_ .57 all ABSTRACT i_1 SIMULATION OF THE CATTLE-CALVES SUB-SECTOR IN A \~/“ DEVELOPED ECONOMY WITH SPECIAL REFERENCE TO THE CANADIAN CATTLE HERD By John James Meek Cattle prices and cattle numbers in Canada have historically demonstrated a regular cyclical time pattern; recently this pattern has become more irregular. This cycle results in fluctuating incomes to producers, fluctuating prices to consumers, and fluctuating con- tributions to the foreign trade sector. While these fluctuations might have been tolerated in an earlier age, modern society demands more stability, more growth, and more management. In order to predict supply or prescriptive right actions, descriptive knowledge of the dynamics of cattle production and trade is required. The purpose of this dissertation is to contribute both descriptive knowledge and analytical tools that may subsequently be employed in prescriptive and predictive applications as well as in future descriptive analyses. The study has three basic objectives; these objectives are realized concurrently rather than sequentially. The first objective is to identify the structure and develop a model of the Canadian cattle herd consistent with specified design parameters. The second is to John James Meek identify, assemble, and explicitly evaluate such data, official and otherwise, as are required to build and validate the model. Thirdly, the model must be tested and found to be valid by specific validation criteria. The third objective includes generation of plausible dis- aggregations of published population and slaughter data. This study was conducted as an element of the sector modeling program of the Economics Branch, Agriculture Canada. While the cattle herd model is designed to interact with other models in this program, it is also designed to provide useful answers independent of these other models. Specifically, the model reflects the supply side of the cattle-calves sub-sector. Modeling of the price determination mechanism, the trade mechanism, and the wheat-feed grain sub-sector are left to the other models with the cattle herd model taking prices and trade flows as given. The cattle herd model is based on the biological growth and production processes as experienced and practiced in Canada. In addition, the cattle herd is separated into its dairy, beef, male and female components. Three geographic regions are recognized; Eastern and Western Canada are modeled explicitly while the third region, the rest of the world, is treated implicitly through the exogenously determined or given trade flows. The herd is further disaggregated to recognize function, production process, and age. The basic functional choice is recognized through allocation of breeding age cattle to either the breeding herd (investment) or to the feedlot for subsequent slaughter (consumption). John James Meek Two feeding processes are modeled: the first simulates a low energy ration such as might be experienced with high roughage feeding; the second employs a high energy ration simulating feedlot feeding-finishing. Finally, the model recognizes age by subdividing calves into ages one to three months, four to six months, and six to twelve months. Further age subdivision is recognized through the above functions and processes. While many aspects of cattle production and marketing are behavioral, three were isolated for explicit modeling. All others are left for subsequent model develOpment. As investment-disinvestment in the breeding herd is central to the study of cattle herd dynamics, cow and bull cull flows and cow and bull replacement flows are estimated econometrically. In addition, the flow of calf slaughter is estimated in similar manner. In order to conveniently adapt the behavioral models to the cattle herd model, a statistical "excess price" model was developed. This latter model is developed from simultaneous supply-demand equations to abstract from "own” price producing a single equation with quantity as the endogenous variable. The excess price model proved to be a good predictor of quantity (flows) but was a disappointing estimator of sign. That is, the estimated sign of the regression coefficients differed from the predicted sign in a high proportion of instances. The technique employed to model the cattle herd is that of generalized simulation. This technique encompasses the system science apuaroach to problem solving. The system science approach is an John James Meek iterative, learning one where concepts or values initially held to be true may subsequently be found to be false or not useful in the context of the study. Should this occur, then a return to a prior stage of the investigation is required. Four tests of objectivity were used as validation criteria; the first two were applied continually throughout the study. These tests are: consistency with observed and possibly recorded experience, logical internal consistency of the concepts used, interpersonal transmissibility of the concepts used and results pro- duced, and workability of the model in the solution of practical problems. Three basic versions of the cattle herd simulator, CATSIM, were built. They differ basically in the method of calculating investment and disinvestment in the breeding herd. The most advanced version, CATSIMB, employs the behavioral models to estimate these flows. Two other models were built. The first, MATRIX, is used to estimate endogenous variables for the behavioral models from known published data using simplifying assumptions. The second, RECON, is used to evaluate the various published data series and other information descriptive of the cattle herd. This second model is based on a single identity. The most substantive results of this study are contained in the structure, parameter estimates, and assumptions of the models. A basic purpose of this study was to develop general models and evaluate historic cattle data in order to solve future practical problems. This objective was met. John James Meek While meeting this basic objective, several useful results were obtained concurrently. MATRIX provided highly plausible estimates of dairy and beef cow slaughter and replacement flows for both Eastern and Western Canada. Eastern and Western bull cull and replacement flows are also estimated as well as beef and dairy calf slaughter flows. These estimates are produced for the years l958 to l972 inclusive. RECON provided valuable insights into the validity of official cattle-calves statistics for the period l959 to l972. In addition, the model provided an opportunity to test certain beliefs about the cattle herd, cattle production and cattle trade. The assumptions made to disaggregate the official data in order to build MATRIX, RECON, and CATSIM, served to accent the deficiency of the official data. Model CATSIM embodies all of the descriptive knowledge of the cattle herd that was assembled. This model generated quarterly popula- tion and slaughter flows for the years l958 to 1972 inclusive. These estimates were demonstrated to be highly credible when compared to the historic official data. These data disaggregations are a significant result. All models serve to highlight deficiencies in the descriptive knowledge of the Canadian cattle herd. Model sensitivity to certain model elements served to rank the importance of the missing elements. While all models developed in this study may immediately be adapted to solve practical problems of the cattle-calves sub-sector, a con- cn1rrent effect must be made to alleviate these noted deficiencies. SIMULATION OF THE CATTLE-CALVES SUB-SECTOR IN A DEVELOPED ECONOMY WITH SPECIAL REFERENCE TO THE CANADIAN CATTLE HERD By John James Meek A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirement for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics and Economics T975 ACKNOWLEDGMENTS The author wishes to thank the members of his guidance and (fissertation committees for their assistance and helpful criticism. mm G. L. Johnson served as chairman of both committees; Drs. W. J. Haley and M. L. Hayenga completed the dissertation committee. With ma Hayenga's departure, Dr. J. N. Ferris ably served as his replacement. Drs. V. L. Sorenson, T. J. Manetsch, A. Y. C. Koo, R. Rashe, and L. Katz served as members of the author's guidance committee. Appreciation is extended to the Economics Branch, Agriculture Canada. The educational leave and financial assistance provided were instrumental in the author's decision to pursue an advanced graduate degree. To Marion, Robbie and Janet for their assistance, patience, and understanding, I am indebted. Their support made this period not only bearable, but very enjoyable. We each gained in our own way from this joint experience. ii TABLE OF CONTENTS Page lJST OF TABLES .......................... vii lJST OF FIGURES ......................... ix Chapter I. INTRODUCTION ....................... l The Problem Setting .................. l The Study Context ................... 4 The Problem Statement ................. 6 Study Objectives .................... l2 Literature Review ................... l3 Dissertation Organization ............... l7 II. METHODOLOGY ....................... l9 The Systems Science Approach to Problem Solving . . . . 20 Feasibility Analysis ................ 26 System Modeling .................. 27 Validation ..................... 29 The Cattle Sub-Sector ................. 32 The Spatial Dimension ............... 32 The Trend-Cycle or Time Dimension ......... 34 The Trade Dimension ................ 39 The Internal Flow Dimension ............ 43 The Calf Slaughter Dimension ............ 45 The Seasonal Dimension ............... 47 The Statistical Data Base ............... 48 The Livestock Survey ................ 49 Calves Born Survey ................. 52 INSPECTED Cattle SLAUGHTER ............. 53 WEST-EAST Cattle-Calf Movement ........... 54 Dairy Correspondents Survey ............ 55 UNINSPECTED Cattle SLAUGHTER ............ 55 IMPORT Data .................... 57 EXPORT Data .................... 57 Chapter Page The Economic Model ................... 59 Investment and Disinvestment ............ 62 Competing Demands and Complementary Inputs ..... 73 Feedback and Cattle Cycle ............. 77 Restatement of the Hypothesized Model ....... 78 III. THE BEHAVIORAL MODELS .................. 80 The Econometric Model ................. 82 Behavioral Model Development .............. 88 Cow SLAUGHTER ................... 90 REPLACEMENTS, Heifers ............... 97 Bull SLAUGHTER and REPLACEMENT ........... 103 Calf SLAUGHTER ................... 105 Modifications to the Specified Models ....... 110 Accounting Identities for Cattle and Calves ...... 112 Generation of Endogenous Variables ........... ll7 Assumptions .................... 118 Description of the Model (MATRIX) ......... 123 The Generated Endogenous Data Series ........ 126 Parameter Estimates and Behavioral Model Appraisal . . . 136 Cow SLAUGHTER and REPLACEMENT ........... 140 Calf SLAUGHTER ................... 144 Bull SLAUGHTER and REPLACEMENT ........... 158 IV. EVALUATION OF THE STATISTICAL DATA BASE ......... 167 Data Base Disaggregation ................ 172 Description of the Model (RECON) ............ 177 Analysis and Evaluation ................ 184 Calf Births .................... 186 Ending Calf Inventory ............... 190 REPLACEMENT Cattle ................. 194 The Sex Ratio of EXPORTS and WEST-EAST Cattle—Calf Movement ............... 195 Yearling Cattle .................. 203 Dairy Heifer SLAUGHTER ............... 206 Model Accuracy ................... 209 V. THE CATTLE HERD SIMULATOR ................ 211 A Model Overview .................... 211 Simulation of the Elements in Cattle Production . . . . 218 Simulation of BIRTHS ................ 218 Simulation of DEATHS ................ 226 Simulation of Calf, Cow and Bull SLAUGHTER ..... 229 iv Chapter Page Simulation of EXPORTS and IMPORTS ......... 233 Simulation of WEST-EAST Cattle-Calf Movement . . . . 237 Simulation of Feeder Cattle ALLOCATION to Feeding Programs ................. 238 Simulation of the Growth Process .......... 239 Simulation of REPLACEMENTS ............. 244 Simulation of Steer and Heifer SLAUGHTER ...... 247 VI. MODEL TESTING AND OPERATION ............... 250 Validation of the Model ................ 251 Model Sensitivity ................... 254 Model Stability .................... 257 Operation in a Deterministic Mode ........... 264 Operation in a Stochastic Mode ............. 267 VII. SUMMARY AND APPLICATION ................. 285 Summary ........................ 285 Program MATRIX and the Behavioral Models ...... 287 Program RECON ................... 290 Program CATSIM ................... 292 Adaptation to Potential Applications .......... 295 Future Model Development ................ 296 Appendix A. PARAMETER INITIAL VALUES ................. 300 Birth Rate ....................... 301 Calving Distribution .................. 302 DEATH Rates ...................... 305 SLAUGHTER and UNINSPECTED SLAUGHTER .......... 306 ~ IMPORT-EXPORT ..................... 307 Allocation to Ration B ................. 311 Allocation of REPLACEMENTS ............... 311 Delay Parameters .................... 313 B. SIMULATION ........................ 316 Simulation of the Modeled System ............ 316 Simulation Building Components ............. 323 C. PROGRAM MATRIX ...................... 335 Appendix Page D. PROGRAM RECON ...................... 347 E. PROGRAM CATSIMZ WEST .................. 366 F. DISAGGREGATE QUARTERLY CATTLE AND CALF POPULATION-- l958-1972, ESTIMATED BY PROGRAM CATSIMZ ........ 384 G. DISAGGREGATE QUARTERLY INSPECTED STEER AND HEIFER SLAUGHTER--196l-l972, ESTIMATED BY PROGRAM CATSIMZ ........................ 392 BIBLIOGRAPHY ........................... 394 vi Table 10. 11. 12. 13. LIST OF TABLES National distribution of cattle and calves, June 1, 1972, eXpressed as a proportion of the national total The stock and flow variable notational convention Notation for and description of behavioral model variables ....................... Coefficient signs implied by the theoretical models Quarterly INSPECTED plus UNINSPECTED Cow SLAUGHTER and REPLACEMENT, l958-1972, estimated by program MATRIX ......................... Quarterly INSPECTED plus UNINSPECTED Calf SLAUGHTER, 1958-1972, estimated by program MATRIX ...... 7. . . Quarterly INSPECTED plus UNINSPECTED Bull SLAUGHTER and REPLACEMENT, l958-1972, estimated by program MATRIX ......................... Adjustments made to Eastern Cow SLAUGHTER and REPLACEMENT data as generated by MATRIX ........ Parameter estimates for Cow SLAUGHTER and REPLACEMENT behavior models .................... Parameter estimates for Calf SLAUGHTER behavioral models ......................... Parameter estimates for Bull SLAUGHTER and REPLACEMENT behavioral models ................... Quarterly INSPECTED plus UNINSPECTED Cow SLAUGHTER and REPLACEMENT, 1959-1972, estimated by the behavioral model ......................... Quarterly INSPECTED plus UNINSPECTED Calf SLAUGHTER, l959-1972, estimated by the behavioral model ...... vii Page 34 50 94 109 128 129 130 131 145 154 165 Table 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. Quarterly INSPECTED plus UNINSPECTED Bull SLAUGHTER and REPLACEMENT, l959-1972, estimated by the behavioral model ..................... Report format for program RECON ............. A comparison of RECON generated Calf BIRTHS with Statistics Canada's semi-annual BIRTH estimates, 1958-1972 ........................ A comparison of RECON generated Dairy Calf BIRTHS with STATISTICS Canada's Dairy Correspondent Survey, "Estimates of Cow and Heifers to FRESHEN This Month,” l958-1972 ........................ A comparison of RECON generated Ending Calf Inventory with Statistics Canada's December 1 Calf POPULATION estimates l958-1972 ................... A comparison of RECON estimated REPLACEMENTS with INVENTORY expressed in terms of a REPLACEMENT Rate, WEST and EAST, 1959-1972 ................. A listing of Eastern and Western Steer and Beef Heifer Feeding "ERRORS" from given parameter settings, 1959-1972, program RECON ................. A comparison of RECON Estimated TRANSFER IN with Ending Inventory for all Yearling Cattle categories, 1959—1972, program RECON ................. A comparison of RECON Estimated Dairy Heifer SLAUGHTER with Dairy Heifer Inventory, 1959-1972, program RECON A comparison of RECON "ERROR" with selected data bases . . Sensitivity test results on selected model parameters-- CATSIMZ, West ...................... Sensitivity test results on selected model parameters-- CATSIMZ, East ...................... viii Page 166 178 189 191 193 196 199 204 208 210 Figure oowow 10. 11. 12. 13. 14. 15. 16. LIST OF FIGURES A simple system with feedback ............. The systems simulation process ............. Eastern Cow Population, June 1, 1954-1972 ....... Western Cow Population, June 1, 1954-1972 ....... Western Cattle SLAUGHTER and Calf BIRTHS, l958—1972 Eastern Calf BIRTHS, EXPORTS, and SLAUGHTER, l958-1972 . Western Ca1f BIRTHS, EXPORTS, and SLAUGHTER, 1958-1972 . . Total INSPECTED Cattle SLAUGHTER, 1958-1972 ...... Expected marginal value product, E(MVP), of a cow Expected marginal value product, E(MVP), of a heifer . . . Price determination given competing demands and fixed supply ...................... The excess demand model ................ The excess price model ................. Quarterly INSPECTED plus UNINSPECTED Beef and Dairy Cattle SLAUGHTER, West, l958-1972, estimated by program MATRIX ..................... Quarterly INSPECTED plus UNINSPECTED Beef and Dairy Cow SLAUGHTER, East, l958-1972, estimated by program MATRIX ......................... Quarterly Beef and Dairy Cow REPLACEMENTS, West, l958-1972, estimated by program MATRIX ......... ix Page 24 35 36 4o 42 44 46 7o 71 73 83 84 132 133 134 Figure Page 17. Quarterly Beef and Dairy Cow REPLACEMENTS, East, l958-1972, estimated by program MATRIX ......... 135 18. Simulation of Calf BIRTHS ............... 222 19. Simulation of DEATHS in a Flow Situation ........ 228 20. Simulation of DEATHS in a Stock Situation ....... 229 21. Simulation of SLAUGHTER ................ 233 22. Simulation of Feeder Cattle ALLOCATION to Feeding Processes ....................... 240 23. Simulation of Feeding-Finishing Process using a Distributed Delay ................... 243 24. Simulation of a Growing Process using a Discrete Delay ......................... 243 25. Simulation of the REPLACEMENT Process (CATSIMl) . . . . 246 26. Simulation of Local Steer and Heifer SLAUGHTER ..... 249 27. Quarterly Beef Cow Population, West, l958-1972, Published, and Estimated by CATSIMl and CATSIM2 . . . . 268 28. Quarterly Dairy Cow Population, West, l958-1972, Published, and Estimated by CATSIMl and CATSIM2 . . . . 269 29. Quarterly Bull Population, West, 1958-1972, Published, and Estimated by CATSIMl and CATSIM2 .......... 270 30. Quarterly Beef Cow Population, East, 1958-1972, Published, and Estimated by CATSIMl and CATSIM2 . . . . 271 31. Quarterly Dairy Cow Population, East, l958-1972, Published, and Estimated by CATSIMl and CATSIM2 . . . . 272 32. Quarterly Bull Population, East, 1958-1972, Published, and Estimated by CATSIMl and CATSIM2 . . . ....... 273 33. Quarterly Beef Cow Population, West, l958-1972, Estimated by CATSIM2 and CATSIM3 ............ 277 Figure Page 34. Quarterly Dairy Cow Population, West, l958-1972, Estimated by CATSIM2 and CATSIM3 ............ 278 35. Quarterly Beef Cow Population, East, l958-1972, Estimated by CATSIM2 and CATSIM3 ............ 279 36. Quarterly Dairy Cow Population, East, l958-1972, Estimated by CATSIM2 and CATSIM3 ............ 280 37. Quarterly INSPECTED Steer SLAUGHTER, West, 1961-1972, Published, and Estimated by CATSIM2 and CATSIM3 . . . . 281 38. Quarterly INSPECTED Heifer SLAUGHTER, West, 1961—1972, Published, and Estimated by CATSIM2 and CATSIM3 . . . . 282 39. Quarterly INSPECTED Steer SLAUGHTER, East, 1961-1972, Published, and Estimated by CATSIM2 and CATSIM3 . . . . 283 40. Quarterly Heifer SLAUGHTER, East, 1961-1972, Pub1ished, and Estimated by CATSIM2 and CATSIM3 .......... 284 xi CHAPTER I INTRODUCTION The livestock sub-sector is a major element in the Canadian agriculture economy. Vast expanses of range lands and apparent ample supplies of feed grains coupled with a growing domestic and world demand for red meat should make livestock, and cattle in particular, a growth sub-sector. But an anomaly appears to be developing. Over the past several years, Canada has been losing its self sufficiency in beef and in fact has incurred several successive trade deficits. This thesis does not intend to examine Canada's comparative advantage in the production of red meat or beef; its objective is much more modest. This study intends to expand or make a contribution to the growing stock of knowledge concerning the dynamics of the Canadian cattle herd. More specifically, it intends to provide both descriptive knowledge and analytical tools that may aid in future prescriptive and predictive applications as well as further descriptive analysis. The Problem Setting The agricultural situation in Canada in the early 1970's could have been described as: (1) unacceptably low net farm income, (2) un- stable income (product prices), (3) uncertainty as to the future, and, (4) inadequate production planning leading to chronic mismatching of supply with demand. The internal economic situation is aggravated by the fact that Canada is a trading nation thus highly interdependent with the world economy. In the agricultural sector alone, it is estimated that 25-30 percent of the nation's total agricultural production is exported. Thus, while current commodity shortages occur largely outside her borders, these shortages (as well as gluts) are felt internally through the international trade sector. These periodic and often unpredictable shocks tend to confound long and intermediate range internal planning. The most vulnerable agricultural sub-sectors are wheat and feed grains as these commodities are largely produced to meet an often volatile international market. This inability is transmitted through various linkages to other sub-sectors, notably livestock, and in fact to other sectors. The sit- uation is aggravated by the fact that wheat, feed grain and livestock production (beef and to a lesser extent hogs) is concentrated regionally in the Prairie Provinces. Because this region, and especially Saskatchewan, is highly dependent on agriculture, the regional economy is prone to unacceptable fluctuations. Fluctuations in the Prairie agricultural economy are transmitted nationwide through balance of payments, the producer durable goods sector, and especially the food element in the consumption sector. While these fluctuations might have been tolerated in an earlier age, modern society demands more stabil ity, more growth, and more management. One noteworthy result of the combined events of the past several years has been the unprecedented trend of growing trade deficits in beef and veal. While trade in these commodities showed a very slight surplus in 1969 and 1970, the deficits became increasingly large into 1973; this is in contrast to substantial trade surpluses in prior years. This situation has been aggravated by continuing declines in the dairy herd in virtually all parts of Canada with the prospects of deficits in milk and dairy products appearing as matters of some real concern. As in most developed countries, the right course of action to pursue concerning the domestic and international agricultural situation has been a preoccupation of government, university, and industry per- sonnel for some 50 years. While the problem has taken many forms through depression, war, and post-war periods, a problem still exists. A most significant study in this regard was produced by the recent (1969) Canadian Task Force on Agriculture.‘ It stated the following hierarchy of values for agriculture. 0 Higher national income per capita; First level all Canadians must have at least a minimum standard of living Functional balance of payments Higher net farm income Full employment Reasonably stable prices Second level 0 Stable farm income Lower cost of production and marketing Increased mobility of labor out of agriculture. Third level lCanadian Agriculture in the 70's, Report of the Federal Task Force in Agriculture, Ottawa, Queen's Printer, 1969. :11! 0.0 a . 1‘9;- n,.. v 1'. T ‘I . s. . O '. .. u t O I .I \ o. . 1., -, O .C a I l . N . ‘1 ‘r. ‘ . ' o . O . ‘ fl) L'- O . 'r. w . - I . . u I .I 0 . 4 SI. .‘ .> _. In addition to these values, it stated specific goals for the non-dairy livestock sub-sectors. These specific goals are: c that a target of 500,000 feeder cattle for export be set for 1980, and a that enough beef and veal be produced in Canada to meet domestic consumption, and . that all tariffs be removed on cattle and beef, and . that Quebec and Ontario dairymen reconsider selling dairy calves as veal in order to market heavier veal or feeders, and ° that resources be diverted from grain production to cattle production, and c that the Canadian Dairy Commission institution incentives for dairymen to move into beef production. Since these recommendations were made, the world and domestic agricultural situation have switched from a surplus to a deficit posi- tion. 15 this a permanent or temporary switch? How should Canada react domestically? In the face of uncertainty and fluctuations, what is the best long and short run resource allocation policy? The Studnyontext Government, especially at the federal level, must take the lead iri ensuring the well being of all Canadians through thoughtful and appropriate policies and programs effectively implemented in a timely fashion. To this end, the Economics Branch of Agriculture Canada has been and is providing increasingly effective input into policy and program planning for the agriculture and food sector. To aid the Branch policy advisors, the Branch has been developing an interactive set of agricultural sub-sector models. These include: 0 feed grain models oil seed models beef models dairy models hog models production adjustment models. In certain instances, several models have been or are being developed for one sub-sector. In the case of the beef sub-sector, at least two models have been developed. The first of these is a short run linear programming model that was initially designed to interact with the feed grains and oil seeds models. In this model, the cow herd is considered as fixed, however, the progeny are allowed to move at several critical stages of the pro- duction process. The initial application of this model was to assist in the development of a national feed grains policy.1 A second beef model is being developed at the University of Guelph.2 This model is a quadratic programing application that considers cattle production, trade, beef and veal consumption, and 1An interim feed grain policy was implemented in August 1973, and replaced by a more permanent policy in August 1974. Both policies were developed with assistance from Economics Branch models. 2G. L. MacAuley, unpublished Ph.D. dissertation, University of Guelph (forthcoming). price determination among three regions, Canada East, Canada West, and United States. While this model is basically a transportation model, the production, and especially the behavioral elements, are well developed. A third study, a simple cattle herd simulator, was begun in mid-1973 to examine the consistency of Canada's statistical data base, related to cattle and calves. This study was curtailed before the completion due to subsequent staff shortages. This third study has been incorporated as an important part of this dissertation. This dissertation research is being conducted as an integral part of the sector modeling program of the Economics Branch, Agricul- ture Canada. It has been designed with general purposes in mind that require something less than a general equilibrium model. While encom- passing the simulator mentioned above, an early attempt was made to ensure general compatibility with the Guelph quadratic programming model. In addition, it is planned that subsequent to this dissertation research, the developed models are to be adapted to meet specific descriptive, predictive, and evaluative needs of the Economics Branch. Some anticipated applications are discussed briefly in the next section. The Problem Statement The problem that is confronted in the dissertation is the con- ceptualization and construction of a dynamic demographic model of the Canadian cattle herd. This model is conceptualized and constructed according to the terms of reference and design criteria stated below. were initially established in consultation with the Economics Branch in light of current and expected future research and policy requirements. These terms of reference and design criteria are discussed below. The model that is developed in this study is partial equilibrium when operated independently of the other Branch models. While it is intended that it be operated interactively with other models, it is to be useful without this interaction. In other words, it is designed as a component, but a self-contained component. The model is based on the biological growth and production process as experienced and practiced in Canada. In addition to this basic departure from prior models,1 the model separates cattle into beef and dairy components, constituting a second major departure. In turn, each of these have a separate male and female component.2 The model has three geographic elements, two modeled explicitly, and the third implied. The two explicit regions are Canada East and Canada West. The third region is the rest of the world and is treated implicitly through the trade component. In Canada, the major trading partner in cattle and calves yhthe United States. In addition to the above disaggregation of the herd, the herd is further subdivided in terms of the (1) age and/or (2) function, 1Most models of the beef or cattle sub-sector are based on and tied to available published statistical data as their main, and usually only. source of information. Most models of the beef sub-sector empha- size beef cattle. Reference to the dairy herd as a very significant source of beef is generally treated tangentially. 2Most models fail to distinguish between steer and heifer beef, cow beef and bull beef; however, veal is normally treated as a separate commodity. and/or (3) process. The basic functional choice is recognized through allocation of breeding age cattle to either (1) the breeding herd or (2) the feedlot and slaughter. The variation in production process is recognized through two separate and distinct feeding rations. The first process utilizes a low energy ration where cattle are grown on grass, hay and other roughage; this process may or may not be terminated by a short finishing period. The second process involves a high energy, high caloric intake ration, such as would be experienced by cattle on full feed in a feedlot. This process assumes that the animal is both grown and finished in such an environment. Some combination of these two processes should approx- imate the actual Canadian experience. In addition, this element of the model allows for a changing combination of the two processes over time. The model is designed to subdivide calves into ages 1-3 months, 4-6 months, and 6-12 months. This subdivision is reasonably consistent with the cattle production and marketing process as practiced in Canada. The major behavioral aspects of the model include: (1) calf slaughter rate, (2) cow and bull cull rate, and (3) cow and bull replacement rate. These major flow elements drive the model and provide it with its basic cyclical and trend nature. The models developed in this thesis, as previously mentioned, areepartial equilibrium. Specifically, the following mechanisms have 131§_been developed: ° the price determination mechanism for beef and veal and for cattle, and ' the trade mechanism for cattle, calves and beef, either internal or external to Canada, and . the major sub-sector which is both competitive and complementary in production has not been modeled, namely, the wheat and feed grain sub-sector. In the first two instances, the model developed by MacAuley1 generates the emitted prices and flows; the output and input matrices of this and the MacAuley model are designed in such a manner that there is potential for the two to be operated interactively. In the third instance, the international grain market provides a major influence on domestic grain price. Because the influence is largely unidirectional, the grain prices, stocks, and outlook can be treated as exogenous to cattle production. The major outputs of the model are (l) a time series of cattle population numbers by age, function, and process cohorts and (2) a time series of slaughter cattle and calf numbers by sex, function, and process.2 The stock values (population cohorts) are determined by a set of flow variables. These flow variables include: 1. calf slaughter rate cow and bull cull rate cow and bull replacement rate export rate 01wa import rate 1MacAuley, op. cit. 2Official Statistics Canada (STATCAN) livestock statistics list seven cattle-calves categories biannually for both Eastern and Western Canada; this model produces 25 categories quarterly. In addition, STATCAN produces six slaughter categories; this model can generate at least 11p for both East and West. 10 6. birth rate 7. death rate 8. feeding-finishing rate. Numbers 1, 2, and 3 are pure behavioral variables. Econometric techniques are used to arrive at parameter estimates. Prices, including cattle prices, are exogenous to the model. Prices provide a feedback mechanism for the cattle production process, and are an element of interaction with other models. Numbers 4 and 5 are taken as exogenous, and provide a second level of interaction with other models. Exports and imports are interpreted to mean interregional as well as foreign trade. Numbers 6, 7, and to a lesser extent 8, are basically biological Technology and environmental influences are of major significance. The impact of economics, especially relative prices and price expectations, have an effect on 6 and 7; their influence on 8 is marked. This latter area is not explored in this study but must be given top priority in future model development.1 Major design criteria involve flexibility to meet future and possibly unanticipated applications. In the extreme, this requirement can invoke undue cumbersomeness. To avoid this result, flexibility features are avoided if they prove to be mildly cumbersome. 1The events in the cattle industry during 1973-74 have demon- \ strated that producers can and do alter feeding-finishing rate in the face of major price adjustment and price uncertainty. This unusual instability leads to further price instability and uncertainty. 11 At the design stage and during model development, specific applications were not known with certainty. This in major part was due to the fact that problems to be addressed, and thus applications, occur in the future. However, several general types of applications were identified. The model is designed: l. to analyze and evaluate existing data series (while this is part of the existing study, additional interaction with statisticians and researchers is planned), and 2. to analyze and assess the impacts on the cattle-calf sub-sector of changing: 0 biological parameters, 0 production processes, - flows values such as exports and imports, and 3. to use the model in an optimum control mode to determine optimal or alternate paths that may lead to present targets such as projected domestic or export demand, and 4. to operate in a forecasting mode, and 5. to operate interactively with researchers in order to heighten their descriptive knowledge and understanding of the sub-sector. These applications are not exhaustive. Since the model is based on the biological reproduction and growth process and since one antic- ipated application set involves the evaluation of changes in biological parameters and production processes, the model must incorporate basic biological parameters and processes. The evaluation mentioned above would be expected to include (1) breeding herd size, (2) breeding herd maintenance, (3) progeny feed intake, and (4) beef and veal output. The basic biological parameters that are indicated include: 12 1. live birth rate birth weight birth distribution heifer calving age heifer calving distribution 050'!wa weaning weight 7. rate of gain 8. carcass weight 9. carcass dressing percentage. While all of these parameters are not modeled either eXplicitly or implicitly, the model must accommodate them with very little altera- tion. In addition, the model must be flexible enough to accommodate additional production and finishing processes beyond the high and low energy streams initially modeled. Study Objectives The purpose of this study is to develop a general simulator of the Canadian cattle herd that can subsequently be readily adapted to meet specific research needs of the Economics Branch and other Canadian institutions associated with the cattle-calves sub-sector. This main objective must be conducted concurrently with or subsequent to other prerequisite objectives which are included below. The following specific objectives of this study are realized concurrently rather than sequentially. This concept is consistent with the systems analysis process to be described in the next chapter. 13 a. Data and Information assessment: 1) to identify and gather such data and information as required to support the hypothesized model, and 2) to attempt a reconciliation of these data and information in order to determine their accuracy. b. Model Development: 1) to identify the structure and develop a general simulation of the Canadian cattle herd consistent with the hypothesized model, and 2) to identify, conceptualize, and estimate those behavioral and biological relationships that are found to be the model's critical parameter and flow variables, and 3) to identify and design into the model those critical elements that are consistent with expected applications and future develOpment. c. Model Testing and Validation: l) to successfully "track" past p0pulation and slaughter daga consistent with the simplifying assumptions used, an 2) to generate disaggregate historic population and slaughter data series and to generate replacement and cull data series that are held to be highly plausible. Literature Review The literature is particularly undeveloped with respect to the problem outlined above. While this is the case, certain related lit- erature is available or is emerging. This related literature falls into five categories. 1. Simulations of agricultural sectors or sub-sectors. 2. Simulation techniques and components. 14 3. Econometric models of the cattle-feed grain sub-sectors. 4. Structure of the Canadian cattle-calves sub-sector. 5. Data description of this sub-sector. A cattle herd model was incorporated as a component of the "Nigerian Model."1 This component modeled both a "traditional" and a "modern" sector in an attempt to develop policy strategies and evaluate policy alternatives. The beef component employed calving rates, death rates, and various marketing strategies with the former two rates being functions of nutritional level. The "modern" beef component utilized a land allocation (allocation between cr0ps and grazing) as a policy variable. The output of land allocated to grazing was a function of input expenditures on it. Supplemental feeding was used as a policy variable as well. Posada2 developed a somewhat similar model for the Northern Columbia beef industry. This industry appears to be a traditional economy; policy instruments include imposition and assimilation of more advanced technology. Credit and export incentives were also employed. Both the Nigerian and the Posada models are explicitly oriented toward policy evaluation; consequently, the identification and modeling 1This model and related study are reported in G. L. Johnson et al., A Generalized Simulation Approach to Agricultural Sector Analysis with Reference to Niggria, East Lansing, TMichigan State University, — 7 . d 2Alvaro Posada, "A Simulation Analysis of Policy for the Northern Columbia Beef Cattle Industry," unpublished Ph.D. dissertation, Michigan State University, 1974. 15 of output and policy variables become a major part of the model. Input demand, a crop element and a price determining element are included as part of both models. The Nigerian study modeled the non-agricultural sectors of the economy while Posada did not. Both of the above studies model one or more sectors of the national economy. As a consequence, the models are highly aggregated; minimum detail is dictated only by policy and output variables that are found to be relevant. A more detailed sub-sector simulation was done by Hovav Talpaz.1 Talpaz developed a hog supply response model subject to both biological and economic constraints. This model tends to more explic- itly model a sub-sector, the hog sub-sector, while taking the balance of the economy as exogenous. He states that "demand for hogs and the distribution and marketing system are beyond the scope of this model." The model does evaluate production response to an identified set of policy variables and ultimately recommendations are made for dampening the hog cycle. Key variables in the Talpaz model are the hog-corn price ratio and volume (rate) of farrowing. The study has two parts. The first used econometric techniques to identify and estimate key model param- eters. Specifically, a Fourier series application to a trigonometric time function is employed. The second uses a time-variant mixed 1Hovav Talpaz, "Simulation Decomposition and Control of Multi- Frequency Dynamic System: The United States Hog Production Cycle," unpublished Ph.D. dissertation, Michigan State University, 1973. .04 16 difference equation system to simulate production supply response. A component model was developed to yield age and weight distributions for market hogs. The sow farrowing variable was found to be the major l l 1 state variable while hog-corn price ratio represented the major input signal. The components and techniques necessary to develop the Talpaz and Posada models, as well as other simulation models not discussed here,1 can largely be attributed to T. J. Manetsch and his associates. These techniques and components were perfected in large part during the execution of the "Nigerian Project" and subsequent "Korean Project." The text, of which Manetsch is joint author, only reflects this knowledge in part.2 Full credit must be given to lectures, seminars, and mimeographed material presented by him and his colleagues. The next chapter deals explicitly and at length with the structure of the Canadian cattle industry and the data base descriptive of that industry. Specific sources and references are cited at that time. Chapter III cites references relevant for the development of the behavioral models. 1One example is D. L. Forster, "The Effects of Selected Water Pollution Control Rules on the Simulation Behavior of Beef Feedlots, 1974-1985," unpublished Ph.D. dissertation, Michigan State University, 1974- 2T. J. Manetsch and G. L. Park, Systems Analysis and Simulation with Application to Economic and Social Systems,TEast LanSing: ‘Michigan State University, 1973. 17 Dissertation Organization The dissertation is organized in such a manner as to provide a general statement of the problem and a specific set of objectives in this present chapter. This chapter has also provided a description of the context in which the study is being conducted as well as a discussion of what is being attempted and what is being left to related models. Chapter II discusses the background necessary to proceed to the detail of Chapters III, IV, and V. Specifically, Chapter II discusses the system science simulation approach to problem solving, provides a historical description of the cattle-calves sub-sector and a discussion of the currently available statistical data base. In addition, the theoretical economic model underlying the cattle-calves sub-sector is discussed in detail. Chapter III develops the behavior models required for the simulation model and provides parameter estimates for the latter model. In addition, the model MATRIX is discussed. This model is required to generate an estimated matrix of endogenous variables for the above behavioral models. The statistical data bases concerning cattle and calves is felt to be less than desirably consistent. Chapter IV discusses a model called RECON that assists in isolating errors and biases in these data series. The implications for both this study and others are considered. ug-pn. . u\ .1‘ .v' u. -~-n. ‘ l - 1\.... .4 u....,. . ~ 6. I ‘ a '1 . a. L’f'v- ., ...‘ . v‘u . .1. , I ... -. - v" 4 x u "9.. u '. i \. '0. . ‘ I x .C '0 ‘ . I‘.- ~ 7 i - t. i o . In s v . I ‘p .I In . a. . " 18 Chapter V discusses the development of the cattle herd simulator, CATSIM. The building of this simulator requires a second set of estimated parameters. These parameters are obtained from sources other than statistical analysis. They fall into two basic categories: the first concerns the basic biological relationships, and the second involves data base disaggregation. A third set is suggested but left to a subsequent study, that is, the statistical estimation of these two former sets. Chapter VI provides an evaluation of CATSIM under various operating conditions. Three basic versions of CATSIM are develOped. CATSIM l operates the basic model under a set of strict and somewhat unrealistic assumptions concerning the rate of breeding herd replace- ment; CATSIM2 relaxes that assumption. CATSIM 3 utilizes behavior models to generate replacement rates and certain other critical rates. The final chapter, Chapter VII, summarizes the study and discusses the modifications required to adapt the model to anticipated applications. Aspects of the model that require further development are also discussed. gnu. .. ‘- ~ .- I CHAPTER II METHODOLOGY The development of a cattle herd simulator, together with its integral behavior elements, requires a description of the sub-sector, a description of the sub-sector's context, and a theoretical basis for analysis. An understanding of the technique of analysis is required as well. It is the purpose of Chapter II to provide this necessary foundation. The first section, The Systems Science Approach to Problem Solving, considers systems science simulation as a problem-solving technique useful for investigating both the normative and the non- normative aspects of problems. It should be noted that while the first section discusses the total method or approach, this disser- tation covers only the first few steps of that approach. The steps involving application are left to future studies, some of which are being developed concurrently and in coordination with this study. The second section, The Cattle Sub-Sector, provides a histor- ical, verbal, and graphical sketch of the Canadian cattle herd, while the third section, The Statistical Data Base, discusses the statistical base descriptive of that herd. It should be stressed that the descrip- tion of the herd is recorded largely in terms of stock and flow data 19 20 series that are proving to be inadequate, incomplete, incompatible, and possibly, in error. The final section, The Economic Model, develops the economics relevant to describing the cattle herd. Special attention is paid to investment and disinvestment in the basic breeding herd and to the relationship between the cattle-calves sub-sector and the wheat-feed grain sub-sector. It is a basic contention of this dissertation that analysis of investment/disinvestment provides a chief indicator of fed cattle supply 24-36 months hence. The Systems Science Approach to Problem Solving The word simulation conjures up a wide variety of concepts or techniques in the minds of those who contemplate it. Lack of concensus or existence of misunderstanding leads to unwarranted confusion. The concept of systems science simulation used in this dissertation follows closely the one developed and applied by G. L. Johnson and his asso- ciates at Michigan State University.1 The systems science simulation approach is general with respect to technique; thus it may use single or simultaneous equation models, LP,.and NLP models, input/output tables, PPB and capital budgeting 1For further elaboration refer to: (a) G. L. Johnson et al., op» cit., pp. 25-37; G. L. Johnson et al., Korean Agricultural Sector Analysis and Recommended Development Strategies, 1971-1985, East Lansing, Mfchigan State University, 1972, pp. 32-46; and M. 1.. Hayenga, T. J. Manetsch, and A. N. Halter, "Computer Simulation as a Planning Tool in Developing Economics," American Journal of Agricultural Economics 50:1755-1759, Dec. 1968. . 1": v4 .1 u. .I 1.. v I! I t. 'i 21 techniques, or any number of other more Specialized techniques. Each is eligible for inclusion at that point at which each is more appro- priate. The approach is also general with respect to data use and data sources. Thus, both time series and cross section data are often employed. Statistical estimation procedures may be used to obtain parameter estimates. Another source of data, used extensively in this dissertation, is informed judgment or data of a judgmental nature implying a Bayesian approach. The method employed in this study utilizes the techniques developed by systems scientists as well as the concept of a system now used generally by most disciplines. While the systems science simulation approach to systems design and analysis was originally developed by electrical engineers, it is increasingly finding favor in a diverse group of disciplines. It is also finding favor in multi-disciplinary problem oriented research as the systems approach allows the diversity to be handled in a comprehensive and coordinated manner, with the logic that is common to all disciplines. Thus, generalized systems science simulation is flexible with respect to kinds and sources of information and technique. The mechanical and logical nature of the process allows adaptation to a wide variety (If modes, including projection, optimization, and optimum control. It has;also been found useful in a normative policy making mode where the following preconditions for optimization, not being present, have hanuaered or even precluded appropriate use of specialized techniques. The preconditions for optimization are as follows: 22 l. A common denominator for the "goods" and "bads" is present. 2. This common denominator is comparable among those individuals or groups affected. 3. The order, or second order condition, is apparent before optimization takes place. 4. A specific decision rule for selection of the optimum is available. The generalized systems science simulation approach continues to be flexible in application; this is important when all possible applica- tions are not known a priori. The systems science approach to simulation is an iterative, learning process. While many, if not most, economists “talk systems," very few actually "do systems." This study provides an example of "doing systems," of laying out the system in explicit detail and simulating the components. The systems approach to accomplishing this task has the appeal of Baygian statistics, that is, it appeals to the logic and thought process of the non-economist or non- econometrician. It accomplishes this by formalizing the learning and corrective process that is the method of all scientists and in fact all entities that learn when reacting to stimuli. A very simple system is presented diagramatically in Figure 1. Three types of problems can be identified with such a system. 1. Synthetic or design problems: given desired output and expected input, design the system to produce the desired output, e.g., a pollution control device for internal combustion motors. 2. Analysis problem: given input variables of the system, find the output variables, e.g., prediction of national crap yields, or the daily weather. 3. Identification problem: given measured input and output variables, find the relation between them. 23 Environmental Inputs Controlled Input Output desired Uncontrolled Variables SYSTEM ‘ Variables undesired System Parameters Controller -J Figure l. A simple system with feedback The identification problem basically is the one of concern in this study. In final application, however, the model will deal with problems of analysis, or even design. The systems analysis approach uses an iterative, learning, problem investigating approach in dealing with all three types of problems. Figure 2 provides a general overview of this process. This study basically includes stages 1 through 3. At each stage interaction takes place between the model builder(s) and the model user. In a policy evaluation mode, the ultimate model user becomes the policy or decision maker. 24 PROBLEM DEFINITION (through (1) interaction between investigator 1 and decision maker) l MATHEMATICAL MODELING AND SIMULATION (2) (and more interaction between investigator and decision maker I MODEL REFINEMENT AND TESTING (and (3) more interaction between investigator and decision maker) l MODEL APPLICATION IN PROBLEM SOLVING (4) (and more interaction between investigator and decision maker) Figure 2. The systems simulation process 25 The method is iterative in that stage 1 takes place before stage 2, stage 2 prior to stage 3, etc. At each stage, however, new or conflicting information may be uncovered that partially or wholly negates information or concepts previously held to be true in earlier stages. Thus, any one step may have to be repeated, possibly several times. Similarly, new information may force a return to a prior step or, in fact, a return to step 1. In addition to the possibility and process of uncovering new knowledge as the overall process takes place, the process accommodates the possibility of uncovering new problems that were not anticipated a priori. These new problems may force a return to a prior stage. As previously mentioned, this study basically does not include stage 4. However, the foregoing applies to stage 4. Thus, in appli- cation, there still exists the critical interaction between model builder and model user. In fact, the human element is not seen as divorced from the process but as an integral part of the process. Thus, even in stage 4, the possibility of new knowledge or new problems may force a reversion to any prior stage. Consequently, the results of this study must be held tentatively. The application of the systems simulation process to policy problems should be noted at this point. Models, including simulation models, normally are thought of as providing knowledge of a non- normative nature. An objective function is normally used to minimize a set of "bads“ and to maximize a set of "goods." This objective function explicitly states what is "good" and what is "bad"; knowledge 26 of the normative is clearly implied. But in policy problems very often it is knowledge of a normative nature that is missing; it is the normative knowledge that must be acquired. To successfully optimize, the preconditions for optimization must be present. In many, if not most, policy applications, these preconditions are not present. In another parlance there is normally an absence of an explicit social welfare function. While the model provides a set or competing sets of production possibilities, no clear rule is present for evaluating these competing sets with respect to social welfare. The problem may be expressed in terms of the lack of knowledge concerning the normative. Systems science simulation can aid in the learning and awareness heightening process by involving the policy maker in the total process from problem formulation to model application. The process forces the accumulation of normative and non-normative infbrmation germane to the eventual policy decision. While the above discussion provides an overview of the general process, more specific steps are required before a problem may be approached, systemized, and eventually simulated. The process involves the following basic steps. Feasibility_Analysi§ This step precedes the commencement of work on any project including this one. It corresponds in part to stage 1 of Figure 2 and includes the following self-explanatory steps: 27 . needs analysis 0 system identification (in very general terms) 0 problem formulation - generation of the systems' concepts (a broad general list) - determination of physical, social, and political relizability . determination of economic feasibility 0 generation of a subset of viable concepts. System Modeling This step receives the set of viable concepts as inputs, the working model is the output. It is basically an elaboration of stages 2 and 3 of Figure 2. This step involves: . concept selection (the final subset) modeling of these concepts parameter estimation or approximation stability analysis sensitivity analysis. From the subset of viable concepts, a further subset is selected that best appears to represent the system being modeled in light of the identified problem. The concepts are individually modeled to collectively produce the model of the system. Systems modeling takes place in terms of the subset of concepts finally selected. This model represents a second level of abstraction from reality. The sequence is: 28 THE REAL WORD MATHEMATICAL MODEL SIMULATION MODEL The mathematical model can be represented in terms of an exact block diagram. The elements in the exact block diagram are modeled in terms of system components1 that in many cases have been developed in the past and are published in the form of specialized systems languages.2 Parameter estimation is a major element in the building of a simulator. These parameters may often be estimated statistically where adequate data are available. Where this is not possible, "guesstimates" and informed judgment provide a second source. In addition, the Simu- lator itself may be deployed to produce parameter estimates with certain optimal properties. If the model output simulates some set of "correct" values, then a formal optimization procedure may be employed to estimate parameter values. If some less precise concept of correctness is held or if highly plausible parameter estimates are available from other 1Appendix B contains a detailed discussion of mathematical modeling, explains the symbols used in expressing the model in exact block diagram form, and discusses, as well, the principle system components used in this dissertation. 2An example is R. L. Llewellyn, FORDYN: An Industrial Qynamics Simulator, Raleigh, North Carolina State University, 1965. 29 sources, then an informal method of parameter adjustment or "fine tuning" may be employed. Viability testing is the first stage of testing. At this stage, generated variable values are checked for correct Sign and approximate magnitude. Validation involves a more detailed test and may include a comparison of simulated output with some known output, as in the case of this study. Sensitivity analysis involves testing the sensitivity of the model to parameter changes. There are two basic reasons for this test. In the first case, the accuracy of sensitive parameter estimates is more critical than those of lower sensitivity. This test then gives some ordering to the allocation of further research resources. In the second instance, the ranking of policy parameters in terms of sensitivity can be very informative to decision makers. Stability testing can take place concurrently with sensitivity testing. This test ensures that the model is stable over all reasonable combinations of parameter values. The dynamic properties of the model should approximate the observed dynamic properties of the system being modeled. Validation The actual process of validation is one of demonstrating that the model fails to be found invalid. Thus, the model may be incorrect in one or more aspects yet superficially appear to be valid. The model may be found incorrect in application; at this stage, corrections or revisions will be made in keeping with the systems process. 30 A simulation model, such as the one being developed in this study, uses information from a wide variety of sources. These include published statistical data, experimental data, as well as the informed judgment of a range of knowledgeable people. The reliability or accuracy 0f any or all of this information is open to question. Unlike specialized techniques, the usual statistical tests do not always apply; where possible, they are used. In all cases, however, less sophisticated but nevertheless useful tests of objectivity are applied. These tests are applied consistently at each stage of model development in order to validate and verify the process that is taking place. These tests of objectivity are: l. consistency with observed and possibly recorded experience (correspondence), 2. logical internal consistency of the concepts used (coherence), 3. interpersonal transmissibility of the concepts used and the results produced, and 4. workability of the model in the solution of problems.1 More specifically, the model's output must be consistent with the official published cattle statistics and users evaluation of these statistics. Also, the process by which the model generates output must 1The following two references are examples of those using objectivity as a validation and verification criterion. G. L. Johnson et al., Korean Agricultural Sector Analysis, pp. 43-45; and G. L. Johnson ande. Leroy Quance,’The OverprodUction Trap in U.S. Agriculture, Baltimore, The John Hopkins Press, 1972, pp. 44-48. 31 be consistent with generally held concepts of how the sub-sector functions. The model must be able to reconcile those various bits of information used in its construction in such a manner as to success- fully reproduce, or change, the commonly held view of the sub-sector. These include generation of short term fluctuations and long term trends. If the model lacks stability or does not reproduce trends and cycles then it fails to be consistent with the real world. In this case the model would fail the consistency (correspondence) test. If the model cannot reconcile the elements used in its construction then it (the model or the elements) fail the internal consistency (coherence) test. The process, the parameter values, and the generated output, must be accepted by a wide range of individuals cognizant of the vari- ous aspects of the cattle sub-sector. This group would include animal scientists, livestock economists, livestock marketing experts, and other knowledgeable industry people. This is the interpersonal transmissibility test. Finally, the model must demonstrate workability or prove to be insightful with respect to specific problems. This means that this model (or some future amended version) is only useful insofar as it can provide useful answers; for a wide range of problems it may be found to be inferior to some other methods or of no use whatsoever. The process of objective validation and verification is never ending. The present stage of development of the model represents a ...Q 32 highly plausible representation of the system. Additional information at some future date may cause this model to be greatly modified or simply rejected. Thus the model's validation will not generally be expressed in a set of well-known and accepted statistics but rather will take an objective truth in the minds of those scientists, policy makers, and others who wish to use it, understand its logic, and contemplate the validity and usefulness of its output. The Cattle Sub-Sector This section describes the cattle sub-sector in terms of its various dimensions. This sub-sector is in interaction with other sub-sectors and indeed with international influences thrOugh its foreign trade dimension; thus, it is ever changing. An attempt is made, consequently, to describe the sub-sector in dynamic terms with emphasis on the external influencing factors. The Spatial Dimension Canada is divided geographically by physical barriers running north and south, giving rise to separate and readily identifiable regions. Within each region, considerable similarity exists with respect to climate, papulation density, degree of industrialization, as well as political and social thinking. Generally, each region is made up of one or more provinces; statistical data collection is conducted on a basis consistent with these regions. 33 For the purpose of this study, two major regions will be identified, East and West. The major elements in the Western region, with respect to the cattle sub-sector, are the Prairies. In the East, Ontario and Quebec are of major significance. Approximately 70 percent of Canada's population lives in the East, mainly in southern Ontario and Quebec, while the remaining 30 percent is spread rather thinly over the Prairies and concentrated in the Vancouver area of British Columbia. In contrast, the June 1, 1972 Livestock Survey indicates that the West had 61.6 percent of the cattle population. This uneven dis- tribution of human and cattle population gives some clue as to the direction of the internal trade in cattle and meat. The relative distributions are even more distorted if the cattle population is split into its dairy and beef cattle components. Table 1 shows the June 1, 1972 distribution on a seven region basis. The West is shown to have the bulk (81%) of the beef cow herd, while the East has most of the dairy herd (79% of the nation's dairy cows). Table 1 provides a static picture only; Figures 3 and 4 Show the trend in dairy and beef cow numbers, both East and West, over the 1954-1972 period. In general, the dairy cow herd has declined over most of the period and continues to decline both in absolute numbers and as a proportion of the total herd. In contrast, beef cow numbers have been on the increase over this same period with irregularity in this rate being the greatest in the West. v. d)- a.” 34 Table 1. National distribution of cattle and calves, June 1, 1972, expressed as a proportion of the national total Milk Dairy Beef beef Bulls cows heifers cows heifers Steers Calves Maritimes .0274 .0457 .0512 .0137 .0127 .0228 .0236 Quebec .1967 .4116 .3529 .0476 .0338 .0341 .0914 Ontario .1446 .3329 .4101 .1237 .2396 .3746 .1772 EAST .3687 .7902 .8140 .1849 .2932 .4314 .2922 Manitoba .0829 .0480 .0467 .1071 .0825 .0885 .0940 Sask. .2121 .0452 .0362 .2884 .2326 .1476 .2488 Alberta .2892 .0805 .0629 .3670 .3453 .3036 .3212 B.C. .0471 .0361 .0401 .0527 .0465 .0289 .0448 WEST .6313 .2098 .1860 .8151 .7068 .5686 .7088 The Trend-Cycle or Time Dimension Marshall1 points out that official estimates of the numbers of cattle and calves in Canada have been kept since 1906. Over that period, milk cow numbers rose smoothly to peak in the mid-1930's and have fallen rather steadily since that date. 0n the other hand, cattle, other than milk cows, have trended upward irregularly since 1906. Marshal goes on to say that these irregularities in cattle numbers, the so-called cattle cycle, is basically a phenomenon of the beef cattle population and thus most pronounced in the West. He identifies the following cycles for cattle other than milk cows. 1R. G. Marshall, Variations in Canadian Cattle Inventories and Marketing, Department of AgricUltural Economics, Ontario Agricultural College, Guelph, 1964. 35 mm _m .mam_-emm_ ._ acne .coepm_=aoa zoo campmam Om mm mm um mm me am mm mm F0 on .m acumen mm mm mm mm mm — a d 1 a d cowpmezaoa zoo emwm covpmpzaoa zoo xgwmo « - q q d u l l l mp mp om Pu mm mm wm PPBH 000‘001 36 .Nmmy-¢mm~ ._ mean .cowpmpsaoa zoo cempmmz .v mgammm mm Pm On mm me No no mo an mm mm _m on mm mm nm mm mm am - q u q 4 A cowpmrzaoa zoo xewmo covumpaaoa zoo mmmm _ _ q _ . q _ q _ q _ . q 1 mm P93H OOO‘OOl 37 upswing 1911-1919 8 years 1911'1928 downswing 1919-1928 9 years _ upswin 1928-1933 5 years 1928 1939 downswgng 1933-1939 6 years _ upswing 1939-1945 6 years 1939 1950 downswing 1945-1950 5 years 1950-1963 uncompleted 12 year upswing (one year decline in 1958) Subsequent analysis Shows that the last continued until 1965. A feur year down turn followed that bottomed out in 1969. An upswing has been in progress since that date. Marshall has been tempted to say that the "conventional” cattle cycle (as occurring 1911-1950) has not been in evidence since 1950. He states, “this apparent deviation from the historical cyclical pattern over recent years, both in terms of timing and magnitude, would appear to negate the automatic properties of the cattle cycle as seemed apparent in the earlier years."1 Petrie characterizes the cattle cycle in terms of slaughter, and from peak to peak.2 _ downswing 1945-1950 6 years 1945 1957 upswing 1951-1957 6 years downswing 1957-1958 1% years 1957"]965 upswing 1959-1965 5 years 1965-1969 downswing 1965-1969 38 years lMarshall, op. cit., p. 11. 2T. Petrie, "Analysis of Seasonal, Cyclical and Trend Variations in the Prices and Output of Cattle and Hogs in Canada," unpublished Master's thesis, Saskatoon, University of Saskatchewan, 1971. 38 Marshall discounts the 1957-1958 downswing as being a product of high exports, therefore, low domestic Slaughter. Beef cow members continued to increase during this period. Both Marshall and Petrie note that the cyclical motion in cattle numbers, generally, is a western beef cattle phenomenon. Petrie goes on to give three basic reasons for this cyclical motion. 1. Producer response to short term conditions. This would include the drought in the thirties, the outbreak of foot and mouth disease in Saskatchewan in 1952, and the drought in 1961. 2. Exports as a response to relative international prices, especially U.S. cattle prices. A low period of exports are noted between 1952-1956 and 1967-1972. The inter- vening period l958-1966 generally was a period of high eXports. 3. Wheat--the competitive condition of livestock in the Western economy. If wheat eXports and prices are average to high, resources are traditionally withdrawn from cattle production in the West. The years 1963-1967 saw high wheat exports and low carryover. Conditions changed during 1968- 1970 as exports were reduced and carryover reached unprecedented levels. Summarizing both Marshall and Petrie, the following events had a significant impact on the Western beef cattle population. 1937-1940 drought 1941-1945 government policy to divert excess grain to livestock 1945-1950 high western grain sales 1950-1962 high grain carryover especially wheat 1963-1967 high wheat sales 1967-1970 high wheat carryover 1970- government policy to divert excess resources to livestock. 39 The recent rise in cattle numbers has in part been sparked by diversification (into livestock) programs sponsored by several provincial governments, as well as the 1970 Lower Inventories for Tomorrow (LIFT) program of the Federal government. Thus, to Petrie's list might be added a fourth item, government programs. These items are in addition to and superimposed on the traditional cobweb model of the cattle cycle. Figure 7 attempts to show the progress through l958-1972 of births, calf exports, calf slaughters, while Figure 5 relates cow-heifer slaughter to calf births and steer slaughter. The Trade Dimension Boswell,1 Boswell and MacEachern,2 and Marshall3 provide a panorama of the changing cattle trade pattern in North America, especially as it affects Canada. Cattle export statistics divide non-dairy, non-breeding stock exports into three weight classes: less than 200 pounds, 200-700 pounds, and over 700 pounds. While these categories will be treated in some 1A. M. Boswell, "The Changing Economic Profile of Canada's Beef and Veal Trade," Canadian Farm Economics 8(5):1-14, Oct. 1973. 2A. M. Boswell and G. A. MacEachern, "Determinants of Change in the North American Feeder Cattle Economy," Canadian Journal of Agricultural Economics, 15(1):53-65, 1967. 3R. G. Marshall, An Assessment of Current and Prospective Trade Patterns, Supply and DemandlSituatTons for Cattle and Beef, Hogs and Pork,_with Reference to Canada's Position in the North American Market, Department of AgricUTtural EconomTcs, University of Guelph, T968. 4O .NNm—lwmmr .mzkam mFmo new mmhzoz<4m mpppmu cgmpmoz .m wgzmwm mm _m on on mm mm mm mm em mm Nm —m cm mm mm . _ . . _ . u _ 1 \Fllur _ .1 II|1IIIJ \\ "IIII‘ mmkxw2<4m zoo mmb:a:oz epmo hm MVPi 1A traditional treatment of investment, business cycles and growth is given in R. G. 0. Allen, Macro-Economic Theory, A Mathematical Treatment, New York, St. Martin's Press, 1968. An excellent review of recent literature on the economics of investment in fixed capital is given in Dale W. Jorgenson, "Economic Studies of Investment Behavior: A Survey," Journal of Economic Literature 9:1111-1147, Dec. 1971. Because the nature of investment and disinvestment in livestock differs in some fundamental ways from investment in industrial capital goods, the method used in this study diverges somewhat from the method and studies cited in Joregenson. The theoretical argument that is developed in this section is presented in a very lucid fashion by Dan Sumner in a mimeographed paper, 'An Empirical Examination Concerning Investment and Disinvestment in Durable Assets: Econometric Analysis of U.S. Milk Cow Herd," Michigan State University, 1973. 2Market price or Pi refers to the asset's rental price. 64 Fluctuations in Pi p:_in MVPi lead either to investment or disinvestment. A revision to neo-classical theory, developed by G. L. Johnson and his associates leads to a third alternative, that of assets (stock) fixed in production.1 The three investment possibilities depend on the existence of two prices, not one. The two prices are referred to as acquisition price, Pa’ and salvage price, Ps’ The divergence of these two prices is attributed to cost of obtaining information, transaction and transport costs. The three investment possibilities now are: Invest 1f Pai < MVPi Disinvest if P . > MVP. S1 1 Neither invest nor disinvest if Psi < MVPi < Pai’ This latter position is known as the fixed asset position where assets are fixed or locked in production for the firm. A firm never plans on being in this position, a position in which it incurs a capital loss. This situation comes about through mistakes made in past investment decisions or where expectations do not materialize. This discussion indicates that net investment takes place in two activities, gross investment in new capital usually of high 1For a detailed description and mathematical treatment refer to G. L. Johnson and C. L. Quance, The Overproduction Trap in U.S. Agriculture, Baltimore, John Hopkins Press, 1972. 65 technological content and gross disinvestment in older capital of lower technological content. Further, this investment and disinvestment con- siders two prices, not one. In addition, the optimum stock of capital is reached when the adjustment is completed with respect to a change in the two prices, Pa and PS, and to changes in MVP. This adjustment process may be represented as1 (17) STOCK - STOCK = (1 —x) (STOCK; - STOCK t+l t t) M .4 O O 7< ‘- II the desired level the accelerator —l I >2 II and (18) STOCKtH-STOCKt = Gross Acquisitions -Gross Dispositions t t This theory may now be applied to the instance of a specific operator or decision maker, making marginal adjustments to his breeding herd. While prices (Pa’ Ps’ and input prices) are determined at a macro level, aggregate SUpply of cull or slaughter animals or demand for replacements is the sum of the decisions made by the micro units. The micro decision makers in the cattle sub-sector are farmers, ranchers, and cattle feeders. Their large numbers and dispersion at the 1This formulation is that of the flexible accelerator. Much of the recent literature on investment uses this formulation with emphasis on the determination of the level of desired capital, the time structure of the investment process and the treatment of replacement investment. 66 cow-calf production level suggests that the sub-sector can be approximated by the competitive model. However, at the feedlot level, competition might be something less than perfect, leading to increasing vertical coordination.‘ The actions of these micro decision makers result in investments disinvestment, and calf slaughter which control the capacity of the sub- sector to subsequently produce more beef and veal. It is their aggregate behavior that is of major interest in these models. It is assumed that the decision makers are utility maximizers, that is, they attempt to acquire and utilize resources in such a manner as to maximize utility over time. It is further assumed that utility is a function of the goods and services that they can command and leisure. This utility function may be expressed (19) Utilityt = f1 (goods and servicest, leisuret). Assuming that profit, however defined, is a good proxy for command over goods and services and, that given leisure, utility is a function of profit, then equation (19) can be written (20) Utilityt = f2 (Rt/leisuret). ‘There is increasing concern that vertical coordination is resulting in less than desirable price reporting due to the lower volume of cattle through public stockyards. Price quotations are given for sales at this point. The concern is eXpressed by C. Mills, "WSGA Market Information Services (CANFAX)," Proceedings of the CAES Workshop, Banff, 1970; and by R. G. Marshall and H. B. Hqu, A NationalTResearch Program for the Marketing of Canadian Cattle and Beef, a restricted distribution publication, SchOOl of AgFicultural Economics and Extension Education, University of Guelph, 1970. 67 The profit function for the dairy or beef (cow-calf) farmer could be depicted as follows: - * (2]) Trt - Pmilk Qmilk + Pbeef Qbeef + Pgrain Qgrain‘ ' f3(Qmilk’ Qbeef’ Qgrain’ other expenses). But each output is subject to the constraint of the production function. Production functions can be written as follows. (22) Qmilk = f4 (dairy cows, grain, forage, labor, housing, non-farm inputs, technology). (23) Qbeef = f5 (cows, grain, forage, labor, housing, non-farm inputs, technology). It will be noted that grain is an input into the production of beef and milk, it also competes for resources with beef and milk production. Thus a production function can be written (24) 0 grain = f6 (land, labor, mach1nery, non-farm 1nputs, weather, technology). The following argument is developed in terms of these basic production functions. It Should be recognized that (1) grain and livestock production are both competitive and complementary in production and (2) that milk and beef are produced as joint products in some proportions. 10* is grain sold, 0 . ' r 'n r duced. gra1n is 9 a1 p 0 grain 68 Substituting equations (22) and (23) into (21) and differentiating (21) with respect to cows, the following is obtained. (25) d = P a Qmilk + 3 Qbeef + a Qgrain d cow milk a cow beef a cow grain a cow 3 P . a P a P . f ( ) m1lk beef grain _ 3 + Qmilk a cow + Qbeef a cow + Qgrain a cow cow ' Since for each farmer %-%-= 0, the fourth to six terms drop out. If P is equated with the value in milk or beef production then the grain third term is cancelled out as well by the last (cost function) term. The MVPcow then equals a Q - 3 Q . f _ m11k beef _ _._3_ (25) MVPCOW ' Pmilk a cow beef a cow cow ‘ Using an adaptation of equation (26) the E(MVP) of a cow can be approximated by the discounted value of all future net returns.‘ ‘This formulation is an adaptation of the familiar capital budgeting discounted present value formula. It is given in many texts including J. C. Van Horne, Financial Management and Poligy, 2nd ed., Englewood Cliffs, N.J., Prentice Hall, Inc., 1968, pp. 53-55. Branson provides a lucid argument demonstrating that utility is maximized by maximizing present value in W. H. Branson, Macroeconomic Theory and Policy, New York, Harper and Row, 1972, pp. 199-203. Branson goes on to demonstrate that the present value criterion is preferred to the marginal effeciency of capital criterion in that the former*exp1icitly considers the Opportunity cost of capital. Because of uncertainty, MVP is seen as a random variable with first and second moments. For this reason, MVP will be expressed as E(MVP) for the balance Of this theoretical development. It should be explained that MVP is the marginal value of a cow over cost thus for an individual farmer it is discrete rather than continuous. This usage differs from the usual definition of the marginal addition to gross revenue made by the last unit produced and sold. The latter is usually thought of as a continuous differentiable function of output. 69 T [E(P 1 - E(c).] E(P ) (1-R(t))"” (27) E(MVP) = z ‘ J . J + 2 T T j=n (1+1)J (1+1) ’" where P1 = price of milk x quantity of milk price of calf x weight of calf, P2 = price of cull cow x weight of cull cow, C = cost of maintaining cow for 1 year plus cost of maintaining calf until sold (1 year or less), R(t) = a risk factor associated with death; assume that it increases with age, - contain the risk associated with conception, medical problems, calving problems. They also are assumed to increase with age, m A v _.1 V Li. I i = the discount factor, a measure of the Opportunity cost of resources, a variable that has a Pa and PS, T = some terminal length of stay in the herd under existing technology, a function of (MVP, PS), and n = current age of cow, N==0 at first calving. In making decisions on whether or not to invest in breeding stock, farmers look largely at the recent past and next immediate year.‘ This is the case as retain-cull decisions can be made almost con- tinuously and are revocable at a cost for the herd. The lower limit is to cull gll_the breeding herd or to completely disinvest; the upper limit is imposed by the capacity of the physical plant. Alteration of ‘While this model does include expected prices, price expecta- tion models are not explicitly incorporated into subsequent applications. All prices that are subsequently considered are either current or lagged, as noted. The author recognizes, however, that a price expectation model is implicitly suggested. 70 the physical plant requires that E(MVP) of the physical plant exceeds its acquisition price.‘ For an individual cow, E(MVP) diminishes with age as n ----+ T, as shown in equation (27) for positive i. This circumstance is shown graphically in Figure 9. Figure 9. Expected marginal value product, E(MVP), of a cow. The dotted horizontal line represents salvage price or cull cow price. At some age, PS = E(MVP); call this age N*. This can be consid- ered as the average or expected length of stay in the herd for any one cow. At equilibrium, (N*)'1 of the herd is replaced each year. If the herd size is k, then culls = k x (N*)" per year. ‘Expansion of the herd through utilization of existing capacity as compared with expansion through investment in additional plant capacity suggests an interesting and realistic dimension to the problem. This question is left for future studies. .£.'1, rd Vi "' ie-I- a... 1 ‘..\ " ‘ ku. ' 1 we . ,I"‘:" A, a . n ‘- '0. I; .- ‘o. h u, '7‘" . °' .‘.1 ~ Q... ’1— 'b' . 5‘s 7‘ 71 At equilibrium (no growth), X = k x (N"')"1 represents a supply of cull cows and demand for replacements. That is, at equilibrium, no net investment is taking place, gross investment covers only the depreciation on the stable stock of capital (the cow herd). Heifers available to enter the cow herd, Q, also have a distribution of genetic desirability. For this reason, E(MVP) of heifers can be depicted as a downward sloping curve as with cows, however, age is constant (say 1-2 years) while quantity is variable. Figure 10. Expected marginal value product, E(MVP), of a heifer. The E(MVP) here represents E(MVP) of a cow. But heifers have an opportunity cost as slaughter animals. This is represented by the dotted horizontal line Pa or acquisition price. Pa = E(MVP) indicates the supply of replacement heifers. This quantity is denoted as 0*. By necessity, Q* 5,Q. 72 The above formulations consider Pa and PS as constants. This is the situation for a farmer in competitive equilibrium. In the aggregate, however, the price is jointly determined with quantity. These E(MVP) curves become the demand curve for stock of cows and supply curve for replacement heifers, respectively. These curves are considered further in the next section. The above discussion develops the E(MVP) formulation and determines that it is a downward sloping function as well. In the case of a stock of (fixed genetic desirability) cows, this downward slope can be attributed to the aging or physical deterioration process. In the case Of a stock of heifers (fixed age), a downward slope can be attributed to a distribution of genetic desirability. Given these downward sloping functions, an optimum stock can be determined, given Pa and Ps as shown in Figures 9 and 10. A shift in Pa of P5 or a shift in the E(MVP) curve would indicate a new Optimum stock. The adjustment process is indicated by equation (17). This adjustment is carried out by acquisitions and dispositions as noted in equation (18). The E(MVP) function is really a distribution function as previously noted. Thus Q* or N* are not known with certainty. Rather, Q* (and N*) represent a range with an upper bound and lower bound. These might be interpreted in terms of Q; and Q: where the subscripts "a" and "s" have the usual meaning. If this interpretation of 0* is used, then a small change in Pa (or PS) or any of the E(MVP) shifters, might not dictate a change in optimum stock. Three situations might be noted: 73 . add to stock if 0* > O; . decrease stock if 0* < Q: - maintain stock if Q* < 0* < O. Competing_Demands and Complementary Inputs At any one time stocks of cows, heifers, bulls, and calves are fixed. This is certainly the case when the time period under consider- ation is short. Facing this fixed supply are competing demands--the market price is that price that will simultaneously satisfy all demands given supply. This situation is demonstrated in Figure 11 for the competing demands of heifers for replacement and the demand for heifers for slaughter. This situation occurs also in the case of the demand for slaughter calves and the demand for calves for further feeding. P ___________ Slaughter Replacement 0:; Qt Figure 11. Price determination given competing demands and fixed supply. .su 74 Thus, the determination of optimum rate of flow (or stock) must simultaneously consider competing demands given a fixed initial stock. From a stock of eligible heifers, 0, only 0: vfill have E(MVP) > Pa' If the sub-sector is in equilibrium then-- k x (N*)" is the demand for replacement heifers 0* is the supply of replacement heifers and Q* = k x (N"’)"1 conditional on Pa’ PS such that this identity holds true. Also, (N"‘)'1 would be the average replacement rate and herd size would be an excellent indication of cows culled and heifers needed for replacement. But the industry is not in equilibrium as evidenced by the cattle cycle. The E(MVP) curve shifts as does the demand for cattle for slaughter. Thus the Pa’ Ps’ and elements in E(MVP) are indicators of the elements to include in the relevant supply and demand equations. A second supply/demand situation might exist where the demand relative to the stock is so small that the supply is essentially com- pletely elastic. This instance might apply to the demand and supply of bulls. For all eligible male calves, an E(MVP) might be drawn that is downward sloping to the right, as is the case with heifers (as depicted in Figure 10). For all practical purposes, that portion of the E(MVP) curVe lying above Pa represents the demand for herd sires with supply being a ..... . o . wv ‘r- 1 ‘0‘ » .11 . 75 unlimited at P = Pa‘ Thus, the demand for herd sires does not effectively influence price; however, price is exogenous to the demand for bulls.‘ A second phenomena germane to the cattle herd model is the concept Of grain (wheat and feed grain, oilseeds) as complementary to the breeding herd in the production of slaughter cattle ppg_as a product competitive with slaughter cattle for land, labor, and capital. The relevant equations from the simultaneous model expressing these two relationships are (1), (4), (5), (13), and (14). Since both grain and slaughter cattle are final products (with respect to the farm firm) and Since both may utilize the same land, labor, and capital, an exogenous rise in the price of grain will raise the MVP of resources employed in grain production. Land, labor, and capital would be expected to shift toward the production of grains and away from cattle production. This same exogenous rise in the price of grain will raise the cost of slaughter cattle since they utilize grain as an input. The MVP of other inputs, especially stock calves, will be reduced. The MVP of the breeding herd is reduced in like manner. In addition, the costs of land, labor, and capital to gll_phases of cattle production rises ‘Commercial beef bulls sell at a small premium over the price of slaughter steers of comparable weight and age. This premium appears to , just compensate the vendor for the additional effect required to market this male animal in the fashion. A few beef bulls earn a noted economic rent due to their unique breeding or intense marketing effect on the part of the vendor. On a national average, these beef bulls are the exception. 1t: .- van... .1 a \. 1' ‘\ 1 ‘ll .. . 1H" 76 because of their Opportunity cost in grain production. Through the processes described above, the MVP of a brood cow is reduced still further. The extent and rate at which resources move out of cattle production and into grain production is a function of their MPP, as well as relative prices. In addition, their degree of "fixity" in the production of grain and livestock is a second consideration. A third consideration is the degree of perception and rate of response of the micro units. A growing specialization would be expected to fix resources in the production of the product utilizing the Specialized inputs.‘ On the other hand, it would be expected that the superior management of larger, more specialized firms would be more cognizant of and responsive to changes in relative prices, as well as being more sophisticated in the formation of expectations. Since both grain and cattle producers have been rather unaffected by technological innovation, and since the ratio of land to labor or capital remains high, it is expected that resources are rather rapidly switched between livestoCk (including cattle) and grain production. This rapid reallocation might be expected to lead to unstable supplies of both cattle and grain. ‘This fixation is due to the higher prOportion of fixed costs, more specialized units and the lower opportunity costs of those resources. Specialized units would be expected to continue to produce even though prices had dropped rather markedly, while smaller, less specialized firms had switched to other products. 77 Feedback and the Cattle Cyple The cattle cycle, if one exists, is an example of the well documented cobweb model initially demonstrated with the hog cycle.‘ The cobweb phenomena is the result of three basic considerations. The first consideration is that of imperfect knowledge with respect to future demand, supply, and thus prices. Consequently, incorrect (in retrospect) production and investment decisions are made. The second consideration concerns the biological production lag between the decision to increase or decrease production and the realization of that increase or decrease. The third consideration, in the case of beef, is that the decision to increase or decrease production through change in the size of the breeding herd, leads to immediate changes in the supply that accentuate the observed price movement. A fourth consideration, not developed by the classic cobweb model, is that of shifting supply and demand functions. These shifters are often largely exogenous to the economy being modeled.2 . The price mechanism can be, and is, influenced by factors apparently exogenous to the cattle-beef economy. Two examples are weather and government policy.3 These influences can disrupt the smoothly functioning cobweb phenomena. In the instance of government ‘Talpaz, Op. cit. 2The model developed in this dissertation does consider shifting supply and demand curves and because of this, cannot be considered as an adaptation of the cobweb model. 3Changes in weather conditions or government policy anywhere in the world may influence domestic demand through the international trade sector. 78 policy, the intent may be to smooth out this traditional cycle. Ill timed or improperly implemented policy may augment the cycle worsening an already unstable resource allocation situation. Major changes in input prices and opportunity costs for resources employed in cattle (and grain) production are specific exogenous variables that will disrupt the cattle cycle, and must therefore be given consideration when anticipating future supplies. These impacts may be felt in equations (1), (2), (3), (4), (5), (13), and (14), of the simplified simultaneous equation model presented above.‘ Restatement of the Hypothesized Model The simplified simultaneous equation model may be used in still another manner to restate what is and what is not to be included in this Cattle Herd simulator. Equation (1) is Simulated. This equation will be expanded to include Slaughter Steers and Heifers, for Beef and Dairy breeds, for both Eastern and Western Canada. In addition, Male and Female Calves will be estimated, once again for both East and West. Future develop- ment will include the economic impacts producing short term changes in Slaughter Cattle supply and slaughter weight. Equations (4) and (5), as well as identity (6), are modeled. They are, once again, subdivided into Male and Female, Beef and Dairy, East and West. The formulation and parameter estimation of these equations make up the bulk of the next chapter. ‘Government policy in Canada normally works through the price system. A stabilization (control) mechanism would typically operate through the variables explicitly recognized. e . 79 Equations (7), (8), (9), and (10), are not included, nor are equations (11) and (12). These elements of the simultaneous equation model are being developed in a complementary study being conducted at the University of Guelph, for the Economics Branch. Equations (13) and (14) are not developed. These endogenous variables are treated as enogenous to this simulation model. The economics Branch currently have models of this sub-sector; however, there are no plans to coordinate them with this study. Equations (2) and (3) are not being developed in the simulation model at this time; however, it is planned that they be developed for one or more of the planned applications. Specific attention must be given to the economic aspects of changes in slaughter weight. Carcass cut out percentage must also be considered. .1 I" e |":1 L3 1‘" ‘u' 'er ‘ m zll‘a ' v ‘1. T. '1. N'l'pl (Q. I. I b), . 101: ‘I I / 1. D I I" '1‘ l .cn 9 1'1 1:. F‘ t . P ' in; I I 3.. (1 '1' 'A. - ere u... t_ . .y. " ,. . n "J lr CHAPTER III THE BEHAVIORAL MODELS In the previous chapter, it was shown that the change in the size of the breeding herd depended on the relative rate of investment and disinvestment. These rates, in turn, are the result of reactions by farm operators adjusting to realized or anticipated conditions in a competitive environment. In addition, it was shown that realized or anticipated conditions have a distinct bearing on whether or not the progeny of this herd were fed out to maturity or slaughtered at a younger age and lower weight.‘ The theoretical behavioral relationships developed in Chapter II are used to develop specific predictive equations for application in the cattle herd simulator. These predictive equations are used to simulate cyclical motion and long term trends; they fall into three basic categories: 1. investment in the breeding herd (by replacement cattle) 2. disinvestment in the breeding herd (by culling) 3. calf slaughter. ‘A third possibility exists in the form of interregional trade when relative conditions among regions change. These flows are worthy of consideration; however, as previously explained, they are taken as exogenous in this study. 80 81 These equations are both predictive and behavioral. Since price and quantity are determined Simultaneously, in this instance, and since only quantity (or flow rate) is required, an econometric model (or models) is/are developed to remove "own price" and thus avoid the need for simultaneous equations. This econometric model is described in the next section. The econometric model requires that both supply and demand equations be hypothesized. The second section of this chapter lays out these supply and demand models, and in addition, specifies the equations that are to be estimated. The theory developed in Chapter II is used to indicate the structure of these supply and demand models and to suggest the types of variables that should logically be included. The outcome of this chapter is a set of predictive equations developed from these behavioral relationships.‘ These econometric models raise a problem in that the current statistical data series are not complete enough to provide the necessary time series for the endogenous variables. The third and fourth sections, therefore, lay out a set of identities, a method, and a computer program (RECON) that generates the required endOgenous data series from and constrained by existing data series. The fifth and final section displays the estimated behavioral model parameters and relevant statistics. This last section comments on the reasonableness of these estimators and provides ex post ‘No attempt is made to retain any structural nature that exists in the supply/demand relationship or to infer back to them from the fitted reduced forms. 82 explanations. Finally the estimated endogenous data series are listed in tabular form. The Econometric Model In static equilibrium‘ for one commodity in a competitive equilibrium, the Walrasian supply-demand model can be given as: dP _ _ (29) af- 1 we) - sum-<1 mm This formulation was expanded to ”n” commodities by Hicks. But the Marshallian stability conditions could be used as a starting point in like manner.2 This Marshallian formulation would be (30) 3% 4 [0(0) - 5(0)] =4 [5(0)] ‘The argument in this section follow closely that of B. T. McCallum, "Competitive Price Adjustments: An Empirical Study," American Economic Review 44:56-65, March 1974. 2The following quote is taken from M. Blaug, Economic Theory in Retrqspect, Homewood, 111., Richard D. Irwin, Inc., 1968, p. 414. "But the Walrasian excess demand treatment which is usually implied in modern text book treatments is no more plausible than the Marshallian excess demand-price treatment." The context of the above quotation indicates that this is true if both price and quantity can vary. In the instances under consideration, the flows do in no way deplete the whole stock even though the stock is fixed for a given period. An example: in time period "t,“ heifers 1-2 years of age is fixed. The flow, or 0*, being added to the cow herd as replacements, can be varied by altering the flow, Q', being fed for slaughter. 83 where D(Q) = demand price; D(S) = supply price; ¢ = an excess price function. This model can also be presented in graphic terms. The traditional excess demand model is shown in Figure 12(b) as taken from the supply-demand model of Figure 12(a). ED' (a) (b) Figure 12. The excess demand model The axis of these models can be reversed to produce an excess price model. The relationship between P and Q is still negative. These relationships are shown in Figures 13(a) and 13(b). In Figures 12 and 13, P and Q are in equilibrium at P* and Q*; excess price is zero. At a quantity lower than Q*, say Q**, the demand price is D(Q**) and the supply price is S(Q**). Since D(Q**) > S(Q**), d excess price exists equal to P**-P*. To restore equilibrium ag-must be negative as indicated by general equilibrium theory. 84 0* Q** Figure 13. The excess price model Thus %%-= a [demand price - SUpply Price] 01‘ 353-- 1» [D(Q) - s1= 9) [5(4)] as given in equation (30) above. Assuming a linear function, o, this differential equation can be specified in discrete difference equation form. Transformation suggests three different models. (3‘) Qt ' Qt-1 ‘ kEt + et 0" (32) Qt ' Qt-1 = kEt-1 l et-1 or a linear combination I" ‘ I "O -o I l "U' 11..” , n. , . 11 . I P‘ s v”: . ; ..,_ ‘r ~. 85 (33) Q,c - Qt_] = AREt + (1-1)1 v 1— 91 are those associated with revenue, namely, milk and veal calf prices. One index of milk price is the price of manufacturing milk for all purposes plus the government net subsidy on such milk. It is expected to have a negative sign. Since this subsidy was introduced during the l958-1972 period, a dummy variable is indicated to express years of subsidy.‘ This variable is intended to reflect the economic impacts of the psychological effects of the subsidy and the expectations asso- ciated with federal government involvement in manufactured milk policy and pricing. A positive sign might be expected. In addition, a quota system was subsequently introduced with penalties applied for production in excess of quota. The years of over quota penalty are recognized with a second dummy variable. A negative coefficient is expected. The value of the calf is recognized by the inclusion of the price of veal calves giving a positive coefficient. A second major element in the calculation of E(MVP) is the cost of inputs. Three major elements are identified: feed, labor, and cost of capital. All are expected to positively affect the CULLING Rate. The feed cost used is the offboard price of barley. This is the local price at grain elevators for non-Canadian Wheat Board sales.2 The labor proxy used was the monthly salary of farm labor without board. ‘The subsidy coincides with the establishment of the Canadian Dairy Commission. This commission is a federal agency which monitors the sub-sector, makes policy recommendations and implements programs aimed at improving the well-being of the manufactured milk industry. 2International and interprovincial sales of prairie grains, including barley, are a monopoly of the Canadian Wheat Board. Within each province, grains, including barley, trade on a competitive basis. It is felt that this offboard price reflects the within-province competitive price. 92 A third element in the E(MVP) formulation is the salvage value of the cull cow. An increase in cull cow price increases E(MVP), thus a negative sign would be expected. However, cull cow price is also PS. As Ps rises, more cows could be culled, thus a positive Sign would be expected. Consequently, the a priori Sign associated with this variable is indeterminate. The price of cull cows is represented by the price of canner and cutter cows. A fourth and final element in the E(MVP) formulation is the opportunity cost of resources. While this variable can be estimated by the interest rate, a more direct proxy is the price of competitive products. For this purpose, the price of barley and the price of hogs provide one index. The coefficient associated with hogs is expected to be negative, while the coefficient associated with barley is expected to be positive. In the West, due to the actions of the Canadian Wheat Board, the back-up of grains in storage on farms is thought to be a good index of the opportunity cost of resources in grain production. Over the period 1958-1972 there have been considerable technological advances in dairying as well as increased incidence of adoption. These changes fall into the general areas of feeding, breeding, housing, and equipment. It might be expected that husbandry and business management, as well, have improved. These changes have resulted in increased milk yield per cow. One proxy for the net effect of technological changes is milk yield per cow; a second might simply be a time variable. v--.. _ u " y .1 a W"- ,‘ I ‘ u 93 The demand for Cull Cows is a demand derived from the demand for beef, especially low grade beef. It would be expected that demand will vary inversely with own price and directly with the price of substitutes and income. The own price is again taken as the price for canner and cutter cows. The price of choice slaughter steers and index 100 hogs are taken as substitutes. Aggregate national income deflated by the consumer price index is taken as the income variable. The supply and demand functions for Cull Dairy Cows are laid out below and manipulated to produce excess price functions as given by equation (35). The excess price function in turn is substituted into the first of the four econometric models represented by equations (31), (32), (33), and (34). The supply function for Cull Dairy Cows isz‘ 'Pm-b'N+b'L-b' C_1 (4°) C“) 3 4 5 6 0 + 11,135“C + béPOPC - b P" + b'7Pb + béI + DOW+bl0M+b111° This function is manipulated into the form required for the excess price functions as follows: (41) PC+c=b +bcc+bPOPC-me-bN+bL-bPv+b b 012 34567p -+b81 + b W+me+b T. 9 11 ‘For a description of the variables used in these equations, "efé‘r to Table 3. 94 Table 3. Notation for and description of behavioral model variables Variable name Symbola Source and description Cow SLAUGHTER (CULLS) CE Revised output of program MATRIX, expressed in head. Bull SLAUGHTER (CULLS) Ch REPLACEMENTS, Heifers Rb REPLACEMENTS, Bulls Rv Calf SLAUGHTER Sh Heifer SLAUGHTER Ss Steer SLAUGHTER S _ ............. P .................................................................. Cow Population POP: Source: Report of Livestock Survey's Cattle, Sheep Bull Population POPh Horses. Expressed in head. Heifer Population POPS January 1 value--published December 1 statistics. Steer Population POP July 1 value--published June 1 statistics. April 1 and October 1 value--average of December 1 and June 1 published statistics. Price of choice slaughter steers P: Source: QUaPterly Bulletih Of-AgFitdltdFdl-StdtiStiES. Price of good heifers E+c Expressed in dollars per pound. Price of canner and cutter cows Pcv Toronto and Calgary prices used except for veal where Price of good stock steer calves P v Edmonton replaced Calgary prices, expressed in dollars Price of good veal calves P per pound. ............................................ ,---------------------------------------_--------------_ Price of index 100 hogs Pfig Source: Quarterly Bulletin of Agricultural Statistics. Expressed in dollars per pound. Toronto and Calgary prices used. Grade A hog prices converted to index 100 by: index 100 - 0.971429 x grade A. Price of barley (off board) P5 Source Economics Branch, Agriculture Canada. L Expressed in dollars per bushel. On farm grain stocks (March 31) K Source: Quarterly Bulletin of Agricultural Statistics. Expressed in millions of tons. The March 31 value is used for the first quarter and the last three quarters of the previous year. ............................ b----------n-----------------------------------—---o---— Price of manufactured milk for P” Source Dairy Review. Expressed in dollars per all purposes plus subsidy hundred weight. Years of milk subsidy N F A zero/one variable. Value of l for the second quarter of 1962 forward. Years of over quota penalty L A zero/one variable. Value of 1 for the second quarter of 1967 forward. Interest Rate I Source: Bank of Canada, Annual Statistics Review. Expressed in two places of decimal. .. - ......... p ---------- p ....................................................... Farm wages (without board) W Source: Quarterly Bulletin of Agricultural Statistics. Expressed in dollars per month. In all cases the value for the fourth quarter is a repetition of the third quarter value. Milk yield per cow M Source: Dairy Review and Report of Livestock Survey's ‘ Cattle, Sheep, Horses. Calculated in hundred weight per annum by the formula: total milk production average dairy cow population The one annual figure was replicated for the four quarters. .................................. 1.----------.-----------------1...-.------------——-------------------- Aggregate real income Y Source: Prices and Price Indices and National Accounts. Income and expenditures by quarters, expressed in J millions of dollars at annual rates. Time T First quarter 1948 - O. “The following superscripts modify the variable symbols: E - Eastern Canada; W - Western Canada; 8 - Beef Cattle and D - Dairy Cattle. 95 The demand function is stated and manipulated in equations (42) and (43). C ' I C+C 1 S 1 hg 1 (42) C a0 - a]P + aZP + a3P + a4Y. _ c s hg (43) Pt - a0 - a1C + aZP + a3P + a4Y. Equation (44) is obtained by substituting equations (42) and (43) into the excess price function, equation (35). 1 l (44) Et = (ao-bo) - (a +b 4 2 3 )Cc + a2PS + a3Phg + a v - b POPC + b Pm b — b I - b w - b V + b4N - b L + b P - b P 8 9 10 5 6 7 M ' bllT. This excess price function is then substituted into the first of the econometric models, equation (31), where CE is now substituted for Q: in that equation. C C _ C S ct ‘ Ct‘] ’ k(ao-b0) ' k(a]+b])ct + k(azp ,oooo, b11T). c c _ c s Ct + k(a]+b])ct - k(a0-bo) + Ct-l + k(a2P ,...., b11T). t = (1+ka1+kb]) I (1+ka]+kb])_Ct-1 + (1+ka]+kb]) s (a2P ,...., bllT)' .3“ me u >\ o,..' “ h l .. 1‘ ‘.' .( e 96 The estimating equation for the Eastern Dairy Cow SLAUGHTER becomes, in reduced form:‘ cDE _ cDE cDE SE th mE E (46) Ct - "0+"lct-l ~112P0Pt +TT3Pt +114Pt +115Pt +1T6Nt -TT7Lt VE bE E E E E I "apt “"gpt "'10‘1; ’"11wt+"12Yt "'13Mt "'14‘t° To Obtain the Western Dairy Cow SLAUGHTER equation, grain stocks are added as an opportunity cost of dairying. 47 cDW = cDW._ cDW sE th mW _ v bW W W W W I “apt ‘"9Pt I Tr10Kt ‘ Tr11‘t ‘ Tr12wt +1T13Yt ' Tr14Mt " "15" To obtain the Eastern Beef Cow SLAUGHTER equation, the price of veal calves is replaced by the price of good stock steer calves while those variables related to milk are dropped. cBE = +1! CcBE POPeBE +11 PsE +Tr4PcE +11 Pth bE (48) Ct 1TO 1t-1'"2 t 3t t 5t ‘"6Pt E E E - 1T7It - '1T8Wt + nth - 1110T. ‘The additions to the superscripts refer to Dairy (0), Beef (B), East (E), and West (W), as indicated in Table 3. 97 Finally, to obtain the estimating equation for Western Beef Cow SLAUGHTER, farm stocks of grain are added. (49) CCB” = 11 +11 $wa t 0 1 M POPEBW+TT Psw+ Pcw’rn Phgw-n Pb” 2 3t TT4t 5t 6t W W W W + n7Kt-n8It-n9Wt-n]0Yt-n]]T. REPLACEMENTS, Heifers As with Cow SLAUGHTER, four estimating equations are required: REPLACEMENTS, Dairy Heifers, East; REPLACEMENTS, Dairy Heifers, West; REPLACEMENTS, Beef Heifers, East; and REPLACEMENTS, Beef Heifers, West. _At any one time, the supply of Heifers available for REPLACEMENT is fixed. Two separate demands face this fixed supply; namely, demand for REPLACEMENT and demand for SLAUGHTER. The supply/demand model for REPLACEMENT Heifers is then: Dreplacements = f(Price, MVP) Dslaughter compet. prod. = f(Price, Price , Income) S = Dreplacements + DSlaughter 98 If at a steady state, the Herd would require a fixed REPLACEMENT Rate. Thus, size of Cow Herd is a good indicator of the required flow of Replacement Heifers. The demand for Dairy REPLACEMENTS is expected to vary directly with milk price, directly with the years of milk price subsidy and inversely with the years of over quota penalty. In the case of Beef Cows, the demand for REPLACEMENTS will vary directly with calf and slaughter cattle prices. The salvage price of cull cows, canner and cutter cow price, is expected to have a positive effect on REPLACEMENT Rate. Labor cost, feed cost and interest costs are expected to have a negative affect on REPLACEMENT Rate, as would the indicators of technological progress. The price of replacement heifers is expected to have a negative effect on REPLACEMENT Rate. The demand for Slaughter Heifers is eXpected to vary indirectly with own price and directly with the price of good substitutes such as choice slaughter steers, veal calves, canner and cutter cows, and index 100 hogs. The demand fOr Slaughter Heifers is also expected to vary with real aggregate income. The REPLACEMENT demand function is: (50) Rh = bb-biPh+béPOPc+b'Pm+bAN-b'L+b'6Pv+b I CV 1 S 3 5 er8P 7 I C+C I b I I I I 99 It is manipulated so that price appears on the left hand side. h (51) P=b " N-b L+b Pv+b PCV+b PS m P+b456 7 8 C O 3 c+c b + b9P "b10P i—b11W-b121-b]3M-b]4T. The SLAUGHTER demand function is: h _ 1 1 h 1 V 1 (52) S — a0 - a1P + a2P + a3 5 1 C+C 1 hg 1 P + a4P + aSP + a6Y. In equation (53), price is placed on the left hand side. h _ h v s c+c hg (53) P - a0 - alP + aZP + a3P + a4P + aSP + a6Y. The above two demands represented by equations (51) and (53) are constrained by total available Heifers.‘ The excess price function thus becomes the difference between the two demands.2 ‘At any point in time the stock of Heifers available for either slaughter or replacement is fixed at level POPh t’ 2The excess price formulation being used is Et = ¢ (Price Replacements - Price Slaughter). If the values in the brackets are reversed, then the excess price function is Et = ¢ (Price Slaughter - Price Replacement). The use of the latter has the impact of reversing all the signs in the excess price function. The former was used as it was felt that demand for replacements "dominated“ SLAUGHTER demand or SLAUGHTER demand was a residual. The use of the former, therefore, retained the signs associated with the "dominant" REPLACEMENT demand. This decision can be viewed as a hypothesis--the predominancy of "correct" or "incorrect" signs on the parameter estimates will determine whether the decision was correct or incorrect. 100 P" + b P“ - a Pc+c - h h v S S c+c hg c m b - 6121-61314- 6141. (54) Et = (-a0+b0) +a1Sh - bth - (a2-66)P" + b7PCV - (a3-b8)PS - (a14-119)Pc+c - asphg - a6Y + bzPOPC + b3Pm + b4N - 65L — amp" - an - b121- b13M - bMT. The constraint is imposed by POPh = Sh + Rh or Sh = Rh - POPh. Et = (-a0+b0) + a](Rh-POPh) - b1Rh ,...., - b14T. (55) )5t = (-a0+b0) +(a1-b])Rh - alPOPh - (a2-62)P" + b7PCV - (a3-b8)Ps c+c hg c m b - (a4-b9)P -a5P -a6Y +b2POP +b3P +b4N -b5L -b]0P -b]]w-b]21-b M‘b 13 14" This excess price function is then substituted into equation h _ (31), where Rt - Qt' 101 h h _ h h (56) Rt - Rt-l - k(-a0+b0)-+k(a]-b])R -+k(-a]POP , ....,-b]4T. h h h __ h h Rt - ka1R +kb1R - k(-a0+bo) +R,c_1 +k(-a]POP 43141. (57) Rh k('a0+b0) 1 h k t = (1-fi]+kb]) I (l-ka]+kb]) kt-l + (1-ka]+kb]i h (-a]POP ,...., - b14T). The estimating equation for Eastern REPLACEMENTS, Dairy Heifers now becomes: hDE _ hDE hDE- vE- SE - c+cE-— th E cDE mE E bE E 117Yt + 118POPt ”9P1. +"10"1;"'11Lt"'12"t '"13wt I T. E t'"15”t"'16 ’ 1'14 The estimating equation for Western REPLACEMENTS, Dairy Heifers is similar except that grain stocks are added as an Opportunity cost for resources employed in dairying. In addition, good stock steer calf price replaces veal calf price. 102 (59) R =11 +11 Rho”- t 011;-1‘T POP‘t‘Dw + 1: PC” f 11 PS“ " 1r PC+Cw Phg“ 2 3t 4t‘5t '"6t w cDW mW w BW ‘ "7Yt +‘T8P0Pt * "9% + "ToNt ' "11Lt ' "12Pt * 1'13Kt w w ’ Tr14“); ' '"15‘t "'16Mt ‘ 1"17" Eastern REPLACEMENTS, Beef Heifers are estimated with a similar equation except that those variables related to milk are dropped. th "6Pt hBE _ hBE hBW cE-+ SE - c+cE -1T7Yw 4' 118%szBE - TT PBE - 1T WE T. t 9t 1Ot'"11‘t"'17 The Western REPLACEMENTS, Beef Heifer estimator includes the farm stock of grain as an index of on-farm opportunity cost of resources employed in grain production. hBW _ hBE hBW CW-F sW-+ c+cW th (61) Rt - 110+TT-lRt--l-112P0Pt +113Pt -114Pt -TTSPt -TT6Pt W cBW BW W ’"7‘1; I "apopt ‘ "9Pt +"10Kt ’ 1"11”1; ' "12‘1: ’ "13" 103 Bull SLAUGHTER and REPLACEMENT The demand for Bulls is derived from a technical requirement fOr the production of Cattle and thus, from the demand for Cows. This latter demand, in turn, is derived from the demand for beef and dairy products. It is expected that if the Cow Herd expands, then more Bulls will be required and vice versa. If Bulls have a fixed useful life, then the demand for Replace- ment Bulls, as well as the supply of Cull Bulls, are indicated by the stock of Bulls, everything else being equal. Since the flow for both SLAUGHTER and REPLACEMENT are influenced by changes in the size of the Cow Herd, factors influencing that Herd would be expected to influence the Bull Herd, and in the same direction. The demand for Replacement Bulls is expected to vary directly with the price of milk, directly with the price of stock calves, and inversely with the cost of barley, labor, and interest. In addition, it is expected that the increased use of artificial insemination and possibly more efficient use of existing bulls, could result in a negative time trend. The demand for Slaughter Bulls is expected to be a competing demand with Replacement Bulls, both constrained by the supply of exist- ing eligible Male Calves. However, only a small proportion of such Calves are required for Herd sires. In addition, the cost of main- taining a Herd sire is a relatively minor cost in the production of Calves, therefore, these cost factors are not considered. 104 The market for Slaughter Steers is not felt to be influenced by the demand for Replacement Bulls; however, the price of choice slaughter steers may represent an acquisition price for Bulls. In the context of the following model, the indicated sign would be negative. However, the price of slaughter steers should directly affect the price of the stock calves and positively influence the E(MVP) of cows. This latter positive influence is felt to be the stronger of the two. The model that is proposed may be represented by Figure 10, of the last chapter, where the E(MVP) curve becomes the demand curve for Replacement Bulls, D-D'. The 0-0' curve is derived from the demand for a Cow Herd and thus the E(MVP) of Cows. The supply curve is infinitely elastic at Pa = f(price of choice slaughter steers). Thus, the estimates for Cull and Replacement Bulls are based on derived demand. The estimator for Eastern Bull REPLACEMENTS then becomes: mE cE c+cE th t +“"spt +a6pt bE bE sE P +a7Pt - CE (62) Rt - a0+a1Rt_1+a2 t +a3POPt +a4P bE E E The estimator for Western Bull REPLACEMENTS is similar with the exception that grain stocks are added as an index of opportunity cost. bW _ bE SW cW mW cW c+cE th (53) Rt - a0+a1Rt +azP.c +a3POPt +a4Pt +a5Pt +a6Pt +a7Pt bW w w ' aBPt +a9Kt'alOwt'alllt'alZT' 105 The supply of Slaughter Bulls is once again thought to be mainly a function of the demand for a Cow Herd and beef in general. Thus, the demand for Bulls as a source of beef will not be considered. The estimator for Eastern Bull SLAUGHTER then becomes: bE _ bE sE CE mE CE c+cE (64) Ct - aOi-alCt4-a2Pt -a3POPt -a4Pt -a5Pt --a6Pt th bE E E - a7Pt ‘Fa8Pt -+a9Wt-+aIOIt-+a]1T. and for the Western Bull SLAUGHTER: bW _ bE SW CW mW CW C+CW (65) Ct - aO-taICt_]-a2Pt --a3POPt --a4Pt --a5Pt -a6Pt th bW W W Calf SLAUGHTER The Cattle Herd simulator requires four Calf SLAUGHTER estimating equations: 0 Male Calf SLAUGHTER, East; . Female Calf SLAUGHTER, East; 0 Male Calf SLAUGHTER, West; and 0 Female Calf SLAUGHTER, West. At any point in time, the stock of Calves available for SLAUGHTER is fixed. There are two major demands facing the stock of Calves. The first of these is the demand for SLAUGHTER, the second 106 is the demand for further feeding. The next Chronological market for Calves, beyond the market for Slaughter Calves, is the market for Stock Calves. The demand for Stock Calves is a function of the cost and availability of feed and the expected price of slaughter cattle. In Eastern Canada, most Slaughter Calves are a by-product of the dairy industry; thus, the Dairy Cow Herd is a good index of the supply of Dairy Calves; this is more or less true in the West also. Thus, the decision to sell Veal Calves is made in large part by dairymen. The following factors might affect their decision. A rise in the price of milk would raise the opportunity cost of milk fed to Calves, thus, promoting sales of Calves at the earliest possible age, i.e., as light Vealers. A rise in the price of other inputs, such as barley, wages, and interest, would have the same effect. On the other hand, an increase in the price of stock calves would raise the opportunity cost of calves devoted to veal production, thus, promoting a negative relationship. Because the two markets for Calves do not operate for the same Calves at the same time (about 3-4 months apart) and historically not for the same Calves (one is largely Dairy, the other Beef), the two demands were pp§.treated as with Replacement Heifers. Another more practical reason also existed; official estimates of Male Dairy Calves are not available. For these two reasons, the traditional supply-demand model is used. The demand function is: (66) 5V = ' - a'PV + a'PS + a'Phg + a' a0 1 2 3 4V: side. (67) (68) (69) (70) 107 Equation (66) is manipulated to place price on the left hand V = _ v s hg P aO a]S + aZP + a3P + a4Y. The supply model is: s" = b' +b'PV-b'Pc+b'POPC -b'Pm+b'Pb 0 1 2 3 4 5 +VW+b I-VT. 6 7 8 Price is once again placed on the left hand Side. v = vl_ c m b _ P bo+b15 bZP + bBPOPc -b4P +bSP +b6w+b71 681. Functions (67) and (69) are now put in excess price model form. - V C c m b V s hg -b7I + b8T +a2P +a3P + a4Y. The excess price function is then substituted into the first statistical model, function (31), where Sv = Qt. t 108 V v _ v c St-St‘] "' k(ao"b0) 'k(a-l+b-|)St+k(bzp ’eeeo’ a4Y). v v _ v c Sv = + Sv + t (1+kb]+ka]) (1+kb]+ka]) t-l (1+kb1+ka]) C (bZP ,...., a4Y). The estimating function for Eastern Male Calf SLAUGHTER then becomes, in reduced form: vE t-l CDE-tn PsE.+" Pth+TT YE va _ (7‘) 5 " t 4t 5t 6t CE t 110 + 1113 + 11th - 113POP mE bE E E ”7P1; '"apt "'9“t"'1o‘t+"11‘° The estimating equation for Eastern Female Calf SLAUGHTER is va _ vE CE CDE SE th E 11 +“lSt-1+T‘2P -TT3POP +114Pt +115Pt +TI6Yt (72‘ St " O t t mE bE E +"7Pt ‘ "8P1; ' "9”t ' T'10‘1; I T'11 T. The stock of grain on farms is felt, once again, to be a good indicator of opportunity costs and is included in the Western model for both Male and Female. 109 Table 4. Coefficient signs inlied by the theoretical models. old-P “10““ air" .33 no ‘0 u 2 2’ 1; .3 an .3 1» 4E .30 COLL nun ““fifitts‘lw‘.‘ oa6.£. ailflflgw' an O 0 ..“== eessosarcc 5553533“ E33 “ “' 312.15 a éé-Eééém- sggasaaecgagewg "massesggggggfia u Uta-I =3: Sésgageassgessss U 00 UU‘DW cams/1m aaccss§s_.._..c...... 0"- NAG-Amr-r—o—o—r—r-e-r— eaiaeeeeaaaassee CowSLAUGHTER-1 ++++ REPLACEMENTS, Heifers-1 e + + + Bull SLAUGHTER-1 + + REPLACEMENTS, Bulls-1 + + Calf SLAUGHTER-1 + + + Population Cows-1 - - - - + + + + - - - + + - - - Pupulation Heifers-1 - - - - Population Bulls-1 - - + + Price slaughter steers-I + + + + +/- +/- +/- +/- - - + + + + + Price can. and cut. cows-1 +/- +/- +/- +/- - - + + Price stock steer calves-1 + + + + + - - + + + + + Price veal calves-1 + + +/- Price index 100th + + + + - - - - - - + + + + + Price manufactured milk + + + + - - + + + + + Milk subsidy + + + + + + + Over quota penalty - — - - Price barley - - - - - - - - + + - - - - - - Grain stocks + + + + - + + + Interest - - - - - - - + + - - - - Farm wages - - - - - - - + + - - - - - - Real aggregate national income + + + + - - - + + + Milk production per cow - - - - Timeb ---- ---- ++-- +++ Season .The excess price function, as specified. reverses the sign of the regression coefficient associated with the exogenous and lagged endogenous variables of the supply function. bThe theoretical models do not include a seasonal variable; the nature of the data and the process being modeled suggest its inclusion. llO va _ unw cw ch sw hgw w mN bw w ”7P1; ' "8P1; + "9K1; ' "10”t ' “11% + "12T° vfw g vfw cw cow sw hgw w (74) St no'tn]St_]-+n2Pt '-n3POPt 'tn4Pt -+n5Pt -+n6Yt mw bw w +"7Pt ' "apt + "9K1: ' 1T10"“: ' "11% + “12T° Modifications to the Specified Models The foregoing models are each modified by the four basic statistical models given as equations (31), (32), (33), and (34). Only model (3l) was developed above for the sake of brevity. Equation (32) has the effect of lagging the demand and supply shifters by one period. Equation (33) has the effect of including both lagged and unlagged supply and demand shifters. And finally, equation (36) has the effect of lagging the endogenous variable both once and twice. The basic period used in establishing the data series is three months or one quarter of a year. The basic production cycle for cattle and grain, and to a lesser extent hogs, is a one-year cycle. Conse- quently, the lag suggested by the econometric model makes little or no basic sense. The fundamental purpose of these models is to generate good predictors, not to test hypotheses. Consequently, the question of the lll appropriate lag is left as an open question. Lags of zero (t) to four (t-4) quarters were considered, and the decision rule used was to select the lag giving the best fit in terms of the "t" statistic. The final model selected is some combination of statistical models (31) to (34). An ex post rationalization for the selected models is given in the final section of the chapter. A second major modification to these models is the addition of seasonal dummy variables. The rationale for adding these variables follows the argument presented with respect to lags and the annual production cycle. That is, the basic production cycle for crops and livestock is an annual cycle highly dependent on the seasons. Response to endogenous and exogenous stimuli is not necessarily immediate nor of a fixed lag, but seasonal. The calendar year was divided into four quarters; these quarters were used to represent the seasonal influence. 112 Accountinggldentities for Cattle and Calves The next major problem to be considered is the availability of time series data for the endogenous variables. In many instances these are not available from any source. The following table indicates the endogenous data series required and those available for both East and West. Desired Available Veal Calf SLAUGHTER Veal Calf SLAUGHTER Bull SLAUGHTER Bull SLAUGHTER Bull REPLACEMENTS no data available Dairy Cow SLAUGHTER Cow SLAUGHTER Beef Cow SLAUGHTER Dairy REPLACEMENT, Heifers . Beef REPLACEMENT, Heifers "0 data ava‘13b‘e Thus, an attempt must be made to generate data series from known information and relationships. The following identity is the main relationship which is employed. (75) POP“.l E P0Pt + REPLACEMENTSt - DEATHSt - SLAUGHTERt + IMPORTSt - EXPORTSt. P0Pt+1 and P0Pt are known from available data series. DEATH Rate is being taken as given from a study of DEATH Rates. EXPORTSt and IMPORTSt are known in an aggregate fashion; they must be disaggregated to meet the needs of the model. Three bases will be used for this disaggregation: 113 l. disaggregate data from l969-1972, inclusive; 2. informed judgment of professional livestock economists; and 3. evidence given by the simulation model(s). Thus, we might indicate that the following models are conditional on a set of parameters (A3,....,xk)1 which are used to disaggregate EXPORTS and IMPORTS. Turning to the Cow Herd, there are two unknowns remaining in identity (75), SLAUGHTER and REPLACEMENTS. Since the size of the Dairy Herd is more stable than that of the Beef Herd, the former will be considered first.2 Over the period under consideration, l958-l972, the Dairy Cow Population has been monotonically decreasing, with the exception of the years 1960-196l. By fixing alternately CULL Rate (A1) and REPLACEMENT Rate (A2), a data series can be generated for the non-fixed element in the identity. If CULL Rate, A], is set at some Rate known to be historically correct on average, then identity (75) can be solved for REPLACEMENTSt. POP +1 = P0Pt + REPLACEMENTS - DR - POPt — A] 0 POP t t + IMPORTSt - EXPORTSt. 1Parameters A3 to Ak are dummy parameters representing whatever structure and parameter values are necessary to disaggregate the pub- lished EXPORT and IMPORT data series. 2This same situation applies in reverse to the Eastern Beef Cow Herd, with the exception of l966, the Herd has been growing at a fairly constant rate since l958. 114 Now solve for REPLACEMENTSt. REPLACEMENTS = P0Pt+1 - POP + DR - POP + A t t 1 . POPt t 2 ' IMPORTS (A3-Aj). + EXPORTS (Aj+]-Ak) J t' (76) REPLACEMENTS ==P0Pt+1-+(DR.+A -1)POPt-IMPORTS(A3,....,A.) t 1 j + EXPORTS(Aj+],....,Ak). In a similar fashion if REPLACEMENT Rate, A2, is known, then identity (75) can again be used to calculate SLAUGHTER (CULLS). t POP = POPt-tA -POP -DR -POP -SLAUGHTER t+1 2 t t t + IMPORTS(A3,....,Aj)t-EXPORTS (xj+],...., k)t SLAUGHTER POP -+A -POP i-DR -P0Pt+ t t 2 t -+ IMPORTS(A3,....,A.) 1 J - EXPORTS(AJ+],....,Ak) (77) SLAUGHTER (1+A2-DR)i-POPt-P0Pt+]-+IMPORTS(A3,....,A.) t J t - EXPORTS(A. 3+],....,A k)t’ If Dairy Cow REPLACEMENT Rate is taken as known (an historical average figure) then Dairy Cow SLAUGHTER can be calculated by identity (75). Since Total Cow SLAUGHTER is also known, Beef Cow SLAUGHTERt t can be calculated. 115 (78) Beef Cow SLAUGHTERt E Total Cow SLAUGHTER - Dairy Cow SLAUGHTERt 1'. Beef Heifer REPLACEMENTS can be calculated by substituting (78) into (75) and solving for REPLACEMENTSt (79) Beef Heifer REPLACEMENTSt = P0Pt+1 - POPt + DR - POPt + Beef Cow SLAUGHTER -IMPORTS(A3,....,X.)t t J + EXPORTS(Aj+1,....,Ak)t. Since Bull SLAUGHTER (CULL) data is published, this figure can be substituted into (75) to calculate Bull REPLACEMENTSt. (80) Bu11 REPLACEMENTS = POPt+1 -POP +DR ° POP +Bu11 SLAUGHTER t t t t - IMPORTS(X3,....,Aj)t-+EXPORTS(Aj+],....,Ak)t. An identity type computer program (MATRIX) was designed to calculate the required endogenous data series from published data using the above identities where required. The rates (Ai's and DR's) previously specified are annual rates ifliile MATRIX requires semi-annual rates, thus, equations (76) and (77) must be slightly modified to fit. POPt and P0Pt+1 now refer to semi- annual livestock figures as do EXPORTS and IMPORTS. 116 A DR 1 2 POP REPLACEMENTSt = POPtH + —.2— - P0Pt + t - IMPORTS(A3,....,AJ.)t + EXPORTS(XJ+],....,Ak)t. A = DR . 2 _ _ (81) REPLACEMENTSt POPti-l + (2 2 1) POPt - IMPORTS(X3,....,Xj)t + EXPORTS(XJ+1,....,Xk)t. A _ 2. _DR. _ SLAUGHTERt - POPt-+ 2 P0Pt 2 P0Pt POPt+1 - IMPORTS(X3,....,Aj)t - EXPORTS(Xj+],....,Xk)t. A2 _ DR (82) SLAUGHTERt = (1 + -2— 7) - POPt - POPtH + IMPORTS(A3,....,X.)t J - EXPORTS(XJ+],....,Ak)t. The resu1ts obtained from MATRIX are conditional on the parameters (A3,....,Xk) used to disaggregate EXPORT and IMPORT data. While the best known estimates will be used initially, subsequent new information may be obtained, some of which may be generated by MATRIX and other computer programs used in this study. This new information will require that a revised set of endogenous variables be estimated. The results obtained from MATRIX are also conditional on A] or These are average or typical values but may not be correct for A2. non-average years; a few, some, or most years, may be non-average. This problem is minimized by selecting that Herd (Dairy or Beef) that demon- strates the most stability in the period under consideration. 117 For non-average years, when A] or A2 do not hold true, the endogenous estimates will be badly biased. Since all endogenous estimates are constrained by published SLAUGHTER and Population figures, manual adjustments can be made to the estimated data series. These adjustments were made in a manner consistent with other known informa- tion such as price movements, unusual conditions or unique expectations. In such a manner, endogenous data series can be generated that are consistent among themselves, consistent within themselves, and consistent with known external influences. The generated endogenous data series will ultimately be verified by knowledgeable livestock economists as reasonable and consistent with their concept of the historical situation. This verification will come at some future date when the models developed in this study are used to solve practical livestock problems. Generation of Endogenous Variables Program MATRIX was developed to calculate the time series of endogenous variables required for the behavioral models and ultimately for use in program CATSIM.l In addition to generating these endogenous variables, the program provides another check on consistency and in this way aids in verifying the models and in determining likely parameter values. 1A listing of program MATRIX is provided in Appendix C. All programs are written in FORTRAN IV compatible with Michigan State University's CDC 6500 computer. 118 MATRIX is a quarterly model utilizing identities. The basic identities used are those developed in the previous section, namely, (75) to (82). These basic identities are normally modified slightly to meet the exact application in this model. To repeat a listing made in the previous section, the following endogenous data series are calculated: Dairy Cow SLAUGHTER East and West Beef Cow SLAUGHTER East and West REPLACEMENTS, Dairy Heifer East and West REPLACEMENTS, Beef Heifer East and West Bull SLAUGHTER East and West Bull REPLACEMENTS East and West Male Calf SLAUGHTER East and West Female Calf SLAUGHTER East and West Assumptions The first assumption made in developing this model is that Dairy Cow SLAUGHTER Rate is basically very stable. An observation leading to a second assumption is that the Dairy Herds, East and West, have been basically declining over the l958-l972 period, ang_the Eastern Beef Herd has been climbing steadily over that same period.1 It is further assumed that the SLAUGHTER Rate on the Eastern Beef Cow Herd has been basically stable over the 1958-l972 period. The above assumptions plus identities (75) to (82) are used in generating a first estimate of the 16 endogenous data series. These are 1As previously noted, a slight upturn in Dairy Cow numbers occurred in 1960- 1961. 119 combined with the various published data series. The most critical of these is the semi-annual Livestock Survey. These data series lead to a fourth and fifth set of assumptions. The fourth set of assumptions concerns the quarterly distribu- tion of REPLACEMENTS. From STATCAN figures, the number of additions (REPLACEMENTS) can be calculated for each of the two six-month periods (December 1-June 1, June l-December 1), however, the requirement is for quarterly estimates. The fifth set of assumptions concerns the disaggregation of the relevant data series to fit the model requirements. Discussion of this third and fourth set of assumptions occupies much of the balance of this section. Calculation of IMPORTS.--The data series used to calculate IMPORTS is the STATCAN annual series Purebred IMPORTS which is available on an annual basis. This data series was disaggregated into first half/ second half, Beef/Dairy, and Male/Female components using available monthly 1969-1972 data as a basis.1 The following parameters and their values are used to disaggregate annual Purebred IMPORTS: Purebred IMPORTS lst half V22 = .526 2nd half V24 = .474 Purebred IMPORTS Female V3 = .90 Dairy VlO = .20 1Appendix A deals with the discussion of data disaggregation and, in general, information relevant to the building of MATRIX and all other models. 120 Calculation of EXPORTS.--The STATCAN annual category Purebred EXPORTS is disaggregated in the same fashion as IMPORTS. The parameters employed are: Purebred EXPORTS lst half V72 = .50 2nd half V74 = .50 Purebred EXPORTS Female V8 = .85 Dairy V9 = .826 A second export category is Other Dairy EXPORTS. These EXPORTS are assumed to be Cows and Heifers Over Two Years of Age. Further, it is assumed that the semi-annual distribution is similar to that for Purebred EXPORTS. The final export category of relevance is EXPORTS, Cattle Over 700 Pounds. It is generally believed that a fairly constant number of these are Cull Dairy Cows, the balance being Steers and Heifers for further finishing and Immediate SLAUGHTER. Observation of the data suggests that at least 11,000 head are shipped annually in this category. These are taken to be largely Cull Dairy Cows. Larger shipments are assumed to be largely Steers and Heifers. This disaggregation was programmed using the following parameters. Proportion of Cull Dairy Vll = .80 Cows in first ll,000 head (East, 3,000 head) (West, 8,000 head) Proportion of Cows in the East Vlll = .lO balance Hest Vll2 = .05 East, 2,400 head) Hest, 6,400 head) 121 An examination of the data also reveals that 57 percent of EXPORTS are made in the first half and 43 percent in the last half. The following parameters are used for that purpose. SLAUGHTER Cow EXPORTS lst half V82 2nd half V84 .57 .43 Calculation of SLAUGHTER.--SLAUGHTER is calculated by summing the UNINSPECTED with the INSPECTED. INSPECTED SLAUGHTER data is avail- able in the form required, however, the UNINSPECTED is only available in highly aggregated form. UNINSPECTED Calf SLAUGHTER is distributed semi-annually by the following parameters. UNINSPECTED Calf SLAUGHTER lst half East V13 = .60 West V14 = .44 UNINSPECTED Calf SLAUGHTER 2nd half East V15 = .40 West V16 = .56 The Male/Female, first quarter/second quarter, and third quarter/fourth quarter allocations are assumed to be the same as INSPECTED Calf SLAUGHTER and are recalculated semi-annually from that source by the MATRIX.program. Cows and Bulls in UNINSPECTED Cattle SLAUGHTER are calculated using the following parameters. Proportion of Cows in UNINSPECTED East V23 = .28 Cattle SLAUGHTER Nest V19 = .25 Proportion of Bulls in UNINSPECTED East V25 = .06 Cattle SLAUGHTER Nest V26 = .06 122 Calculation of Rates.--A set of parameter values, generally described as rates and distributions, are used in constructing MATRIX. The first of these are the quarterly birth distributions. The quarterly distribution of BIRTHS is also utilized in the program to allocate REPLACEMENTS among quarters. These quarterly distributions are: Dairy, East and West lst quarter VALDél; = .262 2nd quarter VALD 2 = .258 3rd quarter VALD( (3) = .222 4th quarter VALD(4) = .282 Beef, East and West lst quarter VALBE(l) = .20 VALBH (l) = .28 2nd quarter VALBE(Z} = .50 VALBNEZ 3 = .64 3rd quarter VALBE 3 = .15 VALBN3 = .05 4th quarter VALBE(4) = .15 VALBN(4) = .05 Two semi-annual Rates are used for DEATHS, one for the first half and a second for the second half. No differentiation is made between East and West. DEATH Rate lst half DRl 2nd half DR2 .008 .006 The final set of Rates concerns that rate at which Cows are slaughtered or culled from the Herd. Rates are estimated for Beef Cows East and Dairy Cows Nest. Beef Cow CULL Rate East lst half V20 = .045 East 2nd half V21 = .055 Dairy Cow CULL Rate West lst half V27 = .08 West 2nd half V28 = .10 123 It should be noted at this point that all parameters including BIRTH Rates, CULL Rates, etc. are used in other programs besides MATRIX. Consistency is attempted among the parameters used in all models thus aiding with their validation. Description of the Model (MATRIX) The model MATRIX attempts to generate plausible time series data for the 16 endogenous variables previously listed. It does this because and in spite of the fact that some of the basic statistical data are not available. The method used in approaching the problem is to make a set of reasonable assumptions. Some of these have been made before; more are made in the balance of this section. MATRIX is divided into two parts. The first calculates endoge- nous variable values for the first and second quarters, the second part for the third and fourth quarters. Structurally, both parts are identical. Calculation of the Cow Slaughter series.--The first two values calculated are Eastern Beef Cow Slaughter and Western Dairy Cow Slaughter.1 The method used is to apply a rate (semi-annual) to the Cow Population to generate that proportion slaughtered. This in turn is allocated quarterly. 1Originally, Eastern Dairy Cow SLAUGHTER was calculated, however, the small errors generated caused relatively large errors in calculation of the much smaller Eastern Beef Cow SLAUGHTER. Calculation of Eastern Beef Cow SLAUGHTER, in this manner, is assumed plausible due to its stable growth over the l958-1972 period. 124 The next two values are calculated using identities (78) and (82). The values generated in this way are Eastern Dairy Cow SLAUGHTER and Western Beef Cow SLAUGHTER. Identity (78) uses the fact that there are only two types of Cows, Dairy and Beef. By the residual method, those that are not the one must be the other. The allocation of SLAUGHTER between quarters is made by allocating the semi—annual in a manner consistent with Eastern (or Western) Cow SLAUGHTER. The seasonal effect is amplified slightly more in the case of Beef Cow SLAUGHTER as opposed to Dairy Cow SLAUGHTER. Examination of monthly Cow SLAUGHTER data shows that Cow SLAUGHTER is low during spring and summer rising during the September-December period. Exceptions occur during periods of rapid expansion or contraction. Calculation of the REPLACEMENT Heifer series.--The calculation of REPLACEMENTS uses a modification of identity (81) where SLAUGHTER is taken as generated above. The REPLACEMENT values generated are Eastern Dairy, Western Dairy, Eastern Beef, and Western Beef. The allocation of REPLACEMENTS between quarters is a problem of some significance. From a priori information it is known that the expected age of a Dairy Heifer at first calving is in excess of 33 months or 2 3/4 years. The data series being calculated is by defini- tion, the rate of flow of 12 month old Heifers, to the Cow Herd via the Bred Heifer stream. It can readily be seen that the two ends of the process differ by 1 3/4 years or 21 months (33 months minus 12 months). If the distribution of dairy cow freshenings is to be maintained over be Or: Q "N :t.:'l r o- l "’1' ,... L‘ b ‘sp‘ N- p P n 125 time, it is reasonable to assume that Dairy Heifers freshen according to the same distribution. It can then be calculated that Heifers entering the Bred Heifer stream in the first quarter (at 12 months of age) will be in the same ratio as Dairy Cow freshenings 21 months later during the fourth quarter. Consequently, Dairy Heifer REPLACE- MENTS are allocated between quarters as follows where VALD is the quarterly birth distribution for Dairy Cows. lst quarter lst half REPLACEMENTS x VALE 4 VALD(l) 2nd quarter lst half REPLACEMENTS x VALD(4) + VALD (T) The same reasoning is used to allocate Beef REPLACEMENT Heifers. In this instance, for lack of better information, it is assumed that Beef Heifers calve at two years of age. Thus Beef Heifers entering the Cow Herd in the first quarter, also enter the Bred Heifer stream in the first quarter. Western REPLACEMENTS are distributed quarterly as follows: VALBW l lst quarter lst half REPLACEMENTS x V LB + V VALBW(2) 2nd quarter lst half REPLACEMENTS x VALBW(1) + VALBW(2) For Eastern Beef REPLACEMENTS, the distribution used is VALBE rather than VALBW. 126 Calculation of Bull REPLACEMENTS.--This calculation utilizes a modification of identity (80). As with Heifer REPLACEMENTS, Bull REPLACEMENTS are allocated using the calving distribution. Since Bulls are assumed to enter the Bull Herd at one year of age, no maturation period need be considered. The distribution used to allocate Bull REPLACEMENTS is VALBE and VALBW in the East and West, respectively. Calculation of Bull and Calf SLAUGHTER.--These calculations involve a manipulation of the INSPECTED and UNINSPECTED SLAUGHTER data as previously discussed. The Generated Endogenous Data Series The endogenous data series generated by MATRIX appear in Tables 5 to 7. Since certain anomalies appear in these data, each data series will be discussed below. The Calf SLAUGHTER series is generated by simply summing monthly published data and in the case of UNINSPECTED SLAUGHTER, disaggregating quarterly and annual data. The only major assumptions of note concerns this disaggregation. These four data series are used directly as endogenous variables in the Calf SLAUGHTER behavioral models. The Bull REPLACEMENT series indicates that most REPLACEMENTS are added during the first two quarters of the year. This occurs to such an extent that negative Bull REPLACEMENT values appear sporadically for the last two quarters. Barring errors in the published data series, the only source of this error can be UNINSPECTED Cattle SLAUGHTER. The Bull proportion of this aggregate series was incremented to 6 percent b 91' . n. It. .i ”Me a.‘- oa- .. p 127 to generate the series presented even though 6 percent is a much higher proportion than that occurring in INSPECTED SLAUGHTER. The only logical explanation that could be found suggested that high demand for Slaughter Bulls came from small UNINSPECTED meat packers producing specialty meats. The remaining negative values can only be inadequately explained by year to year fluctuations. The final data series generated by MATRIX are Cow SLAUGHTER and REPLACEMENT. The assumption that Dairy Cow SLAUGHTER is fairly stable is believed to be reasonably accurate. Since this assumption is used for the West, all Western Cow SLAUGHTER and REPLACEMENT figures are used as generated by MATRIX. In the East, the assumption that the Beef Cow SLAUGHTER rate is stable is undoubtedly a gross abstraction. Consequently, Eastern Cow SLAUGHTER and REPLACEMENT values were adjusted in accordance with a priori information and consistency among these series. These alterations appear in Table 8. Figures 14 to 17 present a visual display of these 16 generated (and adjusted) endogenous data series. 122£3 Table 5. Quarterly INSPECTED plus UNINSPECTED Cow SLAUGHTER and REPLACEMENT, l958-1972. estimated by program MATRIX SLAUGHTER REPLACEKNTS SLAUGHTER REPLACEMENTS Dairy Cows Dairy Heifers Beef Cows Beef Heifers Year Quarter East liest East Hest East liest East lies-t. (5.55) (55.5) (5.15) (55.5) (55.5) (55.5) (55.5) (5555) 1950 ‘ 1 00053 35553 109955 39911 15731 59935 ‘"*7202 57915" 2 50907 30907 99795 37051 13955 50350 12505 132371_ 3 03220"’ 35535 ”95509 39197 15355 59111 23300 51070 5 115155 53555 75753 33725 19550 55575 23079 .51070 1959 1 75255 35090 95559 35033 13513 32555 5331 52351 2’ 59909 30230 57507 33575 12555 3175077 15527 152501 3 73153 37509 75951 55175 12555 52251 27213 29501_ 5 05056 52511 60707 30015 11553 55535 21725 29500 1950 1 75033 ‘33729’ 117535 52553 15535 50951 5911 ”590557 2 55115 29911 105552 39533 15209 35050 9777 135012 3 #1000 37059 09933 53330 9557 53599 29670 55563 5 93953 52551 77355 37255 11571 59055 27375 55553 1951 1 77250 33573 119102 57022 10331 39235 7275 77925 2 59357 30039 110555 53557 5552 51255 15159 175115 3 72395 35390 97055 39573 10355 53590 23955 25555 5 102055 53290 53515 35137 12593 55595 21570 25555 1902 1 ‘101910 35005 112550 31195 ‘110910 55200 ‘0151 ‘70552 2 79930 30155 105555 25952 5925 53095 20379 151590 3 91250 37053 ‘91725 27311 11009 51055 25150““‘57729" 5 117555 51517 75925 23500 13555 70520 22551 57729 1953 1 09523 31970 1155903 35023 11553 52539 9553 72571 2 01792 20350 07553 32539 9553 37315 23959 155552“ 3 90557 35391 90090 32521 11739 59515 19955 73591 5 100560 39909 77519‘""‘20059 ‘15355 ‘52715’ 17110 73591 1955 1 05790 31037 ”135595 31010 ”11979 39920 11577 95150 2 03555 27523 125955 29551 9501 51995 25593 215252 3 09050 35159’ 95529 27275 17303 555551 20151 00125“ 5 111355 35531 75551 23559 22037 75555 19150 00125 1955 1 02059 29535 130795 27755 22259 55593 21300 100952 2 056107 26202 120000 75115 20030 507757 3! 251 230729 3 109555 32335 115553 21295 _J 37555 55019 25555 75957 5 131055 35539'TE“90715—““‘10325‘ r—*50000“"130291"“"25515“—‘“75907" 1355 I 90001 W695 113706 101536 70017 107750 [3051 5b00: ” 2 01357 25515 105755 17129 21750 75555 23102 195755 ”’3 70951 29515’ 91555 20127 21520’ 01909 25957 59052 WWOL 47305 17319 25202 125590 23150 59552 13* 92515 15135 11552’ 50151 10555 "'75502 2 75975 22557 55953 15995__ 9535 50507 25g91 170291__ 3 01735 25975 91255 21535 11920 92055 25539 55579 5 100325 30522 75550 15517 15555 113530 23550 55579 1955 1 55000 23505 . 101597 15753 12575 95070 .13525 75903__ 2 52951 20755"“"‘95299 17551 10205 75775 33550 '“ 173593 3 05770 25239_‘ 101551 22771 12955 95519 11231 53553 5 T042505 25551 7295 19593 15021 109501 0093 53553 1959’ 1 05353’ 22050 111195 50159 12577 509017 20395 52510 2 05553 19552 103305 15720__+_.10372 57157 50995 155523 0 09055 ”23923 97521 31115‘ 13736“"“53305“““15905““—55225“' 5 100555 25977 53535 25773 15759 53550 13575 55225 1970 1 92150 21502 115935 25375 13599 50975 17707 59579 2 90059 19130 105703 22555 1111205 52535 55257 205537 3 55250 23752 50735 20505 15555 51995 31515 52555 5 93571 25010‘ 59509 17903 17555 59097‘“*“20116“““02550“” 1971 1 WWI 2507r 15055 57335 W 2 55750 15275 55910 23295 12325 51553 52135 255095 *0 05571 22917 91203 5523 15036’ 55059 11009 59151 5 91571 25553 75555 5527 19599 75557 7202 59151 1972 1 75535 15525 119990 32505 L.‘556‘ 75505 25500 109755 2_ 00555 15595‘*“’111500"“”""30293”“ 12737""“50371""‘51599“‘"250953"‘ 3 50220 21799 95525 5759 15550 55935 11592 53015 5 91300 25501 55035 7525 20552 75271’ 7509 03010 129 stl0 6. Quartarly INSPECTED plus UNINSPECTED Calf SLAUGHTER. l958-1972. ostlnatad by program MATRIX Ills C0lf SLAUGHTER Fell}. Calf SLAUGHTER Vbar Quartar East East Host (htld) (head) (0500) 1956 126313 56729 2779! 992 10457 H b 1079 5 57071 32 10 115530 44795 20441 1219 5 89636 0 213976 100059 121766 b6 ‘0 222525 116666 116756 126630 216566 116960 166252 157956 213665 #6 217327 96667 125931 110326 17k722 100221 115976 93326 155996 63773 101903 '155225 72509 130 Tibia 7. Ounrtnrty INSPECTED plus UNINSPECTED null SLAUGHTER and REPLACEMENT, l958-1972. cstiuated hy program HRTRlx lull SLAUGHTER auTT REPLACEMENT Yclr Quart-r Rust 19!. 131 000.nm 000.m0 000.0PP 000.0P— 00P.0N 00~.0~ NON.¢N NON.¢F 000.0F w 00¢.F0 00v.~0p —00.0~ ~00.00 n00.0N 500.0P 0N0._N 0N0.pp 000.0F 0 00n.00~ ¢0m.NPF NVO.F0 N¢0.00 NOF.0N 00P.—F 000.PN 005.0 000.NP. 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L op. IAoNp 133 .meh3 vmumswpmm .NNmF-mmm_ .ummm .awkxw=<4m zou xgwmo ucm mmmm omhumamsz: mspa oupumamzH xpgmpgmso .m_ mgamwk mu0~ PNOF on0p 000p 000p n00, 000p 000p «00, 000p NO0F P00? 000p 000p 0m0~ ’ —qqfifiqu—uuudW-d—d-q—qu—q-d—qdq—d.qfi-qu—dqdqdufl—udd—1qq—-4 mzoo mmmm .1 om l O (I) P93H OOO‘l 1 cop mzou zgwma 1 opp g 02. 134 .512: 223.... 2 8.2.33 £378.: 53: 5552...: :8 E3 Ea tom 33225 .2 2.5: N2: :2 22 $2 $2 $2 $2 $2 $2 $2 $2 $2 82 $2 $2 Lomvo: xgwmo \/.\/\/.8 P'afl 000'l J on. mgoypo: yuan . . om— ; 00m A 0NN 135 .mek l were retained. The second property (prediction inefficiency) was not considered as serious in that the five effected models have either high R2 (i.e., .9948, .9208, .9913, .8687, and .9586) or have low impact on the overall situation model, as is the case with the “Bull“ predictors. Cow SLAUGHTER and REPLACEMENT In most of the 16 behavioral models, a lag of more than one period, usually four periods, was found to be most significant, for reasons given above. In the case of Cow SLAUGHTER and REPLACEMENT models, only two of eight have a four period lag, the balance have a one period lag. In the case of Dairy Cow SLAUGHTER and REPLACEMENT, this one period lag can be attributed to a weakness of the seasonal variation. An explanation for Eastern Beef Cow SLAUGHTER and REPLACEMENT lag does not readily come to mind. The price of slaughter steers entered the four Eastern models with a four period lag in three instances and a three period lag in one instance. In the West, the lag on this variable was two period except in one instance when it was three periods. It is interesting to note that farm wages enter both the Eastern and Western Dairy Cow SLAUGHTER models and very significantly so in the East, the dairy region. In this same regard, milk production per cow was a significant variable in the Eastern Dairy REPLACEMENT model. 141 The price of veal calves entered the Eastern Dairy SLAUGHTER model at a very significant level reflecting the significance of this source of income to dairy farmers. As might have been expected, veal calf price was insignificant but stocker calf price was significant in the Western Dairy Cow SLAUGHTER model as well as the Western Dairy REPLACEMENT model. The price of feed, as represented by the price of barley and western grain stocks, were not found to be significant in any of these eight models. It is believed that this is due to the inappropriateness of the statistical index used or to the structure of the model or both. In any case, the real effect of these variables is obscured. The price of hogs enters some models usually with no lag. While price of milk would normally be thought of as a very significant variable, it did not prove to be significant in any one of these models-~this is undoubtedly a result of institutional involvement in price stabilization and its impact on expectations. The imposition of an over quota penalty was not found to be significant; however, the application of milk subsidy had a significant effect in the Eastern Dairy Cow SLAUGHTER model. It was thought that farm wages, interest rates, and milk production per cow would influence SLAUGHTER/REPLACEMENT decisions. With the exception of farm wages, these variables proved to be rather insignificant in most instances. 142 It should be noted that distinct non-linear time trends were observed in the four Eastern models, while the non-time variables proved to be adequate in the Western models. It was observed that the seasonal pattern of Eastern Beef Heifer REPLACEMENT changed over the l958-l972 period. The early part of the period was characterized by high fall REPLACEMENT, while the latter part incurred high spring REPLACEMENT--as in Western Canada. For this reason, one set of regional dummies (the "A" set) was used for the years l958-1967, and another set (the "B" set) for 1968-l972. Serial correlation proved to be a problem with early Eastern Beef Cow SLAUGHTER models. This condition was removed by using time, time2 and time3 variables. While this removes the serial correlation, the basic underlying relationship still remains unidentified. The "h" statistic indicates that the Western Dairy Cow SLAUGHTER model has significant serial correlation. The model used above was attempted but without success. Two different statistics were consulted in an attempt to determine which exogenous, and lagged endogenous, variables were the most important in explaining variation in the endogenous variables. These statistics are the beta coefficient‘ and the R2 delete 1A reference for this statistic is Robert Ferber and P. J. Verdoorn, Research Methods in Economics and Business, New York, The MacMillan company, I962, pp. 994100. TThe authors state, "an idea of the relative imgortance of each independent variable in a multiple regression is o tained through the so-called beta coefficient." "This is not the only means of evaluating the relative importance 143 value.1 While the ranking of these two indices rarely agreed, both identified the same five most important variables in most instances. Dairy Cow Population proved to be very important in both Western Dairy models with Dairy Heifer Population being important in the Dairy REPLACEMENT models. In these latter models real income, price of stocker calves, and the seasonal variable prove important. In the SLAUGHTER model, both fall and spring as well as farm wages were isolated as being important. The seasons fall and summer proved important in the Beef Cow SLAUGHTER model while spring and summer had the same effect in the REPLACEMENT model. Beef Cow Population was important in both with lagged Cow SLAUGHTER important in the SLAUGHTER model. The price of stock steer calves proved to be important in both Beef models, as in both Dairy. In all Eastern Cow models, the time variable (including squared and cubed terms) proved important as did specific seasonal variables in all models except Beef Cow SLAUGHTER. Cow Population proved important in all models except Beef Cow REPLACEMENTS. In the Dairy SLAUGHTER of the different independent variables." Given the model h x] = o] + a2X2 + .f oiXi + E 1-3 the beta coefficient is defined as OX' Bli = “110,.1 1Both the "t" and "F" statistics for the standard error of the regression coefficients provide the same ranking as the R2 delete statistic. 144 model, lagged SLAUGHTER and veal calf prices are noted; Dairy Heifer Population is noted in the REPLACEMENT model. In the Beef models, the two indices fail to agree on the most important variables except as previously noted plus real income. Calf SLAUGHTER The four Calf SLAUGHTER models have consistently high R2 values. In all cases, except Female Calf SLAUGHTER, West, the endogenous vari- able is lagged four periods--in the exception the lag was one period. There appears to be no consistency among the models with respect to lagged Cow Population. In the case of Female Calf SLAUGHTER, East, this variable was not found to be significant. In all cases, the price of stocker calves proved to be a very significant variable. This fact may indicate that dairy farmers, and beef feeders, do consider Dairy Calves as an alternative to Beef Calves for feeding purposes. The price of slaughter cattle was also a significant variable in all four models with a consistent one period lag. This fact may be interpreted to mean that farmers form expectations strongly influenced by recent slaughter cattle prices--these recent prices thus influence whether or not Calves are slaughtered or retained for further feeding. The price of hogs entered both Eastern models but was found to be insignificant in both Western models. This situation may indicate that Eastern farmers and Eastern dairy farmers in particular view hogs as a significant production alternative while this relationship is not so clear in the case of the West. Table 9. behavior modelsa 145 Parameter estimates for Cow SLAUGHTER and REPLACEMENT A. Dairy Cow SLAUGHTER, West 4. Variable Expected coefficient Sign Estimated regression coefficient and standard error Constant Slaughter_] Dairy cow population_1 Price slaughter steers_2 Price hogs_4 Farm wages Spring Summer fiz Standard error h 5239. (2317. 2920** 2045) -.2517** .1024) .0608 -5239.1 .0051) .4407** .2866) .4147 .3081) .3559** .8485) 323** (830.4257) ~42.6815 (1137.0268) 10395.2214* (669.8801) 540.1 -3.1 aAll regression coefficients significant at the 5 percent level are denoted with a single asterisk (*) while those significant at the l per- cent level have a double asterisk (**). This notational convention is continued to Tables l0 and ll. All tests are two-tailed tests. Table 9--Continued 146 B. Replacement Dairy Heifers, Nest Variable Ex ected coe ficient sign Estimated regression coefficient and standard error Constant Replacements_1 Dairy cow population_1 Dairy heifer population_1 Price slaughter steers_2 Price stocker calves_1 Real income_1 Spring Summer ------------------------------------------------ Standard error h +/- 128129.7538** (37202.5045) .2959** (.l204) -.2556** (.0696) .8051** (.2300) -481.4096 (431.7824) 762.6667** (250.1689) -7.4142** (2.1360) 1476.4807 (2407.4369) -2396.8143 (1872.3770) -10070.2533** (2062.8982) b--—-------------------- Table 9--Continued 147 C. Beef Cow SLAUGHTER, West Variable Expected coefficient sign Estimated regression coefficient and standard error Constant Slaughter_1 Beef cow population_1 Price slaughter steers_ Price stocker calves_1 Spring Summer fiz Standard error h 3 -37656.1259** (14268.3452) .5509** (.0942) .0340** (.0082) 1370.9668 (928.8684) -1854.1417** (467.3457) 2528.2616 (4161.3974) 14816.0353** (4554.5544) 21352.8221** (4353.5838) Table 9--Continued 148 D. Replacement Beef Heifers, West Variable Expected coefficient sign Estimated regression coefficient and standard error Constant Replacements_] Beef cow population_1 Price slaughter steers_2 Price c+c cows_1 Price stocker calves_1 Price of barley Spring Summer Standard error DW +/- +/- 72005. (36146. (. -4702. (1699. -3962. (2844. 2873. (1503. -15507. (13923. 107848. (9407. -57797. (21798. -23375. (7932. ------------- 3371** 2612) .2870** .1372) .0496** 0150) 1262** 0234) 3855* 0655) 9203* 3735) 6432 5667) 8030** 3271) 7163** 3628) 2773** 4784) Table 9--Continued 149 E. Dairy Cow SLAUGHTER, East Variable Expected coefficient sign Estimated regression coefficient and standard error Constant S1aughter_1 Dairy cow population_l Price slaughter steers_4 Price veal calves_1 Price hogs Farm wages Years of milk subsidy Spring Summer Fall Time Time squared Standard error h -175450.0196* (99812. 7032) .2109** .0139) .1262** .0483) .6532 .7230) .4092** .3432) .4019** .3366) .1449** .4525) .3600** .9331) .3242** .6800) .4068** .9672) .0833** .2210) .1717** .5361) .5366** .0332) )------------------ ----- Table 9--Continued 150 F. Replacement Dairy Heifers, East Expected Estimated regression coefficient coefficient and Variable sign standard error Constant 779768.2174** 461939.2288** (140060.6315) (112695.9787) Replacements 1 + .1319 .2027 ' (.0669) (.1423) Dairy cow population“1 + -.3607** -.1789** (.0669) (.0416) Dairy heifer population_1 - .3437** .3132** (.0917) (.0980) Price slaughter steers_4 +/- -l408.9147** -1452.9586** (643.1696) (705.6278) Price c+c cows_.l +/- -457.6674 1065.9288 (1030.8904) (1056.3383) Price hogs - 1474.8048** 1175.1190** (363.4522) (379.3627) Milk production per cow - -14.4532* -l9.5076** (8.3878) (7.6607) Spring -9991.5818* -9897.8295 (5626.1975) (6183.2009) Summer -22355.4252** -22645.2115** (4977.9252) (5349.7168) Fall -35404.4679** -37845.2569** (4637.2970) (4710.4716) Time 1530.0588** (503.5889) Time squared -39.1851** (11.6297) -------------------------- ""-""""-‘-"---'-‘-----'--—-('----"'-"------ R2 8764 .8438 R2 .8420 .8091 Standard error 6302.8194 6927.0427 h .4753 ON 1.7345 Table 9--Continued 151 G. Beef Cow SLAUGHTER, East Expected Estimated regression coefficient coefficient and Variable sign standard error Constant -36765.0456 (23493.2732) Slaughter_4 + .5244** (.0773) Beef cow population_1 - .1885** (.0267) Price slaughter steers_3 + -696.5868** (320.4876) Price c+c cows_] -2247.9625** (391.7064) Price stocker calves_3 + 259.3201 (250.6175) Price hogs + 525.8325** (126.9048) Real income + 2.5390** (1.2264) Spring 2725.9907** (1212.2651) Summer 6119.1481** (1466.6370) Fall 6370.4933** (1365.0145) Time -4780.9209** (808.5554) Time squared 101.2289** (22.0375) Time cubed -.8845** (.1971) ............................ 1---_--__-_-__-_-_-__----------------------- R2 8396 82 7900 Standard error 2817.6410 h 1.3984 Table 9--Continued 152 H. Replacement Beef Heifers, East Expected Estimated regression coefficient coefficient and Variable sign standard error Constant 112212.2469** (48163.5818) Replacements_4 + .1176 (.l419) Beeficow population 1 + -.0603 ' (.0476) Price slaughter steers 4 +/- -1393.5692** ' (593.2013) Price c+c cows_] +/¥ -217l.3383* (1305.7785) Price stocker calves_1 + 924.2043 (638.4321) Farm wages - 97.7775 (61.9624) Real income_l - -4.0940*7 (2.4792) Spring A7 15559.7570** (4089.4627) Summer A 18752.6570** (4810.2201) Fall A 32013.6511** (12312.1751) Spring B 27583.4245** (4827.9243) Summer B 4004.7022 (5070.9654) Fall B 26041.7988 (16868.2736) Time 485.1695 (506.3804) Time squaredf 15.4424 (9.6243) ............................ .---_---------_----___---------------------- R2 .8270 R2 .7622 Standard error 5640.5029 h test fails DW 1.6951 153 In three out of the four models, real aggregate income lagged one period was significant while the application of the milk subsidy was found to be significant only in the East. Milk price, price of barley, interest rate, farm wages, and grain stocks proved to be non-significant variables. In all cases, except Western Female Calf SLAUGHTER, a significant time trend was noted. While this trend was downward in all cases, the positive sign on time2 for both Eastern models indicated that the rate of change is slowing. The excess price model proved particularly disappointing in the case of Calf SLAUGHTER in the sense that the realized sign of the regression coefficients were opposite to the predicted signs in most cases. The "incorrect" signs are mostly associated with variables from the underlying "supply" mode1--Dairy Cow Population, slaughter steer price, and stock calf price are examples. The sign of real aggregate income is also incorrect in all instances; however, it serves as a factor in the demand for both_veal and beef. The simplified Calf SLAUGHTER model used in this study did not adequately reflect these two demand functions and their relative income elasticities. Lagged Calf SLAUGHTER was consistently an important variable in all Calf models by both indices. The price of stocker calves was also consistently important by the R2 delete index. Continuing to use this index, the seasonal variable, spring, proved important in Eastern models while fall held the same position in the Western. Table 10. 154 Parameter estimates for Calf SLAUGHTER behavioral models A. Male Calf SLAUGHTER, East Variable Expected coefficient sign Estimated regression coefficient and standard error Constant Slaughter_4 Dairy cow population“3 Price slaughter steers_1 Price stocker calves_] Price hogs Real aggregate income_] Milk price Years of milk subsidy Spring Summer Fall Time Time squared ----------------------------- Standard error h -------------------- 80336.0628 (157301.7436) .4833** (.1032) .0986 (.0756) (21 .6330** .9372) .8488** .7474) .2596* .0427) .8629* .1497) .9538 .3190) .7945** .7433) .1023** .3692) .0444 .3258) .1330** .8357) .8677** (1190. 69. .9653) 8180) 2244** Table 10--Continued 155 Female Calf SLAUGHTER, East Variable Expected coefficient sign Estimated regression coefficient and standard error Constant Slaughter_4 Price slaughter steers_] Price stocker calves_1 Price hogs Real aggregate income_1 Years of milk subsidy Spring Summer Fall Time squared ---------------------------- q R2 'fiz Standard error h 95538. (26234. 9696** 8607) .4582** .0880) .3298 .7172) .5499** .3680) .9670** .2757) .6336* .5608) .8348** .8415) .3015** .1789) .2194 .3352) .9951** .4636) .1973* .2663) Table 10--Continued 156 C. Male Calf SLAUGHTER, West Expected Estimated regression coefficient coefficient and Variable sign standard error Constant 59399.4215** (25761.4252) Slaughter_4 + .4085** (.0729) Population diary + beef - .0132** cows_1 (.0032) Price slaughter steers_1 + -417.1973* (230.8712) Price stocker calves_1 + -503.6313** (157.3257) Real aggregate income_1 + ~12.7213** (5.9461) Spring 1914.7789** (973.3416) Summer 274l.8436** (1041.2650) Fall 3340.8456** (1077.0228) Time -220.5733** (83.7173) ............................ 4__-_-___---_------___-_----_--_--_----__-__ R2 .9458 Ti2 .9352 Standard error 2433 7700 h - 5536 Table 10--Continued 157 0. Female Calf SLAUGHTER, West Variable Expected coefficient sign Estimated regression coefficient and standard error Constant S1aughter_4 Population diary + beef cows_3 Price slaughter steers_2 Price stocker calves_] Price barley Spring Summer Standard error h 8896.0727 (7753.6348) .2835** (.0734) .0150** (.0029) -600.6975* (358.4579) -889.2789** (212.3119) 4379.4108 (2954.2386) -1887.9025 (1454.4207) 2671.5658* (1469.5519) 12084.5311** (1852.4866) 158 For the Eastern models, real income was important by the beta index while the importance of milk subsidy was evidenced by the R2 delete index. In the case of the Western models, the sum of Dairy plus Beef Cow Population was important. In both models, the slaughter steer price was shown to be important by the beta index. Bull SLAUGHTER and REPLACEMENT The least consistent feature of the Bull models is the use of lagged Population as a predictor. In the case of Eastern Bull SLAUGHTER, the sum of Dairy + Beef Cows lagged three periods gave a reasonable fit together with predicted sign. In the case of Western Bull REPLACEMENTS, Bull Population lagged three periods gave the best fit. In the other two instances, a lag of one period on Bull Population was highly significant. The price of canner and cutter cows, price of slaughter steers and price of feeder calves, enter these four models in a rather incon- sistent manner as do hog prices. In the two Western models both inter- est rate and barley price were good predictors even though the sign was "incorrect" in the Bull SLAUGHTER model. Grain Stocks once again proved to be insignificant. A time trend was noted in both Bull REPLACEMENT models; however, the sign was not consistent between them. A positive sign was expected; this occurred in the Western model but not the Eastern. The negative Eastern sign might result from the establishment of a large number of small Beef Herds, each with its own Herd size; this is a hypothesis only. 159 A serial correlation problem occurred with Eastern Bull REPLACEMENTS that could not be removed with either the use of the theoretically suggested variables or by the use of a time trend. The same situation applied to Western Bull SLAUGHTER. The "h" statistic failed in the case of Western Bull REPLACEMENTS: however, the low 0W statistic value and high standard error on the lagged endogenous variable suggest that it also has significant serial correlation. In both Bull SLAUGHTER models, the price of canner and cutter cows was consistently important as were the seasons summer, spring, and fall, and the price of hogs. Lagged REPLACEMENTS was consistently important in the Bull SLAUGHTER models as was lagged Bull Population and time. In both REPLACEMENT models, spring or summer proved important with fall also being important in the Western model. Table 11. 160 Parameter estimates for Bull SLAUGHTER behavioral models and REPLACEMENT A. Bull SLAUGHTER, East Variable Expected coefficient sign Estimated regression coefficient and standard error Constant Slaughter_4 Population diary + beef cows.3 Price c+c cows_1 Price stock calves_1 Price hogs Spring Summer Standard error h 23229.2923** (11535.8110) .1631 (.1142) -.0052 (.0044) -673.4769** (141.2890) 132.4531** (57.9927) 77.3524** (30.2596) 3181.1680** (478.0134) 6716.5654** (907.6478) 3519.1658** (591.4977) 908.6374 Table ll--Continued 161 B. Replacement Bulls, East Variable Expected coefficient sign Estimated regression coefficient and standard error Constant Replacement_4 Bull population_1 Price slaughter steers_1 Price c+c cows_1 Spring Summer Fall Standard error h 69370. (13785. 249. (140. -813. (233. 4653. (1965. -3571. (1324. 1807. (1740. -270. 8097** 8886) .5187** .0948) .4639** .1003) 3419* 6795) 9760** 7458) 4734** 2978) 4345** 9432) 8445 4049) 0263** .7154) Table 11--Continued C. Bull SLAUGHTER, West 162 Variable Expected coefficient sign Estimated regression coefficient and standard error Constant Slaughter_2 Bull population__1 Price slaughter steers_1 Price stocker calves_1 Price hogs Interest Price barley Spring Summer Standard error h 7248.6288** (2098.4868) -.3554** (.1221) .0452** (.0127) 152.0917** (63.2109) -176.3291** (40.6994) 143.2745** (30.6684) .2955** .6899) ~990.3946* (510.6763) 2115.7041** (284.2183) 17l7.3784** .0127) 2023.8506** (367.0365) .8396 678.5276 2.806 Table ll--Continued 163 Replacement Bulls, West Variable Expected coefficient sign Estimated regression coefficient and standard error Constant Replacement_4 Bull population“3 Price slaughter steers_z Price hogs Interest Price barley Spring Summer Standard error DH h 70266.2945** (11677.6818) .5397** (.1430) -.3475** (.1029) -527.0168** (150.5670) -102.4590 (84.6617) -2029.0168** (610.9371) -2922.2334* (1641.2919) 9555.9719** (1843.8523) ~4062.9831** (1405.8923) -6956.0921** (1410.5917) 365.0983** (80.5094) ------------------------ .9586 .9494 2107.3617 1.3924 test fails 164 Table 12. Quarterly INSPECTED plus NINSPECTED Cow SLALSHTER and REPLACEMENT, l959-1972, estimated by the behavioral Iodel WEI! REPLACEMENT SLALGHT ER REPLACEMENT Dairy Cows Dairy Heifers Beef Cows Deei' Heifers . Veer Quarter East West East West East West East ‘ West (head) (head) (head) (head) (head) (head) (head) (head) 1959 1 79963 33623 96196 60763 12907 30032 6269 65591 2 hBMLJ 13L__31621___13567____17.159.___16626__1L6131_ 3 73762 37059 62699 37261 13976 35396 26155 26066 I 91108 “a“ 1: 351 1.0115 11.2.“ 03660 an a; “an _ngn 1 21130 33235 105558 39233 12101 3981.5 1.15:. 50089_ 2 63610 30600 106013 35516 13191 39616 16766 156697 3 11921 314.15 95112 30933 011 6. 6 96329 62532 62653 37710 10371 56295 21669 66206 1961 1 71691 33706 119090 61703 12336 37956 10166 67959 2 12219 31118 110001. «.2351 11111. 33023 23010 1021.23 3 60006 37752 97776 36763 11733 53656 27067 62167 .4962 1 Jane 16066 201882 31125 9893 1.21.32 0253 JSESI 2 62069 31076 102376 26756 11297 36667 22356 172969 3 09531 469M! 93890 201.23 11121. 53585 23939 1.0901 6 111676 61666 72611 26595 12613 66091 20555 67769 1963 1 69569 31630 112666 33663 6609 51666 5606 66679 2 02012 201.02 207,721___35000 9221 63619 217mm 3 91667 36919 97626 36160 11563 55159 20230 50066 —____1 111915 39112 02031 30550 15W “u; fig}: .4366— 1 06691 302.9 1.42911.1__.__301.12.__1823 ’ 66_ ‘ 032. 2 60732 26059 122673 26373 13261 66676 26526 206626 1 90355....13969 102186 30110 16017__.6.601.3____19962_7.9931_ 6 116300 36521 63675 23617 23666 61601 25369 67760 1965 1 90731 29617 119716 26560 22366 75761 16626 96516 .2 65252 26712 116 .i_____13§ ’ 6130. 3 96313 32666 107523 21969 30069 76579 30175 67220 8 121230 m 9"“ “Nil 220“ ““3 _1358 1 91509 21967 128355 10111. 29889 108385 15511. 10208L 2 60031 2659'. 107652 17500 16367 66606 27266 207179 3 0091.1 MLJ933___.17350—..23013__a.uis__82__22221__5690L. 6 97966 33320 77119 15965 25966 101166 22326 59631 1967 1 61767 25561 106330 23061 13376 95976 11616 96637 2 10110 22152 90210 20900 9189 89231 28533 196296 3 76960 27393 63936 19166 9357 76077 26666 56210 WJu—zgm um Ann: mm mm 196 3 3673 106170 2 001 9066 66696 16063 76635 2 10568 20001 96905-_20273_...__107.99_____63601__._..6.3025____.176366-- 3 66075 25766 92662 20619 15607 66931 13666 7 56671 a 1025“ 20952 “a“ ”“5 10.121 100”: 10032 55“; .1169 1 06301_._21002__.116260--- _23.665_.__136LL__._6351.6_ .-_15530_____I_5015_ 2 66331 16991 107596 22967 12257 66921 67775 191169 1. 90 ___36501_2__.252Ll____.16396_____621612....11251_____696n9_. 6 102713 27061 62962 22596 16666 59196 11722 56156 1970 1 69926 21617 121362 25665 16103 65952 26196 99576 2L, 69390_____16226_3__.92712.._.“Z6961,_____9626-_2-_61060m-12267675_.__222165_. 3 66921 23767 63375 21666 15779 56053 20567 69297 *M—flflfi? 113711 ““1 WM 1911 1 01183 20903 90010 2291.2 13058 8111.1 1.1700 10 2 62663 17266 93713 21956 16676 51611 50609 227157 A 63996 23316.._.291067“.___17550m21_-17675.”..213316 m),_19591____.96265_. 6 91516 26069 67526 10166 20726 62967 15536 76299 1972 1 61166 19976 116316 16961 15972 63665 22606 111597 2 08030 15852 101914. 22133 11189 80108 53113 200351 3 76799 22115 93756 15625 16669 76736 11532 76299 if 91616 21.515 821.08 8251 2110L 20519 6665 77220 165 Table 13. Quarterly INSPECTED blus UNINSPECTED Calf SLAUGHTER. l959-1972. estilated hy the behavioral lode H010 Calf SLAUGHTER finnlethlfinAmNflER Veer Quarter East West East West (head) (head) (head) (held) 1959 1 122666 01115 63002 220 71 2 220085 38321 08519 ,21113 3 111075 39620 63906 26952 . 3 91053 35113 37580 38330 .190! 1 122338 30388 88928 28215 2 212327 35595 63136 25296 3 122205 38371 83890 38828 6 103767 36555 61572 66917 1961 1 126309 29710 50263 29609 2 208805 32085 101763 27778 3 126090 36296 50760 35165 6 102830 35305 83387 89115 ._1962 1 115000 28583 87779 30588 ‘ 2 219269 30560 69306 29637 3 127083 32882 53172 ,38050_ 6 113657 29613 67953 66726 1963 1 126766 22750 50132 25566 2 221738, 21211 09583 28125 3 122695 26799 53120 32561 3 ,101131, 129272 ,81311 83511 .4188 L 121739 20150 52003 48031 2 219226 27265 93652 27059 3 120973 29002 51577 38580 6 116203 33031 52275 69103 1965 1 133616 26717 57629 36661 2 220199 33202 91898 30080 3 136292 32961 61615 60999 3 121057 ,56111 ,51588 ,55000 ._1380, 1 ,189082 ,20810 88838 30709, 2 215515 26961 93336 33661 3, 120001 30253 59211 ,36211 6 115120 35355 52666 56216 1967 1 129603 23060 56666 33961 2 ,199669 ,23501 69029 ._29911_ 3 107666 26217 67363 33163 ‘ 8 100822 20709 83000 80392 1966 1 116776 17966 51760 26331 2 200800, 21725 09308, 23825, 3 110736 22931 67167 36531 ,8 99059 23999 83919 85100_ 1969 1 121818 18523, 53898 25171 2 166676 16796 63167 23060 3 92189 ,18839 82338 22233 6 65961 16622 39126 23190 1970 1 116550 11692 52663 10907 2 188193 10089, 15123 0185 3 97633 12951 60966 13256 I ,90880 113020 35331 200.3 ,11911 ,11 ,1106126__- 9016 .63396... 11616 2 156120 9717 69200 10760 3 00181 12810 ,38102 ,1800§_ 6 66996 16269 30931 20009 1972 1 93952 7666 - 36325 6291 2 166636 6730.__”__.mh__..._66536 9233" 3 77266 9662 30506 11661 8 1‘306 121888 29180 15922 166 1’qu 14. Gnu-mu INSPECTED plus UNINSPECTED Bull SLAIEHTER and REPLACEMENT, 1959-1972. «ti-ltd by tho behavioral mac! ‘ luIl SLAUGHTER Bu}! REPLACEMENT Var cum East (had) 1959 0382 15810 CHAPTER IV EVALUATION OF THE STATISTICAL DATA BASE Statistics concerning Cattle and Calves are collected, compiled, and published by several different agencies within Canada.1 Some rele- vant data are collected but only used internally by the collecting agency. Much data that would appear to be relevant to a wide range of problems is not collected by anyone. One question that must be asked by researchers, policy makers, and outlook economists is, do these published data represent a sufficiently accurate, comprehensive, and compatible base for the statistical analysis relevant to the execu- tion of their respective tasks. The implication for statisticians is clear, as is the challenge. These Cattle and Calves data differ among collecting agencies. One such difference concerns the time period of collection. While some series are published weekly, others are published monthly or semi- annually. In addition, some data collection periods coincide with calendar years, others do not. SLAUGHTER and EXPORT—IMPORT data, for example, are aggregated on a calendar year basis while Livestock Pop- ulation data has historically been published on a June 1 to December 1 basis. 1The reader is reminded that the notational convention employed to denote stock and flow variables continues through Chapter IV. This convention is given in Table 2, pages SO-Sl. 167 168 These data differ in definition among agencies. For example, STATCAN's Agriculture Division defines a Heifer in terms of age (l-2 years of age), while the External Trade Division does not report by sex at all. The Production and Marketing Branch of Agriculture Canada, on the other hand, defines a Heifer in terms of certain recognizable physiological characteristics. These data differ with respect to the level and basis of aggregation. As one example, STATCAN's Agriculture Division uses age to designate Calf Population with no differentiation between Male and Female. STATCAN's External Trade Division uses weight, but again no differentiation between Male and Female Calves. The Marketing and Trade Division, Agriculture Canada, uses weight and sex to identify Calf SLAUGHTER. Four related aspects of the overall data problem might be identified. The first of these would be data compatibilityf-this aspect was discussed above. If all data were compatible with respect to time, definition, and basis of aggregation (disaggregation) it would be possible to add and subtract these various data series to generate some desired bit of information. If these data series are not com- patible, then this sort of manipulation may result in such error as to make the end result not only useless, but dangerous. The second aspect concerns data completeness or comprehensive- ness; this aspect was also discussed above and is highly related to data compatibility. The current data base has some glaring omissions. With- out commenting further, it is sufficient to say that missing data can 169 only be generated from the current data base with high potential error due to lack of data compatibility. The third major aspect is data accuracy. Accuracy can be checked by comparing one data series with another. A second method involves periodic completion of a comprehensive and highly controlled survey to generate an "accurate" benchmark. In either case, consistency might be observed, or the two series might differ. If the latter case holds, one series is generally held to be correct and the other incorrect. In the same sense, if the two data series are consistent then they are both considered to be correct. Correct and incorrect are inappropriate words for describing these sorts of consequences. While consistency is necessary for accuracy, it is not sufficient; these data must be believed to be accurate and found to be useful in solving meaningful problems. These data are believed to be correct in a probablistic rather than an absolute sense. The fourth and final aspect of the data problem concerns application to meaningful problems. If the data is accurate, compre- hensive, and compatible, then it may be used for analysis and projec- tion work, among other uses. If the data base were to meet the above three conditions, results of analysis and projections would be held in higher regard and found to be more useful. In attempting to build a demographic model of the Cattle Herd, it is critical that both the builder and the user have some knowledge of the reliability of these basic data series. While it may not be possible to isolate exact errors, it is hoped that the sign and the 170 relative magnitude of biases may be indicated, trends noted, and the deviation in random errors isolated. Information concerning these biases, trends, and inconsistencies could be conveyed to the collecting agencies; this act would constitute an additional payoff to the investigation. To this end, a project1 was initiated in the Research Division, Economics Branch, Agriculture Canada in mid-l973. This work was curtailed in part during early l974, as the economist in charge changed positions. An internal report on this project was produced in mid-1974. The continuation of that project became part of this current study where its basic concepts are retained intact. The model RECON is an attempt to computerize its major features.2 The purpose of RECON is twofold. First, the model attempts to reconcile the various available data series, to note discrepancies, and to evaluate the data series for error, bias, trends, and randomness.3 The second purpose is to obtain one estimate of some of the parameters that will be used in MATRIX and CATSIM. It should be noted that RECON, MATRIX and CATSIM all model the same Cattle Population over the same time period using the same basic statistical data. The difference 1Bruce Lee, "Simulation of Population in Several Sub-Categories of the Canadian Cattle Herd,“ a mimeographed paper, Economics Branch, Agriculture Canada, Ottawa, l973. 2The method of analysis involves providing a visual array of RECON output that may be compared with published official data. 3A listing of program RECON is provided in Appendix D. l7l among them basically involves level of aggregation, although methods of calculation vary also. All three models complement each other and should be generally consistent with each other. By utilizing all three models, it is planned that a dynamic picture of Cattle demographics will appear, together with plausible estimates of critical system parameters. RECON is an annual model utilizing annual data only. All equations are identities using the basic livestock identity (75) from Chapter III. It is reproduced here as follows. (83) Populationt+1 E Populationt-+BIRTHSt-tTRANSFER INt--DEATHSt - SLAUGHTERt-EXPORTStT-TRANSFER OUTt. This identity (in a modified form) is used for each and every row of the RECON output matrix which is displayed in Figure 18. This modifi- cation is shown in identities (84) and (85). (84) TOTAL SOURCES E Populationt-tBORNt'fTRANSFER INt+Il~1PORTSt (85) TOTAL DISPOSITIONS E DIEDt-+SLAUGHTER -+EXPORTSt'+TRANSFER OUT t t + Populationt+]. If identity (83) holds true, then TOTAL SOURCES E TOTAL DISPOSI- TIONSt if not, then an "ERROR" of given magnitude and sign is produced. The "ERROR" will be discussed in more detail later in this chapter. T72 RECON's output matrix is produced for each year under consideration, i.e., l958-l972 inclusive, for both East and West. NEST-EAST Cattle Movement provides one major link between the two Cattle producing regions. This dichotomy allows an evaluation of the completeness of NEST-EAST Cattle-Calf Movement data. In addition, some evidence may be found concerning the sex of Cattle and Calves shipped East. There initially appears to be a duplication with respect to Calves; this is not the case however. Calves have been split into two groups; Calves Born This Year (XCAV stream), and Calves On Hand (YCAV stream). This split assists in tracing the flow as it ages. For example, Ending Calf Inventory must all be due to this year's BIRTHS, while all Calves in the YCAV stream must be disposed of or allocated to non-Calf categories by year end. In the discussion that follows, the calculation of the elements of the RECON output matrix are considered. An important part of the discussion concerns the assumptions made and the initial values of the parameters that are used. As was the case with MATRIX, a critical problem is the disaggregation of statistical data to fit the structure of the model. This disaggregation is discussed in the next sub-section. Data Base Disaggregation The discussion of the data base follows closely the same discussion with respect to program MATRIX presented in Chapter 111. To avoid undue duplication, this discussion will be abbreviated. I73 EXPORT and IMPORT data.--Since RECON is an annual model, only annual data are used. The first export category is Cattle Under 200 Pounds. These are assumed to be solely Male Dairy Calves. A second export category is Cattle ZOO-700 Pounds. This flow is divided between Male/Female and XCAV/YCAV streams. The first case is self explanatory; however, the second may need further elucidation. The XCAV stream refers to Calves born thj§_year while the YCAV stream refers to Calves born la§t_year. Calves exported in this category may be either this year's or last year's Calves. A further assumption is made that only Beef Calves are exported in this category. The following parameters are employed. Proportion of EXPORTS ZOO-700 Pounds from XCAV stream Vl = .90 Proportion of Male Calves in EXPORTS ZOO-700 Poundsl V2 = .l35 The export category Other Dairy EXPORTS is assumed to be solely Dairy Cows and Heifers over two years of age. As such, it is in a form for direct use in the model. The import category Other IMPORTS is assumed to be soley Steers and Heifers for Immediate SLAUGHTER. This category is further assumed to contain only Beef Cattle. The Male/Female separation remains. It is disaggregated by parameter V12. Pr0portion of Steers in Other IMPORTS Vl2 = .65 1This parameter value is the subject of subsequent discussions in this chapter. This value by itself can be very misleading. T74 The Purebred EXPORTS and IMPORTS remain to be disaggregated into Beef/Dairy, Male/Female components. The following parameter values are used. Proportion of Females in Purebred EXPORTS1 East, V3 = .90 West, V4 = .90 Proportion of Females in Purebred IMPORTS2 East, V5 = .80 West, V6 = .80 Proportion of Dairy in Purebred EXPORTS East, V7 = .826 West, V8 = .826 Proportion of Dairy in Purebred IMPORTS East, V9 = .20 West, VlO = .20 The final export category is Cattle Over 700 Pounds. As previously discussed, a fairly stable element in this category is Cull Cows; the transient element is Steers and Heifers for further feeding and Immediate SLAUGHTER. This was programmed using the following parameters. The critical limit referred to is 8,800 head of Cull Cows, 2,400 East and 6,400 Nest. The following parameters are used to model this feature. Proportion of Steers in the non-Cull Cow portion of EXPORTS, Cattle Over 700 Pounds, Vl4 = .35 Proportion of Cull Cows in EXPORT Cattle Over 700 Pounds Under a critical limit, Vl5 = .80 Over a critical limit, East, V16 = .10 West, Vl7 = .05 lThese parameter values differ slightly from the values used ultimately in CATSIM and MATRIX; however, all models prove to be relatively insensitive to these parameters. 2Ibid. T75 SLAUGHTER data.--Calf SLAUGHTER is assumed to be totally Dairy fi Calves. Cow SLAUGHTER must be divided between Dairy and Beef Cows, however; the following parameters are employed. Proportion of Beef Cows in Cow SLAUGHTER, East V20 = .lO Proportion of Dairy Cows in Cow SLAUGHTER, West V21 = .18 While the above applies to INSPECTED SLAUGHTER, a second and major category is UNINSPECTED SLAUGHTER. The following are used to disaggregate UNINSPECTED SLAUGHTER. Proportion of Males in UNINSPECTED Calf SLAUGHTERl East, v22 - .55 West, v23 .50 Proportion of Steers in UNINSPECTED Cattle SLAUGHTER2 (non-Cow, non-Bull UNINSPECTED Cattle SLAUGHTER) East, V24 ' .615 West, V25 .30 Proportion of Cows in UNINSPECTED Cattle SLAUGHTER East, V26 - .28 West, V27 .25 Proportion of Bulls in UNINSPECTED Cattle SLAUGHTER East, V28 - .06 West, V29 .06 WEST-EAST Cattle-Calf Movement data.--The data available on WEST-EAST Cattle-Calf Movement covers only Cattle and Calves moved by rail; however, this is believed to be the bulk of such shipments. The 1These parameters are discussed in detail later in this chapter. These values are very tentative and should be treated as such. 2Ibid. 176 data is divided into Cattle and Calves. Each in turn is recorded as to destination, SLAUGHTER, FEEDLOT, and STOCKYARD. All are assumed to be Beef Cattle. The disaggregation is in terms of sex; the following a priori parameter values are used initially. Proportion of Males in WEST-EAST Calf Movements to FEEDLOTS and STOCKYARDS V32 = .80 Proportion of Males in WEST-EAST Cattle and Calf Movement for SLAUGHTER Calves, V33 = .95 Cattle, V35 = .9 5 'Proportion of Males in WEST-EAST Cattle Movement to FEEDLOTS and STOCKYARDS V = .80 DEATH Rates.--0EATH Rates are assumed to be similar for Dairy and Beef, Males and Females. Differentiation, however, is made between Calves in the XCAV and YCAV streams and Cattle over one year. Calves XCAV stream, East, XDRME1 = .03 XDRFE = .03 West, XDRMW = .03 XDRFW = .03 Calves YCAV stream, East, YDRME = .03 YDRFE = .03 West, YDRMW = .03 YDRFW 8 .03 Cattle over one year, East, DRE = .015 West, DRW = .015 1In all variable names E and W refer to East and West, M and F to Male and Female while B and 0 refer to Beef and Dairy. 177 A further parameter is used to proportion Calf DEATHS between the XCAV and YCAV streams. Proportion of first year Calf DEATHS occurring in the XCAV streams V38 = .60 BIRTH Rates.--Two BIRTH Rates were used, one for Beef Cattle and the second for Dairy Cattle. Beef Cow BIRTH Rate, East, BRBFE = .85 West, BRBFW = .85 Dairy Cow BIRTH Rate, East, BRDYE = .75 West, BRDYW = .765 Description of the Model (RECON)l RECON generates BIRTHS by applying a BIRTH Rate to the Cow Population plus that portion of the Heifer Population expected to freshen during the ensuing year. Dairy Cow P0pulation is taken as an average of December 1 plus June 1 STATCAN Inventory. Beef Cow Popula- tion is taken as the December 1 STATCAN Inventory of Beef Cows. Separate BIRTH Rates are used for Beef and Dairy; in fact, separate Dairy BIRTH Rates are used for East and West. These rates are ini- tially given by a priori knowledge of the sub-sector and then adjusted upward or downward as indicated by the consistency required in the model.2 1The discussion in this section follows the form of identities (84) and (85). Together these identities form one [Qw_in the output format displayed in Table 15. 2The structure of RECON with respect to BIRTHS is discussed in more detail in a subsequent sub-section. T78 mmyaau Jake» .oo:«a«m .ons:u¢~ .oo~sn- .«asc .oonmoa .uoaos .ooauuun .ns@suo~ .ucanw- .«oanm- .oo~sn- .oo: .s«~o~ .-m- .uocno- .«ocnaMN unpopmam .oomnnu .owasuu . .ossau .~oo« .oomnnu .rnmmnu mm>4¢u >0 xu .4om«:« .maaowu .~ .oncnu .000" .ammaaq .ecmuou mm>4au >9 4: o.oo«conu .sosusou .«u: .uuonu .amaaoou .ooaaonn mmsaau um :u .Jowasno .o~o-¢ .no .o«~«« .vou3no .ocuann mmyanu no 4: .onso .msosno~ .on~a«:~ .ssnnou .mn~c .noo- .a:man .msosan~ .m~o~u¢~ Japnhmzm onuomoo ovauabu .nodumu . .«nsa; .:m:n .oaaywu .a««:w« mm>qau >0 an .o««:ou .mamnmu .om .«moon .oocn .muncwu .uuaaou mmsacu >0 4: .naooni .oooou~« .ssannufl .«oadm .uaon . ..-«~ .oooo4~« .oooou~a mm>4¢u an xu .oocnmo .¢oooa~u .ummsso .osooa~ .aom . .ousaw .oocwu~u .oooaumu wm>aau no 4: .co..o .c~mnmoo .aaasmaa .¢:ooun .onnun .soomoou .oksns .-w-a~ .soma~ .nnno4- .uo.mum4 mahhao Jake» ohonuo. .neoamou .aauo~m .nwuc .sou:mo .Nonua .onauwmu .umoou .osamuau .nomumm mmwmpm .ussouu .oounmou .oao.~o .~:os .«-:on .samua .soo~«~u .«uom .mmu~au ...nuom ovunmwu an: no o-so~4 .oon-: . .onno .-~o~¢ .-uo~: munaamw out an .ms~sc¢~ .uouoom~ .aoun. .omNmuN .manon .msss:o~ .oon~ .ocn-a .“nanmi~ mzuu ammo .o~«a«~ .uaooo .«oooo .soo~n .~om« .o~«o«~ .¢~«s«« .rpnr.« mmmuumx >auqo .vnNoom .uoaeoa .oo~«« .cmnao .~«o~ .om~owm .smm ."mooa .....mw mzou >anao .uaoomu .qaaa~« .aao .m~os~ .«au~ .«aooma .~:s .maon» .oo..~u mauao Lassa ca.u.uoaavs nuoucosc. «an agonxu Congas-pm v0.0 «cacao. «Lenin c¢ cue. nuoacosc. .38 9.55 5:23.... ~30» L82!» 2:538 . gnome ensues: so» agape» «sou-x .m— «.4.» T79 Calf DEATHS are calculated for the XCAV stream by applying a DEATH Rate to Calf BIRTHS. Provision is made in the model to have different Male and Female DEATH Rates. In addition, a second parameter is provided to allocate DEATHS between the XCAV and YCAV streams. This parameter, V38, accounts for the proportion of time (Calves x days) between the two streams--it is set by informed judgment. YCAV stream DEATH Rates are set based on a study done by Agriculture Canada. Thus XCAV stream Rates are the Rates that will be varied, if Calf DEATH Rates are varied. Calf SLAUGHTER in the XCAV stream is assumed to be totally Dairy Calves for veal; thus, Beef Calf SLAUGHTER is zero. Calf SLAUGHTER is made up of INSPECTED plus INSPECTED SLAUGHTER; the latter is divided between Male and Female by parameters V22 and V23. Calf EXPORTS are considered next. It is assumed that all Cattle EXPORTS Less Than 200 Pounds are Male Dairy Calves. These are divided between the XCAV stream and the YCAV stream by the parameter Vl. These EXPORTS are further split between Male and Female by parameter V2. Beef calving distribution and other a priori information give initial clues to likely values for these parameters. The final columns considered in the XCAV stream are Ending Inventory and "ERROR." Ending Inventory is calculated by subtracting DEATHS, SLAUGHTER, and EXPORTS from BIRTHS. The "ERROR" is calculated by comparing this figure with the official December 1 Calf Population. T80 Calves on Hand (the YCAV stream).--Beginning Inventory for the YCAV stream in period t is the Ending Inventory of the XCAV stream in period t-l. DEATHS are calculated by applying DEATH Rates to the Beginning Inventory. As previously mentioned, parameter (l-V38) is used to weight DEATHS in the YCAV stream. The assumption is made that no Calves are slaughtered from the YCAV stream. This assumption is applied consistently to MATRIX and CATSIM as well. It is assumed that no Dairy Calves are exported. The EXPORTS from the YCAV stream are based on published Cattle EXPORTS zoo-700 Pounds using parameters (l-Vl), and V2 as discussed under the XCAV stream. I Ending Inventory is zero. This occurs as all Calves on hand January lst must pass one year of age on or before December 315t. TRANSFER OUT is calculated by subtracting TOTAL DISPOSITIONS from TOTAL SOURCES. No consistency check can be made on the YCAV stream as was done with the XCAV stream, that is, no "ERROR" term can be calculated. Bulls,--Beginning Inventory of Bulls is that given by the December 1 official Bull Population. IMPORTS are taken from Purebred IMPORTS by using parameters V5 and V6 to separate Females from total. At this stage there is no reliable information available on the magnitude of these parameters. DEATHS are calculated by multiplying 18l a DEATH Rate by average December 1 and June 1 Bull Population. This same DEATH Rate applies to all Cattle over one year of age. Bull SLAUGHTER is taken directly from published INSPECTED Bull plus UNINSPECTED Cattle SLAUGHTER statistics. In the case of the latter, Only a portion is used. The Bull portion is separated by using param- eters V28 and V29. EXPORTS are calculated from Purebred EXPORTS using parameters V3 and V4 to separate Females from total. Ending Inventory is taken from December 1 Bull Population. The only missing column is TRANSFER IN or Bull REPLACEMENTS. This is the value (number of head) that will equate TOTAL SOURCES with TOTAL DISPOSITIONS. Dairy_and Beef Cows.--Dairy and Beef Cow Beginning Inventory is taken from the December 1 official statistics published for year t-l. IMPORTS are calculated from published Purebred IMPORTS using parameters V5 and V6 to separate Cows from total. Parameters V9 and V10 are used to separate IMPORTS into Beef and Dairy. DEATHS are calculated by applying a DEATH Rate to Beginning Inventory. SLAUGHTER is considered by applying parameters V20 and V21 to separate published Cow SLAUGHTER into its Beef and Dairy components. The method used, whichis consistent with MATRIX, is to calculate Dairy (Beef) Cow SLAUGHTER as a proportion of Inventory. ~Beef (Dairy) Cow SLAUGHTER is the difference between total Cow SLAUGHTER and calculated Dairy (Beef) Cow SLAUGHTER. Total Cow SLAUGHTER includes INSPECTED plus a portion of UNINSPECTED Cattle SLAUGHTER. This portion is separated by parameters V26 and V27. 182 EXPORTS are calculated by using parameters V3 and V4 to separate Purebred Cow EXPORTS from total published Purebred EXPORTS. In addition, Cows are exported in the category Cattle Over 700 Pounds. Parameters V15, V16, and V17 are used to indicate the Cow proportion in this category. In the case of Dairy Cows, there is still another category of EXPORTS, namely, Other Dairy EXPORTS. These data can be used directly. Ending Inventory of the Dairy and Beef Cows is taken directly from published Cow Population for December 1. As in the case of Bulls, the column still unaccounted for is TRANSFER IN or REPLACEMENTS. This figure is the number of Cattle that will balance TOTAL SOURCES with TOTAL DISPOSITIONS. Dairy Heifers.--Beginning Inventory of Dairy Heifers is calculated from published Dairy Heifer Population, December 1, for ,year't-l. TRANSFER IN is set equal to TRANSFER OUT for Female Dairy Calves in the YCAV stream. Dairy Heifer DEATHS are calculated by applying a DEATH Rate to average December 1 and June 1 published Dairy Heifer Population. TRANSFER OUT is set equal to TRANSFER IN for Dairy Cows. Ending Inventory is calculated from published Dairy Heifer Population, December 1 in year t. In the case of Dairy Heifers, the ufissing item is SLAUGHTER. It is the number of head required to balance TOTAL SOURCES with TOTAL DISPOSITIONS. Beef Heifers.--Beef Heifers are divided into two categories: thoseefor REPLACEMENT and those for SLAUGHTER. For REPLACEMENT Heifers, 183 TRANSFER OUT is set equal to Beef Cow TRANSFER IN. TRANSFER IN is set at (l + DEATH Rate) times TRANSFER OUT. DEATHS = TRANSFER IN minus TRANSFER OUT. ' Beginning Inventory for Beef Heifers Feeding is taken from published Beef Heifer Population, December 1 in year t-l. IMPORTS are taken from published Other Cattle IMPORTS by applying parameter V12 to separate Male from total. EXPORTS are taken from published EXPORTS Over 700 Pounds by applying parameter V14 to separate Male from the non-Cow portion of this EXPORT category. SLAUGHTER is calculated from published INSPECTED and UNINSPECTED SLAUGHTER less calculated Dairy Heifer SLAUGHTER. In the case of UNINSPECTED SLAUGHTER, parameters V24, V25, V26, V27, V28, and V29 are used to separate Heifers from total. TRANSFER IN is calculated by subtracting Replacement Heifers TRANSFER IN from YCAV stream Female Beef Calves TRANSFER OUT. DEATHS, and ENDING INVENTORY are calculated in the usual manner. In this instance, all relevant columns have been calculated. A check on consistency is given by comparing TOTAL SOURCES with TOTAL DISPOSITIONS. The difference is given under "ERROR." Stggr§,--Not enough information is currently available to separate Dairy from Beef Steers; consequently, they are considered together under Steers. ‘ Beginning and Ending Inventory, as well as DEATHS, are calculated in the usual manner. IMPORTS are calculated from published 184 Other Cattle IMPORTS by applying parameter V12 to separate the Male portion. EXPORTS are calculated from published EXPORTS Over 700 Pounds, again applying a parameter V14 to the non-Cow portion. TRANSFER IN is calculated by summing TRANSFER OUT from Dairy and Beef Male Calves in the YCAV stream minus TRANSFER IN for Bulls. SLAUGHTER is calculated by summing published INSPECTED and UNINSPECTED SLAUGHTER. In the case of the latter, the Male portion is calculated by using parameter V24 and V25. As was the case with Beef Heifers, all columns have been calculated. Thus, comparison of TOTAL SOURCES with TOTAL DISPOSITIONS provides a consistency check. The difference is given under "ERROR." Analysis and Evaluation The output of RECON is an annual matrix (for each of 14 years, 1959-1972 inclusive) presenting beginning and ending stock values for 15 livestock cohorts together with the interconnecting flow values for seven major flow variables. The purpose of the model is to assess these stock and flow values which are the published statistical data series. The major method of analysis is a test of consistency; to execute the analysis, the concept of objectivity is employed. The results or out- put of RECON also substantiates, at an aggregate level, the results or output of MATRIX and CATSIM. In turn, the knowledge and information obtained from utilizing RECON is Used to construct or revise these latter two models. 185 The analysis of the data base involves applying the four tests of objectivity. Internal consistency is obtained through model design; this has been discussed in the previous sections. External consistency is checked through comparison of RECON output with published data series. Another test of external consistency involves comparison of RECON output with commonly held beliefs about the Cattle-Calves sub-sector. The tests of interpersonal transmissibility and uSerlness cannot be fully applied until RECON is Operated interactively with individuals knowledgeable of the Cattle-Calves sub-sector. This will occur subsequent to this study. To assist with the analysis, the concept of the data as a hypothesis was compromised. One data series, INSPECTED SLAUGHTER, is commonly believed to be the most reliable of all data series used in these models. Two identities, Steers and Beef Heifer Feeding, include INSPECTED SLAUGHTER as the major component on the right hand or DISPOSITION‘ side. An “ERROR" element is calculated for each of these two identities as well as a third "ERROR" element that is the algebraic sum of the first two. This "ERROR" is calculated by sub- tracting DISPOSITIONS from SOURCES.> A negative "ERROR" indicates that SOURCES is too low relative to DISPOSITIONS (believed to be reasonably correct) and vice versa. 1The element SLAUGHTER includes both INSPECTED agd_UNINSPECTED. Later in this analysis, the initial assumptions made concerning lflVINSPECTED SLAUGHTER will be called into question. 186 A very simple objective function is used--it is simply the algebraic sum of the "ERROR“ element for any one identity for the 14 observations (1959-1972 inclusive). Variation in the annual "ERROR" values constitute a significant part of the analysis. Calf Births RECON calculates Calf BIRTHS in the following manner. A BIRTH Rate is applied to Cow Inventory (Cows and Heifers over two years) plus that portion of Heifers (Females 1-2 years) expected to freshen in the ensuing year. For Dairy Cows, the Cow Inventory estimate is the average of June 1 and December 1 STATCAN estimates. No Heifers (Females 1-2 years) are added to this base as a priori information indicated that Dairy Heifers freshen with a mean age of two years nine months. The Inventory of Beef Cows is taken as the December 1 STATCAN estimate. To this figure is added a portion of Beef Heifers (Females l-2 years) as given by STATCAN's December 1 estimates. An examination of observations for l958-1972 inclusive, indicates that an approximate average of 30 percent of Eastern Heifers and 75 percent of Western Heifers enter the Cow Herd annually. The initial BIRTH Rates were selected and restricted by a priori knowledge or beliefs about the sub-sector. First, it was believed that the Beef Cow BIRTH Rate was higher than the Dairy Cow BIRTH Rate. The former would be expected in the .80 to .90 range, while the latter would be expected in the .70 to .80 range. Second, it was believed 187 that the Western Dairy Cow Herd was managed more like the Beef Herd than was the case in the East, at least at the margin. Third, it was believed that WEST-EAST Cattle-Calf Movement statistics underestimated the actual eastward movement. Fourth, there was no reason to believe that BIRTH Rates differed markedly between East and West for Beef Cattle, or for Dairy Cattle for that matter. Finally, the Dairy Cattle BIRTH Rate must be high enough to supply the demand for Replacement Dairy Heifers. Since the West has a very high proportion of Beef Cattle, while the opposite holds true for the East, a "reasonable" Beef BIRTH Rate was selected for the East and the Dairy BIRTH Rate was adjusted until a "small” negative Steer + Beef Heifer Feeding "ERROR" was obtained. The same procedure was used for the West except, in this instance, a "reasonable" Dairy BIRTH Rate was used. The Beef BIRTH Rate was incremented until a "small" positive Steer + Beef Heifer Feeding “ERROR" was obtained. Adjustments in all Rates were made until Eastern and Western Beef BIRTH Rates were equal and the Western Dairy BIRTH Rate equalled the Eastern Dairy BIRTH Rate + .0151 and all rates fell within a priori ranges. In addition, BIRTH Rate adjuStments were made until the Eastern land Western "ERRORS" were equal in magnitude but opposite in sign. As was expected, the Western "ERROR" was positive while the Eastern was 1The constant .015 was arbitrarily selected to fall between the Eastern Dairy BIRTH Rate and the Beef BIRTH Rate, to reflect the assump- tion that the Western Dairy Herd is treated, at the margin. as a Beef Herd. 188 negative indicating that the statistical WEST-EAST Movement underestimated the actual flow. The final BIRTH Rates selected were: East, Beef = .85 West, Beef = .85 Dairy = .75 Dairy = .765 BIRTHS generated by the above process were compared with STATCAN's semi-annual BIRTHS as a test of consistency and a Check on bias and/or trend. The results appear in Table 16. From Table 16, it is Shown that in the West, STATCAN over- estimates Calf BIRTHS by an average of 46,241 head per year or by 1.5 percent of BIRTHS. This could be explained entirely in terms of Calf DEATH Rate.1 The sign of these "differences" is as expected. A priori, it would be expected that RECON would underestimate BIRTHS in periods of expansion (giving a negative Sign) and overestimate BIRTHS in periods of contraction (giving a positive sign) due to the cattle cycle, which is not modeled by RECON. STATCAN overestimates Eastern Calf BIRTHS consistently by an average of 260,000 head. This difference varies from 8-17 percent over the RECON estimate. Part of this difference can be explained in terms of an actual DEATH Rate which might be higher than that used in RECON. I concur with Lee2 that it is unrealistic to expect DEATH Rate ‘The calf DEATH Rate used in RECON are taken from Yang; however, his estimates show some variance. In addition, a priori information would indicate that these DEATH Rates are a lower bound. zLee, Op. cit. Table 16. A comparison of RECON generated Calf BIRTHS with Statistics Canada's semi-annual BIRTH estimates, 1958-1972 West East Year Differencea RECOAEEICEES Differencea RECONeBTEEES (head) (ratio) (head) (ratio) 1958 -136,733 -.0618 -l63,245 -.O8OO 1959 -65,514 -.0294 ~161,279 -.0806 1960 -75,687 —.0330 -l75,675 -.0876 1961 -128,612 -.0539 -202,407 -.1001 1962 -54,818 -.0223 -l8l,94l -.0887 1963 -28,935 -.0114 -219,484 -.1074 1964 19,142 .0071 -271,299 -.1328 1965 51,052 .0177 -324,841 -.1584 1966 -16,975 .0058 -302,268 -.1508 1967 3,695 .0013 -313,196 -.1593 1968 19,592 .0071 -343,923 -.1746 1969 25,330 .0093 -351,317 -.1793 1970 -92,025 —. 0328 -349,554 -. 1784 1971 -191,198 -.0646 -298,657 -.1544 1972 -21,929 -.0069 -24l,7ll -.1256 Ave. -46,241 -260,000 aFormula: DIFFERENCE = RECON BIRTHS - STATCAN BIRTHS. 190 to account for the total discrepancy in this instance, even though Dairy Calf DEATH Rate may be very high. It should also be noted that the discrepancy has tended to widen over the 1958-1972 period. A second consistency check was made against data from the Dairy Correspondent Survey. The annual sum of the Cows and Heifers to FRESHEN This Month1 item from that survey was subtracted from the RECON estimate of Dairy BIRTHS. The results are shown in Table 17. The Dairy Correspondent Survey overestimates BIRTHS by 9 to 27 percent in the West, and by 15 to 29 percent in the East. There is some indication that the difference is narrowing through the survey period. Ending Calf Inventory Program RECON was designed to divide Calves into two categories: those in inventory at the beginning of the year, and those during the year. Only those born during the year would be on ending inventory at year end. Ending Inventory is calculated as follows: Ending Inventory 5 BIRTHS - DEATHS + TRANSFER IN - TRANSFER OUT - SLAUGHTER + IMPORTS - EXPORTS. DEATHS are calculated by applying a DEATH Rate while SLAUGHTER (INSPECTED + UNINSPECTED) is taken as given by STATCAN. IMPORTS 1The freshening ratio from that survey is applied to STATCAN's December 1 and June 1 Milk Cow data series to scale up the actual Dairy Correspondent Survey data. 191 Table 17. A comparison of RECON generated Dairy Calf BIRTHS with Statistics Canada's Dairy Correspondent Survey, "Estimates of Cow and Heifers to FRESHEN This Month," 1958-1972 West East Difference Difference Year Differencea RECON BIRTHS Differencea RECON BIRTHS _ (head) (ratio) (head) (ratio) 1958 -l4l,671 -.2253 -425,308 -.2573 1959 -150,970 -.2460 ~411,223 -.2548 1960 -164,713 -.2690 ~412,639 -.2576 1961 -162,587 -.2711 -479,403 -.2979 1962 -107,516 -.l767 -360,828 -.2232 1963 -115,310 -.2000 -315,394 -.1993 1964 -93,720 -.1679 -317,449 —.2025 1965 -89,605 —.1689 -439,l67 -.2809 1966 -80,331 -.1646 -336,438 -.2193 1967 -75,111 -.1677 —264,550 -.l765 1968 -39,155 -.O94O -27l,866 -.1855 1969 -69,670 -.l769 -255,204 -.l764 1970 -53,080 -.1367 -217,l47 -.1534 1971 -80,624 -.2165 -267,045 —.1991 1972 -60,051 -.1730 -257,174 -.l983 Ave. -98,941 -335,389 aFormula: DIFFERENCE = RECON Dairy BIRTHS - DCS Dairy FRESHENINGS. 192 are zero while EXPORTS are taken as published by STATCAN. These data series have all been discussed previously. The remaining elements are TRANSFER IN and TRANSFER OUT. These elements are entirely made up of Calves shipped from West to East. These shipments are recorded in the data series WEST-EAST Calf Movement for those Calves shipped by rail. As previously mentioned, additional Calves are believed to be shipped by other means. Once again, the "ERROR" in Steer + Beef Heifer Feeding was used to augment rail shipments. A factor of 1.07 (parameter V40 in RECON) is used to scale up rail shipments. This factor has the effect of reducing the above "ERROR" to zero for both East and West, since BIRTH Rates were calculated in such a manner as to make this happen (i.e., equal magnitude but opposite sign). With TRANSFER IN and TRANSFER OUT adjusted by a factor of 1.07, a comparison was made between RECON's Ending Calf Inventory and STATCAN's December 1 Calf Population. These results are shown in Table 18. An average overestimation of 27,362 head occurred in the Western STATCAN Calf Population. This error is fairly consistent with the average overestimation of BIRTHS by 46,241 head. The Sign (or (firection) of the year by year discrepancy is consistent between BIRTHS and Ending Inventory for all years except 1964, 1965, 1970, 1971, and 1972. As previously mentioned with Calf BIRTHS, these discrepancies are largely explained by the cattle cycle. In addition, the average discrepancy is rather small and can be accounted for by a slightly higher DEATH Rate. 193 Table 18. A comparison of RECON generated Ending Calf Inventory with Statistics Canada's December 1 Calf POPULATION estimates l958-1972 West East Year Di fferencea RECiOiquen'veeciiiry Di f f erencea REClOiNf gingham (head) (ratio) (head) (ratio) 1958 -75,301 -.O34O 209,307 .1549 1959 -28,382 -.Ol63 205,789 .1470 1960 -14,975 -.0082 183,436 .1289 1961 -98,886 -.0584 139,835 .0937 1962 -84,989 -.O476 67,324 .0463 1963 -87,357 -.0429 146,292 .0994 1964 -148,205 -.0685 166,459 .1111 1965 ~118,627 -.0564 135,705 .0978 1966 -3,812 -.0018 252,681 .1685 1967 55,997 .0255 253,658 .1662 1968 28,122 .0131 267,021 .1752 1969 21,491 .0094 252,728 .1660 1970 8,736 .0036 326,542 .2073 1971 53,847 .0209 389,228 .2436 - 1972 81,908 .0300 353,237 .2195 .Ave. -27,362 223,283 aFormula: DIFFERENCE = RECON Inventory - STATCAN Population. 194 For the East, the STATCAN data series seems highly inconsistent with RECON. In addition, STATCAN's December 1 Calf Population is highly inconsistent with STATCAN BIRTHS. While it was previously noted that STATCAN BIRTHS overestimate RECON BIRTHS by 8 to 17 percent, STATCAN December 1 Calf Population underestimates RECON by 5 to 24 percent. The trend in these two data series is to a widening discrepancy. REPLACEMENT Cattle In the previous sub-section it was stated that Calves were considered under two categories, the second of these were Calves on Hand at the beginning of the year. By the end of the year, all such Calves, of definitional necessity, must have transferred to non-Calf categories. The following itemizes the possible transfers. 32;;y3311]cgilzgs } to Bull REPLACEMENTS or Steers Dairy Heifer Calves to Dairy Cow REPLACEMENTS Beef Cow REPLACEMENTS Beef Heifer Calves to or Feeder Heifers The calculation of REPLACEMENTS (TRANSFERRED IN) is made through the following identity for Dairy Cows, Beef Cows, and Bulls. REPLACEMENTS = Ending Inventory - Beginning Inventory + SLAUGHTER-tEXPORTS-tDEATHS-IMPORTS-tTRANSFER OUT Since EXPORTS and IMPORTS are minor, errors will be of little :significance. TRANSFER OUT is nil, while Beginning and Ending Inventory 195 is given by the STATCAN December 1 estimates. The major sources of error occurs in dividing Cow SLAUGHTER between Beef and Dairy. Because the method used does not adequately account for the cattle cycle, RECON estimates are inferior to those made by MATRIX in Chapter III. Table 19 compares REPLACEMENTS with INVENTORY. The REPLACEMENT Rates for both Beef and Dairy Cows are inferior to the same ratios that may be calculated from adjusted MATRIX output. This is the case as MATRIX output is adjusted for the cattle cycle, while RECON output is not so adjusted. Nevertheless, the Western Beef Rates do trace out a pattern that is consistent with that cycle. These rates should be tempered by the fact that some Herds are expanding while others are contracting. In general, the Beef Herd is expanding while the Dairy is contracting.‘ The Bull REPLACEMENT Rate differs between the West and the East, with the Eastern Rate being almost twice the Western Rate. No explanation readily comes to mind. The Sex Ratio of EXPORTS and WEST-EAST Ca ttl e-Cal f Movement To this point in the analysis, the "objective" function has been used to minimize the "ERROR“ in Steers + Beef Heifers Feeding. Since these two "ERRORS" were summed, the analysis abstracted from the sex ratio. 1Over the 15 year sample period, the Western and Eastern Beef Herds grew at an average continuous rate of 4.5 and 3 percent, while the Western and Eastern Dairy Herds contracted at an average continuous rate of about 4 and 2 percent. 196 Table 19. A comparison of RECON estimated REPLACEMENTS with Inventory expressed in terms of a REPLACEMENT Rate, WEST and EAST, 1959-1972 A. WEST Dairy REPLACEMENTSa Beef REPLACEMENTSa AgélaSEPOCEEM1NEEZ Year Dec. 1 Inventory Dec. 1 Inventory Dec. 1 Inventory (ratio) (ratio) (ratio) 1959 .1896 .1660 .3479 1960 .2052 .1724 .3321 1961 .2068 .1749 .3139 1962 .1396 .1993 .3337 1963 .1712 .1975 .3530 1964 .1544 .2205 .3719 1965 .1347 .2060 .3311 1966 .1134 .1735 .2814 1967 .1211 .1416 .2523 1968 .1440 .1504 .2308 1969 .1879 .1728 .2860 1970 .1703 .1943 .2539 1971 .1258 .1960 .3362 1972 .1793 .1884 .2936 aFormula: RATIO = REPLACEMENTS (Heifers or Bu11§)_ Inventory (Cows or BullS) ' 197 Table l9--Continued 8. EAST Dairy REPLACEMENTSa Beef REPLACEMENTSa gallaSEPOCEEMTNEOZ Year Dec. 1 Inventory Dec. 1 Inventory Dec. 1 Inventory (ratio) (ratio) (ratio) 1959 .1598 .1664 .5150 1960 .1927 .1507 .4918 1961 .1949 .1774 .5484 1962 .1823 .1800 .4804 1963 .1880 .1580 .5233 1964 .2175 .1456 .5350 1965 .2617 .0948 .5934 1966 .2133 .1019 .5259 1967 .1758 .1915 .5554 1968 .1986 .1372 .5819 1969 .2083 .2020 .5879 1970 .1993 .2248 .6217 1971 .1988 .1543 .6242 1972 .2458 .1706 .6186 aFormula: RATIO 8 REPLACEMENTS (Heifers or Bulls) *TTnventory (Cows or Bulls) 198 A priori information concerning the sex ratio of WEST-EAST Cattle-Calf Movement for SLAUGHTER were 90-100 percent Male, while the Cattle and Calves for FEEDLOT and STOCKYARD were 80 percent Male. A priori information about EXPORTS of Feeder Cattle to the United States indicated a sex ratio of 35-42 percent Male. The procedure used to confirm or reject these ranges involved adjusting the sex ratio of WEST-EAST Movements until the Eastern "ERRORS" summed algebraically to zero. The sex ratios that provide this balance are 95 percent Male in SLAUGHTER and 80 percent Male in FEEDLOT and STOCKYARD Movements. The resultant "ERRORS" are given in Table 20A. An attempt was then made to bring the Western "ERRORS" into balance by adjusting the sex ratio of EXPORTS, Cattle ZOO-700 Pounds. This was unsuccessful in that there were still excess Western Heifers on the average, when 100 percent of the above EXPORTS were considered as Heifers.1 These “ERRORS" are listed in Table 208.2 For the East, the average "ERRORS" are close to zero for both Steer and Beef Heifer, with the sign and magnitude of the "ERRORS" producing no distinct trend. 1This aspect of CATSIM was modeled using a step function with :some success. For 1958-1965 inclusive, EXPORTS were considered to be 60 percent Male; after 1965, EXPORTS were considered 0 percent Males (i.e., 100 percent Female). 2While the sex ratios of WEST-EAST Movements are not constant between Table 20A and Table 208. this minor discrepancy does not effectively mask the inconsistency that is being revealed. 199 Table 20. A listing of Eastern and Western Steer and Beef Heifer Feeding "ERRORS" from given parameter settings,a 1959-1972, program RECON A. WEST EAST Year Steers Heifers Steers Heifers (head) (head) (head) (head) 1959 79,991 -87,038 38,352 75,044 1960 6,151 -4l,786 50,287 33,649 1961 46,475 -36,991 1,684 3,433 1962 48,108 -92,521 -13,408 30,165 1963 32,503 ~122,023 -60,898 26,773 1964 -43,981 -32,813 -37,276 -32,251 1965 11,314 -24,258 -60,896 -l34,891 1966 -55,931 -17,687 -95,157 -51,857 1967 -30,161 135,979 72,083 23,527 1968 -2,636 21,436 75,289 -4,323 1969 -34,366 13,936 38,231 -23,835 1970 -61,437 130,840 -51,103 385 1971 -l,403 89,496 10,198 58,546 1972 -49,691 129,013 34,879 4,100 .Ave. -3,933 4,685 162 605 aWEST-EAST Cattle and Calf Movement set at 95 percent Males, FEEDLOT, and STOCKYARD Cattle and Calf Movement set at 80 percent Males. EXPORTS, Cattle ZOO-700 Pounds set at 35 percent Males with UNINSPECTED Male SLAUGHTER at 0 percent (100 percent Female). Table 20--Continued 200 B. . WEST EAST Year Steers Heifers Steers Heifers (head) (head) (head) (head) 1959 127,100 -l34,147 34,729 78,667 1960 -10,l97 -25,438 46,766 37,169 1961 16,641 7,157 -3,159 8,276 1962 82,332 -126,746 -15,927 32,684 1963 54,938 -144,458 -69,376 35,251 1964 -94,105 17,312 -39,501 -30,026 1965 -54,287 41,343 -53,319 -l42,468 1966 -42,199 -31,410 -91,846 -55,168 1967 -40,108 145,925 83,522 12,089 1968 -67,061 85,861 86,026 -15,06O 1969 ~105,366 84,936 48,156 -33,759 1970 -l57,119 226,523 -51,736 1,019 1971 -92,613 180,706 8,011 60,732 1972 -145,882 225,204 29,708 9,272 Ave. -37,709 38,461 861 -94 aWEST-EAST SLAUGHTER Cattle and Calf Movement set at 100 percent and STOCKYARD Movement 85.5 percent Males. Cattle 200-700 Pounds set at 0 percent Males (i.e., 100 percent Males, FEEDLOT Females). UNINSPECTED Male SLAUGHTER at INSPECTED level. EXPORTS, 201 The Western data presents an anomaly. The a priori assumptions used do not work; on the average there are too many Beef Heifers and too few Steers-~by about 38,000 head annually. In addition, a distinct time trend is evident, that is, from 1960 through 1972 the Heifer surplus increaSed. More Heifers could not have been shipped to the United States because these shipments were set at 100 percent Heifers in the model. One logical conclusion is that UNINSPECTED SLAUGHTER is made up of more Beef Heifers and less Steers.l The procedure used to explore this latter alternative was to initially accept a priori assumptions about sex ratios. Thus, for WEST-EAST Movements, SLAUGHTER was set at 95 percent Male and FEEDLOT- STOCKYARD Movements at 80 percent. The sex ratio of EXPORTS Cattle 200-700 Pounds was set at 35 percent Male. The Eastern Female UNIN- SPECTED SLAUGHTER2 ratio was incremented until the Eastern "ERROR" came into balance. A separate Western Female UNINSPECTED SLAUGHTER ratio was then incremented until the Western "ERROR" also came into balance.3 The results of this analysis are displayed in Table 20A. These results indicate that even at 100 percent Female, the "ERROR" (Western) does not come into balance, although it is close. 1The original assumption was that UNINSPECTED SLAUGHTER had the same ratio as INSPECTED SLAUGHTER. 2For the balance of this sub-section UNINSPECTED SLAUGHTER refers to the non-Cow, non-Bull portion. 3The sex ratio of INSPECTED SLAUGHTER (excluding Cows, Bulls, and Calves) over the 1959-1972 period ranged from 25.3-30.9 percent Heifers in the East and 25.4-34.2 percent Heifers in the West. 202 The logical conclusion is that the a priori assumptions do not hold. The Steer content in EXPORTS Cattle 200-700 Pounds must be between 0 and 35 percent concurrently with the Heifer content in UNINSPECTED SLAUGHTER being between 30 and 100 percent. An infinite number of linear combinations would work. One such linear combination is 20.5 percent steers in EXPORTS, Cattle 200-700 Pounds and 70 percent Heifers in UNINSPECTED SLAUGHTER. A distinct trend in the "ERROR" still remains and must be resolved. An assumption was made that the sex ratio in UNINSPECTED SLAUGHTERl is constant over the 1958-1972 period. Consequently, the sex ratio of EXPORTS, Cattle ZOO-700 Pounds must change over this period. A linear time trend was fitted with the sex ratio being about 50 percent Heifers in 1958 rising to 100 percent in 1972. This tact appeared to be successful for the years 1958—1966; however, the flow of EXPORTS dropped off from 1967-1972, severely reducing the impact of this change. Consequently, the discrepancy remained for those latter years. The results of this run are not listed. The only possible conclusion, given the above assumptions, is that the sex ratio of both_EXPORTS, Cattle 200-700 Pounds and UNINSPECTED SLAUGHTER changed over this period with both_exhibiting a high Heifer proportion in the period 1967-1972. 1This appears to be the case in the East; some degree of similarity might exist between East and West in this regard. 203 YearlingCattle The ratio of TRANSFER IN/Ending Inventory gives some index of the average length of stay in the Yearling categories. Theoretically, Replacement Heifers (1-2 years) should stay exactly one year in this category. Thus, the above ratio for Replacement Dairy Heifers Should be one. This same ratio for Beef Heifers (the sum of Replacements plus Feeders) and Beef Steers would be less than one, if the average length of stay is less than one year and vice versa. Another alternative involves believing in the reliability of flows (i.e., TRANSFER IN, SLAUGHTER, etc.) and using an a priori notion of average age of Feeder Cattle.' Holding these beliefs then, the reliability of stocks (Begin- ning and Ending Inventory) can be tested for consistency. Since the author does not have any strongly held beliefs concerning the latter alternative, the former will be used. The results of this analysis appear in Table 21. The Western Dairy Heifer ratio is about as expected for 1959-1965 but then becomes much "too high" and subsequently "too low." The explanation does not likely involve age of Heifer but rather clas- sification of both Heifers and the Female offspring of Dairy Cows, some of which may be more Dual Purpose or crossbred Beef than Dairy. The ratio is substantially above one during the Herd contraction period, 1965-1969, and substantially below one during the subsequent expansion, 1970-1972. 204 Table 21. A comparison of RECON Estimated TRANSFER IN with Ending Inventory for all Yearling Cattle categories, 1959-1972, program RECON A. WEST Year Dairy Heifersa Beef Heifersa Steersa 1 (ratio) (ratio) (ratio) 1959 .9604 .9697 .4956 1960 1.0284 .7146 .5589 1961 1.0461 .6652 .5048 1962 1.0233 .8816 .5918 1963 .9349 .9413 .6016 1964 .8535 .7180 .6016 1965 1.0697 .6137 .6137 1966 1.3340 .6666 .5826 1967 1.1574 .5791 .5862 1968 1.5539 .5576 .5618 1969 1.3095 .5644 .5631 1970 .8279 .5723 .5264 1971 .6613 .6193 .5360 1972 .6870 .6057 .5418 aFormula: RATIO = Ending Inventory__ TRANSFER IN 205 Table 21--Continued B. EAST Year Dairy Heifersa Beef Heifersa Steersa (ratio) (ratio) (ratio) 1959 .9195 1.0809 .8581 1960 .9144 1.0405 .7892 1961 .9423 1.0459 .8642 1962 .9073 1.0692 .9305 1963 .9337 1.0103 .0227 1964 .9420 .9677 .8925 1965 .9471 .8442 .8274 1966 .9517 .9310 .9309 1967 .9173 .9971 .7881 1968 .9506 1.0278 .7749 1969 .9639 .9348 .7771 1970 .9151 .9853 .8592 1971 .7961 1.1522 .8629 1972 .8597 .9991 .7685 aFormula: RATIO = Ending Inventory . 206 The Dairy Heifer ratio for the East is very stable except for 1971-1972. If Inventory and classification are correct, then a ratio of slightly less than one might be expected to account for DEATHS and culling of Heifers. The Beef Heifer and the Beef Steer ratios for Western Canada will be biased by the sex ratio errors noted in the previous sub-section and listed in Table 20. If this bias were removed the effect would be to make these ratios even more consistent through time. Taking a typical Steer value as .5, this would imply that the average Steer is 1.5 years or 18 months old at slaughter. A typical Heifer value is .7, this value is made up of Replacement Heifers ang_Feeder Heifers in about equal proportions. This would imply that the average Slaughter Heifer is slaughtered at about 1.4 years of age or 16-17 months. The Steer and Beef Heifer ratios for Eastern Canada are substantially higher than for Western Canada. A typical Heifer value is 1.0 while a typical Steer value is .85. If TRANSFER IN is accepted as correct, and it seems to be consistent with SLAUGHTER, then either Ending Inventory is high 93_Eastern Cattle are slaughtered at an older age than Western Cattle. Dairy Heifer SLAUGHTER An initial assumption was made that all Calf SLAUGHTER was of Dairy breeding. At another point in the analysis of RECON, it was stated that Dairy Cow BIRTH Rate must be adequate to generate Replacement Dairy Heifers. 207 Since the residual element in the Dairy Heifer identity is Dairy Heifer SLAUGHTER, this element merits examination in light Of the above assumptions. It is generally believed that few Dairy Heifers are slaughtered. One explanation might be that some progeny of "Dairy Cows" might be from Beef sires. Table 22 lists Dairy Heifer SLAUGHTER and compares SLAUGHTER to Beginning Inventory. Dairy Heifer SLAUGHTER in the East appears to be more stable than in the West. The one negative Eastern value (1965) can be attributed to a model design that underestimates Beef Cow SLAUGHTER, leading to an overestimation of Dairy Cow SLAUGHTER thus making an unusual demand on Dairy Heifers. This explanation would also apply to 1964 and 1966. In most other years, from 15-30 percent of Beginning Inventory are slaughtered. The rather eratic nature of Dairy Heifer SLAUGHTER in the West can possibly be traced to two sources. First, some misclassification might occur, so that the offspring of the Dairy Herd might oscillate between Dairy and Beef, depending on economic outlook. In addition, a given Heifer classified as a Dairy Heifer on one occasion might be classified as a Beef Heifer on a second occasion, depending on the farmer's intentions. Second, some Female Calf SLAUGHTER may come from the Beef Herd. This would increase the number of Dairy Heifers on Inventory. A wide fluctuation in Beef Female Calf SLAUGHTER would thus cause wide fluctuations in the ratio being considered. The effect of these two 208 Table 22. A comparison of RECON Estimated Dairy Heifer SLAUGHTER with Dairy Heifer Inventory, l959-1972, program RECON WEST EAST SLAUGHTER a SLAUGHTER a as proportion as proportion Year SLAUGHTER of Inventory SLAUGHTER of Inventory (head) (ratio) (head) (ratio) 1959 25,340 .1445 164,707 .3485 1960 3,229 .0183 123,080 .2505 1961 2,737 .0152 109,286 .2188 1962 53,497 .3075 162,831 .3185 1963 52,223 .3090 128,775 .2597 1964 66,303 .4196 72,583 .1455 1965 42,222 .2833 -34,133 -.O702 1966 23,768 .1801 36,491 .0798 1967 30,807 .2525 117,163 .2690 1968 —7,852 -.0689 75,128 .1680 1969 , -l4,815 -.1347 63,219 .1391 1970 32,884 .3224 105,861 .2357 1971 80,171 .8181 171,116 .3903 1972 49,502 .5500 24,485 .0633 aFormula: RATIO = Dairy Heifer SLAUGHTER Dairy Heifer Beginning Inventory ' 209 possible errors could conceivably provide the variation noted in Western Beef Heifer SLAUGHTER. Model Accuracy The overall accuracy or variation in RECON is demonstrated by summing algebraically the Steer plus the Beef Heifer Feeding "ERROR." This data is displayed in Table 23. Two bases of comparison are used. In the first case, the "ERROR" is compared to total Steer plus Dairy Heifer plus Beef Heifer SLAUGHTER. As the major output of the system, SLAUGHTER seemed like a reasonable basis. The second comparison is between "ERROR" and TOTAL DISPOSITION of Cattle. Since "ERROR" is the sum of all_the errors in all_data series, for the seven Cattle series, this also appears as a reasonable basis for comparison. Since the first basis has a much smaller denominator, the relative "ERROR" appears larger. In the West, with the exception of 1963 and 1967, the relative "ERROR" is 6 percent or less. The "ERRORS“ appear reasonably random. The "ERROR" in the East appears less random and reaches major proportions in 1959-1960 and 1965-1967. When the second basis of comparison is used, the relative "ERROR” becomes very small (less than 2 percent) in all but two cases. Generally, this simple model constructed entirely of identities and naive relationships may be considered as quite consistent internally with the data series being acceptably accurate except where noted. 210 Table 23. A comparison of RECON “ERROR" with selected data bases WEST EAST ERROR ERROR as a proportion of as a proportiona of Year Error SLAUGHTER DISPOSITION Error SLAUGHTER DISPOSITION (head) (ratio) (ratio) (head) (ratio) (ratio) 1959 -7,048 -.0102 -.0013 113,396 .1469 .0198 1960 -35,635 -.O450 -.0063 83,935 .1000 .0147 1961 9,484 .0105 .0016 5,117 .0062 .0009 1962 -44,414 -.0549 -.OO75 16,757 .0195 .0028 1963 -89,520 -.0972 -.Ol43 -34,125 -.O38O -.0057 1964 -76,794 -.O699 -.0112 -69,529 —.0691 -.0109 1965 -12,945 -.0123 -.0018 -195,787 -.l7l7 -.0307 1966 -73,609 -.0635 -.0104 -147,014 -.1421 -.0244 1967 105,817 .0882 .0155 95,610 .0942 .0161 1968 18,800 .0199 .0028 70,966 .0670 .0118 1969 -20,430 -.0155 -.0030 14,397 .0134 .0024 1970 69,404 .0510 .0100 -50,718 -.0487 -.0084 1971 88,093 .0627 .0120 68,743 .0667 .0117 1972 79,322 .0527 .0102 38,979 .0361 .0065 aFormula: RATIO = Steer + Heifer Feeding "ERROR" SLAUGHTER 9: TOTAL DISPOSITIONS ' CHAPTER V THE CATTLE HERD SIMULATOR The computer program that simulates the dynamics of the Cattle Herd is called CATSIM.1 It is the main or focal program in this study. Because of the sheer bulk of the program and the initial requirement to build and debug, the program was built in four parts. The parts are Dairy East, Beef East, Dairy West, and Beef West. The two Eastern parts were subsequently merged to form CATSIM East; and similarly, the West to produce CATSIM West. A comprehensive knowledge of the simulator can only be gained by a line by line study of CATSIM. The purpose of this chapter, however, is to provide an appreciation of the model through a general discussion of its parts, their interrelationships, the assumptions made, and the parameter values used. The first section of this chapter provides an overview of the model; the second section discusses the model in detail. A Model Overview The model of the Cattle Herd, that is Simulated by CATSIM, is divided into four parts: lThree versions of this basic model are developed. They are CATSIMl, CATSIM 2, and CATSIM 3. Unless otherwise indicated, this chapter will use the name CATSIM when referring to all three versions. A listing of CATSIM 2 West in provided in Appendix E. 211 212 1. Beef Cattle West, 2. Dairy Cattle West, 3. Beef Cattle East, and 4. Dairy Cattle East. The structure of each is deliberately designed to be virtually identical. Thus, the following discussion applies to any or all the four parts. It also follows Figures 18 to 26, which are the exact block diagrams of the above four parts of the model.1 The basic element in the model is the Cow Herd.2 The size of the Cow Herd changes with SLAUGHTER (CULL), IMPORTS, EXPORTS, DEATHS, and addition of Replacement Heifers. The size of the Cow Herd increases due to favorable expectations; there is a reduction of Slaughter Heifers as additional Heifers are retained as REPLACEMENTS. After a two or three year lag, allowing for gestation and progeny maturation, the SLAUGHTER flow is increased. Since ceteris paribus, prices move in the opposite direction to quantities, adverse prices might now reverse the process after appropriate lags. These changes in the size of the Cow Herd lead to further changes in prices and price expectations, which lead to still further changes in the Cow Herd. Thus the Cow Herd is basic to the phenomenon known as the cattle cycle. Consequently, investment (REPLACEMENT) and disinvestment (CULLS) form a major part of this model, providing it with its cyclical motion. 1Appendix B discusses exact block diagrams and explains the symbols used. 2A notational convention is followed to denote stock and flow variables. This convention is given in Table 2, pages 50-51. 213 The Cow Herd is defined as female stock two years and older (Beef and Dairy). This allows comparison of the simulated Cow Herd with Statistics Canada's semi-annual Livestock Survey. Generation of a Calf crop is produced by breeding the Cow Herd and allowing for a nine month gestation delay. Three aspects are considered at this point: 1. the nine month gestation delay, 2. the birth distribution over the year, and 3. the live BIRTH Rate. Observation of the exact box diagrams will reveal that First Calf Heifers are treated differently than Mature Cows. This is so with respect to: (1) that portion of gestation occurring after two years of age, and (2) live BIRTH Rate. The former is due to the structure of the model and the age at which Heifers are bred. This structure is discussed in detail in the next section. The latter is a hypothesis that may or may not be true. The BIRTHS from First Calf Heifers and Mature Cows are combined to produce the Calf crop. This in turn is split between Male and Female Calves. Initially, it is assumed that the sex ratio is .5; this also is a hypothesis and thus subject to subsequent Change. The Calves are subsequently aged through a series of discrete (fixed length) and continuous (variable length) delays,1 simulating the 1Delays and simulation of delays are discussed in detail in Appendix B. 214 growing and feeding-finishing processes until they are either slaughtered or added to the Breeding Herd. Through time, addition and attrition occurs due to EXPORTS, IMPORTS, SLAUGHTER, and DEATHS. The following discussion follows these processes looking at each of the several identified stages (delays). Shortly after birth a certain number of Calves are exported. These Calves are mainly Dairy Males ("bob" Calves) from the East to the United States, although increasing numbers are being shipped to Europe. In addition, the model allows for attrition due to DEATH at the beginning of each period. At the end of the first period (three months of age) a number of Calves are slaughtered for veal. While Veal SLAUGHTER is currently Male Dairy Calves, it has not necessarily been the case historically. In addition, all Veal is not necessarily slaughtered at three months of age; however, this is a reasonable approximation. At the end of the second period (six months of age), Calf numbers are adjusted for the flow of Stock Calves. This includes EXPORTS mainly to the United States, as well as Movements from Western to Eastern Canada. This point in time approximates weaning age as well as the first point in time at which Calves are normally placed on feed. At this point also, the Calves are directed along one of two streams which correspond to ration and method of feeding. The first stream is called Stream A and the ration fed, Ration A. This ration is high roughage, low energy, and is received by all Cattle not placed in a feedlot. It is assumed that all future Breeding Stock will be derived from Stream A. 215 Ration 8 (fed in Stream 8) corresponds to a high energy, high feed intake ration such as would be fed to Cattle on full feed in a feedlot. It is assumed that none of these Cattle are used for breeding purposes. Stream 8 Cattle are matured to Finished Cattle through a variable length delay process. This "continuous" delay provides for: (1) an expected time on feed, and (2) a distribution about this expected value. This continuous delay attempts to approximate the effect of the different feeds and feeding practice used, as well as variation in genetic growth rates. As the Finished Cattle leave the feeding-finishing process (continuous delay), they are added to Cattle matured on Ration A to produce total Steers and Heifers Available for SLAUGHTER. Steers and Heifers Available for SLAUGHTER are adjusted by EXPORTS AND IMPORTS of Slaughter Cattle to produce Steer and Heifer SLAUGHTER for each region (Local SLAUGHTER). Six month old Calves ngt_going directly into a feedlot proceed to mature along Stream A, on Ration A. The next stage of the growth process is six months in length. This period is simulated by a fixed length or discrete delay. At the end of this period, when Calves are one year of age, adjustments to their numbers are made for EXPORTS and WEST-EAST Movements. It should be pointed out that EXPORTS, IMPORTS, and WEST-EAST Movements do not occur at discrete points in time (age) but occur more or less continuously. Thus the model abstracts from reality to simplify the study. 216 The numbers of Calves generated by the model may be summed at this point to compare with Statistics Canada's semi-annual Livestock Survey category, Calves Under One Year Old. This summation includes: calves one to three months calves four to six months calves seven to twelve months Ration A calves seven to twelve months Ration B (a portion of total Ration B Cattle) At this stage (one year of age) a decision is assumed to be made as to whether or not Calves will be added to the Breeding Herd or finished for slaughter. Those ngt_added to the Breeding Herd are matured through a continuous delay process and subsequently added to the flow of Steers and Heifers Available for SLAUGHTER. This was discussed above in connection with Cattle fed on Ration B. The number of Yearlings entering the Breeding Herd are calculated in the following manner. Their numbers are large enough to provide for DEATH losses and just provide the necessary additions to the Breeding Herd. In actual practice morg_than this number would be allocated to allow for non-breeders, poor type and to provide flexibility. Thus, this model deals only with actual REPLACEMENTS, flgt_intended or potential REPLACEMENTS. One year old Bulls are added immediately to the Bull Herd. The size of the Bull Herd generated by the model may then be compared with Statistics Canada's semi-annual Livestock Survey category Bulls, One Year or Older. 217 One year old Heifers are matured for one more year before being added to the Cow Herd. During this period they are bred. AS was discussed in connection with MATRIX, the assumption is made, at least initially, that Beef Heifers are bred at 15 months to calve at 24 months. Thus, all Beef Heifers are assumed to calve immediately upon leaving the one year maturation period. This assumption and subsequent modeling will be followed until new information is found to the contrary. In the instance of Dairy Heifers a more SOphisticated and realistic approach is used. From a priori knowledge, an expected calving age and distribution about this expected age have been deter- mined. Thus, as Dairy Heifers leave the one year delay they enter another continuous or variable length delay with an expected value and dispersion as indicated above. This second delay models the period of time between two years of age and parturition. For various purposes, all First Calf Heifers are added to (or deleted from) the Cow Herd at three points. In the first instance, Heifers are added to the Cow Herd to provide a total which can be com- pared with Statistic Canada's semi-annual Livestock Survey category Female Stock Two Years Old and Older. In the second instance, they are deducted from the above total so that different BIRTH Rates and gestation lags can be applied to First Calf Heifers and Mature Cows. In the third instance, the Calves from both groups of Cows are summed to provide the total Calf Crop. 218 Simulation of the Elements in Cattle Production The elements in the Cattle Herd simulator are described in detail in this section.1 The structure of each element, the assumptions made, and the system's key parameters are given together with plausible estimates of their value.2 This structure is also displayed in the form of exact block diagrams which indicate the relationships of stocks, flows, and system parameters. A rationale for this structure is provided in many instances. Simulation of BIRTHS BIRTHS are simulated by applying a BIRTH Rate to the available stock of Cows and Heifers. The first assumption is that BIRTH Rate is a function of the age of the Brood Cow. This model identifies two ages of Brood Cow; namely, First Calf Heifers, and Mature Cows. Different BIRTH Rates could be used for these two ages. It is initially assumed that the Dairy Cow breeding cycle was approximately 13 months; this figure is based on a priori information. It was then assumed that, everything else being equal, the First Calf Heifer BIRTH Rate would be the Nature Cow BIRTH Rate x 13/12. This was roughly translated to provide a BIRTH Rate differential of .08 for Dairy. The same assumptions were not made for Beef. 1One versiOn of CATSIM, namely CATSIM2 West, is listed in Appendix E together with an explanation of key stock and flow variables not described in this chapter. 2These parameters also include those that are required to disaggregate published statistical data in order to generate certain stock and flow variables. 219 It was further assumed that Eastern and Western Beef BIRTH Rates do not differ. This assumption was made for lack of information to the contrary. Subsequent testing resulted in a Slight differential being introduced. Finally, it was assumed that the Western Dairy Herd was managed somewhat like a Beef Herd, at least at the margin. For this reason, a Western Dairy BIRTH Rate was selected that fell between the Beef and the Eastern Dairy BIRTH Rates. The Rates used in this model and their variable names are listed below.1 Dairy Birth Rate Cows, East BREDC = .72 West BRWDC = .76 Heifers, East BREDH = .80 West BRWDH = .84 Beef Birth Rate Cows, East BREBC = .85 West BRWBC = .84 Heifers, East BREBH = .85 BRWBH = .84 The second assumption is that BIRTH Rate is constant over time. This may well be unrealistic in two respects. First, there may be a long run trend and, second, BIRTH Rate could well be expected to have 1Appendix A contains a detailed discussion of the derivation of BIRTH Rates and of many other parameter values used in CATSIM as well as RECON and MATRIX. The parameter values listed in this chapter, in many instances, were derived or at least verified, through the operation of programs RECON and MATRIX. The sensitivity analysis described in the next chapter also influenced the selection of the values listed. 220 both a predictable and a stochastic element. These two aspects were not considered in constructing CATSIM. A third assumption concerns sex ratio. It is initially assumed that this ratio is 1:1 or Calves are Male and Female in equal numbers. A major element in simulating Calf BIRTHS is the quarterly distribution. Various estimates are discussed in Appendix A. CATSIM uses a monthly distribution that is subsequently aggregated to produce the required quarterly distribution.‘ Dairy birth distributions, East and West, are initially assumed to be equal, however, the Eastern Beef birth distribution is assumed to be more uniform than the Western Beef birth distribution.‘ The array "VAL" indicates the monthly BIRTH Rate at the beginning of each month (note that VAL(l) = VAL(13)). VALDE(1), VALDW(l) = .088 VALDE(7), VALDW(7) = .054 VALDE(Z), VALDW(Z) = .093 VALDE(8), VALDW(B) = .069 VALDE23), VALDW(3) = .069 VALDE(9), VALDW(9) = .077 VALDE 4), VALDW(4) = .112 VALDE(10), VALDW(lO) = .097 VALDE(S), VALDW(S) = .089 VALDE(11), VALDW(11) = .096 VALDE(6), VALDW(6) = .065 VALDE(12), VALDW(12) = .094 VALDE(13), VALDW(13) = .088 ‘An integration subroutine, INGRAT, is used to calculate the proportion of BIRTHS for any stated period of time. This subroutine is described in Appendix B and listed in Appendix E. 2The characters 0 and 8 refer to Dairy and Beef while E and W refer to East and West. This convention is followed in all variable names used in all programs. In addition, M and F are used to denote Male and Female. 221 VALBE(1) = .05 VALBW(1) = .01 VALBE(Z; = .06 VALBW(Z) = .04 VALBE 3 = .06 VALBW 3 = .11 VALBE(4) = 10 VALBW(4) = .25 VALBE(S) = 20 VALBW(S) = .39 VALBE(6) = 20 VALBW(6) = .11 VALBE(7) = 10 VALBW(7) = .04 VALBE(B) = 04 VALBW(8) = .01 VALBE(9) = 04 VALBW(9) = .01 VALBE(10) = 05 VALBW(10) = .01 VALBEéllg = 05 VALBW(11) = .01 VALBE 12 = 05 VALBW 12 = .01 VALBE(13) = 05 VALBW(13) = .01 Figure 18 is an exact block diagram of the birth generation process. After a stock of Cows are bred, a gestation period is realized. This period is approximately nine months in length or three DT's.‘ The gestation period is simulated by a discrete delay process2 that essentially retains the generated BIRTHS for nine months before emitting them. First Calf Dairy Heifer BIRTHS are delayed through a continuous or distributed delay. This process which was used as the age at which First Calf Heifers calve, describes a distribution. Since this distribution is known, it is modeled with a continuous delay.3 ‘The model CATSIM simulates the Cattle Herd in time increments of three months or .25 of a year. Each time increment is termed a DT; a 01 is the same as the At used in other contexts. 2A BOXC subroutine is used. This subroutine is described in Robert W. Llewellyn, FORDYN, An Industrial Dynamics Simulator, Raleigh, University of North Carolina, 1965, pp. 52-56. The BOXC program is listed in Appendix E. 3The subroutine used was VDELDT. A similar subroutine DELDT is described in Llewellyn, o . cit., pp. 40-51. A complete discussion of VDELDT is contained in Appenaix B; the program is listed in Appendix E. 222 .mzhmmm upmu mo newuapasww .m— «Lamp; mzpmum upau apnea“ m u on ovum co.uznvgumwu mezuzuu<4au¢ :pmum gugpn zapou cameo: Levee: »_meca:o cmvuuumom L... _ 3 LII? 5:3 E j _ 85.253 _ ; 4mg . mu.\4ua u .mHH mung 558 _l m 1 \ + a _ E. + uhuaumna zo_h<4=aoa :8 35. 85323:. . :pxum =»L.a ampuo sou xpguucoac covaaumom mbaau mpxoax~ mhzoaxu m. a _n zoo 260 you mxp¢~m mpuu opus 223‘ The expected value of this Dairy Heifer gestation delay is approximately .85 years beyond two years of age. This is modeled by the use of the following parameters. DELEDH, DELWDH = .85 The distribution is very flat, with some BIRTHS occurring before two years of age and as late as four years. The parameter that provides, the shape to the distribution is: KEDH, KWDH = 3 For lack of proper information, no delay is experienced with First Calf Beef Heifers. It is assumed that they immediately calve Upon turning two years of age. Information received in the future may allow this element of the model to be developed more accurately, possibly along the lines of the Simulation of First Calf Dairy Heifer BIRTHS. Figure 18 Shows that First Calf Dairy Heifers are added to the Cow Herd at point A and subtracted again at point B. The purpose of this structure is to allow the model to both conform to STATCAN sta- tistics ang_provide the differential birth process. In the first instance, Heifers are added to the Cow Herd at two years of age. This allows comparison of Simulated "Cows and Heifers, Two Years and Over," with the published figures. In the second instance, First Calf Heifers are subtracted after being multiplied by a constant in 224 order to generate BIRTHS in an accurate manner consistent with actual practice. The rationale for this structure is described below. By definition, Cows are considered to be females over two years of age, kept primarily for milk and for producing Calves. At first glance, BIRTHS would appear to be a product of Cow times BIRTH Rate. That is: BIRTHS = Cow Population x BIRTH Rate. This formula assumes, however, that only Cows over two years of age produce calves; in fact, only Cows two years or older are bred. If Heifers are bred at 15 months, they drop their first Calf at two years. Thus, tw9_groups of Females calve: Replacement Heifers under two years, plus Cows over two years. If Cows only are considered, BIRTHS are understated by the Calves produced by Heifers bred prior to two years of age. On the other hand, if Cows do not produce their first Calf until they are 3 3/4, then BIRTHS will be overstated if the above formula is used. This occurs as Females two to three years of age do not produce Calves at all. Sine the possibility of different BIRTH Rates exist for First Calf Heifers, as opposed to Mature Cows, the following formula may be used. Cow BIRTHS = (Cow Population - Heifer Population‘) x Cow BIRTH Rate ‘Refers to the stock of Replacement Heifers, not total Heifers. 225 Heifer BIRTHS = Heifer Population x Heifer BIRTH Rate Total BIRTHS = Cow BIRTHS + Heifer BIRTHS. This formula applies only to the situation where a Cow has its first calf at approximately 2 3/4 years. It does not apply to the above "early" and "late" calving instances. To do so it must be altered--the critical point is the breeding age of 15 months. At this breeding age, Heifer Population is ngt_subtracted from Cow Population in order to calculate Cow BIRTHS. If bred at two years, then Heifer Population j§_subtracted; if bred at three years, then Heifer Population is subtracted approximately EEiEE: The generation of BIRTHS can be reformulated as follows to handle all the above instances mentioned. Cow BIRTHS = (Cow Population - Heifer Population x A) x Cow BIRTH Rate Heifer BIRTHS = Heifer Population x Heifer BIRTH Rate Total BIRTHS = Cow BIRTHS + Heifer BIRTHS where = 0 if Heifers bred at 15 months, 1 if Heifers bred at 24 months, J> J> :> 11 2 if Heifers bred at 33 months. The continuous delay parameter DEL is used to indicate the expected age of First Calf Heifers at calving, by measuring time from two years onward; thus, DEL is used to calculate A. 226 A = DEL/.75 where .75 represents gestation period in years, the same unit as DEL. Thus, if Heifers calve at two years of age, as it is assumed Beef Heifers do, DEL 0, and A = 0. If Heifers calve at 2 3/4 years, then DEL = .75 and A = 1; this is roughly the case with Dairy Heifers. If DEL is unknown, but all other elements in the birth genera- tion process are known, it may be possible to optimize on A. DEL would then be estimated by the formula: DEL = A x .75. Simulation of DEATHS DEATHS constitute a continuous, but not necessarily constant, depletion of the Cattle Herd. The major parameter of concern is the DEATH Rate, usually expressed in annual terms as a proportion of the Herd. The DEATH Rate is most likely a function of the age of the animal, possibly its sex, possibly its function, and quite likely its environment. Due to the lack of information concerning DEATH Rate, several assumptions are made to accommodate the simulated process and the available data. The first assumption is that Male and Female DEATH Rates are equal. A second assumption is that for East and West, all Cattle under one year of age have the same DEATH Rate. All non-Fed Cattle over one year of age have a second and different DEATH Rate. 227 A third assumption is that all Cattle on Feed, East and West, have a third DEATH Rate. A final assumption is that the DEATH Rate for the first six months of the year is at a high level, a lower level is used for the last six months. The best initial estimates of annual DEATH Rate of Calves are as follows, together with their variable names. DRMBCE‘ lst quarter = .048 DRMDCE 2nd quarter = .048 DRFBCE 3rd quarter = .022 DRFDCE 4th quarter = .022 DRMBCW lst quarter = .040 DRMDCW 2nd quarter = .040 DRFBCW 3rd quarter = .020 DRFDCW 4th quarter = .020 Lower annual DEATH Rates are used for Cattle over one year and all Cattle on Feed. The DEATH Rate variables and their annual rates are listed below. DRCATE(1) = .015 DRCATW( (1) = .016 DRCATE(Z; = .015 DRCATW§23 = .016 DRCATE 3 = .012 DRCATW 3 = .012 DRCATE(4) = .012 DRCATW( (4) = .012 DRCATF(1) = .014 DRCATF(2) = .014 DRCATF(3) = .012 DRCATF(4) = .012 ‘The annual Rates are stored in a set of subscripted variables whose names commence with CY, i.e., CYMBC(1). The DEATH Rate parameters take on different values each quarter. The value of the parameters are changed quarterly by a CBOX subroutine which cycles the subscripted CY variables. This CBOX subroutine is explained in Appendix B as well as in Llewellyn, op. cit., pp. 52-55. The CBOX program is listed in Appendix E. 228 DEATHS are simulated by generating the flow at the beginning of each period, for each age, and/or function cohort. This is done by multiplying the net inflow rate by the annual_DEATH Rate then by the lgngth_of time in that cohort. If the cohort is represented by a stock value (i.e., Cows and Bulls) then the stock_value is multiplied by an annual_DEATH Rate. These two types of simulation models are shown in the following exact block diagrams (Figures 19 and 20). EXPORTS IMPORTS DEL IN _ + K OUT FLOW _ l FLOW f Annual DEATH Rate x DEL Figure 19. Simulation of DEATHS in a Flow Situation. Some inaccuracy is introduced as the whole DEATH flow is deducted at the beginning of the period as a continuous process is being simulated by a discrete process. This inaccuracy, however, is not felt to be significant in light of the possible error in the estimated DEATH Rate. 229 Cow Cow Cow EXPORTS IMPORTS CULLS Cow + Population _ _ Heifer -e S 2 + REPLACEMENT Rate Figure 20. Simulation of DEATHS in a Stock Situation. Simulation of Calf, Cow and Bull SLAUGHTER Simulation of SLAUGHTER is not so much a problem of method or model structure as one of data or of obtaining estimates of the magnitude of the flow variables. The technique used to estimate the flow variable, Calf SLAUGHTER, is to employ published statistical data or at least available statistical data. The data basically fall into two categories: INSPECTED and UNINSPECTED. Both categories have previously been discussed in Chapter II. INSPECTED data are available on a monthly basis, East and West, Male and Female. The only remaining problem is to allocate it between Beef and Dairy. Good estimates are unavailable; consequently, 230 the following parameters are used in CATSIMl to generate the necessary flows.‘ Proportion of Male Calf SLAUGHTER that is Beef East, V41 = .10 West, Vl = .10 Proportion of Female Calf SLAUGHTER that is Beef East, V42 = .10 “ West, V2 = .25 The second category of data is UNINSPECTED SLAUGHTER. These data are estimated by STATCAN under the classification, Farm Killed and Eaten, and Farm Killed and Sold. The latter two data series are available only on an annual basis, while the former is available on a quarterly basis. All are available on an East/West separation but not on a Male/Female basis. The problem then is to estimate a quarterly distribution and a Male/Female separation. While this matter is discussed in detail in Appendix B, the first estimates were made by simply applying the comparable rates from INSPECTED SLAUGHTER. The parameter values used are as follows: Proporion Females in UNINSPECTED Calf SLAUGHTER East, V43 = .55 West, V3 = .50, before 1966 V3 = 1.00, after 1965. Quarterly Distribution of UNINSPECTED Calf SLAUGHTER =.25 (included as a structural element, not as a parameter). ‘This sub-section is largely devoted to describing the method of estimating SLAUGHTER (Calf, Cow, Bull) flows for CATSIMl. SLAUGHTER flows for CATSIM2 and CATSIM3 have previously been estimated by program MATRIX and the behavioral models, respectively. 231 The allocation into Dairy and Beef follows the same distribution as INSPECTED Calf SLAUGHTER. CATSIMl re-calculates this latter distribution quarterly. Calf SLAUGHTER flow values for CATSIM2 and CATSIM3 are taken as generated by MATRIX and the relevant behavioral models, respectively. These flows are given in Tables 6 and 13. The allocation of Cow SLAUGHTER into its Dairy and Beef com- ponents represents a further data problem. In CATSIM2, Cow SLAUGHTER flows are calculated by MATRIX; these data are given in Table 5. Cow SLAUGHTER flow data for CATSIM3 are generated by the behavioral models; these data are listed in Table 12. Finally, CATSIMl calculates Dairy Cow SLAUGHTER in the West and Beef Cow SLAUGHTER in the East by select- ing fixed values (constants) that maintain the respective Cow Herds at published levels given REPLACEMENT Rates. The replacement process and Rates are discussed below in sub-section Simulation of the Growth Process. SLAUGHTER Rates are determined by REPLACEMENT Rate plus or minus a constant. The former Rate is then applied to the appropriate Cow Population to determine SLAUGHTER flow. The constants are minus .06 for Eastern Beef Cow and plus .022 for Western Dairy Cows. Calculation of Western Beef Cow SLAUGHTER and Eastern Dairy Cow SLAUGHTER is the residual given the published Total Eastern and Western Cow SLAUGHTER. Program MATRIX corroborates the estimates for these flow values. As with Calves, UNINSPECTED Cattle SLAUGHTER also contains Farm Killed and Eaten and Farm Killed and Sold estimates. This flow 232 must be disaggregated into its Cows, Bulls, Steers, and Heifers elements. The calculation of Bull SLAUGHTER follows the pattern of the calculations for Calves and Cows. That is, SLAUGHTER flows for CATSIM2 and CATSIM3 are taken as estimated by MATRIX and the behavioral models. These flows are listed in Tables 7 and 14. For CATSIMl, the UNINSPECTED Bull SLAUGHTER is added to the published INSPECTED Bull SLAUGHTER. It was initially assumed that Bulls occurred in UNINSPECTED SLAUGHTER in the same proportion as in INSPECTED SLAUGHTER. This assumption was modified as the result of new information obtained through the use of program MATRIX leading to the following parameter values. Proportion of Bulls in UNINSPECTED Cattle SLAUGHTER East, V75 .06 West, V35 .06 Flow values for UNINSPECTED Heifer SLAUGHTER is required, as well as for Steers. The Heifer value is the residual after UNINSPECTED Steers, Cows, and Bulls have been accounted for. The following parameters are used for this purpose. Proportion of Steers in UNINSPECTED Cattle SLAUGHTER East, V76 = .40 West, V36 = .207, before 1966 V36 = .00, after 1965 It was assumed initially that 25 percent of UNINSPECTED Cattle SLAUGHTER was Cows, the balance was Heifers. Program MATRIX indicated an upward revision in the case of the Eastern Cow value. 233 Proportion of Cows in UNINSPECTED Cattle SLAUGHTER East, V45 .28 West, V11 .25 The allocation of UNINSPECTED Cow SLAUGHTER between Beef and Dairy is the same as that for INSPECTED SLAUGHTER. When the SLAUGHTER flow has been estimated in the disaggregate form required of CATSIM, it is deducted from the IN FLOW by the simple operation of subtraction. This is demonstrated in Figure 21. IN FLOW OUT FLOW Z *' + SLAUGHTER Figure 21. Simulation of SLAUGHTER. Simulation of EXPORTS and IMPORTS As with SLAUGHTER, the major problem encountered in attempting the simulation of EXPORTS is the determination of magnitude of the flow. SLAUGHTER statistics are available in a fairly disaggregate form for the years 1969-1972 inclusive and in a highly aggregate form for the years 1958-1968 inclusive. The 1958-1968 data is available on an annual basis only. The first set of parameters provide initial quarterly estimates. 234 Quarterly distribution of Purebred IMPORTS East and West, 01(1) = 01(3) 01(4) Quarterly distribution of Purebred EXPORTS East and West, 02(1) = .18 02(2) = .28 W( ) = 24 02(4) = .30 Quarterly distribution of Other Dairy EXPORTS East and West, 03(1) = .16 032 = .32 0333) = .30 03 4) = .22 Quarterly distribution of Other IMPORTS East and West, 04(1) = .31 04(2) = .26 Q43( ) = 03 04(4) = .40 Quarterly distribution of EXPORTS, Cattle Under 200 Pounds East and West, 05(1 W 1111111 —-l—-IU'| OGDN 05(4 Quarterly distribution of EXPORTS, Cattle 200- 700 Pounds East, 0631; = .14 West, 0621; = .04 Q6 2 = .16 062 = .04 06(3) = .29 06(3) = .08 06(4 = .41 06(4) = .84 Quarterly distribution of EXPORTS, Cattle Ov ver r700 Pounds East, 07(1) = .14 West, 07(1) = .31 07(2) = .34 07(2) = .22 07(3) = .26 07(3) = .18 07(4) = .26 07(4) = .29 The next problem is the division of EXPORTS into Male/Female and Beef/Dairy. 235 Proportion Females in Purebred IMPORTS East, V59 = .90 West, V19 = .90 Proportion Females in Purebred EXPORTS East, V58 - .85 West, V18 .85 Proportion of Dairy in Purebred IMPORTS East, V55 = .20 West, V25 = .20 Proportion of Dairy in Purebred EXPORTS East, V56 = .826 West, V26 = .826 The EXPORT category, Cattle 200-700 Pounds, contains Cattle that range from Weaned Calves to Yearlings. A parameter is needed to make the basic division Between six month old Calves and one year old Calves. Proportion of six month old Calves in EXPORTS, Cattle 200-700 Pounds East, V46 .90 West, V6 .90 A parameter of major interest, as it has historically hampered Herd expansion possibilities, is the proportion of Male Calves in EXPORTS, Cattle 200-700 Pounds. Proportion of Males in EXPORTS, Cattle ZOO-700 Pounds East, V44 - .145 West, V4 .50, before 1966 V4 .00, after 1965 The EXPORT category, Cattle Over 700 Pounds, contains a variety of Cattle. To make this division, the following assumptions are made. 236 East: 1. Of the first 3,000 head shipped annually, 80 percent are Cull Dairy Cows. 2. Of all Cattle over 2,400 head (80 percent of 3,000) only 10 percent are Cull Dairy Cows. West: 1. Of the first 8,000 head Shipped annually, 80 percent are Cull Dairy Cows. 2. Of all Cattle over 6,400 head (80 percent of 8,000) only 5 percent are Cull Dairy Cows. ALL EXPORTS, Cattle Over 700 Pounds that are not Cull Dairy Cows are assumed to be Steers and Heifers for Immediate SLAUGHTER. Proportion of Cull Dairy Cows in EXPORTS, Cattle Over 700 Pounds below a fixed critical figure East, V53 - .80 West, V13 .80 Proportion of Cull Dairy Cows in EXPORTS, Cattle Over 700 Pounds above a fixed critical figure East, V531 .10 West, V131 .05 Proportion of Steers in the non-Cow portion of EXPORTS, Cattle Over 700 Pounds East, V54 .35 West, V14 .35 In addition, the Dairy/Beef proportion of EXPORTS of Cull Cows is assumed to be in the same ratio as Cows in the general population. Other assumptions include: (1) all EXPORTS of Cattle Under 200 Pounds are very young Male Dairy Calves, and (2) all EXPORTS of non-Purebred Dairy Cattle are Dairy Cows. 237 Finally, consideration must be given to the proportion of Males in IMPORTS, Cattle Over 700 Pounds. It is assumed that this category only contains Cattle for Immediate SLAUGHTER. Proportion of Males in IMPORTS, Cattle Over 700 Pounds East, West, V16 = .70 Simulation of EXPORTS and IMPORTS is done by the same subtraction operation as was the case with SLAUGHTER. Simulation of WEST-EAST Cattle-Calf Movement Closely related to foreign trade are the internal trade flow variables. The following assumptions are made concerning the published data. 1. Eastern Movements by rail are something less than total Cattle Movements. The scale of coefficient for WEST-EAST Cattle-Calf Movement is: East, V9 1.07 West, V7 1 .07 2. Calves shipped for SLAUGHTER are assumed to be slaughtered immediately. Calves shipped to FEEDLOTS or STOCKYARDS are assumed to be placed in a feedlot or on grass. 3. Cattle shipped for SLAUGHTER are assumed to be slaughtered immediately. Cattle Shipped to FEEDLOT or STOCKYARDS are assumed to be placed in a feedlot or on grass. The remaining problem is the Male/Female division. The following parameters are used. Proportion of Males in Calf Movements for FEEDLOT and STOCKYARDS V5 = .80 _ Proportion of Males in Cattle Movements for FEEDLOT and STOCKYARDS V12 = .80 238 Proportion of Males in Cattle and Calf Movements for SLAUGHTER V15 = .95 As with SLAUGHTER, EXPORTS, and IMPORTS, WEST-EAST Movements are simulated by a simple arithematic operator: in the case of the East, the recipient, an addition operator; in the case of the West, the shipper, a subtraction. Simulation of Feeder Cattle ALLOCATION to Feeding Programs As previously discussed, CATSIM models the feeding and finishing of Cattle using two processes. The first or Ration A is a low energy ration. The second, Ration B, is a high energy ration. While a whole spectrum of processes are used in practice, these two processes in some proportion are felt to reasonably represent cattle feeding and finishing in Canada. The decision point comes at approximately six months of age when the Calves are weaned and are brought in off the range. An assumption made in constructing the model is that all REPLACEMENT Cattle are taken from the low energy or A Stream. Thus, at least enough Cattle must remain in this stream to comfortably provide for REPLACEMENT flow. An extension of this assumption is that no Dairy Heifers are diverted to the high energy 8 Stream. Appendix A provides a discussion of the initial values used in allocating six month old Calves to the two feeding-finishing processes. These parameters and their values are: Proportion of BeefoMaleS to Ration 8 East, V47 West, V7 .60 239 Proportion of Daizy Males to Ration B East, V67 = West, V27 = .70 Proportion of Beef Females to Ration 8 East, V48 = .30 West, V8 = .20 Proportion of Dairy Females to Ration 8 East, V68 = 0.0 West, V28 = 0.0 The simulation of Feeder Cattle ALLOCATION to Feeding Programs is demonstrated in Figure 22. Simulation of the Growth Process One of the most important processes in cattle production is that of growth (and feeding-finishing). This process can be of varying length depending on genetic stock, feed intake, disease and environmen- tal factors and the cultural or husbandry practices followed. Three observations might be made. One, for any group of Cattle, the growth (and feeding-finishing) rate varies from animal to animal. This is true for one feedlot as well as for the total Herd. A second observation is that given constant cultural practices, the average length of the growing period might shorten over time, due to techno- logical improvement in feeding and breeding and wider adaptation of superior techniques. A third observation might be that the shape of the distribution of cattle coming out of the growth process might change for the same reasons as were used to support the hypothesis that the growing rate was increasing. 240 .ooomooaoa oewooou 0» one4DR if BR=DR if BR C) c) C) PPBH 000‘ Ol l 0.2 . w. 85an o o o -92 2:35 ...-------.. e.g— u szmh3 umpmevumm ucm .vmsmwpnzm .Nnmpupmmp .pmmm .mmhzo:<4m mewm: xpgmpgmso .o¢ mnm— Pump , ONmP momp moor Romp mom? mom— comp mom? Nmmp pomp —4du—1111—q1114‘—-ufi—1qql41qqd-u4—+q-—d-J‘-uq—-qu 353250 0 0 2:35 1:3-.. 1, L: 1 X $| .o . o NszHs¢v >s.o >s.o a: .o .o as a: United 3271’: 3:33 3:23 ‘5? 1633 "8g gin; E23)? States 8151 83. 33. 3m 33 go. mo 1.1.0 (head) (head) (head) (head) (head) (head) (head) (head) .‘2 East 20,972 11,163 776 9,233 3,817 414 6,776 1,443 2 West 1,422 202 11 3,885 2,974 3,814 6,521 28,271 a East 31,074 16,006 1,426 1,719 465 164 3,079 112 2 West 2,143 427 14 3,012 2.764 2,701 7,127 2,731 ;: East 36,441 22,440 3,160 129 2: West 2,334 294 7,967 182 :2 East 33,069 22,283 2,677 129 52 West 2,930 327 12,876 3,397 g East 19,673 19,148 1,626 119 ... West 2,226 660 23,936 14,546 8 East 13,965 13,286 6,488 86 2 West 585 217 26,295 21,456 S East 11,810 11,569 2,334 106 52 West 301 180 7,223 10,736 :3 East 19,389 18,772 8,441 258 52 West 486 275 28,133 61,692 8' East 14,178 17,952 23,766 788 2 West 896 494 31,101 94,193 g East 12,965 16,283 14,952 513 2 West 1,085 542 12,162 17,516 {3 East 11,244 16,607 7,862 141 9: West 281 318 9,188 28,916 g East 14,639 15,509 7,558 34 ... West 296 269 19,649 44,624 S East 16,889 19,140 450 125 3 West 14 97 28,812 86,595 311 Allocation to Ration B The best evidence of the proportion of Cattle placed on a high energy ration might be given by an examination of the proportion of Slaughter Steers and Heifers falling in the top two grades (choice, good). This analysis is given in the following table. Proportion of Slaughter Steers Year Heifers in top two grades 1961 .7472 1962 .7177 1963 .7520 1964 .7644 1965 .7413 1966 .7622 1967 .7742 1968 .7968 1969 .8339 1970 .8479 1971 .8449 Allocation of REPLACEMENTS The following table shows the annual change in the Dairy Cow Population (June 1 data). Annual Year 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 Annual % change 1957-1973 change in Dairy Cow Population--June 1 Change in Eastern Change in Western M9 (head) -149,500 -7,300 '8 9400 52,200 59,000 -227.500 —46,500 -2,000 -11,000 -61,100 -50,900 -43,000 -19,000 -50,000 -115,500 -20,500 -36,000 -1.821 Cow Herd (head) -51,500 -10s500 -13,000 2,000 15,000 -53,000 -36,000 -26,000 -38,000 —60,000 -54,000 -37,000 -28,000 —3.000 -18.400 -23,800 -22,800 -3.98 Canada -2.337 The following table calculated the ratios for selected years. = INSPECTED Cow SLAUGHTER Average Cow Population INSPECTED Cow SLAUGHTER AverageIHeifer Population Ratio A Year East West 1964 .1279 .1036 1969 .1264 .1070 1972 .1167 .0945 19219.8. Year East West 1964 .4185 .381 1969 .3861 .423 1972 .354 .339 313 Ratio C Year East West C = INSPECTED Bull SLAUGHTER Average Bull Population 1964 .288 .208 1969 .347 .175 1972 .358 .193 Ratio D Year East—~—___West D = INSPECTED Bull SLAUGHTER ' Average Steer Population 1964 .052 .0354 1969 .0464 .0314 1972 .0434 .0365 Delay Parameters The calculation of the parameters for the continuous delays are based in most part on a set of more or less realistic assumptions con- cerning the process being simulated. The exception is the simulation of First Calf Dairy Heifer BIRTHS--a distribution was obtained from ROP in this instance. The parameters in question are DEL and K. These are described in Appendix B. Given the erlang distribution, the purpose of this section is to consider initial expected values and distributions. Ration A and B Delays Initial assumption--Ca1ves weaned at 180 days Male Calf weaning weight 375 pounds Female Calf weaning weight 350 pounds Ration B--on full feed Hales to 1,050 pounds ADG range 1.9 to 2.4 pounds Days on feed 281 to 355 t / at“ 314 Females to 950 pounds ADG range 1.7 to 2.1 pounds Days on feed 285 to 352 Ration A--1ow energy ration for all or part Assume at 365 days Males 600 pounds Females 550 pounds At one year these Cattle may be placed in a feedlot or may be placed on grass for a further four to six months. This option increases the ADG range; thus, the distribution being simulated is flatter than the above "full feed" distribution. Males to 1,100 pounds ADG range 1.5 to 2.25 pounds Days on ration A 222 to 333 Females to 1,000 pounds ADG range 1.4 to 2.00 pounds Days on feed 225 to 321 The above ranges provide a bound for expected value; it might also be expected that at least two-thirds of the distribution would fall in this range. The shape of the distribution might be expected to be skewed to the right possibly suggesting an order (K) of five. In the case of Ration 8, this provides mean of 3.33 DT's or .82 years variance of 2.22 DT's standard deviation of 1.25 DT's or .3125 years The distribution associated with Ration A might be expected to be f1atter--an order of three is suggested. mean of 3 DT's or .75 years variance of 3 DT's standard deviation of 1.75 DT's or .4375 years 315 Dainy Heifer Birth Delay The ROP Section of Agriculture Canada provided the following age distribution for First Calf Heifer FRESHENINGS. month range. of three. These parameters would provide: mean of about variance of about standard deviation of about Age Range Proportion of Total (months) under 21 .00278 21-24 .01719 24-27 .10542 27-30 .16005 30-33 .15536 33-36 .11261 36-39 .09634 39-42 .12149 42-45 .12652 45-48 .10078 The distribution rises rapidly, then slowly tails off. quite flat and is in fact bi-modal suggesting two distributions. Half this distribution falls below the mid-point of the 33-36 The flatness of the distribution suggests the order (K) DT' DT's 's s or .85 years or .5 years APPENDIX B SIMULATION Appendix 8 describes several different aspects of simulation pertinent to an understanding of this thesis. The first section describes the implied mathematical model and the exact block diagram. The second section describes several common simulation building components used in the models. Simulation of the Modeled System The simulation model is the second level of abstraction from reality. The sequence is: THE REAL WORLD 1 MATHEMATICAL MODEL 1 SIMULATION MODEL There is thus an implied or possibly explicitly expressed mathematical model of the system under investigation. The mathematical model in turn is the model that is simulated. In actual practice, exact expression of the system in mathematical form is most often skipped. The development, performance, consideration, and theoretical 316 317 discussion of the simulation components, however, takes place in exact mathematical form. The dynamic aspects of a biological growth process, such as a cattle herd, probably can most precisely be expressed in non-linear differential equations. Their solution, however, even with advanced numerical techniques, can be unduly complex. If the relationship is essentially a function of time, it is usually possible to pick a time period of short enough duration so that the non-linear system can be modeled in linear terms. The basic mathematical representation of the cattle population is developed in terms of linear differential equations and the related first order difference equations. The matrix representation of a first order linear differential equation could be given as follows: (%) fifi1=gxu1+pmu where x(t) = a vector of state variables U(t) = a vector of rate or stimulus vectors A, 8.: matrices Or in first order difference equation form as: (m) MtH)=AxU)+BMU where the symbols have the same meaning as above. 318 The terms state and rate variables are used in systems parlance to represent stock and flow variables, respectively. The state variables are described as the product of the integration of rate variables. In the specific terminology of this study, stock (or state) variables refer to cattle numbers at a point in time; flow (or rate) variables refer to number of head per unit of time. An nth order linear differential equation is used to represent lagged response to a stimulus. This can generally be represented as: (88) a Mi- a 93:13:59.... “..., aOY(t) ___ b de(t) " dt" "’1 dt m dt'" ,...., +b0U(t) where x(t) = the stimulus, y(t) = the response. Since differential equations are difficult to solve or manip- ulate, a method is used by engineers, called Laplace Transformations.‘ This is a transformation whereby differential equations can be converted to ordinary algebraic equations, manipulated, and then transformed back to differential equation form by an inverse Laplace Transformation. 1The basic Laplace Transformation is by definition L[x(t)] = x(s)=fox(t)e-5tdt 0 All other transformations are derivatives of this formula. 319 If a Laplace Transformation is performed on equation (87), the following form is obtained bms'“ + + b0 I.C.(s) (89) Y(S) = m x(S) + m anS + ,...., + a0 anS + ,...., + a0 where I.C. = the initial conditions. If I.C. = 0, then (90) Y(s) = G(s)X(s) where G(s) = ratio of two polinomials known as the transfer function, itself a polynomial. The transfer function, G(s), determines the response of the system being modeled by the nth order differential equation and thus the model's dynamic properties. This transfer function is used to design into the model both stability and the required response characteristics.‘ With respect to the overall Cattle Herd simulator, the foregoing discussion is strictly theoretical as the system is much too complex to be modeled in terms of differential and difference equations and assessed 1For a detailed discussion of Laplace transformations and the dynamic properties of differential and system control equations, see T. J. Manetsch and G. L. Park, op. cit., especially Chapters IV and VII. 320 in terms of their Laplace transformations. Rather, the system is simulated using system components with known properties and the complete model is then subjected to a series of validation, sensitivity, and stability tests to assess its dynamic properties and to fine tune it accordingly. The simulation of these linear differential equations that represent the dynamics of the Cattle Herd essentially involve solving them at discrete points in time. Such a model is called a discrete model and the simulation essentially becomes a difference equation model. Block and exact (mathematical) block diagrams are commonly used to display and represent the system being modeled. These diagrams allow lines and direction of causation to be shown, feedback loops to be displayed, as well as stock and flow variables to be represented. The exact block diagram displays the simulation components that are the differential (difference) equations or transfer functions. For demonstration purposes, a simple block diagram is shown below. It involves a vector of state variables, X, an exogenous rate vector, u, and an output rate vector, y. In addition, the model has a feedback loop. Feedback involves an output of the system influencing an input, usually a delayed influence. Most, if not all, real world systems involve feedback loops together with controller mechanisms. A system without a feedback loop is called an open loop system, a system with a feedback loop is a closed loop system. A complex system may involve both open and closed loop components. 321 The feedback mechanism is closely associated with system performance and stability. If changes in a system's output are felt almost immediately through a short "delay process," then the controller can act quickly and so provide smooth performance as does a governor on an engine. If the system has long delays and slow controller response, as does the price mechanism in the economic system, then cyclical motion may result. With poor feedback and an ineffective control mechanism, explosive behavior or a complete collapse may be observed. Feedback can be of either a positive or of a normative nature-- usually both are present in a system of any complexity. The behavioral response of individuals and firms in the economic system represent a positive response to largely normative stimuli. When certain outcomes are observed and evaluated as being good or bad (with respect to some welfare function, largely unspecified), specific adjustments are observed. Thus, in this model, beef farmers represent the controller, adjusting Herd investment and disinvestment as well as Calf SLAUGHTER and certain other variables under their control. A larger model can be visualized representing the aggregation of all beef farmers, as well as other immediate elements in the economic system. In the larger model, the Federal government, their advisors, and operating agencies are the controller. Let x represent the vector of the various age cohorts in the Cattle Population, u represent the vector of EXPORTS, and y, the vector of Slaughter Cattle. Then H is a matrix of SLAUGHTER Rates and A, a matrix of BIRTH and DEATH Rates. In differential equation and exact block diagram form, the model may be represented as follows: 322 dx _ EE-AX+U y=|_i_x E5 RAJ In difference equation form, the model is x(t+l) = A_x(t) + U(t) ”H = fl x(t) U(t) x(t+l) UNIT x(t) n m) — Z DELAY * 1_5-J + J—l IAF 323 The symbols used in representing a model in exact block diagram form are <::) summation (negation) ,LZJ product (::> division integration .2399—a- variable name, stock or flow Simulation Building Components Integration The dynamics of the Cattle Population can be visualized as a series of stocks and flows. Stocks are quantities at a point in time, flows are quantities pg§_unit of time. Stocks result from the integration of flows. Mathematically, this process can be modeled by differential equations such as: <91) dt = f(x) where F(x) = a stock. f(x) = a flow. 324 Differential equation (91) states that the change in the stock is a function of the flow. If both sides of (9l) are integrated from time 0 to time t+DT, the following is obtained. t+DT (92) F(t+DT) — F(O) = j" f(x)dx. 0 Assume F(O) to be zero and rewrite the right hand side t+DT (93) Mt+DT) j'f(x )dx + j' f(x)dx. t This form, (92), can be related directly to cattle population by specifying: F(t+DT) = cattle population at time t+DT, t ] f(x)dx = cattle population at time t, o t+DT 1' f(x)dx = the flow of cattle over the period t, t+DT. o This in turn can be rewritten as: t+DT (94) F(t+DT) = F(t) + Jr f(x)dx. t 325 Expression (94) can be simulated by a series of integral simulators that vary in degree of accuracy.1 For the application used in this study, the simplest possible formula was used initially. It is called Euler integration and assumes: (l) DT is small, and (2) f(x) is constant over the interval (t, t+DT). Since neither of these conditions hold, some inaccuracy may result.2 The form of the Euler integral is: (95) F(t+DT) = F(t) + DT -(f(x)). Delays The second major building block is the delay. The delays, as used in this study, are of two basic types. The first is "discrete," where a flow is delayed for a finite or discrete period while a process or function takes place. The second basic type is called "continuous" or "distributed." In this instance, the delay is of variable length; however, the output is of a fixed distributional character. Discrete delay§:--Delays are associated with flow variables. A discrete delay may be represented by 1T. J. Manetsch and G. L. Park, op. cit., pp. 9-l9 to 9-43. zEuler integration was only used in CATSIM to calculate Cow and Bull Population; in all other possible instances it was found to be inaccurate. Rather than employ a more sophisticated integration, all other Populations were calculated by summing the storage (Train Values) in the delay sub-routines. 326 (96) 0(t) = I(t-DT) where 0(t) = output of the delay in period (t); and I(t-DT) = the input to the delay in period (t—DT). For a poli-period delay, a series of such delays would be utilized. 0(t) = 11(t-DT) 01(t) = 12(t-DT) On-l(t) = In(t-DT) where 01(t) to 0n_t(t) are intermediate values. This delay procedure is simulated by the BOXC subroutine. The call statement for BOXC is as follows: SUBROUTINE BOXC (BINR, BOUTR, TRAIN, NCOUNT, N CY, LT, SUMIN) where BINR = the unlagged value, I(t); BOUTR = the lagged value, 0(t); TRAIN = the array of LT-l intermediate values 01(t) ,.... 0LT-1(t)i NCOUNT = number of DT's since last indexing of the TRAIN; 327 NOCY = number of DT's per indexing of the TRAIN; LT = number of sub-delays in the total delay; and SUMIN = sum of the inputs since the last indexing. This delay might be demonstrated graphically as TRAIN TRAIN TRAIN BINR LT , LT_1,....,_._ 1 BOUTR ,_ A second discrete delay is used called CBOX. It is used to cycle a series of values such as seasonal or monthly values. It might be depicted graphically as: CYCLE (T) CYCLE (T-l) L—C- ,...,-H CYCLE ('l) The call statement for CBOX is SUBROUTINE CBOX(CYCLE, LT, NCY, NK) where CYCLE = an array of LT values; LT = the number of elements in the array; NCY = the number of DT between indexings; NK = a counter that records the number of DT's since the last indexing. 328 Both subroutines, BOXC and CBOX are described and the programs listed by Llewellyn.1 Continuous delays.--A continuous delay can be defined as a linear differential equation. k k-T (97) x(t) = a ngle—+ a g___yjjj_+ ,...., + a y(t) k k k-l k-l 1 dt dt where x(t) = the unlagged value, and y(t) = the lagged value. This delay is defined by its order, or the size of K. The output of this type of delay is distributed over several periods; the output y(t) thus adjusts slowly to changes in input x(t). The difference between the output of a discrete as compared to a continuous delay may be demonstrated by the following diagrams, where x(t) is input, y1(t) is the discrete response, and y2(t) is the continuous response. X ---- 1R. W. Llewellyn, op. cit., pp. 7-50 to 7-54. 329 Y1 I t Y2 t If x(t) were a non-sustained flow, then the y(t) function might look like the following: x(t) The shape of the y(t) distribution depends on the order of the differential equation (97) that represents the delay. 330 The delayed output has an erlang distribution‘ with parameters a and k, k being the order of the delay. f(x) = Laflk x(k'])e'kax defines the erlang distribution. (k-l) ! where _ l E(x)-—a—-s l V(x) = -—§-; and ka -11-.1 mode - ak . The parameter k allows this distribution to represent a whole family of distributions. The following figure provides examples. A rather sophisticated continuous delay subroutine is used in CATSIM to simulate continuous delays that have an erlang distribution. The subroutine is VDELDT. SUBROUTINE VDELDT(RINR, ROUTR, CROUTR, DEL, DELP, IDT, DT, K) where RINR = the unlagged value x(t) ROUTR = the lagged value Y(t) CROUTR = the array of intermediate values 1T. J. Manetsch and G. L. Park, op. cit., pp. l2-9 to l2-ll. 331 mcowpoczu prmcmo mo prsmm mcmfigm mg» m we. w m. P m m P I, ’I \ \\ \\ \ (II I \ \ '1” [All]! \ flh’I/I I'll, \ \ MI. \ \ NI. IIIVIII, I’I‘ \\ .I\ Ix / II, II, II \\ z/ x \ // z / ~ \ ux 1 I // L x z // \ ’ //II\\~ ’ n ~ , S V_ c z s , ~ , x o ’ x ’ x s I , x H \ m: ,( 332 DEL = the mean delay at (t); DELP = the mean delay at (t-DT); IDT = a parameter to subdivide DT; DT = the increment in the model; and K = the order of the delay. DEL is related to ”a“ of the erlang distribution by the relation DEL = %-. The DEL, DELP feature allows the average length of the delay to change each DT. The IDT subdivides DT; the purpose of this feature is to provide for stability in the model,1 by meeting the stability conditions for distributed delays. The K defines the order of the underlying differential equation and is the same parameter as used in the erlang distributions. Stability of Delay Subroutines One source of instability in a simulator is the continuous delay. The nature of the continuous delay subroutine must correspond to the size of the DT or the model will be unstable. This source of instability is derived from the size of the OT and the order of continuous delays and integrators. There are no hard and fast rules, however, various authors2 have given rules of thumb that are calculated to minimize the probability of instability. 1Manetsch gt_al,, op. cit., pp. ll-l to ll-lS. 2These authors would include J. W. Forrester, Industrial Dynamics, Cambridge, The Massachusetts Institute of Technology Press, l96l; T. J. Manetsch and G. 1. Park, op. cit., Chapter VIII; and R. W. Llewellyn, op. cit., Chapter VI. 333 For Euler integration, Forrester's criterion is:1 DEL L.___ DT — K Manetsch and Park indicate that for Euler integration the rule should be: Min - _ DEL. J‘] ,....,p l! >DT>O Kj which is the same as Forrester's rule except that it is extended to include all the delays in a more complex system. Llewellyn states his criterion as: Min i=1...... 9 [W] >DT>0 where IDT is a parameter used in certain continuous delays to subdivide DT.2 A different stability rule is required if a higher order integrator (higher than an Euler integrator) is imployed. These stability criterion are a function of the roots of the differential equations underlying the model. 1DEL and K are parameters of the continuous delay. 2CATSIM utilizes the continuous delay subroutine VDELDT which has the parameter IDT. This subroutine was used to retain stability while employing a relatively large DT. 334 CATSIM proved to be stable under all conditions imposed during construction including the sensitivity tests.1 The INGRAT Subroutine This sub-function integrates over a distribution and is used in this model to calculate the quarterly calving distribution. The call statement is: INGRAT (IBEG, IEND, VAL) where IBEG = the lower bound of the integral; IEND = the upper bound of the integral; and VAL = the array describing the distribution. 1As an example, in the sensitivity tests, the largest K employed was K=7, the smallest DEL was DEL= .59. Since IDT= 10 for all delays, the stability formula is: .59 x l0 2 x 7 = .4214>.25. APPENDIX C PROGRAM MATRIX Appendix C provides a listing of program MATRIX. This program shares the matrix of published statistical cattle-calves data with program RECON and CATSIM; the statement required to dimension core storage and to read this data matrix into core are common to all three programs.1 Because this matrix of published data is central to this study, as well as to all programs, the variable names of these data are listed below. A description of these data is provided in Chapter II, the third section. June 1 and December l Population Data K = year; 1946 = O; L = quarter; lst quarter = l CALVE, CALVW, CALVT Calves Under One Year Old, East, West, Total STRSE, STRSW, STRST Steer One Year Old or Older, East, West, Total BHFRE, BHFRW, BHFRT Beef Heifers, East, West, Total BCOWE, BCOWW, BCOWT Beef Cows, East, West, Total DHFRE, DHFRW, DHFRT Dairy Heifers, East, West, Total 1All programs were written in FORTRAN IV compatible with Michigan State University's CDC 6500 computer system. 335 336 DCOWE, DCOWW, DCOWT Dairy Cows, East, West, Total BULLE, BULLW, BULLT Bulls, East, West, Total June 1 and December 1 Calf BIRTH Data K = year; l946 = O; L = quarter; lst quarter = l BIRTHE, BIRTHW, BIRTHT = Calf BIRTHS, East, West, Total INSPECTED SLAUGHTER Data I = year; l946 = O; J = month; January = l SCAVE, SCAVW = SLAUGHTER, Calves, East, West SCATE, SCATW = SLAUGHTER, Cattle, East, West SBULLE, SBULLW SLAUGHTER, Bulls, East, West K = year; l946 O; L = month; January = l SMCAVE, SMCAVW SLAUGHTER, Male Calves, East, West SFCAVE, SFCAVW SLAUGHTER, Female Calves, East, West SSTRE, SSTRW SLAUGHTER, Steers, East, West SHFRE, SHFRW SLAUGHTER, Heifers, East, West SCOWE, SCOWW SLAUGHTER, Cows, East, West SBULLE, SBULLW SLAUGHTER, Bulls, East, West WEST-EAST Cattle-Calf Movement Data K = year; l946 = O; L = month; January = l ZCTSLR, ZCTFD, ZCTSTK, ZCTTOT Cattle Movements for SLAUGHTER, FEEDLOT, STOCKYARDS, and TOTAL ZCVSLR, ZCVFD, ZCVSTK, ZCVTOT Calf Movements for SLAUGHTER, FEEDLOT, STOCKYARDS, and TOTAL 337 Dairy Correspondent Study Data I = year; l946 = O; J = month; January = l FARME TCAHE CAHMKE CAHCVE CAHFSE CWBCHE Number of Farms Reporting Total Cows and Heifers for Milk Cows MILKED Yesterday Cows and Heifers in Calf Cows and Heifers to FRESHEN This Month Milk Cows BUTCHERED This Month UNINSPECTED SLAUGHTER Data I = year; l946 USRTQE, USRTQW USTKEE, USTKEW USTKSE, USTKSW USRTQE, USRTQW USRTAE, USRTAW USRVQE, USRVQW USVKEE, USVKEW USVKSE, USVKSW USRTQE, USRTQW USRVAE, USRVAW Annual IMPORT Data I = year; T946 VPBRDE, VPBRDW VOTHRE, VOTHRW O; J = quarter; lst quarter = l UNINSPECTED Cattle SLAUGHTER, East, West (excludes the following sub-categories) Farm Killed and Eaten (Quarterly) Farm Killed and Sold (Quarterly) Farm Killed, Eaten, Sold (Quarterly) Farm Killed, Eaten, Sold (Annually) UNINSPECTED Calf SLAUGHTER, East, West (excludes the following sub-categories) Farm Killed and Eaten (Quarterly) Farm Killed and Sold (Quarterly) Farm Killed, Eaten, Sold (Quarterly) Farm Killed, Eaten, Sold (Annually) O Purebred IMPORTS, East, West Other IMPORTS, East, West Monthly IMPORT Data I = year; 1946 YPDRYE, YPDRYW YPBFE, YPBFW YOTHRE, YOTHRW Annual EXPORT Data Monthly I = year; 1946 WPDRYE, WPDRYW WPDBFE, WPDBFW WPBRDE, WPBRDW WODRYE, WODRYW WCAVEZ, WCAVWZ WCAVE7, WCAVW7 WCATE9, WCATW9 EXPORT Data I = year; 1946 XCAVEZ, XCAVWZ XCAVE7, XCAVE7 XCATE9, XCATW9 XOTDYE, XOTDYW XPDRYE, XPDRYW XPBFE, XPBFW 338 O; J = month, January = l Purebred Dairy IMPORTS, East, West Purebred Beef IMPORTS, East, West Non-Purebred IMPORTS, East, West 0 Purebred Dairy EXPORTS, East, West Purebred Beef EXPORTS, East, West Purebred Total EXPORTS, East, West Dairy, NES, Weight 200 Pounds and Over Cattle, NES, Weight Less than 200 Pounds Cattle, NES, Weight ZOO-700 Pounds Cattle, NES, Weight Over 700 Pounds O; J = month; January = l Cattle NES, Weight Less than 200 Pounds Cattle, NES, Weight ZOO-700 Pounds Cattle, NES, Weight Over 700 Pounds Dairy, NES, Weight 200 Pounds and Over Purebred Dairy EXPORTS, East, West Purebred Beef EXPORTS, East, West 339 The model parameters, their descriptions, and initial values are listed next; further explanation is provided in Chapter III. A number of intermediate values are calculated requiring a set of variables. While these will not be described, the output variables are listed below. HFRDEl = REPLACEMENTS, Dairy Heifers, East HFRDWl = REPLACEMENTS, Dairy Heifers, West HFRBEl = REPLACEMENTS, Beef Heifers, East HFRBWl = REPLACEMENTS, Beef Heifers, West BULLEl = REPLACEMENTS, Bulls, East BULLWl = REPLACEMENTS, Bulls, West SBULEl = SLAUGHTER, Bulls, East SBULWl = SLAUGHTER, Bulls, West SCVMEl = SLAUGHTER, Male Calves, East SCVMWl = SLAUGHTER, Male Calves, West SCVFEl = SLAUGHTER, Female Calves, East SCVFWl = SLAUGHTER, Female Calves, West BCSCEl = SLAUGHTER, Beef Cows, East BCSCWl = SLAUGHTER, Beef Cows, West DCSLEl = SLAUGHTER, Dairy Cows, East DCSLWl = SLAUGHTER, Dairy Cows, West The last element in the variable name, a "l" or "2," refers to the quarter. In the first half of the program ”1" and “2" refer to the first and second quarter while in the last part of the program they refer to quarters three and four. 340 FROG?!" VITRTXTIMPUToOUTPUToTAPE1l COMMON VlLOTBIoVALDETBI.VAL‘llhl OF PUDLTSHEO STATISTICAL DATA HITRTX DIMENSION TM ’ 0| ' ' \l . Z r-T‘l ,.le, 1| IV“’. 1.52 "TL 94.. I 0‘ 3 r017 v 77). F 037.7 9.2L 4, 9‘2 0".) ’ch’T‘ ..HV '(o‘LH 3.?Pl TF QLV rFZ I‘D 7U“ QHH 9 0.. ).n’q0)p\~.)) 7“ I OS? 9 '2 ,.HHVI’ '1’-.. 1| lax-10‘! I).1_ I P 11.. 91 v 115' «(QT/12 O 9’ r 963... O(”l| 4’ O(’H9Ls cl nZTHZV‘l‘O OTRLIAHHT )ol OLF...va-vl LHVUVFLflrl) OOZJAPIIIJ. :42 7C‘ 9C Owned 915 ’ORTPJTF. ’, 0 1‘ 9.41u 7.. 0))..7 1,0 ' '1)?1z HQYr, 081 9‘ O or)?h71 '7 T C, Ola 0).. 9,710 15.-(TC 7T7).l\'l O‘qu/HQITV.V TH oLTV‘..T.r. “H’JT 3.17132 7P“! TU Lnl; ‘0 9‘0: ,4 “Wed/‘1‘ T 0..) OT. 0..) O .1 “)0 'l |..J\l’ . N “T7 0). 95(27 n OVJO \IQLTCLIAGL 39’ OT“ 9,. 9 ill 41.)T .71/7‘ 9(“V72 '27....- ,.L OL1_(7 ‘(S bacilli»; HJV OW)..LNV‘)F,H 7Ciounwttl Gen T’Tffiunxho 0 II QDBPFOCJZ, FTP? Orgrv D 9,... ugflrn .S”1 n 90..- t) 0...? O c, OTTO I117 “.2," [~12 D 02 (5V 9 017,1‘ vl O .7, liq/NJ 27.27.,Tl‘: FZCTI‘LFD v NH‘ opt—ETD LC OJH’HVF61 32 H XXL-INNS... o HTF lKCOSC) OQHIINC 022 c OUZHSSI v1 1234‘56'89 C see .. II. 77 T 0L2 H O OIII‘ CI, \ITLC (“ 7 .55: VI Q 9.19. P), (3.1 J2 ”Pep 9" YHH 2 9 V 0’51, ”TTTGaVTL )...x’)< 0“ ’Y-7 —‘..'lllq {Ir-v.37.) EOCU 0‘ O OHHHIF.- H O O '78“ r)’,?< O 0777(V7 V428..v)7_ D((lIAdUII THQ1T 9H 7VHHCTO 07,1 73‘, 4947.75 0 2 O‘l‘ITUl‘ ’H7?.L 9“ 7r HHSTE n10. vYKHK (Odor. vV HPCOSIS ndflduzu a 0 9 D 0:! O O’TTDH- 3777,07 OF CP 575 CH H H UZU 121.23.. “III, 0‘s. V.u1»7—.H|r J.C1?HAZ Ct OTLC1 1 QINAL O O Vila; Vol-7 92‘? 01.2 ’13.”)111 7.28:7..d cart-vast,“ O9-“ 0 O?” "-4',(’ ZHKZZFH CV- OEFC... 123“.)6 C E READ JUNE 1 IND DEC 1 POPULATION DATA (Is (‘ (( ‘( UH NH .5“ Q.“ Ox) .(9 T.« T... S‘. .3:- O O O 0 T, "1 LL LL . . . ' KK. KK (‘ “ flu. ...... SH ,eaH «in: «(0 Tab Tau SQ. S) O O O O ,’ ” LL LL I O O 9 KK (‘ “ “ vlvl .lvc UR VR Lr. LF AH AH CB he Q ' 9 I ‘1’ ” LL LL 9 0 O 0 << << 0“ " H“ "H VR VK LF LF AH 5H (0.. C9- . O O 9 3 ‘1' T, LL LL 0 0 O O D T ‘K <‘ ‘II '0‘ o o a. —. ...—s Pu VDx a! '9. , LF 0 LF 0 ‘H 0 AN 0 fin: O. CH 1 0 F O o TDZ in, o LL01 LL 7.! o O 9 9 0 oz 0 K“ (‘0 o OH -(Tl all“ 0 11c LTTCA “TTOL I 31' Crawls 13”..” HKT IROT IROHN P. H ‘TFuA TTCCI. TZS “SUN "SOT-l T. ‘2‘ O 99 “I 0 DIN H05 8 EDI-O .. Flo-H0 SDILRLLF LRLLSC ‘3 2 O I K K ls 1| H H H H 3 9 so c a) 0 O O I: cl L L . . ‘ K ( ( ... _u. d H 3 0 Pa C ‘1 n1 0 D T, ,’ LL LL 0 9 O 9 (‘ 1“ l“ ‘1‘ TT TT RL RL FL FL HU NU 01.1. ”a O D O O "l ,’ LL LL 0 D O O <‘ (K 1“ (It "H H“ 9 L RL ..rL C L "U HU 08 N 8 I O O O 9 I!) II- LL LL 0 O O O 0 cl KK K‘ T‘ I.“ o ...—l r...- G «(L o L T FLT FL 0 HUD HU 0 On 0 n“ 1- 09 V 0 Tc ’ 0 Ln! L 75 O O 0 oz 0 (‘ ‘0 O O" ’0‘... ’1‘ 0 11C 5T1 BT05 .. ...! OHI‘ 9H..U "Kl. 0.0T IOHN c H TCA Ernaacl T7.) In '2‘ OQB‘ CTN HOFxFDO..E|-HO salku'kusc .9 7 CALF NIQTH DlTI JUN‘ I lNO DEC 1 REID CCC OTDT‘YETVQL) oUIQTHH‘KoL, OBIQTHTTxoL’ GTDT‘SETMQLTOBT‘TTHH ‘KDL’OBIR'HT‘KOL’ 13 (22.2? 1 1 RFID TNSpECT'O SLAUGHT'“ DATA CCC ETTQJTQ 3ULL AV'lT.JO.SCAVHTIoJIoSCATFTToleSCATHII.Jlo Xv2'10-0o101o2F10.0l h a rio.o.1 ’QL SMFAVHIK.L).SFCAVEIKoLToSECAJHTKoLl "10.01 ’0 ‘9 : : .(Trhr. KL inU ITNN ”apathy-T. .QuF-{C((.LI,SHFQJTKOLTOQC‘JQEI K.L) (0L) WULLHI ill-’(KHJ ."'T°H( UHULLri$<€2>$:. ==..:::..:U I?13Ti(T?N ... FE... HHHHT. VVVVV'VVT OSOQ::§OSOREJ SREgggbsSC. E CALCULATE BEEF AND DAIRY CON SLAUGHTER c LE-IDBOT'VIII LH'ZTSDT'VIIZ Zl’VZI'.B5 J csLsx . O D BCDHH DCHH=DCOHH BCHH RATTJZ C 1=SCHH1-DCSLHQ SLH dCSLHZ‘SJHNZ-DCSLH? C CALCULATr P C ’LACEHFNT HEIFE?S TOTDZCLH10?CSLHZ -JQTOEXPDR H’ ?TODR?'0COH A'VT‘VIDOH009 VALD(TTT ’TODRP'DCOH. b'VS‘VIOOHODR VALD(JTI 000 3415 CALCULATE NULL REPLACENENTS BULEIBULLFtJJ.tT-ven90£(JJT°vz~'I1.-v3)otSaLEtOSnLEZToHPnROECJJI A’V'b'Tt.-VHI-BULLE(JJ OZT‘TAo‘DRZT auLflantlLLHiJJ.hT—V3n°DWIJJT'VZA’i1.-V3)O¢SBLHIOSOLH2)OJPBQDHTJJI “s ‘1. -VAl-BULLH(JJ-1.?T‘T1.-OQ’) BULLE1=3ULE'VALRL(VT/TVALRET31oannETu)I 8ULLE2=JJLE'VALBFTQTI(VALDE(BTOVALDE(A!) BULLN1=3ULHPVALBH(’TI(VALRHISTOVALDH(LT! BULLu2=3utw-VAL9HI.II(anawtsioVAwaIbTI CALCULATE INSPECTED PLJS UNINSPECTE) CALF SLAUGHTER RAT103:(SHCVFIOS"VEZTICfiVCVEIOSNCVE? SFCVSIOSFCVEPT RATIOAITSHCVHIOSMCVHZTITSMCVH105NCVH? Schw1vSchw3) RATIOS:(SNCVEIOSFCV¢1TicsnchIosncvtzoSch€1+SFCVEPI RAT106=TSHCVWLOSFCVHIlI1SMCVHIOSHCVHZOSchwitsFCVWBI SCVNE13S‘CVEIOUNSL°F"15'R3TIOT'PATIOS SCUHH185‘CVH19UNSLQH‘VIG'RATIOC'DATI06 SCVFE1=SFCVEIOUNSL°E‘VIS'(1.-°ATTOT)'PATIGR SCVFH185‘CVHIOUNSLRH'V16'(1.-RATIO~)'DAT106 SCVMFZSSMCV520UNSLRE'V13'RATIOS'l1.-°ATTOS) scvudz=sscvw2ounsL2w'v15°°AT104'II.-RATIOoI SCVFL2=SFCV620UNSL(€'VIS‘li.-QATIO'1'(i.-RATTOSI SCV‘NZ:S:CVNZOUNSL,H'VTD'TAQ‘RATTnHT'TI-‘KATTOBT PRINT THE LAST THO QUARTEDS L" 'RT‘TT 3030 LonrRDETouFQOuTVNFQDCAOHFRDNTQRULLEAQ'T’JLL‘TlognLETo TSBLNL. S:V~EA.SCVNN19SCV‘EIOSCVEHToDCSLETQDCSLHAQDCSLELQOSSLHI L" ’pT-‘TT NC! LQHFRDEZQH:°DH,QNT’RUE?¢HEDDNZODJLLEZonJLLHZo ‘AL’. 20 ASBLIZ. s T162.SCV‘HZ.schEZ.chrw2. BCSLElchSLHZ. acch- .DCSLH? watts:10.JISIocSLSI.1c.LuI.IcsL: 1.uCSLu1. NFRa£1.RrR1w1. area: 1. 1MFR8WI.SDL€1.5HLW1.BULLE1. DULLHI URTTETIJ 3151 OCSL'? ocspuzfi ACSL- 2. ecSsz. uraacz. u= Rawz. HF°3=2. AHFR9H2.S serz. 5 Hz. éu JLL 2 LL H2 C 310 CONTINUF END APPENDIX D PROGRAM RECON Appendix D provides a listing of program RECON. The first statements in the program dimension the output variables, as well as the variables that are the matrix of published statistical data described in Chapter II, the third section. The variable names used to describe these data are listed in Appendix C. The next set of program statements read the published statistical data matrix into core. The parameters of program RECON are briefly described in comment statements; the initialization of these parameters occupy the next set of program statements. The number of intermediate and output variables preclude their listing, however, the logic of the output variable names is given below. The program calculates the elements in the output format matrix displayed in Table 15; each row of this matrix is an adaptation of identity (83). The first part of the program calculates the four "Calves Born This Year" rows on the XCAV stream elements. These row elements are: XBMCV + E or W + l to 9 or P or M Male Beef Calves XBFCV + E or W + l to 9 or P or M Female Beef Calves XDMCV + E or W + 1 to 9 or P or M Male Dairy Calves XDFCV + E or W + l to 9 or P or M Female Dairy Calves. 347 348 The E or W refers to East or West while the l to 9 or P or M refers to columns of the output format matrix. These columns are: Beginning Inventory BORN TRANSFER IN IMPORT TOTAL SOURCES 'Uwa—J DIED SLAUGHTER EXPORT TRANSFER OUT Ending Inventory TOTAL DISPOSITION Zoooucxm The second part of the program calculates the "Calves On Hand” rows or YCAV stream elements. YBMW Male Beef Calves YBFW Female Beef Calves YDMW Male Dairy Calves YDMW Female Dairy Calves E and W as well as l to 9, M and P make up the last two characters of the variable name. Using these same last two elements in the variable name, the remaining rows of the matrix are listed. 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CSCOPE¢27. 12I. SCOHH(?7.12). SBULLF(?7. 12). SBULLH(27. 12I. SHFRE¢2L 12 7I.SSTRE(27.12I.FSTRH(27.1?I.SCAT:(27.12I.SCAIH(27.12I.SHFRut27.12I O.ICTSLR<27.12I.ZCYFD(27.12I.ZCTS[K(?7. 12L zcrvor¢2L 12I. ZCVSLR(27. 012IoZCVFDC27.12I.ZCVSTK(27.12I.Z.UYOT(27.12I - ,;"3 conrou vPaRnucz7I. VPBRDE(27I. VOTHRH(27I. vovuRE(27I:HPonVH(27I. 1HPDRYE(27I.HPDurw(27).HPDRFE(27I.uonavut27I.uoonve(77).HCavu2(27I, 2HCAVEZ(27I.HCAVH7¢27I.HCAVE7(27I.HCAYHOtZ?).HCAYE9(27I.HPBRDE(27I. suPaRoH(27I.H:RYUZ(27I.HDRYEZ(27I. HDRYH9(27I.HDRYE9(27I. 2USIYEEIZ7I.USYKSE(27I.USRYOE(27.¢I.USRTAE(27I.USTKEH(77I.USTKSHI 327IoUSR79H(?7.4I.USRTAH(27).USVK:E(27I.USVKSEI27I.USRVOE(27.¢I. OUSRVAEIZ7I.USVKEH(27I.USVKSH(27I.USRVOH(27.4I.USRVAH(27I COHKON 7PDRYE(27.12I.VPDRYH(27.12).YPBVEC27.12I.YPRFU(27.12); IYOYNRE(27.12I.YOYHRHC27.12I.XCAv:2(27.12I.XCAVH2(27.12).XCAVH7(?7 2.12I.XCAVE7(27.12I.XCATE9(27.12I. XCATU9(27.12I.XPDRYEC27.12L XPRF SEIZL 12I.XPFFH(77.12I. XPDRYH(27. 1?). XOTDYEI27. 12I.x01nYH(27. 12). QVARVECZ7.12I.FARHH(27.12I.TCAHE(£7.12).TCAHH(27.12I.CAHNKE(27.1?I, SCAHFKH(27.12I.CANCVE(27.12I.CAHCVH(27.12I.CAHFSE(27.12I.CAHFSH(27. 612I.CHBCHE(27.12I. CuacuutzL 12I.AA(27I. 98(27I. ccc27L 00(27I C C READ JUVE 1 AND EEC 1 POPULAYION DAYA. C SHIYCH31.0 DO 2 “.1027 [F(SIIYCH.EO.1.0IGO 70 3 U2 ‘ IFABC1.4I C‘LVE(KIL,oCALVH(K0L’oC‘Lv'tKoL,OSYRSE(KoL,.SYRSH(K! 1LI.51R51(K.LI.aHFRE(K.LI.8HFRH¢K.LI.8HFR1IK.LI.8C0HE(K.LI.acouHIK. 2L’0PCOHYC“0L’ . '0RVL'C11X01279.0’ I LOO . REIPCC.4) CILVE‘KoLIoCILVHCKoL’oCALVICKoL’oSYRSECKnL)oSYRSHIK, 1L’057R5'(“0LIOBNFRE(K0L’99HFRH(K0L)oBH'R'CxoL’OBCOHE‘KIL)oBCOHUCK. 2L’oFCOHY(“0L’ SHITCHIH.O 2 CONYINUE 3'IYCH'1oC DO 7 “.1027 L'2 . RFAD(1.0I DHFRECK.LI.DHFRH(K.LI.DHFRY(K.LIoDCOHE(K.LI.DCOHH(K. 1LI.DCOHY(K.LI.BULLE(K.LI.BULLH(K.LI.BULLY(K.LI . '0RVATC11X09F9oo) 9 L04 IEAD(1.0I DHFPE(KILI.DHVRH(K.L).DHFRTCK.LIIDCOHE(K.LI.DCOHHCK. 1L).DCOHY(KILIoUULLCCKILIoBULLH(KIL)oBULLTCKILI SUITCH'0.0 7 CONYINUE C C lElD JUNE 1 AND CEC 1 CALF BIRTH DAYA. DO 13 K'ZIZ7 LIZ REAPC1.14I BIRYHE(K.LI.8!RTHH(K.LI.BIRYHT¢K.LI 14 FORPAY(11!.3710.0I L04 RFAD(1.14I BIRTHFtK.LI.BIRTHH(K.LI.BIRYHYIKILI :3 courxuue GOG GOO 000 35] READ INSPECTED SLAUGHTER DATA DO 11 I'3012 Do ’2 J'1012 aaar(1.15Iscavs¢I.JI.scavu¢I.JI.scar£¢1.4).scntuc1:4).830LLEII.JIL 1SRUlLH(!.JI 15 FORFAYt01.2F1o.o.1ox.2r1o.o.1ox.2r1o.oI 12 CONTINUE 11 CONTINUE DO 18 K812.26 DO 19 L'Iol? READI1o71ISNCAVEtloLI.SHCAVHCK.LI.SFCAVEIKILI.SFCAVH(K.LI 21 Fonra7(11x. 2F1o.o.1ox.2F10.oI 19 CONTINUE 10 continue DO 24 Ku12.26 Do 75 L'lal? READ(1.27I SSTREIK.LI.SSTRH(K.LI.SHFREIKoLIoSHPRH(K.L).SCOHE( 1‘0LIoSCOHHIK0LIOSBULLEIKOL,oSBULLHIKoL’ 27 FORWATIIIXIOF10.II 25 CONTINUE 24 CONTINUE READ HEST'EASY CATTLE-CALF NOVEHENT DATA DO 31 ”.2026 no 32 L-I.12 RFAD(1.347 ZCTSLR(K.LI.ZCTFD(KLLI.ZCTSTK(K.LI.2CTTOTCK.LI.ICV 18LR¢K.LI.zcvrn(K.LI.zcvsrx(K.L).tcvrortu.LI 34 FonrAtc11x.ar12.oI 32 CONTINUE 31 continue REOD DAIRY CORRESPONDENTS STUDY DATA no 30 II1O.27 Do 39 J'loI? aFAD(1.42I FARHFII.JI.ICAHE¢I.JI.CAHHKE(I.JI.CAHCVE(I.JI.CAH IFSEtloJI.CHPcHE(I.JI 42 VGRHATI11X.V15.0.5F20.0) 39 courtuuF 30 CONTINUE DO 45 l-1o.27 no 46 4:1.12 nFAn¢1.42I FARHH(I.JI.TCAHH¢I.J).CARHKHII.JI.CAHCVH(I.J).CAH IFSHCI.J).CHHCHN(I.JI 46 CONTINUE 45 CONTINUE READ UNINSPECTED SLAUGHTER Data no 53 [-10.26 00 54 J'104 If(J.Ea.4.0)co TO 53 RFICI1o55) USRTOEIIIJIoUSPIOJIIoJ) 55 '0RPATI17X.40X.2FI°.1I 00 T0 5‘ . 5. RFADI1359) USTKFEII).USTKFH(I)aUSTKSEIITIUSTKSHIITIUSRTOEIIIJI 1.USPTOH(I.JI.USRTAE(II.USRTAH(II 59 FORVATI17x.ar10.1I 54 c0N11nuF 53 CONTINUE DO DZ I'10.26 DO '8 J'Io‘ IrIJoFO.‘o°IGO To 97 READI10‘5’ USRVOEIIoJIoUSRVORIIoJ’ 00 TO DO . 92 RFADI1059) USVKFEIII.USVKEHIIIoUSVKSEII).USVKSH(II0USRV°EII0JT 1.usnvou(I.JI.USPVA£xxeFCvuoIT-II YDNCVEI(II:X£HCVEO(I-II TDNfVNIIIIaxc"cvuo(I-1I YDFCv51IIitchCVEOII'1) TDrchIIII-xnrcvu9II-1I on To 321 YRHCVEIII)80.D YBHFVN1IIICO.O YBFCVEIIII80.0 YBFCVN1IIII0.0 YDHCV51(I)IO.0 YDHCVH1(IIl0.O YDFCVEIIIIIO.° VDFFVUIIIIIO.0 SHITCN-0.0 CONTINUE TOTALIIOAO TOTAL2I0.0 DO 322 JNIAO TOTALIITOTALIOIZCVSTKII.JIOICVFDIIoJIIov40 CONTINUE DO 323 JIIOJ TOTALZCTOTALZOZCVSLRIIIJI0V40 CONTINUE TaurVESIIIaTDTAL1cv32oTOTAL2.v33 YRVCVEJII).TCTAL10(1.-V32)6TOTAL£-(1.-V33) TDNCVHOIIIsTCTALI-vxonOTAL?.v33 TarcvuacIIaTCTALI-T1..v32IoTOTALzA(1.-v33I YDHCVESIIIUO.0 anch3III-D.D TDNCVNOIII-o.o TDECVHDIII-o.o TBNCVEPIII'VBHCVEIIIIOYBHCVEJII) YBHCVNPIIIIYSHCVN1II) YBTCVEPIIIIYBFCVEIIIIOYRFCVEJII) TRECVHPIIIATaFCVNIIII TDHCVEPIII-TCHCVEIII) TONCVNPIII-TcNCVNIII) TOTCVEPIII-vcrchIIII YOTCVNPIIIIYLFCVNIIII YRNCVESIIIIYEUCVEICIIOYDRNEOIIo‘VSOI VBHCVU5IIIIYBUCVHIIIIOYDRHNCIIo‘VSOI Tn'rVESIIIIYSFCVEIIIIOYURFEOIIo'VBBI VHFCVUSIIIIYEFCVH1(IIOYDRFNOIIo'ISBI YOHCVESIIIOYCHCVEIIIIOYDRHE'IIA-V3B) YDHCVNSIIINYCHCVNIIIIOYORHH.I1.-438) YDFCVHSIIIIYCFCVNIIIIOYDRFN'IIA'V3B) TDFVVESIIIIYCTCVEIIIIOYDNTEOIIA'V38I 324 358 TOTALS-0.0 TOTAL4-o,o TOTALS-0.0 ‘TOTALOI0.0 DO 32‘ J3103 TOTAL3ITOTALJOSNCAVEIIAJI {OTAL4-T0TAL4oSFCAVFIIoJ) TOTALS-TOTALsoSHCAVHII.J) TOTALGITOTALOOSFCAVNII.JI CONTINUE YOTAL7IU5VKEEIII/AOUSVKsEIII/A‘U59VOEIIA1I TOTALOIUSVKENIII/AOUSVKSNIII/AOUSRVOHII.1I YONFVEOII)80.0 TanrvubtlI-D.o VBFCVEOIITI0.0 YBFCVHOIII'OQO YDNCVEOIIIsTCTALSOTOTAL7-v22 TDeruocIIaTCTALSoTOTALOovzs YOFCVEOII)xTOTALAoTOTAL70(1.-V2?I TorcvuocII-TcTALooTOTALOoI1.-v23I TOTAL93NCAVEZIII0.0A TOTALIO-NCAVNZII)0.04 TOTAL113NCAVE7III TOTALIZINCAVNTII) YBNCVE7IIIITCTAL110TIA’VIIOV2 YBNCVHTIIIITCTAL120(1.°V1I'V2 VRECVE7II)ITOTALIIOI1.~V1I0¢1.'V2) YBFCVU7CIIflTCTAL1?'(1.'V1)0(1o’Ve’ VDNCVETIII'TCTAL9 VDNCVH7IIItTCTAL10 TDFCVETIII'O.I VOFCVHTIII!0.0 SUBTOHE-TRNCVESIIIoYBHCVEbIIIoTRNCVE7III SURTBNNSYRHCVHSIIIOYBHCVNOIIIOYONCVHTIII SUOYOFE-TPFCVESIIIoTchvEOIIIoTRCCVE7IIT SUBYBFN-TRFCVNSIIIoTachuocIIoTRTCVUTIII SUOTDHEtvnNCVESIIIoTDHCVEOIIIoTONCVE7III SUBTDHN-TDNCVHSIIIoTDNCVNOIIIoTDTCVH7III SUBTOFE-anchSIIIoTDFCVEOIIIoTOFCVE7III SUOTDFNI'OFCVHSIITOYDFCVNOIIIOTDFCVNTIII TaerEOIII-TONCVEPIII-SUOTOHE YBNCVHOIIIIYEHCVHPTII-SUBTBHN TOECVEOIIT-TNFCVEPIII-suavarE TarrvHaIII-varcvupIII-suaveru TDNfVEaIII:TCHCVEPIII-suaTDHE TDNCVHOIII-TDHCVNPIII-SURTDHN TDrchOIII-TDTCVEPIII-SUDvDrE YDFCVHOIIIIYDFCVNPIII-SUBYDFN YBNCVENIIIIYBNCVENCIIOSUBYBHE VRNCVUNIIIIYBNCVHBIIIOSUUYBHH TRFCVENIIISYOFCVEHIIIOSUBYBFE TOFCVNNIII-TOFCVNOIIIASUOTOFN VDNCVENIII'YCHCVEfl‘II'SUUYDHE TONCVHNIIIschCVNOIIIosuavDNN YDFCVEHI[I'VCFCVEBIIIOSUBYDFE yorchNIII-TchVNNIIIASUeTDFH vchvsgIIIAvachEIII)oTRFCVE1¢I)oTOchEIIII0YDFCVEIIIT VYCAVEJIIIIvaHCVESIIIOTRFCVESIIIOYDHCVESIII°YDTCVEJIII TTCAVERIII-veNCVEDIIIoTRTCVEPTIIoTDHCVERIIIoTDrchPIII VVCAvEsclIaTaHCVESIIIoTRFCVESIlIoTOHCVESIIIoTnFCVESIII TTCAvEOIIIsvaNCVEOII)oTnFCVFOIIIoTUHchOIIIoTnFCVEOII) TYCAVETIIIIYBHCVE7(IIOYOFCVE7IIIoYDHCVE7IIIovnFCVE7II) 'vcvaa(|):ybHCVEA(IIOTRFCVFBIIIOYUHCVEO(IIOYDFCVEB(II TYCAVENIIlIYbHCVEHIIIOTBFCVEHIIIOYUNCVEHIIIOYDFCVEHIII 000 cvn 359 'TTCAVNIIIIITONCVNIIIIOTR'CV'ICIIOVDHCVVIIIIOTD'CVHIIII YTCAVHPIIIOYBNCVNPIIIOYRFCVNPIIIOYDHCVNPIIIOTDFCVNPIII TYCAVUSIIIIYBNCVNSIIIOYHFCVHSTIIOVONCVNSIIIOYDFCVNE(II TVCAVHOCIIIYBHCVHOIIIOYHFCVUOIIIOYDHCVNOIIIOYDFCVUOIII YVCAVN7IIIIYaNCVNTIIIOYRFCVH7IIIOYDHCVNTIIIoYDFCVN7IIT TTCAVUOIITIYBHCVHB(IIOYBFCVH8(IIOYDNCVNBIIIOYDFCVNOIII TTCAVHNIIIIYBNCVNNIIIOYBFCVNHIIIOYONCVNHIIIOYOFCVNNIII CALCULATE BULLS AND CULL nEPLACEHENTs: IULLE1(II'BULLE(I’1043 CULLNIIII'BULLHII‘IAAI TOTALS-UsTKEEIIIOUsTKsEIIIOUsRTAétI) TOTALQ-USTKENIIyoUSTKSNIIyoUSRTAAIII 'TOTALSIVPHRDEIII TOTALOIVPBRDNIII IULlE4(I)'TOTAL50(1.-V5I IULIHAIII8TOTAL60¢1.-V6) BULLESTII'I(8ULLEII-1.4)~BULLE(I.2)I/2)0DRE OULINSIII-IICULLNII-I.4IoaULLNII.2I>/2IoDRN 'TOTALTANPRROEII) TOTALO-NPBRONII) BULLETIII'TOTALTOIlo'VST IULLN7III3TOTALOOIlg'V4I ’TOTALCI0.0 TOTALIOIO.I DO 325 JI!.12 TOTAL9ITOTAL9°SBULLEIIoJI TOTALIOtTOTALIOOSBULLNIIoJT 329 CONTINUE IULLEGIII-TOTALooTOTAL3.v7a IULLNOIlItTOTALIOoTOTALO-v29 IULLEOIII-BULLEII.4I IULLN9IIIIBULLNIIAAI IULLEHIII-RULLESIIIoaULLEOIIIoBULLETIIIerLLEQIII IULLNHIII-OULLNSIIIerLLNAIIIoUU.LN7IIIoBULLNQIII IULIE3III-aULLEHIII-DULLEIIII-DULLEAIII IULLNJIII-BULLNHIII-BULLNIIII-UULLNAIII OULIEPIII-UULLEIIIIoOULLEJIIIoBULLEAIII IULINPIII-BULLNIIIIerLLNDIIIoaULLNAIII CALCULATE CONS AND REPLACEMENTS DCOVEIIII'OCCHEII'IAAI DCOUNIIII8DCCHNII-IA4I OCOVEIIIIEBCCHEII-1.4) CCONNiIII'UCCHH(I°104I OCOVE‘III'TOTALSOVSOVO DCONN‘III3T0IAL60V60VIO CCO¥E4IIItTOIAL50V50(1.-V9) CCOKN‘III3TOTAL6OVOOIIo-V10) DCOVESIlItIDCONFII-1.4IADCONEII.¢II/2ADRE DCOVHSIIIRIDCONHII-IAAIODCOHNIIal)I/2009N OCOVESIII-DCCNETI-1.4IoDRE OCONNSIII-OCONNII-1.4I-DRN TOTAL1O'OAO DO 330 JIIoIz T0TAL9ITOTAL9°SCONEIIAJI TOTALIOITOTALIOOSCOHNIIoJI 330 CONTINUE non 000 36“) DCOVUOIIIOIDCOUUII’Io‘I‘DCOUNIIoZJIIIOVZI DCOUEGIIIIDCOHEIICIARIOYZO DCOHEOII)OITOTALOOTOTAL'0V26I-9CJHEOIII DCOVNGIII'ITOTALIDOTOTAL40V27IODCONNCIII TOTALaE-NCATEDIII TOTALBNINCATI9(II IrIToTALaE.LE.JDDOI TOTALCEuTOTALREAVIB IFITDTALDH.LE.DDDDI TOTALCN-TOTA.OE.v1s ITIToTALaE.CT.soDnI TOTALCEt24000(TOTALRE-2400I0V16 IrIToTALaN.CT.JODoI TOTALCN-o4ooocTOTALaN-bcooI-v17 RATIOS-DCONEIIo2I/(DCOHEII.2I°BCOHE(I.2)I RATIoo-DCONNII.2I/(DCONNII.2IoDCJNNII.2II OCOHETIII- TOTAL70V30V7OTOTALCE04ATIOSoNODRYEII) DC0¥u7IIII TCTALCOV40V70TOTALCNOIATIOOOHOORYNII) OCONETIII- TcTAL70V30(1.oV7)oTOTALCE-(1.vRATIOST ICOVH7IIII TOTALO~v¢o¢1.cvanToTALCN-II.-RATI06I - ”COHEQII,.DCO"E‘IO‘I DCOPN9III'DCDHNTIAAI DCOVE9III'DCONEIIA4I ICOUN9III'DCONN(I04I DCOUEHIII-OCCHESIIIOOCOHEOIIIODCONETIIIOOCOHEOII) DCOHNHIII-DCCHNSII)oDCONNOII)oOCJNN7IIIouc0uu9(I) DCOVENIIIIBCCNESIIIOBCOHEOIIIOBCJNE7IIIOOCOHEOIII RCDUNNCIIIDCOUNSIII‘DCOHNOIIIODCJNN7IIIOUCONN9III DCOVE3IIIODCDHENIII-DCOHEIIII00CJNE4II) -DCONN3III'DCONNNIII-DCONN1III-DCJNNAIII DCOVESIII'DCONENIII-DCONEIIII-BCJNEAIII RCDVNJIII'OCONNNIII-DCOHNIIII-BCJNN4III DCOVEPIII'DCCNEIIII‘DCOUESIIIODCJHEAIII DCONNPIII'DCCHUIIIIODCOHNJIII’DCJNN4(I) DCOVEPIII'UCOHEIIIIOBCONEJIIIOBCJHE4III RCOUNPIII'DCOUHIIIIOBCONNSIIIQBCJNNAII) CALCULATE DAIRY NEIFER AND DAIRY HEIFER SLAUGHTER DNTPEIIII'DHFREII°1A4I DNTPNIIII'DNFRNII-IAQI DUFFEJIIIUYOFCVEDIII DNFPN3IIIIYJFCVHDIII DHVTEPIIIIDNFREIIIIODHFREJIII DNFPNPIIIIDNFRNIIIIODHFRHJII) DNFPESIII'IIDN'REII'IA‘TODH'REIIo2IIIZIODRE DHFFU5IIIIIIDHFRNII-1.4)onHFRN(IAZIIIZI'DRU DH'PEOIIIODCONEBIII DNTPNDIII'DCCHNBII) DH'PE9III'DHFREII04T DNFPU9IIIUDNFRNIII4I DNFPEGIII'DNTREPIII-DHFRESIlI-DHEREOIII-DNFREQIII DNFPNOIII-ONTRNPIII-DNFRNSIII-DHFRNOIII-ONFRNOII) DHFPEHIIIIDHTRESIIIODHFREOIIIODNFREBI[)00HFREOII) ,DNTruHTIT-DNTRNsIIIoDNTRNATIIoDNrRNOITIoDNTRUDIII CALCULATE BEEF NEIrEns AND BEEF NEITER SLAUCNTER DNFP'EIIIIIBHFREII'1.4I DN'F'UIIIIIDNFRNII.IAAI - CHFPREGIIIID.D DHFIRHOIIIID.D DNFPRE8(IIIDCONE3(II DNFPRUOIIIIDCONHJIII TOTAL9IO.O TOTALIOIO.0 DO 335 J-1.12 ToTALOUToTALDoSHrREII.JI TOTALifltTOTALIOOSHFRNIIoJI 3:5 CONTINUE GOO 000 337 336 36'! 'TOTALIIIOAI TOTALIR'RAR Do 837 401.12 TDTALIIITDTALIIOSSTPEIIAJI TOTALIIITOTAL12OSSTRNIIAJI CONTINUE INFPTEOII)oToTALOOTOTALSAII.-V26-V28I.CI.ovaI -DHVRE6III CN'RFNOIIIITCTALIOoTOTALQOII.-V2/-V29)0(1.Uv25I -DNFRN6III DNFPFEAIIIIVCTHRETI)O(1.-V12I ONrPFH4III-VOTNRNIIIoI1.-VI2I oNrPrETIII-ITOTALRE-TOTALCEI-I1.-v14) INFPFNTTITIITOTALNH-TOTALCHIOI1.UVIAI CHEFREJIIIIBHFRPEDIIIGIIAODREI INFFRH3IIICRLFRRHBII)o(1.oDRH) DHFPRESTIIIRNFRPESII)-BHFRREB(II DNFPRUSIIIIBNFRRNSIII-DHFRRNDII) TOTALT'Dofl TOTALIDlool DO 336 J31.I2 TOTALOCTOTALOQICTSLR(IIJIOY‘D TOTALID'TOTALIDOIZCTSTKII.J)02CT7DIIAJIIOVRD CONTINUE .N'P'EJIII'TDVCVEOIII°BHFRRFSIIIOTOTAL90I1.‘VJSIOTOTALIDOIIU'VJ‘I IHFPFNJIIIIYGFCVHBIII-BHFRRHJII) DNVPFEPIIItRhFRFEIIIIRBUFRFE3(IIOBHFRFE4III DH'FFHPIIIIRNFR'NIIIIoBHFRFNJ¢II9RHFRFN4III nurRrNaIII-TcTALOoII.oVJSIoTOTALIOOTI.-V34T .N'FREPIIIIBhFRDE3(II INFERNPIII-REFRRNJIII DNfr'ESTIIIIIRHTREII-1AAIOBHFRETIAZIIIZIODRE INrPrNSIII-IIBHTRNII-1.4I°8NTRNII.ZIIIZI-DRN INTPFEOIIIOONFREIIoAI INfPfN’IITIRNFRHIIA4I INFPREHIII-ORERRESIIIoBNrRREOIII INVRRNNIIIaRyrRRNSIIIoaNrRRNOIII .NrrrENIIIaaNrRrESIII.eNrRrEo¢IIonnrRrETIIIoBHFRFE9III IHrErNNIII-RNrRrNSIIIoBNrRrNOIIIoeNrRrNTIIIoaNrRrNDIIIoNNrRrNOIII CALCULATE STEERS AND STEER SLAUONTER SUN sTRSEIIII-STRSEII-1.4I 8TRSN1III-STRSNTI-I.4I OTRSE9III-STRSETI.4I 8TRSN9III-STRSNII.4I STRSEJIIICYDNCVEDIIIOYDHCVEDIII’iULLESIIIOTOTALOOVSSOTOTALIDOVJA CTR5N3III'YDRCVUDIIIOYBNCVNDIII-DULLN3III CTR$E4III3VDTHREIIIOVIZ CTRSN‘III'VOTNRNIIIOVIZ STRSEPTII-STRSEITIIoSTRSE:III.$T+5EATII QTRSNPIII-STRSNIII)oSTRSNJIIIoSTISNAII) ITRSEsTII-TSTPSETI-I.AIoSTR5EII.¢II/2cDRE STRSNSIII-ISTRSNTI-I.‘Io$TR5NTI.¢II/2ADRN UTRSECIII'TDTALIIOTOTALJOIIo-VZG-VZDIOV24 CTRSHOIII'TDTALIZOTOTAL4.II.-V27-V29I0V25 3TRSE7III'ITCTALBE'TOTALCEI0VIQ STRSHTIII‘ITOTALBH-TOTALCHI'VI4 CTRSNNIII'TDTALQOVJSOTOTALIOOVJA CTRSEHIII'STRSE5IIIOSTNSEOIIIOSTNSETII)0STRSE9III 'TRSNNIII'STRSNSIII’STRSNOIIIOST45N7III‘STRSH9IIIOSTRSNOIII Cous.flULLs.NEIrER3 AND stEER; IFOINVEIIIIRLLLEITIIODCONEITIIODNrnEIIITOBCONEITIIOBHFg'EITIIO 362 IOTRSEIIII TRANINEIII-DLLLEJIIIoDCONEIIIIoDNtREJTIIoOCONEJTIIoONrRREJIIIo IINFRFEJIITOSTRSFJIII TINPTEIII-OULLE4IIIoDcouEAIIIoacquaIIIoaNrRrE4IIIoSTRSE4¢II IOUECEIII-BULLEPIIIoDCONEPIIIooNrREpIIIoOCONEPIIIoaNrRREPIII. 1INfRFEPIIIoSTRSEPII) YDTrDEII).QULL55({IoocoussglIODHFRE5IIIOBCONESIIIOBNFRRESIIIO IDNTTCEOIII.STR555(IT TsLRETII-RULLEAIIIoDCONEocIIoDNrAEOIIIoBCONEOIIIoBNFRFEOIIT° 13TR566III TExPTEIIIIBULLETIITODCONE7IIIOUCJNE7IIIOBHFNFETIIIOSTR$E7TII TRNOUTETIT-DNTREOTI).aNarEATII ENDINVEIII-OULL69IIIoDCOUEDTIIoDAtRE9¢IIoaCONEDTII~DNrRrE9TIIo ISTRSE9III TDSPNEIII-DULLE~¢IToDCONENIIIoDNrRENIIIADCDUENIIIoDNrRRENTIIo :DNrRrENIII.sTRSEN¢II DEOINVNIIIIDULLHIIIIODCONNITIIODNFRHIIIIOBCONHIIIIODNFRFNIIIIO ISTRSNIIII TRAPINNIITIBLLLHSIIT¢DCONUJIIIODNFRNSIIIOBCOHHSIIICOHFRRu3II)o IONFPFHJIIIoSTRSNJII) TINPTHIII-BULLHAIIIODCOHNAIIIOBCJNNAIIIODHFRFN4IIIOSTRSUAIII SOUPCNIII-OULLNPIIIoDCOHNPIIIoOHrRNPIIIOOCONNPIIIOONTRRHPIIIO IINFPEHPTIIoSTRSNPII) TDIFDNIII'DULLNSIIIODCOUHSIII.DHFRUSIIIODCONNSIIIOCNFRRUSIIIO IDNTPFUSIIIOSTRSNSTI) TSLPNIIIORULLUOIIIODCONHOIIIODNFQNCIIIODCOHNOIIIODHFRFNCIII° ISTRSNOIII TEIPTNIIIADULLHTIIIODCOHU7IIIOOCJNN7III‘DN'RFH7IIIOSTRSN7III TRNDUTNIIIIDhFRHGIIIOBHFRRNDITI ENDINVNTIIIBCLLNVIIIODCONN9(IIODNFRNOIIIOBCDHNDIIIODHFRFNOIIIO 18TR5N9III TDSPNNIIIIDULLHNIIIODCONNNIIIODNFRNNIIIODCDNNNIIIODHFRRNNIIIO ICNFPFNNIIIOSTRSNNIII 3!. CONTINUE PRINT TUE LIVESTOCN RECONCILIATION NATRII.NEST DO 33. I012A26 o and on J019460I PRINT STIAJ 37D 'ORVATIOI0AOLIVESTOCK POPULATION-STOCK AND FLOH-RECONCILIATION HAT IRIX 70R THE YEAR o.IOa2!.0HEST0I PRIET 371 37: FDRHATI0-0.17XAOBECININCOAOXAOBDNNO.2X.OTRANSFEROAQXAOIHPORTOASX.0 ‘YOY.L.'5‘D.DlED..2x..SL‘UGHTER.D‘x..EXPORY.02‘..TR‘~ern.o“O.E~D' INCODS‘AOTUTAL'IIAI7TAOINVFNTORYOAICXA0I~00ISXAGSDURCESOAJ7NAOOUT0D 33!..‘uVENT0RYODZXA0DPSITIONO,4XAOERROROI P'INT 372ABULLNIIII.BULLN3IIIAUU.LH4(ITUBULLHPCIIDBULLUDIIIABULLHO 1‘T’OBULLu7IIDIBULI-HQI ')08ULLH"( II 372 TORNATIO-OoOBULLSOAIOXAFIO.0.10X.6710.0.10X.2710.OT PpIWT 373.DCDNNIIII.DCOHN3III.DCDNN4III.DC0NNP¢II.DC0NN5III.DCOHHO IIIIoOCONN7III.DCONN9III.OCDNNNIII 375 FDRHATI°D°DODAIRY CONSOASXDFID.0010XAOFID.D.10X.2'10.DI PRINT JTCADNFRNIIIIaDHFRNSIIIADHFRNPIIIoDHrRNSIIIADNFRNGIIIoDHFRHD IIIICD"'RN9IIIAUHFRHHIII 3’. FOR”‘T‘...O.BRIRY HEIFERSO.ZX.FIU.D.IDXATID.DAIDX.3F10.D.IOX.3'10. 10) PRINT 375.860NN1II).8C0HH3(II.BCUNN4(IIAOCONNPIII.BCOHN5II).8CONN6 IIII.OCONN7III.UCONN9III.aCDNNNIII . :79 FORMATIOOO.08EEF CONSO.6X.TIO.OAIOX.OFIO.O.IOI.2FIO.II C PnIWT STOUDNTRRUSIII.CHTRRHPIIIAUHFQRNSIIIARNanNGIIIaBNVRRUOIIIA IDHFFRHHIII 376 TORNATIO|O,OOF NPR REPLACECAZIXATID.D.10X.JrllgDoIDKAFID.DalOXA 1'1...) 36KB AIINFnrHPIII-ONrarNNIII DISTRSNPIII-STRSNNIII CISOURCNIII-TOSPNNII) D'AXCAVNOIII-CALVHII.AI EIRXCAVN2III-TDIRTNHII) PAINT 377.8HTRFHIIII.HNTRTN3IIIIUHERFN4III.ONPRFNPIII;BNERFNSIII. 1INFFFUA(IIADHFRFN7(ITaBHFRFHOIIIABNFNFNHIII.A 377 FORFATIAAA..sr HFR FEEDING-.Ix.r10.o.1ox.or1o.o.1ox;3r10.oI PRINT 378ASTRSHIIIIASTRSNBIII.$T(SH4(IIASTRSNPIIIASTRSNSIII.STRSH6 IIIIASTRSN7IIIASTRSHQIIIASTRSNNIIIAB 37. FDRPAT(OO0AOSTEERS'A9XAF10.0.1flxabF10.OAIOX.3PID.DI PRINT 379.8FCINVNIIIATRANINHII).TTNPTH(II.SOURCNIII.TDIEDH(I). ITSLRNIIIATEXPTN(IIATRNOUTNIIIAENUINVNII)oTDSPNNIIIIC 379 PORHATIOOOAJXAOTOTAL CATTLEO.710.DAIOIAIDFID.DI .PRIVT 380.!8HCVN2II), XBMCVHPIII.!8NCVN5III.XBNCVH6(IIA IXINCVNTIIIAXDNCVNRII).XRNCVH9(IonaflCVNNIII.BRIII DOD PORPATI0-OAONL BF CALVESO,13XA FID.D.20X.8710.0) PRINT 351.xDrCVN2¢I). AarcvupcII.xarCVN5¢II.xarcvuo¢IT. 1!RPCVN7(II.XGFCVNO(II.XBFCVH9III.XBFCVNNIII,DDII) 8|: FORNATIOIOAOFN or CALves-.13x. FID.D.2D:.OFID.OI PRINT 302.!DPCVNZIII.XDNCVNPIII.lDNCVN5(IIARDNCVNGCII.XDNCVU7II). IXDNCVUDIIIAXCHCVNNII) 302 FORPATIODEAONL DY CALVE50913XAF1O.D.ZDXAQFID.DAIDXIZPIO.0) PRINT 303aXDFCVHZIII.XDFCVNPIIIIIOTCVHSTIIAXDFCVUOIII.XDFCVN7III. I’DPCVH’IIICXCHCVHHIIIOE 303 rORrATIoDo..rN OT CALVES..13x.rID.o.2ox.4r10.o.tox;3:10.0I PRINT 384.!XCAVH2IIT.XXCAVHRIII.IXCAVN5¢II.:XCAVNAIIT.XXCAVH7TII. INXCAVNOTIIAIICAVN9IIIIXXCAVHN¢IIAD ' and TORNATIACA.4x.-suaTOTALo.13x.r:o.o.20x.ar10.o: PRINT aas.Tnncvu1TIT. TONCVUPTII.TDNCVN5TIT; IYDNCVUTIIIAYONCVNHIIIAYRNCVNHII) ' 309 TORFATIO-OAOIL Dr CALves-.3x.rzo.o.30x.2710.I.on.2rzo.o.aox.rao.I PRINT DOC.TDTCVH1TII. TOTCVNPIIT.TDTCVN5III. :TRTCVNTIIT.TDTCVNOTII.TarcvuncII‘ . IDA TORHATIvo.ATN er CALVEs..3x.r10.c.30x.zrao.o.aox.2rao.o.10x.rao.I PRINT JRTAYDHCVNIIIIAYDNCVNPIIIAYDHCVNSIII.YDNCVN6(II.YDNCVH7III. 1YDNCVHDIIIAYCNCVNNII) 3.7 PORNAT(0|0.ONL DY CALYESOAJXAVID.DASDX.SFID.OA10XAFID.DI PRINT 300.anCVN1III.TDFCVNPIII.TDFCVN5III.TDrcvuoIII.TDchu7III. lyOFCVHOTIIovCFCVNHTI) 800 TORNATT000AOFN DY CALVEs-.3x.rxo.o.30x.sral.o.xox. rxo.oI PRINT 309AYYCAVU1IIID YYCAVHPIIIAYYCAVNSIIIAYYCAVUOIIIA IYYCAVU7IIIAYTCAVNRIIIATYCAVHHIII 3.. 'DRHATI0|..4x.OSURTOTALO.JXAFIDoDoJDX.SPID.D.IDIAEID.DI TOTALPsXXCAvuPIIIoYYCAVNPTII TOTALS-xxCAVNSIIIoTYCAVHStIT TOTALO-XKCAVAOIIIoYTCAVUOIII TOTALTIXACAVN7IIIOYYCAVNIII) ’TDTALNIXICAVNNIIIOYYCAVNNIII PRINT 390ATTCAVN1II).XXCAVN2III. TOTALP.TOTAL5.TOTAL6.TOTAL7 CQTTCRVHOII’oRxCRVH9IIIoTOTRLH 390 TORNATIO-O.3x.OT0TAL CALVESO.2F10.D.ZDX.7P10,II 380 CONTINUE C50“ 364 PRINT TUE LIVESTOCK RECONCILIATION HATfllioEAST DO 339 IOIZAIA JII’AOOI PRINT JAIAJ COO TORHATTOIOAOLIVESTOCK POPULATIONoSTOCK AND FLON-RECONCILIATION NAT IRI! FOR THE YEAR OAIOAZXAOEAST-I PRINT 341 341 FURNATIO-O.17!.OBECININGo.OX.OBO+NO.2X.OTRANSFERoo4xooIHPORTo.5X.o 1'0T‘L.0,xl.DIED.02xD.SL‘UGHTER.D‘x..EXPORT..2x0.TRRNSFER..‘xp.ENDT 2N6¢.5X.UTOTAL0.I.17X.oINVENTORY0.18X.oINo.13x.OSOURCES0.37x.oOUTo; 33!.0INVENTORTO.2X.ODPSITIONo.4x.IERROR.) PRINT 342.8ULLEITII.DULLE3III.8ULLEAIII.CULLEPTII.OULLE5IIT.OULLEA IIII.DULLE7TII.8ULLERIII.9ULLENTIT 342 TORFATIO-OAOBULLSO.10X.F10.0.10x.6F10.O.1ox.2r10,l: PRINT 343.0CONEIIT).OCOHESII).DCJNEA(I).DCONEPIII.DCOUEOIII.OCOHEO 1(IIADCONE7IIIADCOHEOII)ADCONENCII 343 FORPATIOOOAOCAIRY CONSO.SXAFIO.OAIOX.OF1O.0.10!.2F10.OI PRINT 3C4.DNTREIIII.DHFRE3¢II.DHrREPII).OHFRESIII.ONTRE6III.OHFREO ITII.DNFRE9(II,DHFREN(II :44 rORNAT¢.o.,.DAIRT NEIrERs..2x.r10,o.on.F10.o.10x.3r10.o.xox.3rao. III PRINT 345AUCCUEIIIIADCOHEBIIIABCDNEAIIIoDCONEPIIIADCONEOIIIADCONEO IIIIADCOUETIIIAUCOHE9III.BCONENIII 34’ VORPATIOOOAOEEEF CONSOIOIoFIO.OAIDXIOPIO.OglOKo2f1030I PRINT JAOADNFRREJTIIADNFRREPIIIADHFRREOIII.RN'RRE6III.DHFRREO¢IT. IRNFPRENIII 34‘ rORVATIOOO.oIr NFR “EPL‘CE..21‘OF‘0...‘0‘."1.0.01°‘O':o0.01.‘l IPIOAOI A'DHPR'EPIII-DH'RFENIII DUSTRSEPIII-STRSENII) CISDURCEIII-IDSPNEIII DIIXCAVEOIII-CALVEIIAAI EINXCAVEZIIIoTBIRTNEIII PRINT 347.0NTRTEITII.aNrRrE3III.$H79754¢II.ONrRrEPIII.BNFRFESTI). IONTPTEOIII.RRTNTE7III.aHrRrE9(II.aHrRrEHIII.A 347 rORrATI.....gr NrR TEEDINC..Ix.rID.D.10x.orID.o.on.3r10.oI PRINT 345.5TR5E1III.STRSE3ITI.STTSEATII.5TR3EPIII.STR5E5III.$TR5EA IIID.sTR5E7III.STR5Eo¢II.5TR5ENTII.9 340 TORNATI-D-,osTEER5o,9x,rzo.o,IDx,orxo.o,10x,3r10.oI PRINT 349.856INVEIII.TRANINEIII.IINRTEIII.SOURCE(II;TDIEDEII). ITSLPEIII.TEXPTEIII.TRNOUIE(II.ENUINVE(II.TOSPNEIII$C 349 TORNATI-0o.ax.oToTAL CATTLEo.rID.o.IDx.10r10.oI PRINT SSngflNCYfizIII.XBHCVESIIIAIRHCVEPCIIIXBNCVESIIIAxRNCVEOII). INRNCVETIIIAXENCVE9(IIAXHHCVENIIIAAAII) 35D FORHATI0-0AONL 8f CALVESO.13X.ZTIO.0,10X.‘F1O.O.IOX,3P10.OI PRIFT 351.XDFCVF2III.XBFCVE3(II.KRFCVEPIIIAIDPCVESII).XRPCVEOII). IXBVCVETCII.XBPCVE¢(II.XRFCVEN(IIACC(I) 351 'ORPATI¢IOAOFH BF CALVESOAIJXAZFIDo0.IDXARPIO.DoIOX.3PIO.OI PRINT 352oXDNCVF2IIIAXDNCVEPIIIAADNCVESIIIAXDNCVEOIII.XDNCV57(IIA IXDNCVEOIIIAXCHCVENIII 352 PORNATI0OOAORL DY CALVESO.13x.FIU.O.20X.47I0.0.10fl32'I0.0I PRINT 353.!DFCVE2III,XDFCVEP(IIAXDFCVE5(II.!DfCVE6III.XDFCVE7II). IxDrrVEDIII.XCNCVENIIT.E 383 rORrATIoo-.0NL DY CALves-.13x.r1o.o.zox.4710.o.10x:3710.oI pnIuy SSAAXXCAVEZIII.XXCAVEJIIIAXXCAVEPIITDXXCAVESIII.!XCAVE6(IIA. 3Efl5 IXICAVETIIIAXICAVEOIIIoXICAVENIIIAD 39. PORNATI'I'AQID'SURTOTAL'01310271UoODIOXAQPIO.OAIOXISFIO.OI PRINT 355.YRNCVEIIIIATDNCVESIIIAYDHCVEPIIIATDNCVESIIIATDNCYEOIIIA IYRNCVETIIIAYBNCVEDIIIaYRNCVENTII 35$ PORNATIo-o.oflL 8F CALVESO.JX.FIO.O.1O!.PIO.O.10x.5PIO.OA1O!.rlO.OII PRINT JSAITRTCVE1TII.YOTCVE3¢II.TOFCVEPIII.TarcvesIII.TarCVEAIIT. ITDTCVETTII.varCVEA.. oh INOFC IXOoo R NT QR F AAAA AA AA A A AA H o HICNIC VIEVZ J .II 5 o.SSOA 0 V VVVV VU vv V V VV 9 1 0.00.9 oNTC ou‘IJJ P IIQEIQ 9:50 C o o o o v o c v . . II ofiJ o BUCZD ”IJ v v V. IIELT ENN z 3333 00 00 9 o o o K. J CJICJI 1 E IN I... IIIEAAO HI... 6 1111 11 I... 7 7 77 o J PIAPI“ VNPKA. 7SIII NIUQTHDHT EE I o 9 o o o I oh 9 9..» v IST 0 HEIHH IIRQSE H33 3 0033 I o 9 o 9 o 0 o I H IHIIHL 1 VSOLVVAQQ 034 :03 0 A 1111 77 77 I 1 11 A I 0 An.A0. SSTVFSALQTH YRPOF TE COD J IIII II II I I II o A H IoHJoHJ ILNCTTCATAT PBHVEF L RR 0 TTTT IT IT T T TT 0 1 O 0 .ICJICJ VLUZCCXCACO r5 EESA YFE 1 AAAA AA AA A A AA .52 . 1 C S . a I . n I 0U 7.2 CXY BAVNNBEFH PHH . 9‘9 R9 919 PR P R RD 1. o J . P FJ oHJ 0H JRNN NOX 20 TI BLE I J GmGC (6 as G G an .o J J o OJIRJIO I IINNIL NM V N H AF AuL J NhNN NN NN N N NN A o) I J I U(ARIAP VF VAT. ONT... FISSO‘NH 00L I III... II. It I I. II 25 I7 1* T “ rul I» I. or, .035 S I 80 FFr.o\ Y CU K 0.00. 9.0 oo o a o o .....5 I? H H o . IHIHHIHO ... 2:535? . SS V YLLTEvo F 8 S T CCA r PC C. C C CC 1 . . VV 1 n... I Fu. .... n. .0 . VNELFELSSEE .VRAASTOI Or E S 33.00 68 00 6 3 00 u u 1 . . F o. . FJ .FJ on. IDEALLAOHLL 7OIWHFSTA r... 9 V HHHd UH dH H H H“ 7. a .IIC F J NCJICJIC AITflAAuHOAA ZIATCHFAD NFH U C RQWR P? 9R 9 Q 9R 7?! IIIao H J OPIAoIA? VTS HM SCH" VTOFF Hn TRT C 2 8338 96 an 8 0 ad Vvv IIvv. P I Ioi..1o1 GIF. F ox F F 9 I o o... a. to o o .o oo- u-ouI . H TIHIIHI. ...OFOCFOFFF“ rdFFFOFFo OFF F T TT’T Til ” T T T- Til, TTII.“ , III, 0 ‘ Od.“\u.x ID? no 0000 VPnnn 00 P00 J AAAA AA AA A A AA AAA AAAA. A AAA H L.IJ.rJI V0 M. N '0 N N O N I 0900 0' I. I O to 09! 0'00... O 000 O UIFIJICJO OONONNOIIINNN qDNNNfl "No RN” 0 CA .51.]... 0.51 1‘ CL 1 1|. 10A... 11111. {A 111 c o .p‘ufll‘l 50.19010110 IPGOOIOOI 300 I . .... .. .. . . .. ... ....J . ... P 0115]....)0 IoITITYIIII V.IIITIIT .II T J JJJJ JJ JJ J J JJ JJJ JJJJJ J JJJ I pJIHJIHO VoTRTToTITT o.YTT{It{ .II A J JJJJ JJ JJ JQJ JJ JJJ JJJJI J JJJ I IAJIAG. 9‘{n1.1)\aJJ\-‘J( 5XI730010 Zul)‘ L 1| TII‘ TI TI TVT II III ITII“ II III III, ti .II. 9C1: Orri- SJODUOPOOfiO IIOOOPOOP 2300 U K HHHH HM NH new UN HRH HHAHP fl HHH AAA 6 "HICHICF V.urfinOPoPnP VoPpPJDnD VvPP P T an AM NH Hu Haw an p.30 ......dHF .< LHH oco o I.-P.:..uJ .IOQOOQ0OJO .I110Q00K 9300 O . S 0000 00 00 0V0 00 09:0 oafiOH F LOO 111 I flfiJcfiJoI 6 .2 1.4009 QRR 6 .R9 Pr 9. no 1 .9? P V CCCC CC CC C. C CC ITH . TIrCn. H ”CC . .. . NCJICJI o ISPOOPOPPPP 25999. PP. «(COP TIITTT c ”"00 03 no 8 8 on. SSdo $0.;qu D 84.0 JJJ J TPTQPInflB VF. so u o. o 0 o VF. o o 90 o o VF. o G 1111.11 II = = ._ .. .. .. .. .. ..I .. .. .. .. .. .. : = : .. .. .. .. .. .. .. JJJ J r. 92. o 93 I O. 0‘ 00v! 9 0|. 0' 090x 0 0x 999' N IIITI‘ .3 TTII .II Ill ’7’ TI. Ila” .II-III! I! -II III II FLHITVI ' SI‘I‘XSXKXX SXXYYIXXI. IXXX I HHHHHH 90 blobs AA A“ QVB AA AAA.» 55th 9 “Ah HRH U Wod...0.2 Tfitn '31. 933‘.) 9h1319330 331.3 N CCCCFQ. 9LJ 9000 00 90 o. v to 9900 90900 o 090 80L n. 013’ OWJT v 0 03 O 03 I I I O v 0 v I 03 O 93 v 0 O 0 N anyonTT 0‘ O 1111 I.C.. 1|. .1 01 Isl. 11.11; 10511.4.- 1 1.1.1 "HI. H QWCJIP.J 0 003.33 .3333 90331. .33. 9033 I NFHFCC o 7TI .... .. .. .1. .. .... ..... . ... OOU n o IPI.PI0 .5..S.... 70...5..5 10.. G YYYYVV . :0. JJJJ JJ JJ JIJ JJ JJJJ JJJJJ J JJJ PC? C OIIorJgs. A. : FCSFGGS.) A. 55.22. .2? 50 G.) F. CCCSCC 0 JT J... JJJJ JJ JJ J. J JJ JJJJ JJJJJ J JJJ PPP P 57. IIdJIdo “F 'F‘ .FFFF B‘FFF 'FF 0 31“; 8 I 2 2 = 2 I .. ..JU III“ ‘0‘ ‘l‘ TQ‘ T‘ T“‘ T‘IIII II T“ 2 = 3 8 “S l“ “1..-I‘M”! I 0X 00! 990' T 00.x '0‘ T 90 NHHHFH 9 “GIN 111.1 22 2?. 3L...» 33 96%“ )IIHHS 5 “NH 1’3 1. O I OHH OHT TAXSXXbAXXX TAXXXSXXA TAX! E ZCCCCTT L ILOI HHHH NH flu HAM HH HHHH dwlfidfiu LnD LLL 0 JTAYICLILA ""5 9‘5 05.555 "”555 9.55 "”55 T Iflano“ ‘ '3an 9300 BB 00 HTG‘OD "080 BOO 987° LHH 3“ I. JNHN . O L o P" Tic/onto... IRooo/ooo IRoo A AnfiFNFCC T TNN HFHF Hr HF HOFOAF NHFF fiHFFF.F UnO TIT T :IoIJcUJoI OI’II””’ OOIIIIII’ 90” L 8’9 RRDD‘R 0 acre cccc cc cc CTC 0cm ”ECG CCNHCTC ecc ono ‘ ”ROPJInJu—co F o o o o v o o o 9 PF 0 o o o o o 0 PF 0 0 U LJODOOOO I DTZC PPPP PP PP P .Po P PPP PPPPP- P PPP R96 R HPFPIAPIAF Colt-(3.0.97.9 1235567 12 c I I. I. 1. 17.335 ‘ 7 u); M u 0 I. a. 5 7 7 3 3 3 c 3 3 I. C C C CCC C C CC C C C C C C C C 375 CALCULATE VILUES IN OELlYS AND QFGINNING FLO“ VlLUES F0! IVYEGRitEQS LOlO 'RAIN FOR HESYERN CALF BIPYHS TNU36111819COHH1JJ-1. 2108C0HH1JJ°1.Q1|/Z’ NGPATIbo7oVALOH1'b'WRHUC YNHOC111310C0H31JJ°1921.“CnHHIJJ‘ 1.811/2’ NGRAT‘bo7oVALDHI'B'QRHDC 1' .8 1IN:JC(2131800IHCJJ-1021OBCOHHCJJ- 1.“)1/2’INGRA717913o VlLafli'b- c lzggggéz);1nCOHH(JJ- 1 2)."COHH1JJ-1.b1)lZ'INGRAT‘ToIGo VALOHD'Q trgwncé3;IKBCOHUIJJ-1..LIoflcnuutJJ .2:)Izvrncanrcxo.13.VAL3un'L 1:gu0&é:):(0€0flfl(JJ’ 1.5160CORH1JJ .211IZ'INGRA7110g13oVALOH1'b PP IN NY ‘52 352 FORMAT('-’. ’TRAIH FO° HESTEQN CAL? BIRTHS’) 9 NY 393.TVHBC(1).TNH9C121.YNHBCI3)oTNHDC‘l)QTNHOCIZigTNHDCCBD 353 FORHAY1'0'96F10oC LOAD YRAIN FOR CALVESl1-31 11CALVE1I((BCONH1JJ°Zo~1OBC0HH1JJ-1o2D1121'INGRAY1 1.5. VAL8H1'8 1ICALVEB'HOCnflulJJ-Z.bDODCOHUHJJ-ioZ)1/2)’INGR§T( 1.5. VALOH1'B 1IggLVF?=((BCOHH(JJ-nglORCOHH(JJ-19211/21'IN6RA7110.13.VAL3H)‘6 1YCAth~81(”COHHIJJ°Zoh1.DCGHNIJJ-1 Z,1/21'INGRA7110013oVIL0H1’B H1=TCALV61'. s-t1.-oo~nnu-nv: ACFQa1=YCALVE1'. %'(1.-UQF"CH'“T) Leaou1=r3ALvsx .5't1.-0QPO'H'UV) acrnu1=ranv;3'. §'(1.-DQFnrw-0!) ucwau1=ranvc3'. s'¢1.-02~9ca'or) acreu1=tCALvrz'.<'c1.-nawncu~or» RCHOH1=YCALVFB’."11.-D°'4DPH’DT) acrow1=ICALvru'.60t1.-oarocu00t» tunquxttp-Acnnux INFBH1(1)-ACF1H1 YNHDJLIlisncfiflwt turouxtzrcncrowz para? 368 35L roowat¢'-- .-ronx~ to: ussvszu CALvrs 1-3') PRINI 355 ncnwa: Atroux ncvuux.screw:.ecneux.acrau1.acnou1.ncr0u1 355 Fovnntt'c ‘.~FLu.5/urtc.fii c LOAo IRIIN to: ursrcan CALVES|b-6) OW‘L13000 oran:o.o IsJJ Ls: no 311 {a} ‘zggngz 3"3L105NCIJH11.J!ocUSVKEHCIDI:’OUSVKSHIIDIiZoUSRVQw11olD igggebgévouwosrcnvucI.“owsvxcuu)newsmanunzwsovqun.L) 31: couxzuuz IOIIL3=0.0 10taL~=a.o 1=JJ-1 K=JJ Ls!- on 312 1:15 1:2:9L2=Y3;:[3osncnvucx.J)Otusvxsuttt112+usvxsu(II/xzousavoth. .L) 1Eggghghouuosrcmm.”Husvxru(nuzwsvxsutnnzousavwu.u 312 couvaur ccnauz:(ncwoux-VOVALL'VL'LI-t1.-oanqcu°ntb ccwoxzzcncnwua-vovtL10«1.-v13-L)-:1.-oonocu-ot| ccrnuzzt33fifiu1-IOI1LZ'VZ'ui'(1.-0°FGCH'DI) CCFOd2=LBCFOH1-IOYALZ'(1.-VZD'R)'(1.-DQFDCH'OT) nggaxg’lt(WCOHI1JJ-1ooZIOBCOHHIJJ-Z. til/Z1'INGRAIL 7.10. ansuv-u ’IgngEnz ((DCOHHIJJ- 1. ZDODCOHHCJJ- 2.611121'INGRA11 7 .to.anJw»¢L H ncnnu2=¢tnnLves'. s-(1.-ovn~cu-orv-r1tnL3'v10u»-:1.-12nacw-nvr ncnnuz=ctcaLvs«-.s'(1.-wonqu.ot:-t01ALt-¢1.-vx)-u»-t:.-nowwcwcor» OCFHH2=(13ALV‘3'.5'(1.-0°F“CH'UYi-TOYALw'v2‘91'(1.-)QF33H'WY) 0cr0u2=¢lanVEw'. 5'11.-OPFUCH'HID-101AL~'11.-VZD'u)‘l1.-D°:)3H'DIi tnnauz¢1v=ccwawz vnrnuacavzccsnuz tuwou2¢11=ccwouz lurnu2(ti=CCfOH2 rain! was 35¢ rownarc'--.'t°aru rno ucsvran CALv rs U-e yum! 137,rr‘1.m7 c:rmc.cr:~ 0H2. CCF 0H2. nonnuzmcruuz. OCflnHZ DCFOH2 357 rouna1t'c'.«rxa.8/ur10.0) OWK1 c E OCH1 (“10 376 CALCULATE VALUES FOR CALVES 7-12 F HBHJ: PCHnHVtJJ-1.h1112'fl'1 F HOH3= Pcfiow31JJ-1.:II(Z’OT) FCFQHJaPPFnH‘(JJ- -1. kiltz'nli FCFDu33PCFOH'CJJ-1.bbl(2'0!) YN19H311D=FC“HHJ tNHOHSC118'CWOH3 :NFQw3t11aFCFnH3 NFDI311DIFCFOH3 YNHfid3¢ZDI‘CNNH3 INHOHJCZDSF010H3 turgustzvarcrgw3 INF ustthcFOHB GCH923:P:!0H3(JJ-1.uiItZ'Ot) GCHDd3=PCHnH3(JJ-1vkbl(Z'OTD GCF8H39P3F8H1(JJ-1.~)I(Z'OT) GCFOH3=PCFOH3LJJ-1.k)I(Z'DTI CALCULAIE YHE SEGIMMYNS VALUFS KCHBHB=PCHWH51JJ-1.BIIDLNBHQ KCHGHB=°FN"HB(JJ-1ob)IOLNOHB KCFFHLIPCFfiHo(JJ°1.B)I0LFRHk KCFOdhzchOHh(JJ-1.b)lULFOHh LCHOthPCHDd*(JJ-1.k)InLHOHQ LCHBHk= PCHQHh¢JJ-1.h)IDLNng LEF 8H3: P;FRH~(JJ-i.b)/DL‘°HB L F Fou.(JJ- .ADIOLFOHB CALCULAYE YHE REGINNING VALUES FOR CAYTLE ON RATION A HCHBHS: PCH345(JJ-1.b$/OLHHN§ HCHOflS=°CfifiwquJ-1ok)IOL”DHS MC‘WH‘ PCFQH51JJ-1.~!IOLF°H6 HCFOHS: P:F0a5(JJ-1.b)IOLFOH5 JCHRHS=PCHnHfitJJ-1.h1IULHSH‘ JCH0A5=P31nufitJJ-1.bbIDLwfiHS JCF9H5=PCFQNSIJJ-1.B)IDLFQHG JCFOHSIPCFDISCJJ-l.hIIOLFDH< ABULLHe RPL°PLutJJ.ID°L ‘ IFIAUULLd. Lt. 0.9) ABULLu:0.0 CALCULAIC BEGtNNING HEIFE° VALUES RHF91 H: RanroothJo1.11's BHFDnH-PHHFQDHtJJ61.1I’b CHFR1H=R1HF40HIJJ.1)’L CHFRWfl=9OHFH°NCJJo1)’b INHRHP¢Liza~Fonu INHOHOLLI=nHF°nu Inwanv(3)2°sufoothJ.hi'h INHOMC('l:°0uF°Pu(JJ.~)'~ INHUHP(?)=°'JHF°Q‘41JJ.VI’B INHOHRIZD=PJHF»OH(JJ.Bl'h TnunH211139|HF°°H11.1.21.3 INH0H9111sanHF9QHCJJ.21’b PPXNT 35b 36:. Foo-unh- .-mam ma HE'IFRN Harm-5., M6; OHFW‘H. TNHIHDECHFnflfl. .BHFOOH. YNNOHR. CHFQOH DIN! 365 FO’HA11'0'00‘11.0o/96F1 LOAD BEGINNING VALUES ‘09 COHS AND SULLS IOIALB= H,AYH91JJ1 '07111 TOVAL23HqufiN1JJD'72111'11.-V?‘) IOTAL3=V33°0'4(JJ1'11I11’11.-V25) IOIAL5=V9J")J(JJD‘)1(1I'V2G YOYALE=HPQ°QH1JJ|')2111’VP5 IOIAL7=HOO°YH1JJ)’1I(11 1F1'0Y‘Lao 1E.20001 TOVALC=TOYAL9’V13 [F(YOIA L1. 61.2C001 YOVALC=160091YOTA SCOUWH=RWCH§LH(JJ.11'E SCORfiflz°fiCW§LH1JJ¢11’h ICOHQH=YGYAL2'V1A'holOFALC'3ATIO1'h ICONIH=IOYHL3'V1%'oOVOTALC'Clo‘QA I YCOH$H=‘QTAL"V19’B VCWHOH:Y$YAL5'V1Q'Q ”COH"H:PCOH|H(.)J‘1ohl'0°CAYH OCOHOH= ’COHU‘IJJ-1oBI'ORCATH SHOULL”)L’L°H1JJ.11’Q FOR CAITLE ON QATION B L8-16001’V131 f 011'AOYOYAL7'B 377 XBULLH=TOTAL?'(1.-V111'LOYOTAL"I1.-V18)'b VBULLuetntavac1.-V1wavuovntnL. --. ‘05 non 71119 L982 xtm 33$ QHB HWHMIJ nantJ ‘19“, '10“, «-II N 11" an. VON 008 BB UL"BH61/ OLHDHBII 211 Can mama MNHH MHnH \\ HH 336 253V ltPO zmwm 2mm I not 0440 OM40 Dado Odd rno ussvre~ CIYYLE narrow no) cvnauc Jcnaus.ncrau§.crraus.acraus.ucwnus.cvwows. nu5.Jc&owr 0.1.12‘10.0./.12F19.0./.12F10.0| p ‘ ‘8“‘ 0000 anno 0000 0008 U 0 ‘ I 70’ H‘SY‘QN CAYYLEgRATIOV 8’1 C'NJthLCN3RR.KCF"HE.CYFBH“.LCF9H5.KC1DHQ.CV‘OHB. QUB.LCFUHL 0o].17F10.0./.1?'10.0o/.1ZF10o0) FER FRESHENIVGS V HOD-C 02:2 1021: "OOH ‘DJU NOW“ «ow tflbfl ’tdbd "It“ thu Httu HLI 1L0! 353 FOQHA 0110 (nan P c , o a :1 A 9 I 3 fi 0 D x D 336 I‘1oKH CIRUJH111‘ICINHDHPC110'NflUHR1216YNHDH91310lNHOHQIkiilh 'HQHOHI 1/10! 338 CONTINU‘ PRINY 36R 36. FOQNA11'-' 'YRAIN ‘OR HESTFQN HEIFFQ FPESHENINGS'I PRINI 363. YPHWH 369 FOR‘A‘C’O'o10F10oOI PRINT INI'YAL 9ATES.YRA1N AND "900'? VALUKS point 37? 372 FO°NAY('1'. ova-.uv.vnunov-.r .'PCFRHL'.?K.'PCFiH10.2!.'?211H2' .?X.'Pcrnu?¢.?x.-Pcwau!-.2x.-Pcrquxv.2x.-Pcnguuo.’v.-pcrqaav 21"PbfidH9'.2X.'P7FIHG‘.2(.'9HF°QH'.PX.’PCOHWH’.31.'°1JLWH’.I. ‘ 'DLHHHI..?X.'9CFQH1' PX.'PC*0H2’.?X.'PCFOHZ'.31.'°3‘WH“.1xo' r u3-.9x,0=cwouL-.zx.o&cr)uuo,7:.opcnous- 2x.oncruus0.2x.-puraou 21"PCanH’.?¥.'“W1LWH’ ut.'SLi ' éLR «r2- : YntAL anvts'.2x.'ac UAL CAL x.°rv - c}UAL St"s acruaL strrzs-.2x. c1 cows-.2x,°lc S .1!.°A SLQ Mr.) E EXECUYION oNASE E°QODS=Oofl (RROnH:OO 0 FR?0°1=000 0000 OVOJtuNn ' 99LL3’01x9.‘ COUNVP=o.o LOH=1 LHIGH=R DQJJQQ JJ'12026 O “R ck 378 CVCLE 0E1!» QAYES c 2 COHEHCJJoLIOPCONDHIJJoL11 6: 1111'”, 22 KKKKVKK CC VV VVNVVNV 30 .. 00...... NH 006‘ YYYYYYY TT 1122 c. acr.rr.c ..PC 11vv 1 1!” NNNNNVN "N .... J”JJJ 009.00! I. 1111 OJJOOO HHHHHHH VT oifiwflwl 7"!!! 1111111 no 1‘1111‘ a 111111 0900000 A. [121211 0 911HHU T'YY11' 171’ 17001u1 k HVHYY' LLLLLLL LLLL LQOOIIQ TFFQQD 00.99.! “A... 9. O o 01:19.0".1 HHHHHH“ -1111, TTJJ J111111 'I copppo rrFWCCU 111111 5 OOJJ JIIITII XXYXYX 0.111091 111111 a 9.9.11 1111111 0 .06... NFCCNFC HHHHHH 0 ::HH HQHHHHH G 1?!«:7 VYYYYYY CCCCF3 C 1110 3H0309Y 1 3 LLLLLL CCCCCCC 051071 LLHN H103??? 3 v AAAAAA 1111111 N‘FFCC F 1000 OAQJJQD 20000001(TTVT11 XXXIXK! YYYYYV 0 JJC3 CCDDPPO ooooooozoflo3003 0000000 CZCCCC JJPP DHNVHVN YOUOOOCKQTYTYTYFE INQUQJQ t::::: N 11:: ::::::: L=::::: 1::::::UU CCCCCCC HHHHFN 0 HH1Z 1R?3B€7 .823h570NU23BN7NN CCFCTT I 10LL OLLLLLL LLLLLLJULLLLLLYI LLLLLLL BHBOAA 1 NNAA 1AAAAAA 1AAAAAA60AAAAAA11 LLLLLLL "NFFCC A 00f! TVTITTT ITWYTYY CYWTTTYNN AAAAAAA DOPRRR L COO A000000 F0000000300000000 0000000 000000 U PRR RYY'YT' IIYIYYTOJVVYTIYCC m on A 00 CL 60 6 CCC cc c 3 ALB-16001'V131 1 Y 'QATIO1'6 C'Clo-RA11011'QO'01AL7'Q HHIHR.Hch INHUH9,NCOU’ C l 1 V oanhtfli'h “ODCATHD'A 1H 1H “0 o OOIALIOHV’NEYHQL CILL VOKCCuHFIUH.CMrwJN H1LHLI “OTNHQH K1 K1 Q( Sothfinflt L! LL wrvsuovcnuLu-xcowuH-ucownu—nnnwwu ‘47"!H'11.-WDCA curonu :Cr urtunL=curwou'1.gocovcounu-xuouou-scounu-ncouow iSCOHFHtSCFHBN SCONUNéQRCNSLNCIoni’B UHrRIN UHFQJH7LHFHQH.(1,-MOUA XNFR“N XHFDUH=CHFDWH NTYNIL‘AflUlLH'C.Q7C0VNULLN‘YnNLLH-QHHULL’UWULLH CALL noxttswrunu,nurou C CALCULAYION OF HEIF‘RS(BQEO AND FOR RREEOINGD "le E CALCULAYION 9F 5ULLS C C 379 s CALCULATTON 3F CALVESC1-31 -!HFPBNODT‘VBL’BD'RRHBC'INGQAT(L0H.LHIGH. 'C=(PCONONlJJcLD-XNFRDH’OT'V~0’~I'BRHOC'INGfiAT(LONoLNISd. H 1 N d U 303 J0L18AC” J9L13ACN J9L130CF JOL1'AC' H15H0LT016160 T0 Huh )0L u=xurouu-nr-aruau.u l'b NSXHFRUN'OT’BRHOH'b “C21P0036H1JJcLI EONILHIGH ulGuaLHIGHOS SUNIN1 H.5U41N1 1 H 0 8T 6T nocv.Lr NOCY LT 0H.oé°u .NCOUNT. O NanNY . HDHoOFLH P=LR 1JQDNOHun 91HN885THH3C0690H3H THHO QGHQC.QTHH ROHOCoRTHH 010010‘HOH1 QTHHOCOQTHNOH NiCH:QTHH§'.‘ an5cw=uluun'.5 ardenxrtuufl'.$ BFOCH=814HO’.‘ 8 ODD HBCN1=JfiaCH'fi =dFP¢H'U gracwx:nrnca'oq cuauxzanecu-on FBCn1 o-ucu1=3wocuvo 8 E CALCULATION 0‘ CALVESIh-SI ,vnwawz.ncnuuv.no Donacu-nt nouncu'nt 'HDFpCH'QY I'NQFOCV'DT -V?1'B 00H1H2.TNN1H?.NCOUNV.NO “DHZ.0CH)H’ GCH7-nracu? JHZ.0¢FJH2.tNr1H?.VCOUNt.Nn ONZQOCFDHZoiflFOHzoNCOUNI.NO 1H2. E CALCULATION OF CALVES17-121 0N RATTON A §SSSCCSLHHFF C..C3J3313....C 099R11110300 .. = = o. = 2 : 2 2 : 2 : 2????2222222 HHHHdHHHHdHH onfiuo1Tl5lo 0.0010001 000 .. K111 .. 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K‘AA. 1.”, 000001711 LLLL 000010000 0009 0000:1TTT JJJJ : ......Kt:: ..rJJJJ 123k 1Z1AU1111 1111A1111Nk6h6 LLLL1LLLLYHHHN AAAA6AAAAT6080 TTTT [TTTVNQFF OOnOOOOOOOCCCC TVTTDTTYTCPPPP ~ 1 0 -nLrnwu) '0L‘0Hk1 6'3H6.Lcrnuh.cvrnuu.nLFHu&.opraH 0‘00“ '0LO0H01 'DLfith1 "HFF QJ~J~ VQJ ...E‘E ,xrquu) 9(‘0301 ,(1quu1 Q‘NOHQ’ HHA.CT“WHB.OLHBH“.DPHJH DHB.CTNPN3.OLNOHB.OPWDH FOHE.CTF016.OLFDHA.OPFnd C CALCULATION OF FEL3ER CATTLE.°AIION A ‘ q .Unvfiu C 0000KTT11F :::: ::=:U 123B1123kN LLLL1LLLL1 AAAASAAAAT 1111 1111" 0000000000 YTTTOTTT'C 1 1 6 ::=: ’0’, LLLL O O 0 0 JJJJ JJJJ 10“ 5559 HHHH 8000 WHFF CCCC PPPP LSOZCTrotngD.ICTSTKIIoJ1 TDJIC IOTAL63H3AVUT111 .17111 3100 TO 606 .3 ALfiOXCAVN71loJ1 .2 .o :1 ox at 10K?!::: 11 C1NN Fonznoo I'DJTCC 70 00 66 XHBCN5=TOTAL6’l1.-V61'Vk'h AHVOHH HS-AHFROH 0LHOH5.U°ND nLFGuS.nPFq :HS-ARULOH H3-nraCH3- HS-OFO O H5.DL‘BH5.0PNR H5.0LFOHS.OPFD H‘, H5 381 E HS'ZNBCHS-AQULBH)'OQCATF ’DLWBH5 o°V12|’V9'§ Z'V9'6 I.°Vfi)'l1.-VB).6 H3-XVU‘H5-7HOCH5-GWULQH)’DRCATF 'UL50H: u;-xrnPHG-zwanuc-AHFRWH)'fiRCAYF ’OLFBHS ux-xrfiqu-erch-AHFOHH)'DOCAYF 'OLFDHS K-XHucws-rvgcus-OHQCHC-AQULqu u't1.-i|r!01i S-IHJCH5-Z“OCHG-"NO '3-XF5Cd5-1'1 3-XFOCAS-ZFO LH'°ITIGI L HJ-Xfid vIvIru-I 0000 o... 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R t DQWIL ' ’c C . 0 V(YUE Tn I1 6 L C(IO 0! (A P E E Yo. IXKK: ' D NNALL 0019', U V IOOEELoIRIUI 0 .IILUUFC: N ..OI‘CR E USF‘C0:JIIPPB:N N 0N:sx=° K CYAQR I REYIOPT?81:U:YU I BHOLLLU N CONU'O U UIICEFOOIOBRIOEN 0 50X000ROROICQRRE R 8 12 U 5 E g FUNCIION IN63I7 G.YENO.VAL) 1990 KKK f E OCOEPCI!ODEP(IOIi)/2 I V a 1m: V‘LttnEGoKD & RO‘KOOKC‘KD‘CICF 1 0 2 APPENDIX F DISAGGREGATE QUARTERLY CATTLE AND CALF POPULATION—- 1958-1972, ESTIMATED BY PROGRAM CATSIM2 Appendices F and 6 display the output of CATSIM2 for the parameter settings given in Chapter V. These are not necessarily the correct settings; the correct setting is undoubtedly a function of a wide range of factors not considered at this stage of development. Indeed, the structure of CATSIM may be in substantial error and itself a function of both exogenous and endogenous factors. These appendices are included to demonstrate the sorts of output possible from a model such as CATSIM2. 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