SIMULTANEOUS EQUATIONS SYSTEM ESTIMATION: AN APPLICATION IN THE CATTLE - BEE—F SECTOR Thesis For The Degree Of Ph. D. MICHIGAN STATE UNIVERSITY SAML‘EL a. L’NGER 3968 THESE? This is to certify that the thesis entitled 'M‘t.-\A~H*‘-‘-“‘l y n. -— k ‘szn‘ 0 1r“ “7 _. L I“ 1.} 1 ‘e .t 1 A 1 l I Michigan State University Simultaneous Equations System Estimation: An Application in the Cattle-Beef Sector. presented by Samuel Galen Unger has been accepted towards fulfillment >4 of the requirements for Agricultural 112'..— degree 111M //‘) g JM/ Major professor j Date—S-s-SS— 0-169 _/.,/r/ ff’z’L/ ABSTRACT SIMULTANEOUS EQUATIONS SYSTEM ESTIMATION: AN APPLICATION IN THE CATTLE-BEEF SECTOR by Samuel Galen Unger The underlying problem to which this thesis is addressed is broadly a need for improved knowledge of basic economic interrelationships between producer segments of the agricultural economy and the marketing and consumer segments of the general economy. This study focuses principally on interrelationships within the cattle-beef sector of the economy; but account is taken of other sectors by incorporating economic relationships of the cattle-beef sector in a simultaneous equations system framework. Aggregative United States beef cattle producers' behavior is postulated as consisting of three parts: production for slaughter, production retained (inventory) for feeding pur- poses, and production.retained for non—feeding purposes; and three corresponding behavioral relationships are specified. Marketing firms' composite behavior is treated analytically as a single aggregative marketing segment equation; and con- sumers' behavior is summarized analytically in a specified retail beef demand equation. A similar set of equations is Samuel Galen Unger specified to explicitly incorporate behavioral relationships of an aggregated other livestock-meat sector; and finally two iden- tities are Specified to complete the system of equations. Several alternative statistical estimation procedures are used to obtain estimates of parameters in the specified struc- tural equations of the model. Namely, the procedures employed are Ordinary Least Squares (OLS), Two-Stage Least Squares (ZSLS), Unbiased Nagar K—Class (UNK), Limited Information Single Equa— tion (LISE), Three-Stage Least Squares (3SLS), and Iterative Three-Stage Least Squares(IBSLS). These alternative sets of estimates are presented and compared; and the 3SLS (beginning with ZSLS) estimates are evaluated in further detail. The equations of the model were fit using United States annual time series data for a sample period from 1936-41, 1949-63. All data used were secondary, primarily from the records of federal government departments and agencies; although some data series were transformed to meet the special needs of this study. Major findings include a structural form elasticity of slaughter beef supply with respect to current average farm price of -.137. A further analysis of the producer—segment relationships led to similar elasticities of +.1127 and +.3284 for 3-year and 5-year adjustment horizons, respectively. Sta— tistically significant (and different) coefficient estimates SIMULTANEOUS EQUATIONS SYSTEM ESTIMATION: AN APPLICATION IN THE CATTLE-BEEF SECTOR by Samuel GJNUnger A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 1966 ACKNOWLEDGMENTS I gratefully acknowledge the guidance provided by the chair- man of my graduate committee, Professor R. L. Gustafson. His willingness to share ideas and his constructive suggestions help- ed make the preparation of this thesis a rewarding experience. The constructive participation of other committee members, Pro- fessors L. V. Manderscheid, H. R. Riley, T. R. Saving, and J. H. Stapleton is sincerely appreciated. Many thanks are extended to Professor L. L. Boger and the Department of Agricultural Economics faculty for their educa- tional program and financial assistance while I was a student at Michigan State University. Financial assistance through the N.D.E.A. program is also gratefully acknowledged. Professor W. L. Ruble provided invaluable computational assistance. Without his computer programming develOpments, this study would not have been feasible. Further computational and typing assistance, provided by the computer staff and the secretarial staff of the Department, is appreciated. Special thanks are extended to Mrs. Dorothy Helms and Miss Connie Griesbach for typing preliminary drafts of this thesis. I am especially grateful to my wife, Beth, for her cease- less encouragement and support. She unselfishly assisted me while continuing her career in the computer field. To both Beth and my son, Mark, I acknowledge the sacrifices they will- ingly made to make my graduate study possible. ii ACKNOWLEDGMENTS. . LIST OF TABLES . . LIST OF LIST OF Chapter I. II. III. FIGURES. . APPENDICES TABLE OF CONTENTS INTRODUCTION . . . . . . . . . . . . . . . . Objectives . . . . . . . . . . . . . . . . Methodology. . . . . . . . . . . . . . . . The Simultaneous Equation System Approach. THE CATTLE-BEEF SECTOR . . . . . . . . . . . An Overview of the Cattle-Beef Sector. . . The Production Process . . . . . . . . . . The Marketing Process. . . . . . . . . . . Marketing Livestock . . . . . . . . . . Meat Packing. . . . . . . . . . . . . . Meat Wholesaling. . . . . . . . . . . . Meat Retailing. . . . . . . . . . . . . The Consumption Process. . . . . . . . . . Summary. . . . . . . . . . . . . . . . . . Literature Review. . . . . . . . . . . . . THE ECONOMIC AND STATISTICAL MODELS. . . . . Definitions and Concepts . . . . . . . . . Specification of the Economic Model. . . . 1. Demand for Beef at Retail . . . . . . 2. Marketing in the Cattle-Beef Sector . 3. Slaughter Supply of Beef Cattle at the Farm. . . . . . . . . . . . . . 4. Inventory Demand for Beef Cattle 5. Inventory Demand for Beef Cattle Not Retained for Feeding at the Farm. . Retained for Feeding at the Farm. 6. Demand for Other Meat at Retail . . . iii Page ii vii ix 13 13 14 25 25 29 32 34 37 42 46 52 52 56 6O 64 67 69 72 73 Chapter IV. V. APPENDICES 7. Marketing in the Other Livestock-Meat Sector. . . . . . . . . . . . . . . . 8. Supply of Other Livestock at the Farm . 9. Other Livestock-Meat Sector Identity. . 10. Cattle-Beef Sector Identity . . . . . . The Statistical Model. . . . . . . . . . . . EMPIRICAL RESULTS. . . . . . . . . . . . . . . Structural Form Parameter Estimates. . . . . 1. Demand for Beef at Retail . . . . . . . 2. Marketing in the Cattle-Beef Sector . . 3. Slaughter Supply of Beef Cattle at the Farm. . . . . . . . . . . . . . . 4. Inventory Demand for Beef Cattle Retained for Feeding at the Farm. . . 5. Inventory Demand for Beef Cattle Not- Retained for Feeding at the Farm. . . 6. Demand for Other Meat at Retail . . . . 7. Marketing in the Other Livestock- Meat Sector . . . . . . . . . . . . . 8. Supply of Other Livestock at the Farm . Summary of Statistical Tests for the Identi- fiability of the Structural Relations. . . Long-Run Beef Supply . . . . . . . . . . . . Further Evaluation of the Fitted Structural Model. . . . . . . . . . . . . . . . . . . Reduced Form Estimation and Forecasts. . . . Comparison of Results from This Study with Other Studies . . . . . . . . . . . . SUMMARY AND CONCLUSIONS. . . . . . . . . . . . BIBLIOGMPIN . C O O O O C O C O O O O O O O C O O O O 0 iv Page 73 75 77 79 80 90 92 93 99 101 104 107 110 113 116 119 122 132 146 160 167 177 202 Table LIST OF TABLES Distribution of the Total Number of Beef Cattle and Calves on Farms, January 1, 1964, by Leading States and Divisions. . . . . . . . . Distribution of the Number of Beef Cows 2 Years and Older, and the Number of Cattle and Calves on Feed, January 1, 1964, by Leading States . Percentage Distribution of All Cattle Sold by Farmers through Different Market Outlets, by Geographical Regions, 1955... . . . . . . . . Percentage Distribution of Commercial Cattle Slaughter (Liveweight) by Regions, 1947 and 1962, United States. . . . . . . . . . . . . Estimated Distribution of Sales by Meatpackers to Different Classes of Customers, for Selected Years. . . . . . . . . . . . . . . . Per Capita Consumption of Food by Major Groups in Selected Periods . . . . . . . . . . . . . Schematic Summary of the Economic Model. . . . . Definitions of Variables . . . . . . . . . . . . Schematic Summary of the Statistical Model . . . Demand for Beef at Retail: Coefficient Estimates and Related Statistics. . . . . . . Marketing in the Cattle-Beef Sector: Coefficient Estimates and Related Statistics. . . . . . . Slaughter Supply of Beef Cattle at the Farm: Coefficient Estimates and Related Statistics. Inventory Demand for Beef Cattle Retained for Feeding at the Farm: Coefficient Estimates and Related Statistics. . . . . . . . . . . . Inventory Demand for Beef Cattle Not-Retained for Feeding at the Farm: Coefficient Estimates and Related Statistics. . . . . . . . . . . . Page 17 18 28 31 33 39 57 58 83 94 100 102 105 108 Table Demand for Other Meat at Retail: Coefficient Estimates and Related Statistics. . . . . . . Marketing in the Other Livestock-Meat Sector: Coefficient Estimates and Related Statistics. Supply of Other Livestock at the Farm: Coef— ficient Estimates and Related Statistics. . . Summary of a Test for the Identifiability of the Structural Relations (Hood and KOOpmans Pro— cedure) . . . . . . . . . . . . . . . . . . . Summary of a Test for the Identifiability of the Structural Relations (Basmann Procedure). . . Long Run Beef Supply Functions: Generated Data and Estimated Slaughter Supply Price Elasticities. . . . . . . . . . . . . . . . . 3SLS(ZSLS) Reduced Form One-Period Forecasts (Ex Post) for 1964 and Related Statistics . . Comparisons of Estimated Retail Demand Price and Income Elasticities for Beef with Other Studies . . . . . . . . . . . . . . . . . . . Comparisons of Estimated Farm (and Retail) One Year Supply Price Elasticities for Beef with Other Studies . . . . . . . . . . . . . . . . vi Page 111 114 117 120 122 130 159 162 165 Figure 2.1 LIST OF FIGURES Time-Paths of Beef Cattle Inventory and Slaughter Beef Production . . . . . . . . . . Estimated Long Run Slaughter Beef Supply Functions . . . . . . . . . . . . . . . . . . Structural Equation 1: Demand for Beef at Retail. 0 O O O O O O O O O O O O O O O O O 0 Structural Equation 2: Marketing in the Cattle- Beef Sector . . . . . . . . . . . . . . . . . Structural Equation 3: Slaughter Supply of Beef Cattle at the Farm. . . . . . . . . . . . . . Structural Equation 4: Inventory Demand for Beef Cattle Retained for Feeding at the Farm. Structural Equation 5: Inventory Demand for Cattle Not-Retained for Feeding at the Farm . Structural Equation 6: Demand for Other Meat at Retail . . . . . . . . . . . . . . . . . . Structural Equation 7: Marketing in the Other Livestock-Meat Sector . . . . . . . . . . . . Structural Equation 8: Supply of Other Live- stock at the Farm . . . . . . . . . . . . . . Reduced Form Equation 1: Price of Beef at Retail. 0 O O O O O O O O O O O O O O O O O 0 Reduced Form Equation 2: Price of Beef Cattle at the Farm . . . . . . . . . . . . . . . . . Reduced Form Equation 3: Quantity of Beef Produced for Slaughter. . . . . . . . . . . . Reduced Form Equation 4: Inventory of Beef Cattle Retained for Feeding . . . . . . . . Reduced Form Equation 5: Inventory of Beef Cattle Not-Retained for Feeding . . . . . . . vii Page 15 131 135 136 137 138 139 140 141 142 151 151 152 152 153 Reduced Form Equation 6: at Retail . . Reduced Form Equation 7: stock at the Farm Reduced Meat Reduced Meat Reduced Meat Form Equation 8: Produced Form Equation 9: Consumed Form Equation 10: Consumed viii Price of Other Meat Price of Other Live- Quantity of Other Quantity of Other Quantity of Beef 0 Page 153 154 154 155 155 LIST OF APPENDICES Appendix Page A Additional Equations . . . . . . . . . . . . . . 178 B 38LS(ZSLS) and IBSLS Reduced Form Fitted Equations (and Rz's). . . . . . . . . . . . . 184 C Data Sources and Data. . . . . . . . . . . . . . 187 D Simple Correlation Coefficients between Pairs of Variables. . . . . . . . . . . . . . 195 E Additional ZSLS and 3SLS(ZSLS) Structural Equation Estimates. . . . . . . . . . . . . . 198 ix CHAPTER I INTRODUCTION Relationships in the aggregate cattle-beef sector in the United States and interrelationships of this sector with other economically related sectors are specified and estimated in this study. The relationships postulated are treated as a system of simultaneous equations and alternative estimators are employed for obtaining the structural form parameter estimates. It is believed that a simultaneous equations system approach to eco— nomic analysis of the cattle-beef sector is a practical and use- ful method for discovering and measuring the extent of the inter- dependent nature of some nationally important economic variables and relationships. The underlying problem to which this study is addressed is the need for increased knowledge of some of the basic interrela- tionships among the producer segments of the agricultural econ- omy, and the marketing and consumer segments of the general economy. Basic relationships within the cattle-beef sector in particular have been difficult for researchers to formulate ac— curately and estimate from time series data. A major contention in this study is that beef cattle pro— 2 ducers' supply response, price relationships arising from mar- keting firms' behavior, and consumers' behavior are sufficiently jointly related so that procedures which analytically treat the corresponding behavioral relationships simultaneously can be use- fully employed. Economic models are, of course, subjective for- mulations; but they are based upon economic theory, a knowledge of the sectors being studied, and various institutional constraints placed on the system. Evaluation of the estimated relationships in an economic model is likewise subjective; however, the burden of the "proof" rests with the analyst and only after prOper evalu- ation can any one approach to the underlying problem be regarded as useful for understanding and explaining basic economic rela- tionships. Objectives The main aim of this study is to investigate the endogenous mechanism of the cattle-beef sector by first prescribing an eco- nomic model to represent the endogenous mechanism and then fitting the model using simultaneous equations estimation methods. Ulti- mately, in a study of this kind, the researcher usually has the purposes of predicting future values of economic variables and of predicting the consequences of various prOposed economic policies. The results of this analysis will be used to some extent for such prediction purposes. In addition to the main objective of the study there is 3 also a set of intermediate or "working" objectives which were derived in order to more effectively approach a successful com- pletion of the main objective. Implicitly, the researcher trusts that the discipline of fulfilling the intermediate objectives leads to fulfillment of the principal aim and the ultimate pur- poses of prediction. The intermediate objectives are described as follows: (1) (2) (3) (4) (5) (6) To postulate a set of relationships within the cattle- beef sector (and the other livestock-meat sector) which meaningfully represent the aggregate behavior of beef cattle producers, marketing firms, and con— sumers; To estimate parameters, both structural form and re- duced form, which will contribute to a better under- standing of these economic interrelationships, par- ticularly those within the cattle-beef sector of the general economy; To employ alternative simultaneous equations estimation methods, compare estimates from the alternative esti- mation procedures, and ascertain the apparent advan- tages of any particular estimation method; To utilize and relate the results of other analyses in this area when formulating and evaluating the fitted relationships; To explore alternative specifications of the relation- ships postulated with the belief that valid improve- ments may be discovered (model construction is unques- tionably a subjective process and an investigator's initial specifications may not be the most suited formulation of the model); and To utilize and evaluate the reduced form coefficient estimates in the final model as a means for predicting changes in various economic variables. Methodology Six alternative estimators are used for estimating the structural form parameters of the specified relationships in this study;l and they will be referred to as Ordinary Least Squares (OLS),2 Two—Stage Least Squares (ZSLS),3 Unbiased Nagar K-Class ’(UNK),4 Limited Information Single Equation (LISE),5 Three—Stage Least Squares (3SLS),6 and Interative Three-Stage Least Squares (I3SLs).7 1These estimators (except IBSLS) have been discussed in the literature so no attempt will be made to detail their development here. The assumptions and the statistical properties of the par- amater estimates depend on the estimation method used, however; and these aspects of the estimators will be discussed in the sta— _tistical model section of Chapter III. 2See, for example: Johnston, J.: Econometric Methods, New York: McGraw-Hill, 1963, Chapter IV; and Goldberger, A. S.: Econometric Theory, New York: John Wiley and Sons, 1964, Chapter IV. Theil, H.: Economic Forecasts and Policy, Amsterdam: North Holland (second revised edition), 1961; and Basmann, R. L.: "A Generalized Classical Method of Linear Estimation of Coefficients in a Structural Equation," Econometrica, Vol. 25, January 1957. 4 . . Nagar, A. L.: "The Bias and Moment Matrix of the General K-Class Estimators of the Parameters in Simultaneous Equations," Econometrica, Vol. 27, October 1959. Anderson, T. W. and Rubin, H.: "Estimation of the Para- meters of a Single Equation in a Complete System of Stochastic Equations," Annals of Mathematical Statistics, Vol. 20, March 1949; and KOOpmans, T. C. and Hood, W. C.: "The Estimation of Simultaneous Linear Economic Relationships," in Studies in Econ- ometric Method, Cowles Commission Monograph No. 14, W. C. Hood and T. C. KOOpmans, editors, New York: John Wiley and Sons, 1953, Chapter VI; and Chernoff, H. and Divinsky, N.: "The Computation of Maximum Likelihood Estimates of Linear Structural Equations," in Studies in Econometric Method, Cowles Commission Monograph No. 14, W. C. Hood and T. C. KooPmans, editors, New York: John Wiley and Sons, 1953, Chapter X. 6,7 See following page. 5 The OLS method is strictly a single equation technique which does not account for a particular equation being embedded in a system. Theoretically, this method will be unsuited for all but one of the relationships in this analysis, but it will be used for all the equations for comparative purposes.8 OLS estimation has been the most widely used method in agricultural economic research to date; and because relatively little is known about the small sample characteristics of the other estimators, there seems to be a general interest (and usefulness) in presenting the OLS estimates in addition to the others. 6Zellner, A. and Theil, H.: "Three-Stage Least Squares: Simultaneous Estimation of Simultaneous Equations," Econometrica, Vol. 30, January 1962; and Rothenberg, T. and Leenders, C. T.: "Efficient Estimation of Simultaneous Equation Systems," Econo- metrica, Vol. 32, January 1964. Iterative Three—Stage Least Squares refers to a procedure which successively utilizes the (N-1)—Stage Least Squares para- meter estimates in order to derive the (N)-Stage Least Squares estimates. This procedure is a logical extension of 3SLS. William Ruble, who programmed this procedure for Michigan State University's CDC 3600 computer system, has termed the procedure IBSLS; and his forthcoming Ph.D. thesis will include the compu- tational details of this estimator (and the other estimators used herein). Further, he has planned to investigate the theoretical prOperties of this estimator; so, anticipating the "apprOpriate" theoretical basis for this procedure, I3SLS estimators are in— cluded in this study for "future" interpretation. 8A theoretical problem arises with OLS estimation if more than one endogenous (jointly dependent) variable is specified in an equation. The problem arises because the endogenous variables are generally considered to be correlated with the disturbance (random error) term. In such cases the parameter estimates are said to be biased and inconsistent. OLS estimation is considered strictly applicable when only one dependent (endogenous) variable is specified as a function of independent (predetermined) vari— ables. 6 The ZSLS, UNK, and LISE methods are also single equation estimation methods, but in each case the method takes limited account of the equation being embedded in a system. In this sense, these estimators are simultaneous equations estimation methods. Another general classification by which each of the first four estimators can usefully be described is that each is a (k)- class estimator.9 For the OLS and ZSLS methods the k—values are known constants, namely k = 0 in OLS estimation (hence, it is a trivial case), and k = l in 2 SLS. The k-values for the UNK and LISE procedures have to be determined for each of the single equations to be fitted, however. (In the UNK method, Nagar has prOposed that the k-value should be calculated as k = 1 + Lil', where L is the number of predetermined variables in excess of the number of coefficients to be estimated and where T is the number of observations.10 Nagar shows that this k-value can be expected to reduce a small sample bias of ZSLS (to the order of T—l) in most simultaneous equations studies. (Alternative k-values have been proposed by Nagar, but they are not included in this study). For the LISE procedure, the k- values will always be greater than one for over-identified equa- tions (and equal to one for just identified equations). In one context, the k-value is derived in a manner such that it corre— sponds to a minimum ratio of residual variances, i.e., the 9Theil, H.: op.cit., 1961, pp. 231-237. 10Nagar, A. L.: Op.cit., 1959. 7 residual variance from regressing a linear combination of the endogenous variables on the predetermined variables in the equa- tion, divided by the residual variance of the game linear com- bination of the endogenous variables regressed on all the pre- determined variables in the system.11 In another context, the k-value also corresponds to a minimum characteristic root of a determinantal equation. Turmhugto the BSLS method, this estimator is generally referred to as a simultaneous equations system method since the parameters of all the identified structural equations are esti- mated simultaneously. This method also makes use of restrictions on the parameters of the full system in estimating each struc- tural equation and in this sense BSLS is also termed a "full- information" method.13 The 3SLS method was develOped by Zellner and Theil in 1962.14 The 3SLS method requires initial estimates of the coefficient parameters and the disturbance covariance matrix in order to 11 For a more complete account of this interpretation, see Hildreth, C. and Jarrett, F. G.: A Statistical Study of Live- stock Production and Marketing, Cowles Commission Monograph No. 15, New York: John Wiley and Sons, 1955, p. 69; and KooPmans, T. C. and Hood, W. C.: Op.cit., pp. 166-177. 12For an account of this derivation, see, for example, Goldberger, A. S.: Op.cit., pp. 340-341. 13For a concise summary of the characteristics of system methods of structural estimation see Goldberger, A. S.: Op.cit., 1964, pp. 346-356. l4Zellner, A. and Theil, H.: Op.cit., 1962. 8 obtain estimates in the "third-stage" of this method. Zellner and Theil have shown that the 3SLS method is expected to be more efficient than ZSLS, and they recommend that the ZSLS estimates be used as the starting estimates for BSLS. A logical extension of the 3SLS procedure is to establish an iterative process by successively utilizing the UJ- l)-Stage Least Squares (e.g., 3SLS) estimates in order to derive (N)- Stage Least Squares estimates (e.g., 4SLS). Zellner and Theil refer to this procedure as a possibility in their concluding remarks: "One can set up a new stage based on this estimator (BSLS). . . and proceed iteratively."15 Pending further theo- retical development they did not conjecture any further expected advantage from employing such a procedure. Despite the lack of an apprOpriate theoretical foundation for proceeding with the above mentioned iterative scheme, such estimates will be presented and the method referred to as Itera- tive Three-Stage Least Squares (IBSLS). The main reason for doing so is strictly intuitive at this time;16 namely, given that 3SLS estimates are "more accurate" than ZSLS estimates, then re- application of the same method using the "more accurate" esti- mates as starting estimates would reasonably seem to support the 15Ibid., p. 77. l . . . . 6Also, the marginal cost of obtaining IBSLS estimates was reasonably low with the computing routines and facilities avail- able. 9 procedure. Application of the IBSLS method is admittedly an ex- periment and a "tangent" analysis in this study, but future re- search and development in this area may disclose its applicability in simultaneous equations studies of this kind. This selection of estimators does not exhaust the currently known alternative procedures for fitting simultaneous equations. Other known systems methods include Full-Information Maximum Like- lihood, or more generally, the Full—Information Least Generalized Residual Variance method; and Linearized Maximum Likelihood, which is another version of the generalized method.l7 Because computer routines were not yet available at the time of this study, no fur- ther attempt was made to include the other known estimation pro- cedures.18 17 . . . . The Full-Information Least Generalized ReSidual Variance method was developed by the following authors: Koopmans, T. C.: Rubin, H.: and Leipnik, R. B.: "Measuring the Equation Systems of Dynamic Economics," in Statistical Inference in Dynamic Eco- nomic Models, Cowles Commission Monograph No. 10, T. C. KOOpmans, editor; New York: John Wiley and Sons, 1950, Chapter II, pp. 53- 237. The Linearized Maximum Likelihood version was developed by Rothenberg, T. and Leenders, C. T.: op.cit., 1964. 18All of the estimation methods employed were programmed for use on the Michigan State University CDC 3600 computer system by William Ruble (Assistant Professor, Department of Agricultural Economics). These routines are part of the MSU-STAT System, and they are written with double precision arithmetic (1 word = 48 'bits). Additional estimation procedures are presently being pro- grammed by Mr. Ruble, and a complete documentation of all the procedures are presented in Agricultural Experiment Station Pub- lications (in cooperation with the MSU Computer Laboratory). 10 The Simultaneous Equations System Approach With the advent and deve10pment of electronic computers the prospects for more elaborate quantitative economic research have become computationally feasible. Together with economic theory, statistical data and modern methods of statistical inference we have the tools for estimating the parameters in equations of eco- nomic behavior. Perhaps one of the brightest prospects for the use of these econometric tools lies in the area of equation sys- tems where the primary objective is to recognize and discover the interdependent nature of economic theory and the working of the real world. The main feature of the simultaneous equations system approach to the study of economic processes is to account for the joint or mutual determination of changes in economic variables. The simultaneous equations system approach of econometric investigation involves three important steps: (1) specification of the model, i.e., a system of relationships believed to be responsible for generating the observed data; (2) establishment of the identification of individual equations in the system; and (3) estimation of the parameters of all equations or of a subset of the equations in the system simultaneously. Specification of the model relies heavily on a_priori in- formation about the commodity and markets involved together with theoretical knowledge of the econometric relationships and other 11 relationships relevant to the study. Also it is important to consider how well the observable data represent the theoretical variables both conceptually and with regard to numerical accu- racy of the data. Identification is essentially a matter of formal logic and mathematics. Definite procedures are available for determining whether a particular equation in a system of equations is identi— fiable. Three classes of identification for linear structural equations have been enumerated: (1) under or not identified, (2) just identified, and (3) over identified.19 Sometimes the latter two classes are grouped and called "identified" equations. Statistical estimates of the parameters in structural equa- tions of simultaneous equations models are derivable in alterna- tive ways for identified equations. Many of the known methods of estimation were referred to above in the section on methodology, but many other deve10pments were not discussed. Only in the recent past have simultaneous equations estima- tion methods come into somewhat general use in economic research. Despite the many desired asymptotic prOperties of these more com- prehensive analytic procedures a major problem remains: the bridge See, for example: KOOpmans, T. C.: "Identification Prob- 1ems in Economic Model Construction," in Studies in Econometric Method, Cowles Commission Monograph No. 14, W. C. Hood and T. C. KooPmans, editors, New York: John Wiley and Sons, 1953, Chapter II. 12 between the theoretical asymptotic properties and (the more real- istic) small sample properties of these estimators has not yet been satisfactorily built. Many efforts are being made toward this end, but until more knowledge is acquired in the profession and generally, simultaneous equations estimation has this most pressing limitation. 20 Because the small sample benefits from applying the more comprehensive simultaneous equations methods are yet to be ascer— tained, the generally higher estimation cost is another factor that has restricted the widespread use of these methods. CHAPTER II THE CATTLE-BEEF SECTOR The purpose of this chapter is to describe major aspects of the cattle-beef sector in the United States as it has evolved in the recent past and as it exists currently. The United States agricultural economy has in general been undergoing rapid deve10p- ment and transition in this century with marked shifts in agri- cultural resource-use patterns. Remarkable developments have occurred in the cattle-beef sector of the economy, but many of the changes in this sector could not have feasibly occurred with- out concurrent developments and achievements associated with the growth of the general economy and of other segments in the agri- cultural economy. Consequently, it is to be understood that the cattle-beef sector is but a component of a much larger economic system. An Overview of the Cattle-Beef Sector The cattle-beef sector can be viewed as three interconnected processes: production, marketing (in a broad sense), and con- sumption. On a year-to-year basis we can observe a flow of beef cattle for slaughter arising from the production process. Through an interaction of the production and marketing processes, farm 13 14 prices for beef cattle are established and, simultaneously, the liveweight level of beef production for slaughter is determined. After slaughtering, processing and distribution, beef—meat prod- ucts flow on to retail outlets where the marketing and consumption processes interact; with retail beef prices and the level of dressed weight consumption being established in this case. With this sim- plified account of the basic processes that are involved, a more realistic description of the processes and their interrelation- ships as they have evolved and as they exist is presented. The Production Process Viewed in the aggregate, total farm production of beef cattle flows either into production for slaughter or production for in— ventory, with the inventory component becoming then an input for future total production. This dual use of beef cattle is clearly an important aspect of the production process to be considered. The following graph depicts the historical cyclical nature of beef cattle inventories and beef cattle slaughter as they have been observed since 1920. Typically these variables have moved together, i.e., slaughter in year t has increased with increased beginning period inventories, and the same movement has generally occurred during the downturn in the cycles. How- ever, at the turning points of the inventory cycles the direction of the slaughtered beef variable has not always been the same. Various causual factors and economic conditions can be reviewed BEEF PRODUCTION (BIL. LB'.) m. m. k. mth 0000m 0000m DDDD: DDDDm DUDDE DDDDK DDDDm an on gm mm m: a: a: an mm mm :m owe. self-let‘s.) I N I .3 I; 5 x _3. x as: ss ’ u s 1 t v s . x p \s. s.~ \. x. s N l . ,, ., . l < ,. 11 lIIIIEEzw>zH mntmo ummm. J .1 _.. .inI 23538... “mum \ flee ..\ 1 ‘005 C x s. L :thqu. ZOHHUDn—omm umwm «melonmnm 02m >aoe2m>2H m.:.._.mo “mum .10 mIEn. mzfl. ..m mane: I NUMBER I BEEF-CHTTLE INVENTORY JHNUHRY 16 and conjectured as having influenced this phenomenon whenever it has occurred1 and, parenthetically, it is an objective of this study to "explain" as much of this variation as possible with a limited number of the alleged most important economic variables and relationships. Another aspect of the beef cattle production process has been the geographical location of the major producing areas. One indication of the geographical distribution of the total beef cattle herd is the number of cattle and calves held as inventory on January 1, by leading states and by the divisions of the United States. This distribution is shown in Table 2.1 for 1964. However, the total beef cattle inventory distribution as indicated does not accurately portray the fact that important differences in location have existed with regard to the cow (breeding) herd versus the feeding herd. Table 2.2 shows the leading states based on the number of beef cows 2 years and older, and based on the number of cattle and calves on feed for 1964. Without tracing the actual movement of stocker and feeder cattle, the data in Table 2.2 implicitly reflect that a sizeable inter farm and inter state movement of beef feeders has been a See for example: Lorie, J. H.: "Causes of Annual Fluctua- tions in the Production of Livestock and Livestock Productsf'Uni- versity of Chicago Press, Studies in Business Administration, Vol. 17, No. l, 1947. See, also: Maki, W. R.: "Decomposition of the Beef and Pork Cycles," Journal of Farm Economics, Vol. 44, August 1962. 17 Table 2.1 DISTRIBUTION OF THE TOTAL NUMBER OF BEEF CATTLE AND CALVES ON FARMS JANUARY 1. 1964. BY LEADING STATES AND BY DIVISIONS Number Percent of Division Rank State 11000 head) Total Classification 1 Texas 9494 12.4 So. Central 2 Iowa 5818 7.4 W. No. Central 3 Nebraska 5604 7.1 W. No. Central 4 Kansas 4917 6.2 W. No. Central 5 So. Dakota 3686 4.7 W. No. Central 6 Oklahoma 3676 4.7 So. Central 7 Missouri 3432 4.3 W. No. Central 8 California 3320 4.2 West 9 Illinois 3072 3.9 E. No. Central 10 Montana 2516 3.2 West 11 Colorado 2425 3.1 West 12 Minnesota 2300 2.9 W. No. Central 13 No. Dakota 1831 2.3 W. No. Central 14 Kentucky 1731 2.2 So. Central 15 Mississippi 1628 2.1 Leading 15 States 55,450 70.3 Percent of- Rank Division Number Total 1 W. No. Central 27,588 35.0 2 S. Central 22,065 27.9 3 West 16,389 20.8 4 E. No. Central 7,174 9.1 5 S. Atlantic 4,989 6.3 6 No. Atlantic 697 .9 United States 78,902 100.0 (48 states) Source: Consumer and Marketing Service: Livestock and Meat Statistics, Supplement for 1964 to Stat. Bull. No. 333, USDA, September 1965, p. 7. 18 Table 2.2 DISTRIBUTION OF THE NUMBER OF BEEF COWS 2 YEARS AND OLDER, AND THE NUMBER OF CATTLE AND CALVES ON FEED JANUARY 1, 1964, BY LEADING STATES Beef Cows, 2 Cattle and Years & Older Calves on Feed Rank State (1000 head) State (1000 head) 1 Texas 5170 Iowa 1731 2 Oklahoma 1839 Nebraska 1022 3 Nebraska 1812 California 946 4 Kansas 1549 Illinois 716 5 So. Dakota 1521 Colorado 508 6 Missouri 1396 Minnesota 487 7 Montana 1287 Texas 478 8 Iowa 1155 Kansas 388 9 Louisiana 936 So. Dakota 329 10 California 927 Arizona 324 11 Mississippi 923 Missouri 260 12 Colorado 887 Indiana 250 13 No. Dakota 834 Ohio 210 14 Florida 813 No. Dakota 166 15 Kentucky 788 Michigan 162 Leading 15 Leading 15 States 21,837 States 7,977 United States 31,729 Total States 9,391 (48 states) Reporting (39 states) Source: Consumer and Marketing Service: Livestock and Meat Statistics, Supplement for 1964 to Stat. Bull. No. 333, USDA, September 1965, pp. 7 and 14. 19 characteristic of the production process in the recent past. To a large extent beef cattle feeding Operations and beef cow-calf enterprises have, in fact, become essentially separate (but economically related) Operations. Beginning in the 1930's and particularly in the postwar period, fed beef production has increased steadily in the United States. The number of cattle and calves on feed on January 1 in the 26 major producing states averaged about 3 million head in the 1935-39 period (or about 9.4 percent of the total cattle and calves inventory). In contrast, in the 1960-64 period an aver- age Of about 8 million head were on feed on January 1 (repre- senting about 11.4 percent of the total).2 The absolute changes are more striking than the relative measures, but neither of these measures adequately reflect the impact of cattle feeding enterprises Which have been expanded throughout the period. Commercial cattle feedlots where large numbers of cattle are fed, usually on a year—around basis, have been expanded greatly during this period, especially in some areas. Namely, the growth of cattle feeding Operations has been substantial in some Western states (California, Arizona and Colorado), in some Based on data from: Consumer and Marketing Service: Livestock and Meat Statistics, Supplement for 1964 to Stat. Bull. No. 333, Washington: USDA, September, 1965, Table 23; and Agricultural Marketing Service: Livestock and Meat Sta- tistics, Stat. Bull. No. 230, USDA, July 1958, Table 23. 20 Northern Plains states (Nebraska and the Dakotas), and more recently in the Northwest and the Southern Plains areas. Tradi- tionally, the Corn Belt farming area has led in beef cattle pro— duction for slaughter and it has continued to be the dominant area of such production. Nevertheless, substantial growth in fed cattle production has occurred outside of this area.3 There are many ramifications of the changing locations of production and changing types of beef feeding enterprises. These ramifications extend not only within the beef cattle producer segment but perhaps to an even larger extent through the market- ing segment. For example, many of the large commercial cattle producers' (especially in the West) who may feed 30,000 to 50,000 or more feeders in a single Operation often have coordinated directly with packers and retail Outlets in the marketing seg- ment, and thus, bypassed established markets. Another impact deals with feeder cattle procurement practices and feeder cattle movement patterns. In this brief description of the production process many details must of course be omitted, yet a thorough knowledge of the sectors being studied is essential when a researcher seeks to prescribe a meaningful and valid set of relationships cor- reSponding to those sectors. See, for example: Williams, W. F. and Stout, T. T.: Economics of the Livestock-Meat Industry, New York: The Mac- millan COO, 1964' pp. 286-291. 21 Viewed broadly again, the main agricultural feature of the states leading in the size of the breeding or cow herd is the vast areas of grassland and ranges in these states. When the 15 leading states are classified by their division or region of the United States, there are 6 leading states in the West North Central, 5 in the South Central, 3 in the West and l in the South Atlantic division. In contrast, the main agricultural feature of the states leading in the number of cattle and calves on feed is the large amount of land suitable for feed grain production and/or'other concentrate-type feed production. In this case there are 7 states in the West North Central division leading in the number of cattle and calves on feed, 4 in the East North Central, 3 in the West, and l in the South Central division. Typically, feeders have been shipped into the feed producing areas rather than the shipping of feed products into the prin- cipal breeding herd areas where many calves are raised. Some of the factors which have influenced this general pattern of move- ment are overall shipping cost considerations, the heavy con- centration of meat packing and processing facilities established near the feeding areas, the nearness of large metropolitan con- suming centers where the finished beef products are principally distributed, and the availability of labor for the meat packing and distribution agencies. 4Williams, w. F. and Stout, T. T.: cp.cit., pp. 82-85. 22 SO far no mention has been made of price relationships which are certainly relevant to the production process. To do so re- quires a discussion of other attributes of the production for slaughter component. First, there have been seasonal variations in total production for slaughter; and second, there have been seasonal variations in classes of slaughter. The total slaughter of cattle and calves has been reasonably well distributed through— out the year, but the composition of slaughter has varied more from month to month than did total volume. Slaughter of all cattle and calves has been normally the greatest in October, principally due to the many cows slaughtered during that month. Cow slaughter has been the most highly sea- sonal class of slaughter and has given the total slaughter a seasonal swing from a Fall high to a late Winter or early Spring low. More steers have normally been slaughtered in the Spring than at other seasons; while heifer slaughter has been greatest from October to February. Calf slaughter usually has been the highest in October and November, and has been the lowest during January and February.5 Associated with seasonal variations in slaughter (especially by classes of slaughter) were seasonal variations in prices received by farmers for the various classes of livestock. It is Breimyer, H. F. and Kause, C. A.: Chartinggthe Seasonal Market for Meat, Washington: USDA, Ag. Handbook No. 83, June 1955. 23 through variations in livestock prices that producers of beef cattle have been most affected economically and their decisions regarding future production adjusted. The trend toward higher levels of feed beef production on a year-around basis has reduced seasonal variations in total slaughter; yet the practice of marketing many cattle at the end of the Summer grazing period has continued to cause a Fall high in total slaughter. Conceptually, any production process requires inputs in order to produce an output; and in beef cattle production, feed, labor, land, and capital and equipment are the most important resources used. Consequently, one can readily perceive that economic conditions prevailing in the feed economy, the labor markets, and the capital goods and equipment markets assuredly have an important bearing on the cattle-beef sector. In this study, conditions outside the cattle-beef sector prOper are generally taken as given, i.e., predetermined; except for rela- tionships in what will be referred to as the other livestock- meat sector. In the aggregate, other livestock6 producers often compete 6Other livestock refers to hogs, sheep and lambs, chickens, turkeys, and dairy calves (for veal) in this study. Chickens and turkeys are not normally referred to as livestock. Dairy calves (as a "by-product" of the dairy industry) are the dom- inant source for veal meat products; hence, veal production and consumption are aggregated with the other livestock-meat sector variables, rather than the cattle-beef sector variables. 24 directly with beef cattle producers for such resources as feed and in many cases for labor and capital resources. Thus, another dimension is added to the study of the production process of the cattle-beef sector. While this interrelationship of beef cattle and other livestock enterprises is believed to have been impor- tant, it is believed that to an even larger extent, there are. important indirect factors affecting the beef cattle and other livestock production processes. Beef and other meat products are considered in the aggre- gate to be relatively close substitutes in consumption.7 Move- ment along one demand function (e.g., other meat) results in a shift in the demand for the other (e.g., beef). But since the farm demand for these two different groups of livestock are con- sidered to be derived demand functions, there is a corresponding shift in the demand function (e.g., beef cattle) at the farm level. Consequently, it seems apparent that an analysis of the cattle-beef sector must simultaneously involve an analysis of the other livestock-meat sector. This study treats the other livestock-meat sector more directly than other sectors of the general economy, by incorporating demand and supply relation— 7By relatively close substitutes in consumption, we mean that cross-price elasticities of beef and other meats are rela- tively large (but far from 1) as compared to similar elasticities for beef and non-meat foods. See, for example: Brandow, G.E.: "Interrelations among Demands for Farm Products and Implications for Control of Market Supply," Pennsylvania Ag. Expt. Sta. Bul- letin 680, August 1961, p. 17, for a comparison of cross-price elasticities for various food groups. 25 ships of this sector in the model that will be develOped. The Marketing Process In a broad sense the marketing process can be viewed as a provision of services by firms in the marketing segment that facilitate the movement of cattle-beef products from producers to ultimate consumers. A wide range of institutional arrange- ments exist to carry out the basic functions of the marketing process in order to provide the ultimate consumer with beef products in the form, place, and at the time desired. A vital feed-back function is implicit in the marketing process, in that marketing firms and institutions are the principal mode for reflecting consumer demands to the producers of beef cattle. The marketing process, i.e., the processing and distribution of livestock and meat, is normally classified into four broad functional categories: (1) marketing livestock, including trans- portation, (2) meat packing, (3) meat wholesaling, and (4) meat retailing. The degree to which these functions may be vertically coordinated is a subject that is being continually studied, but for the purpose of this study, a brief description of each of the four functional categories should suffice to indicate that the mar- keting process involves a complex pattern of interrelationships. Marketing Livestock In most areas where beef cattle are produced, producers 26 usually have several alternative outlets (channels) available for marketing their animals. These outlets include terminal public markets, auction markets, and various forms of "country selling". Country selling includes sales by producers direct to packers, to livestock dealers, and to other farmers.8 Changes in the structure and in the pattern of livestock marketing during the past forty years have resulted in a decline nationally in the relative importance of terminals as a market outlet. This decline has been characterized as a trend toward a decentralized marketing structure. Increased volume of mar- keting through country selling methods occurred initially in the 1920's and early 1930's, and this method of selling has been expanded. The most dramatic change in livestock marketing which contributed to the relative decline of the central markets, how- ever, was the rapid growth in the number of livestock auction markets since 1930. In 1930, only about 200 auctions were in operation, but by 1937 the number had increased to 1,345. The number of auctions continued to rise rapidly until a peak of about 2,500 was reached in 1952. A decline to 2,322 auctions occurred by 1955, but since then the number has risen slightly.9 8A general reference of the livestock-meat economy on Which much of the following discussion was based is the following: Williams, W. F. and Stout, T. T.: Op.cit., 1964, pp. 802. This book contains an extensive bibliography. 9Engelman, G. and Pence, B. S.: "Livestock Auction Markets in the United States," Washington: USDA, Mktg. Res. Rpt. No. 223, 1958, pp. 37. 736 27 The early growth of auction markets was concentrated in the North Central region, but the develOpment soon spread into the South, Northeast and West. By 1955, livestock auction markets were located throughout the United States. Several factors provided stimulus for the develOpment of the decentralized livestock marketing system. Extension and improvement of the highway network and increased reliance on trucks for transporting livestock have provided considerable flexibility to producers when choosing their marketing outlets. Expansion of the Federal Livestock Market News Service and im- proved market news dissemination have greatly facilitated the "non—terminal" outlets in attracting producers' sales. (Current market news about changes in prices at major terminals and other major marketing centers has in general been a basis for adjusting Offerings for livestock at "non-terminal" outlets. Consequently, non-terminal marketing outlets have generally been looked upon by producers as representative of the broader regional and national marketing system demand and supply conditions.) Another factor contributing to decentralization of livestock marketing has been the relocation (and decentralization of firms in the meat packing industry. Whether or not the decentraliza- tion of the meat packing industry was a cause or a result of the decentralization of livestock marketing is debatable, but perhaps more accurately, the decentralization of both was concurrent. These newer meat packing facilities were generally located in areas 28 near major sources of slaughter animals, which are also the areas where the most recent livestock markets have been established. There~have been differences by geographical regions in the principal market outlets used by producers; and further, there have been differences with regard to species of livestock. For cattle (including dairy), the percentage breakdown by regions and by type of market outlet in 1955 were as follows: Table 2.3 PERCENTAGE DISTRIBUTED OF ALL CATTLE SOLD BY FARMERS THROUGH DIFFERENT MARKET OUTLETS, BY GEOGRAPHICAL REGIONS, 1955 Percentage Sold Through Market Outlets Country Sales Terminal Public Direct to Local Total All Region Markets Auctions Packers Dealers Farmers Cattle Sales Other Northeast; 21 36 3 22 15 40 3 North Central 54 22 11 6 6 23 1 South Atlantic 4 68 8.. 13 6 27 1 South Central 16 46 6 11 19 36 2 Mountain 39 22 11 10 10 31 8 Pacific 17 8 39 16 17 72 3 Source: Phillips, Victor B., and Engleman, Gerald: Market Outlets for Livestock Products, ng. Res. Rpt. No. 216, Agric. ng. Ser., USDA, March 1958, p. 23. In summary, terminal markets were the major outlets for cattle sales in the North Central and Mountain regions. In the South Atlantic and South Central regions, auctions were the principal market outlets. In the Northeast, both auctions and country sales were dominant methods of marketing; and country sales led 29 substantially in the Pacific region. (A limitation of this data should be mentioned: percentage distributions of sales by pro- ducers do not account for interfirm or interagency sales or ship- ments of livestock; and consequently, do not completely portray the relative importance of the various marketing channels. Never- theless, it is clear that no single type of market outlet is com- pletely representative as the major producer marketing channel in all regions of the United States). . Meat; packing "Meat packing", as a functional category, refers to a com- bination of slaughtering and processing operations. The term originated prior to the develOpment of modern refrigeration when most livestock were slaughtered during the winter and the product was "packed" in salt or brine for consumption during the warmer seasons. Even though modern slaughtering and processing Opera- tions are markedly different from the past, the term "meat packing" is still generally used. Slaughtering Operations have been classified in numerous ways.10 One indication of the sc0pe of the slaughtering plant Operations is the number of livestock slaughtering plants by type of slaughter and the relative importance of each type of slaughter. In 1960, there were 3,144 commercial slaughtering plants in the United States. Of these, 530 (16.9%) were IO p. 62. See, for example: Williams, W.F. and Stout, T.T.: Op.cit., 30 Federally Inspected plants, which accounted for 77.4 percent of all cattle slaughter. Another 902 (28.7%) plants were classified as wholesale, and 1,712 (54.4%) were local plants.ll'12 Combined, the Wholesale and local slaughtering plants accounted for 20.0 percent Of the cattle slaughter. The remaining 2.6 percent of cattle slaughter was farm slaughter. The general acceptance and expansion of the Federal Meat Grading System for carcass beef, especially in the post World War II period, has been a major factor contributing to the high proportion of beef cattle that are slaughtered under federal in- spection. Not only have consumer preferences thereby been re- flected more accurately back through the marketing system to producers, but also the marketing process has been enhanced be— cause graded beef meat products can be purchased by retail out- lets On a specification basis (i.e., buying and selling by description rather than through personal inspection). Another consequence largely attributable to the Federal Meat Grading System has been the decline in the concentration within the meat packing industry, with less dependence being placed on private labels for quality assurance. 11Ibid., p. 63; and also in Agricultural Marketing Service: "Number Of Livestock Slaughter Establishments, March 1, 1960," Washington: USDA, August 1960. 12Wholesale plants are those slaughtering 2 million pounds Of liveweight or more annually; and local plants are those slaughtering less than 2 million pounds liveweight annually but more than 300,000 pounds. 31 The changing structure of the meat packing industry can be observed in part by noting the changing geographical percentage distributions of commercial cattle slaughter (liveweight) by regions over time. Table 2.4 PERCENTAGE DISTRIBUTION OF COMMERCIAL CATTLE SLAUGHTER (LIVEWEIGHT) BY REGIONS, 1947 AND 1962, UNITED STATES Cattle Region 1947 1962 Per Cent Change North Atlantic 10.5 8.6 -l.9 North Central 57.4 55.2 -2.2 E.N. Central 25.0 18.3 -6.7 W.N. Central 32.4 36.9 4.5 South 16.4 15.6 - .8 S. Atlantic 4.7 4.6 - .1 E.S. Central 3.2 3.8 .6 W.S. Central 8.7 7.2 —l.5 West 15.7 20.6 4.9 Mountain 4.4 7.8 3.4 Pacific 11.3 12.8 1.5 United States 100.0 100.0 Source: Statistical Reporting Service: Livestock Slaughter, Number and Liveweight By States, By Months, USDA Annual Series. The major areas with gains in the relative level of com- mercial cattle slaughter from 1947 to 1962 were the West North Central, Mountain, and Pacific regions. Those regions with the largest relative losses were the East North Central, North Atlan- tic, and West South Central. These interregional shifts in lo- cation of slaughter volume are an indication of the decentrali- 32 zation of the meat packing industry that has occurred concurrently with shifts in livestock marketing patterns (discussed above). Meat Wholesaling The meat wholesaling function is principally the sale and distribution of meat products from the meat packing plants to retail outlets. Again, a Wide range of institutional arrange- ments and marketing channels has been utilized in providing this service. The major channels which have been used in the past include (1) direct sales by packers to retailing outlets and to H.R.I. (hotels, restaurants, and institutions), (2) distribution through packer branch houses, and (3) distribution by independent whole- salers and jobbers. Some important structural changes also have occurred in the wholesale distribution system for meat and meat products. The more significant changes have been a decline in the relative importance of packer branch houses as wholesale meat distributors, and an increased share Of meat products moving through independent wholesalers. Also, direct sales by packers to retailing outlets and to H.R.I. have generally increased during the past 30 years. For all meat and meat products the following data on esti- mated distribution of sales by meatpackers to different classes of customers gives some indication of the changing structure in the meat wholesaling industry over time. 33 Table 2.5 ESTIMATED DISTRIBUTION OF SALES BY MEATPACKERS TO DIFFERENT CLASSES OF CUSTOMERS, FOR SELECTED YEARS Packer Independ- Owned ent whole— Institutions Branch salers and Retail and Other Ex- Year Houses jobbers Stores Large Users ,port Total (percent) 1929 47 14 32 4 3 100 1935 34 ll 46 8 l 100 1939 30 ll 49 8 2 100 1948 20 ll 59 9 l 100 1954 l9 16 55 9 l 100 Source: Agricultural Marketing Service; Marketing Costs and Margins for Livestock and Meats, Mktg. Res. Rpt. No. 418, USDA, 1960. When some of the factors which contributed to the changing structure of the meat wholesaling industry are reviewed, the ex- planations cited are generally much the same as those cited as factors contributing to the changing structure in other segments of the livestock—meat sector. Namely, (l) the improvement and extension Of the highway system and trucking equipment (with modern refrigeration units) have facilitated the movement of meat direct from packers to retailers, and (2) the develOpment of the U. S. meat grade standards facilitated the sale and dis- tribution of meat on a specification basis. Procurement practices of the large-scale retailing organ- izations, who require high volume, fresh, uniform quality meat, have been such that direct purchases have been economically 34 feasible. Also, the demand for the types of specialized services Offered by many of the independent wholesalers has increased sub- stantially and their role in meat distribution has increased in importance in the recent past. Another recent facet of the meat wholesaling industry has been vertical alignment with retail food chains that involve centralized processing (e.g., breaking and packaging) before deliveries are made to the individual stores. Meat retailing The final functional category of the marketing process to be briefly discussed is that of meat retailing.l3 Major outlets for meat products to consumers have been retail grocery stores; ho- tels, restaurants, and institutions; meat markets; and other food stores. Since the early 1940's grocery stores and the H.R.I. trade have accounted for increasing shares of retail sales. Meat marketing practices in retail grocery stores have changed substantially since the 1930's with meat sales account— ing for about 25 percent of the total dollar sales in most modern retail supermarkets. The increased importance of meat retailing by supermarkets is a major aspect of structural changes that have occurred in the food retailing industry since the first appearance of supermarkets in the 1930's. Prior to this time a 3A general reference on the following discussion is again: Williams, W. F. and Stout, T. T.: Op.cit., especially Chapter 16, "Structural Changes at Retail," pp. 402-426. 35 very small proportion of fresh meat was distributed through grocery stores, with considerably more being sold through Special- ized meat markets. A supermarket "era" emerged as the nation's larger retail food chains became established and increasingly accepted by the public. The total number of grocery stores increased during the 1930's with the largest increases occurring among stores handling fresh meat. World WarII inhibited many adjustments and changes but the pressure for larger retailing units continued to mount. At the War's end, with the sharp population increase and the exodus to the suburbs apparent, shopping centers with supermar— kets increased. By 1948, grocery stores with fresh meat had increased and the average size of these stores had risen sharply. Another major develOpment that occurred in meat retailing in recent years was a trend toward self-service Operations. Again, the larger chains apparently led this develOpment with increased emphasis placed on quality, uniformity and variety. Economic pressures continued on smaller grocery store units; and the number of grocery stores drOpped 28 percent to about 260,000 in 1958, from about 360,000 in 1948. Even more dramat- ically, the average volume of sales per store, in constant dol— lars, more than doubled between 1948 and 1958, from about $80,000 per groceryustore to approximately $170,000.14 By 1958, 14Ibid.; p. 406; and also, Bureau of Census: "Retail Trade," U. S. Census of Business, Washington: U.S. Dept. of Commerce, census issues for 1948, 1958. 36 nearly all of the larger grocery stores handled fresh meats. The original concept of supermarket food merchandising re— ferred mainly to a way of doing business, rather than so much emphasis on size. Originally, supermarkets were characteristi- cally thought of as discount houses for food products. However, in the postwar period, with increased competition among the larger retail chains and supermarkets, there were pressures for retail stores to increase both the number of items distributed and the services Offered. In the recent past, added services have been Offset partially for meat by self-service merchandising and economies in procurement, cutting and handling. Many of the in-store meat cutting, trimming and wrapping Operations have be- come highly mechanized and routinized. 0n the other hand, there has been some shift of the processing services back to packers and other distributors; and increased centralized processing among chain-stores. These factors may lead to important develOp- ments in the structure of the meat wholesaling industry. Many other developments in the retail food industry have had and are having an impact on the structure of the industry. Other segments of the retail trade for meat include H.R.I., delicatessens, the food locker industry, and various types of home freezer plans. H.R.I. has been by far the most important segment of this group in recent years. About 18 percent of the food sold to U. S. civilians is handled by eating establishments, 37 including public and private institutions. Meat products are an important part of these sales, but no data are available on this consumption by commodity groups. It is known, however, that a high percentage of dining establishments purchase meat through jobbers or specialized hotel supply houses. Also, some of the larger firms buy direct from the packers. The complexity of the overall marketing process for meat products poses some particularly difficult questions in studies of this kind where a main objective is to simplify and tie to- gether into a limited number of economically meaningful vari- ables and relationships the underlying dynamic processes of meat production, marketing and consumption. But, before "build- ing-the-bridges" in the form of an economic and statistical model, we should consider the last of these processes; namely, the consumption process. The Consumption Process Meat and meat products account for about 25 percent of family food expenditures. Beef meat products have accounted for the largest single-species share (both by weight and by value) of the meat consumption in the United States since 1947, and the per capita consumption of beef has increased relative to the other red meats in the postwar period. In the decade from 1952 to 1962 the per capita consumption of beef rose 44 15Williams, W. F. and Stout, T. T.: p. 420. 38 16 percent, from 62 to 89 pounds. Further increases to 100 pounds per capita were reached in 1964, a new record level of beef con- sumption per capita.17 The phenomenal increases in beef consumption per capita are the result of many factors. Part of the increase was associated with a shift to beef consumption relative to other meats, and also, associated with shifts from other food groups to higher levels of total meat consumption, particularly beef and poultry meats in recent years. Some of the major trends in food consump- tion patterns are evident in the following table (Table 2.6) Where the per capita consumption of food by major groups in selected periods are presented. In summary there have been increasing trends in per capita consumption of beef and poultry meats. Fish, dairy products, fats and oils, vegetables, potatoes and sweet potatoes, and sugars and sweetners have been food groups that remained es— sentially stable in recent years. Finally, other meats (in- cluding pork, veal, lamb and mutton), fruits, and flour and cereal products consumption per capita have been generally declining over the periods shown. 16Based on data from: Economic Research Service: "U. S. Food Consumption, Sources of Data Trends, 1909-63," Washington: USDA, Stat. Bull. No. 364, June 1965, p. 22. 17 Preliminary estimate as cited in: Consumer and Marketing Service: "Livestock and Meat Statistics," Washington: USDA, Supplement for 1964 to Stat. Bull. No. 333, September l965,p. 146. 39 .em .mm .opma .:Omo .nma .oz .xoonecmm .6: ..m:umuumm w unemue coauassmeoo amps. .mo:>umm mcflumxumz :musuHsoflum: can we .«« .mm .mmma .«omo .eom .oz .225: .umum ..moumomd .mpcoua paw mama mo mmuusom .coflumfiomcoo poom .m.D: "moa>umm noncommm owaocoom "muupbm As: can: 883.: As... 3833-33» 6 “223 :oootoameo. Au uoEmw :o mambo 03:00 02:05. no: 30G 5855 BE £52 .28 .32, atom 30305 "Emma: 82:8 3 “Emma: ”30.80 A: o. 2: a: «.2: «58 p.22 22 as 22 33 2.2. «.3 82 28: 32 p.22 3.8 «.32 22. S2 22 v.5 A.:. 22 «p2 2.2: p: o. o: 318 3.2 4.2. 22 1.2 amp v.2. 28 S2 was: S: 28: o. 2« 3.2 22. m2 «.2 5a 23. 93 82 .28: 2: 28: 2:8 p.«2 «.2 8« «.2 22 «.2. «.«m 2-52 m. «.2 A: l..«2 .922 5.8 22. pm« «.2 v.«« 22 23 2-22 m. o: 1.8 3.2 :42 852 «.2 «o« 12 «.2 «.2. 22. 2-22 92: :2 o.«2 a.2« p82 25 :2 5.2 22 p. 8 2% 2-32 :2 :2 .38 o.8« «:2: 28 E: «.2 22 s. 8 «.3 2-82 A: A: A: A: A: A: a: A: A: A: A: :33. :23. ”Son. Jon 32.6 28:08 .825 c825 =2...— bugom .333 “com a .0928 «5:32: masses «52:23 .0 o masses. 1. manage :88. :38. 82233 as»: :38. :22 I 550 265326 .650 32605 3080 3880a Hoo3m moEuuofio> 83$ 50 an as". 82695 >95 d stm a» SoE d 3838 .Em bygon— :32 il‘iillri )lilllllllllililrlll mQOHmmm QMBUSmm 2H mgOMO MOE Nb DOOM m0 ZOHEngOU Jan—”20 mam m . N OHQMB 40 A wide variety of economic and sociological factors are generally believed to have accounted for these shifts in per capita consumption, particularly for beef. Among these are pro- duction characteristics, the level of consumer disposable in- come, prices Of beef relative to other meat and meat products, beef (and other meat) prices relative to prices of other food, changes in tastes and eating habits, effects of urbanization, size and age distribution of the family, occupations, race, religion and nationality.18 Since most beef consumed in the United States has been fresh meat and not well suited for storage for long periods of time, "current" consumption has been closely tied to "current" slaughter at the farm level. In the short run, slaughter pro- duction largely determines consumption. On the other hand, in the lOnger run situation, consumer demand largely determines the level of farm production at specified prices, and in this sense changes in consumer demand have influenced production trends. Most of these factors are briefly discussed by: Williams, W. F. and Stout, T. T.: Op.cit., Chapter 4, "Meat Consumption," pp. 86-105. Also see, for example: Stout, R.G., Purcell, J. C. and Fishel, W. L.: "Marketing, Slaughter and Consumption of Livestock and Meats in the South," Southern Cooperative Series, Southern Regional Expt. Stations Bull. No. 66, August 1961; Agricultural Marketing Service: Meat Consumption Trends and Pat— terns, Washington: USDA, Ag. Handbook No. 187, July 1960; and Lanahan, Thomas J., Jr.: "A Review of 1955 Survey Data on House- hold Meat Consumption," The National Food Situation, April 1957. 41 The increased level of consumer disposable income apparently has been one of the main factors responsible for the shifts to higher levels of meat consumption. Our marketing and consumption processes effectively merge only when the consumers' preferences are backed by their ability to pay for the goods desired. The higher costs of meat production relative to production costs of other foodstuffs with equivalent nutritive-values has meant that consumers both prefer and are able to purchase meat products. Beef and other meats are relatively close substitutes in consumption and the relative prices of the various meats have influenced consumers' choices and demand for alternative meat products. Likewise, meats and other foods are substitutes to some extent, but generally not to the same degree as the various meats. Meat consumption patterns have been further influenced by the availability of many processed forms of meat (e.g., luncheon and variety meats, wieners, meat pies, and others). Processed meat consumption has increased steadily since the late 1930's, and price interrelationships among alternative forms of meat have been affected. (Most processed meats are pork products, however; whereas beef has been marketed primarily as fresh meat). Increased consumption away from home in various kinds of dining establishments, both private and institutional, has also affected meat consumption patterns and interrelationships. 42 The other factors mentioned have been cited as phenomena influencing meat consumption patterns, and some factors have been important in particular areas of the nation. For example, teen- agers consume more meat than the average adult; consequently, the changing composition of population should be a consideration in studies aimed at explaining demand for meat. Another example of a factor which should at least be considered is the effect of the kosher trade, especially in the Northeast, on the overall consump- tion levels of meat. These factors and possibly many others com- plicate efforts to simplify and quantify aggregate demand rela- tionships. Summary In summary, three interrelated processes of beef production, marketing and consumption have been briefly reviewed. Each pro- cess, by itself, was seen to be a source of many complex patterns of involvement, and each process is linked to the others. Beef production was viewed as the raising of beef cattle for one of two uses; either production for slaughter or produc- tion for inventory. The inventory component then was considered as an input for future total beef production. Geographically, the beef breeding herd was seen to be principally located in the grassland and range areas of the country; while the feeding herd was seen to be located primarily in those areas where feedstuffs, such as feed grains, are grown. These differences were considered 43 relevant to the overall production process. Variations in seasonal slaughter of beef cattle were con- sidered as important to producers of various classes of livestock (but this study is based on annual time series data, so the full affects of seasonal variations will not be accounted for in this analysis). However, the trend toward larger feeding herds, espe— cially on a year around basis, has tended to reduce seasonal vari- ations in slaughter. Producer sales out of first hands normally have flowed into alternative marketing outlets, with terminals, auctions and country selling methods each being important marketing channels. The relative importance of each was seen to vary across regions of the United States. The marketing of livestock was discussed as the first func- tional category of the marketing process. Three other broad categories of the marketing process discussed were meat packing, meat wholesaling and meat retailing. Meat packing referred to a combination of slaughtering and processing operations, which was but an intermediate step in the marketing process. The meat packing industry was seen to be well distributed throughout the United States and a changing structure of the industry was char- acterized as a trend toward decentralization. Packing plants have been substantially relocated over time and new locations have generally been closer to major producing areas of beef 44 cattle and other livestock. Meat wholesaling refers to the sale and distribution of meat products from packers to retail outlets. Direct sales to retail stores and institutions, independent wholesalers and jobbers, and packer owned branch houses are the main channels. As the nation's highway system develOped, as trucks with modern refrigeration units came into use, as the Federal Meat Grading System expanded (thereby allowing the smaller packers to merchandise meat with- out a well known brand name), and as the meat packing industry became decentralized, the meat wholesaling industry has likewise been decentralized. The major relative decline occurred in sales moving through packer owned branch houses, with both the inde- pendent wholesaler and the direct sales channels gaining relatively. Meat retailing has changed markedly since the 1930's with the growth and develOpment of supermarkets. Retail grocery stores have become the principal outlets for meat wholesalers, with hotels, restaurants and institutions becoming somewhat more im— portant over time. Larger retail grocery stores, namely chains and supermarkets, have dominated however, and their procurement practices have had reverberations throughout the meat economy. Implementation of self-service merchandising in the postwar period has been a major develOpment in meat retailing and its widespread adOption, combined with the large scale retail out- lets, has resulted in considerable structural change in the food 45 retailing industry; mainly in the reduction of the total number of stores and large increases in the average sales volume of the remaining stores. The meat retailing industry has direct access to consumers and here the marketing and consumption processes interact. Con- sumption of meat (beef in particular) has increased sharply in the postwar period. In fact, meat products (including poultry) as a food group is the only group with rising consumption per capita from the 1930's to the present time. Many factors are believed responsible for this rise in con— sumption of meat, especially beef. In the short run, meat con- sumption is closely tied to slaughter production; but in a longer run situation, the level of consumer demand affects the level of production. The level of consumer disposable income seems to have been a major determinant of increased demand for beef. Also, relative prices of beef and other meats, and of beef and other foods have had additional influences on the level of beef con- sumption.‘ Changes in tastes and eating habits, composition of the population, and several other factors were briefly mentioned as sources Of influence on the changing demand for beef by con— sumers. With this brief background on the cattle-beef economy, and its relation to other sectors of the economy, there are some guides, or perhaps more accurately, some constraints, within 46 which an economic model of the cattle-beef sector may be dev- eloped. An Objective of this study is to consider a system of relationships which integrates some of the interrelationships between the consumer, marketing and producer segments. Clearly, these segments are interrelated. Literatu;e,Review Numerous studies have dealt with various aspects of the cattle-beef sector or interrelationships of the cattle-beef sector with other sectors of the general economy. These studies have differed in the approach taken, in the time period analyzed, in the level of aggregation, in the estimation methods employed, and in the types of interrelationships considered. The purpose of this section is to report on only a limited number of previous studies which had a bearing on development of this study. Later in this report some findings of these and other studies will be compared with results of this analysis. A pioneering effort employing national aggregate variables of the livestock and feed grain economies in a simultaneous equations framework was reported by Hildreth and Jarrett19 in 1955. Their effort focused attention on the economic inter- dependence of the average price of livestock produced, quantities of livestock produced and sold, and prices of feed grains and 19 Hildreth, C. and Jarrett, F. G.: A Statistical Study of .Livestock Production and Marketing, Cowles Commission Monograph DR). 15, New York: John Wiley and Sons, 1955. 47 protein feeds. A similar more recent study was developed by Feltner20 (1964) to account specifically for changes in aggregate livestock inventories. Two other early studies which were formulated within a structural model simultaneous equations framework at a lower level of aggregation were those by Nordin, Judge and Wahby21 (1954), and by Judge22 (1954). In the former study, the authors considered interrelationships of retail demand and supply func- tions of pork, beef, poultry products, dairy products, oleo- margarine and feed grains; plus a production function for feed grains. Their main focus for estimation was on derived demand relations for pork, beef, and poultry products. Judge's study considered aggregate demand and supply interrelationships for eggs, meat, and other foods at the retail, commercial and farm levels. Both of these studies emphasized develOpment of eco- nometric models. 23 Working (1954) discussed interrelationships among demand functions for various meats, although a simultaneous equations 20Feltner, R. L.: Alternative Models of the Feed-Livestock Economy, North Carolina State University, Raleigh, Ph.D. thesis, 1964. 21 Nordin, J. A., Judge, G. G., and Wahby, 0.: "Application of Econometric Procedures to the Demands for Agricultural Prod— ucts," Iowa State College, Ames, Ag. Expt. Sta. Res. Bull. NO. 410. July 1954. Judge, G. G.: "Econometric Analysis of the Demand and Supply for Eggs," University of Connecticut, Storrs, Ag. Expt. Sta. Bull. NO. 307, 1954. 3 . . . . Working, E. J.: Demand for Meat, Chicago: UniverSity of CHIicago Press, 1954. 48 application was considered only in an appendix discussion. Fox24 (1953) presented a few simple simultaneous equations systems, but his emphasis was on appraising the applicability of single equations methods for fitting demand functions for agricultural commodities. The dates of the above references were noted to emphasize that these studies (except Feltner's) were developed prior to modern develOpments in estimation procedures and prior to major advances with computers. Wallace and Judge25 (1958) presented two more comprehensive models, each involving twelve relationships of the beef and pork sectors of the economy. Demand and supply relations at both the farm and retail levels were considered, and alternative estimators (LISE, ZSLS, OLS) were applied to a selected set of equations from the systems. Cromarty26 (1959) introduced an econometric model that ex- amined twelve product categories (involving demand, supply and price relationships) within the agricultural economy. His study was a continuation of a comprehensive project begun by Klein and 24Fox, K. A.: "The Analysis of Demand for Farm Products," USDA, Tech. Bull. NO. 1081, 1953. 5Wallace, T. D. and Judge, G. G.: "Econometric Analysis of the Beef and Pork Sectors of the Economy," Oklahoma State University, Stillwater. Oklahoma Ag. Expt. Sta. Tech. Bull. No. P-75, August 1958. 6 . Cromarty, W. A.: "An Econometric Model for United States Agriculture,” Journal of the American Statistical Association, Vol. 54, Sept., 1959. inc den of the Se: 27‘ I 9‘. 49 Goldberger27 (1955) which linked both the agricultural and non- agricultural sectors of the total United States economy within a system framework. The primary purpose of such grand or "master" models was to measure major relationships within and between the agricultural and non-agricultural sectors of the total economy. These latter two references illustrate how one might proceed to integrate less-aggregative components of a system to the more- aggregative "master"-model of an economy. Other researchers have taken alternative approaches to ac- count analytically for interrelationships within the cattle- beef sector and with other sectors. Recent related research includes a study by Maki28 in 1962, Where he concentrated on develOping market forecasting procedures by decomposing beef and pork production cycles into several interacting components. Nine multivariable equations were specified to obtain estimates of the functional relationships for the beef-pork economy; and the method of least squares was employed in fitting annual, semi-annual and quarterly data for the 1949-1960 sample period. Variables used in the study involved a more detailed breakdown of livestock classes than had previously been attempted in similar studies. 27Klein, L. R. and Goldberger, A.S.: An Econometric Model of the United States, 1929-1953, Amsterdam: North Holland, 1955. 28 Maki, W. R.: "Decomposition of the Beef and Pork Cycles," Journal_of Farm Economics, Vol. 44, August 1962, pp. 731-743. . 13‘: bee rel 50 Maki29 presented another econometric model of the beef and pork sectors in 1963, with the particular emphasis of demonstrating its empirical application in analyzing and forecasting cyclical fluctuations in livestock supplies and prices. An important aspect of this analysis was the use of inventory relations in a comprehensive forecasting model of the livestock economy. Prior to the develOpment of the final system of prediction equations in the study, a series of inventory and cobweb models of the beef and pork producing sectors, and a series Of vertical price relationships were specified and fitted using the least squares method. Combining the production and supply relationships at the farm level with the vertical farm and wholesale price rela- tionships, a recursive system of 44 prediction equations was obtained to generate the principal endogenous variables of the overall model. Crom and Maki3O have developed a semi-annual dynamic model of the livestock-meat economy, which is adjusted so as to im- prove its predictive ability. Such models may be recursive, simultaneous, or both (recursive and simultaneous subsets); but in any case the develOpment of such dynamic models has relevance 29 . . . . . Maki, W. R.: "Forecasting Livestock Supplies and Prices with an Econometric Model," Journal of Farm EConomics, Vol. 45, August 1963, pp. 612-624. 30 , Crom, R. J. and Maki, W. R.: "Adjusting Dynamic Models to Improve Their Predictive Ability," Journal of Farm Economics, Vol. 47, November 1965, pp. 963-972. 51 to studies like this one. A recent study by Petit,31 which in- cluded a recursive model formulation of the beef cattle producer segment, is another example of an alternative analytical approach. We discuss Petit's methodology and some of his findings in more detail later in this report. 1 g o o I Petit, M. J.: Econometric AnalySis of the Feed—Grain Livestock Economy. Ph.D. Thesis, Michigan State University, 1964. CHAPTER III THE ECONOMIC AND STATISTICAL MODELS Definitions and Concepts In order to discuss econometric model construction and sta- tistical inference more efficiently and accurately, it is helpful to use language that has been developed to consider statistical analysis of economic relationships. Some basic defintions and concepts will be presented in this section. Concepts of a model and a structure are fundamental. A model is a more general concept that refers to a set of struc- tures. A structure is defined as the process by which a set of economic variables is generated. A structure can be thought of as a unique representation of the model, i.e., it is a member of the set of structures. This distinction is useful in that em- pirical analysis is aimed at determining a single structure, including estimates (via statistical estimation or by assumption) of all unknown parameters of the model. ‘ The number and nature of the parameters of the model have to be ascertained. Two types of specifications are essential for Obtaining meaningful parameter estimates: (1) economic specifications, and (2) statistical specifications. Economic 52 53 specifications are generally summarized in terms of an economic model. Economic theory and knowledge of the economic institutions and characteristics pertaining to the sector(s) being studied, are important in this phase of the analysis. In addition, the researcher is required to make statistical specifications (or assumptions, e.g., functional forms of the relationships, form of the variables, distribution of random variables, and others). About which a priori economic knowledge and theory may Offer little if any guide. Since statistical specifications are supplementary to economic specifications, then the combined specifications are generally summarized in terms of a statistical model. In the simultaneous equations system framework the components of an ecOnomic model can be classified into categories of vari- ables, endogenous and predetermined. The variables Whose values are explained by the structure are called endogenous variables. The predetermined variables are further classified as being either exogenous or lagged endogenous. The variables Whose values are determined outside the structure are called exogenous whereas those variables whose values are determined by the struc- ture prior to the current period are called lagged endogenous. In other words the endogenous variables are to be explained by the syStem of relationships while the predetermined variables are specified as being determined at the time they enter the 54 structural relationships. There is a third type of variable which enters in the sta- tistical model called a disturbance or shock variable. This is a random variable that is not directly observable but its prob- abilistic behavior can be described or assumed. In actual sta- tistical analyses it is seldom true that the structural relations of the economic model specify an exact functional relationship. We normally deal with stochastic rather than functional relations. Assuredly not all variables that might affect an economic rela- tionship are included in the economic model Specification, only the alleged most important variables are included. To allow for this incomplete specification statistically it is assumed that this disturbance random variable enters in to the structural relations of the statistical model. Another concept important in this study is a complete model. Simply stated, it is a model that contains as many equations as there are endogenous variables. In general, complete models are required when we want to estimate the reduced form equations for prediction or for other analytical purposes. Also, from an eco- nomic viewpoint, a complete set of equations more clearly indi- cates the logic underlying the endogenous mechanism that is being modeled. Once we have specified the statistical model, there remains at least one more critical consideration; namely, the identifi- 55 ability of the structural parameters. The concept of identifica- Eigp is briefly as follows. The structural parameters of a model are said to be identifiable if their values can be deduced from complete knowledge of the distribution function of the observa- tions, or, in the case of a linear structural model (such as is Specified in this study), from complete knowledge of the para- meters of the reduced form. Identifiability is usually achieved in linear structural models by imposing a priori restrictions on the values of the structural parameters, in particular by speci- fying that some parameters are zero. The restrictions may be such that the parameters in a given structural equation are 295 identified (pr under identified), just identified, or over identified. Sometimes just identified and over identified equa- tions are referred to simply as identified. If all of the struc- tural equations in a linear model are identified and if that model is complete, then the model is also said to be identified. Koopmans has derived a necessary condition for the identi- fiability of a particular structural equation in a system of equations.1 Let g be the number of endogenous variables ap- pearing in the equation; let k be the number of predetermined variables appearing in the equation; and let K be the number of 1KOOpmans, T. C.: "Identification.Problems in Economic Model Construction," in Studies in Econometric Method, Cowles Commission Monograph NO. 14, W. C. Hood and T. C. KOOpmans, editors, New YOrk: John Wiley and Sons, 1953, Chapter II. 56 predetermined variables in the system of equations. Then the necessary condition for identifiability is K—k :g—l. I.e., if K-k g-1. Sufficient con- ditions for identifiability require values of pOpulation para- \ meters which are unknown, but can be tested statistically. Specification of the Economic Model The economic model summarizes the economic specifications made by the analyst. A description of the variables and the structural relationships of the model will be discussed in this section. The specified model is formally complete and it con- tains ten relationships: eight behavioral equations and two identities. Table 3.1 summarizes in a schematic form the ten endogenous variables, the twelve predetermined variables (including a con- stant term), and the ten specified relationships of the final form of the model (note that checks indicate included variables and that circled endogenous variables are selected as the nor— malizing variables). Definitions of all the variables are pre- sented in Table 3.2. The equations can be grouped as six equations pertaining to the cattle-beef sector and four pertaining to the other live— stock—meat sector. Within each sector three major segments are I 5'7 IL'BLI X ZS'LOP- S'EIZ9T 96'PII ZI'IZ VS'BL 89'99 9'8689? 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OHZOZOUM ME? ho Nfltzxfim 0H3¢Zfimom H.n Danna 58 Table 3.2 DEFINITIONS OF VARIABLES PBEEFR QBEEFC POMEATR PBEEFF QBEEFP IBEEFFZ POMEATF IBEEFNFZ QOMEATC QOMEATP CONSTANT DISPY CMKTGM IBEEFFl IBEEFNFl PPROTEIN ARANGECI POMEATFL O. O. .0 Price of BEEF at Retail deflated by CPI (Con- sumer Price Index, l957-59=lOO); cents per pound ‘ - Quantity of BEEF Consumed, excluding veal (carcass weight); million pounds Price of Other MEAT at Retail (weighted aver- age of pork, lamb and mutton, veal and poultry meat) deflated by CPI; cents per pound Price of BEEF cattle at the Farm level de- flated by PPFI (Prices Paid by Farmers Index, l957-59=lOO); dollars per cwt. Quantity of BEEF cattle Produced for slaughter (carcass weight); million pounds Inventory of BEEF cattle retained for Feeding at the end of the current period; thousand head Price of Other MEAT at the Farm level deflated by PPFI; dollars per cwt Inventory of BEEF cattle Not-retained for Feeding at the end of the current period; thousand head Quantity of Other MEAT Consumer (carcass weight); million pounds Quantity of Other livestock (MEAT) Produced for slaughter (carcass weight); million pounds A CONSTANT term identically equal to one Consumers DISPosable income (Y) deflated by CPI; billion dollars Cost of MarKeTinG Meat deflated by CPI; cents per pound (y6 lagged), Inventory of BEEF cattle retained for Feeding at the beginning of the current period; thousand head (Y8 lagged), Inventory of BEEF cattle Not- retained for Feeding at the beginning of the current period; thousand head Weighted Price of PROTEIN feeds deflated by PPFI; dollars per thousand pounds TDN (Total Digestible Nutrients). Average (of August, September and October) RANGE Condition Index of the current period; reported as percent of normal (y7 lagged) Price of Other livestock (MEAT) at the Farm level, deflated by PPFI, Lagged; dollars per cwt. 59 Table 3.2 (con't) M X8 = PFEEDIDL : Price of FEED InDex Lagged (l-year), deflated by PPFI, l957-59=100 (y1 lagged) Quantity of Other livestock (MEAT) Proguced for slaughter Lagged (carcass weight); million pounds NOMIMPORT: (yg - ylo) Principally Net Other Meat IMPORTS (carcass weight); million pounds x11 = NBIMPORT : (y2 - y ) Principally Net Beef IMPORTS (car- cass weight); million pounds X = QOMEATPL : X II rwecognized: producer, marketing and consumer. That is, the de- nuand relations at retail correspond to the behavior of consumers it) the consumer segment; the marketing relationships corresponds tc> the behavior of firms in the marketing segment; and the supply ecztlations at the farm correspond to the behavior of producers in tries producer segment. In addition, two inventory demand equations are postulated as. also representing the behavior of producers in the producer Secjiuent of the cattle-beef sector. Finally, two identities are flP€3<3ified to account for differences in the levels of production an(3_ consumption in both the cattle-beef and the other livestock- "EBEit; sectors. The principal reason for a difference between the se two variables (both measured in million pounds of carcass Wei~ght equivalents) has been the influence of the export—import mo\Iement. of these meat commodities. The net level of imports fCXr each is considered to be predetermined in this model, and 60 the inclusion of the two identities serves to make the model for- mally complete. 1. Demand for Beef at Retail From consumer demand theory, retail (consumer) demand for beef is postulated as a function of the price of beef, prices of close substitutes, prices of all other goods, consumers' income and.the number of consumers. In this relation, the quantity of beef consumed (QBEEFC) and the average retail price of beef (IPBEEFR) are specified as being jointly dependent (endogenous) veariables. A weighted average retail price of other meat (POMEATR) is; specified to reflect the prices of close substitutes, and it is: also considered to be an endogenous variable in this study. Ck>rlsumers' income is represented by an aggregate disposable in- come (DISPY) variable. A constant term is included in this rela-. tion (as will be the case for all the equations in the model). The number of persons eating out of civilian food sup- _ 2 PlJ-ees was initially specified to represent the number of con- sun1€3rs. However, in the final model this variable was not 2 Additional specifications were considered for all of the eQIléations in the structural model. (We include some of the al- tel?11ative specifications in Appendix A.) The final specifications preEEBented here are, therefore, selections from sets of possible altlulation as separate predetermined variables. We regard this alt:ernative as one which might be preferred over our final sPecification and we recommend that research in this area con— Etl1~ne and population is also quite high: .9958 for the 1936-41, 1949-63 sample period. 62 series data may not be causal factors, thus a trend term might remove the "non-causal” influences of an explanatory variable which is spuriously correlated with "trends". We know of no general guiding rules in this regard, and our choice to omit trend terms is admittedly only one alternative. Some of the equations were also estimated including trend terms, as an al- ternative specification, and the results (using ZSLS) are re— ported in Appendix A.) The above digression has a direct bearing on this par— ticzular equation, in that DISPY and a linear time variable, TIDdE, i.e., 1936=l, l937=2, l938=3,..., were simply correlated to the degree +.9953.w Under such empirical conditions, we would hesitate to conclude that distinguishable individual (DISPY and TIth) effects were reliable even if "statistically significant" Coenffficient estimates were derived. (To a lesser, but sub- Stan tial, degree TIME was simply correlated with other explana- tor33' variables in this study, so that in each equation one or more; specified variables are believed to have "captured" trend eff€3<=ts, which may or may not have been causal with regard to the Specified variables). Prices of "other goods" are represented indirectly by def:Lating all retail prices and other (non-farm) monetary vari— akfiLees with a consumer's price index (and farm price variables were deflated with a prices paid by farmers' index). Or, in 63 other words, all monetary variables are expressed in "real" terms. This procedure seemed desirable given the period spanned by this study, i.e., 1936-41, 1949-63; and it is a generally accepted practice in cases where, for example, we believe that a doubling of all price and income variables would have no effect, on consumption.4 So far the above discussion of the retail demand equation Ines led only to an implicit expression; namely (in the usual way of summarizing the relations implied by the economic model): Y1: yz. Y3: x0. x1 (1) wheare y1 = PBEEFR,. y2 = QBEEFC, y3 = POMEATR, x0 = CONSTANT, and x = DISPY. 1 In this expression a comma should be read as "and," and a semi— colon should be read "appear in relation with." The variables on 1:]ne left of the semicolon are current endogenous variables and those on the right are considered predetermined within this Particular model. (Most of the estimation methods used in this Studile' require that a single endogenous variable in each equation be 8elected as a "normalizing variable"; the asterisk (*) in eac11 relation indicates this normalizing variable.) The advan- tages of stating the economic model relations in this way is that we (it: not become involved in essentially statistical problems, ___~__¥ S See, for example: Foote, R. J.: Analytical Tools for wing Demand and Price Structures, Washington, USDA, Ag. ancibook No. 146, August 1958, p. 27. 64 e.g., stating the algebraic form of the relation, deciding whether or not to use actual data or logarithms, deciding how "disturbances" in the relations will be specified, and others. 2. Marketing in the Cattle—Beef Sector When viewed in the aggregate, the composite behavior of firms in the marketing segment is conceived as representing, simultaneously, (1) a supply of beef (plus services) response at: retail, and (2) a derived demand for beef cattle at the farm. Thug basic idea here is to postulate a single behavioral relation cozrresponding to the composite behavior of firms in the market- ing; segment of the cattle—beef sector. The derived demand at tine farm (and consequent domestic supply of beef and services at retail) is further conceived as a function of (a) the "margin", (b) the costs of providing associated marketing ser- Vic<3:s, (c) factors associated with shifts in the derived demand for Ioeef, and (d) factors associated with shifts in the supply of sseervices relative to the actual amount of meat products in- VOlVed . In terms of observable variables this relation is specified as the price of beef cattle at the farm (PBEEFF) being jointly determined with the price of beef at retail (PBEEFR) . Both of these endogenous variables are in turn specified as being deter— mined jointly with the quantity of beef produced for slaughter (QBEEFP). Consumers' disposable income (DISPY) is specified 65 and considered to be a factor related both to shifts in the de- rived demand for beef cattle and to shifts in the supply of ser- vices (relative to actual meat supplies). Finally, an indicator of changing marketing costs is our CMKTGM (defined below) variable. USDA sources publish a data series named the total meat marketing bill,5 which is estimated by first dividing cash receipts for farm animals for slaughter by a market basket measure of the farm value of meat relative to the retail value for corresponding quantities. This provides an estimate of the retail value of all red meats, and the difference between the aggregate retail and farm values is then a marketing bill estimate. This measure (annual) was divided by total red meat conSMption to get an (indicator) estimate of the cost of marketing meat per pound (CMI'C'I‘GM), as used in this study. While the total meat marketing bill estimate (above) is broken down into components (e.g., labor C031: 5, transportation costs, etc.), that which is not accounted for explicitly is classified as "other costs" (which includes profits to firms in the marketing industry). Hence, this vari- able (and our CMKTGM variable) includes some factors which are “Ot really predetermined, thereby weakening our specification Of c:DfiC'I‘GzM as a predetermined variable. However, adequate data are not available for the desired "predetermined" components \ t Derivations of marketing bill estimates are discussed in She following: Agricultural Marketing Service: "Farm-Retail preads for Food Products," USDA, Misc. Pub. No. 741, 1957, p.49. 66 over the entire sample period, and the CMKTGM variable seemed the best choice among the available alternatives. A related concern was that using CMKTGM really implied "fitting" a near-identity relation, i.e., PBEEFF = PBEEFR - CMKTGM: but since the CMKTGM variable is based on all red meats, the identity does not of course hold exactly for any one. It is believed that this variable does capture major year-to-year changes in those costs of marketing, which are largely determined outside of the sectors being studied, and that the endogenous components are at least partially cancelled out by the process of averaging over all red meats. (Alternative specifications of this equation were attempted, including variables such as an average hourly wage index in the food marketing industry and a unit labor cost index for marketing farm food products,6 but we regard the specification presented here to be the most suited given our preliminary findings.) In summary, the composite marketing behavior relation of the cattle-beef sector is specified as follows: I *0 7 o o 2 Y1 Y4 y5 x0 x1 x2 H where y1 = PBEEFR, y4 = PBEEFF, y5 = QBEEFP, x0 = CONSTANT, x1 = DISPY, and x2 = CMKTGM. 6These results (using ZSLS) are reported in Appendix A. 67 3. Slaughter Supply of Beef Cattle at the Farm Total beef production in this study is considered as a flow into three components: slaughter, inventory of beef cat- tle for feeding purposes, and inventory of beef cattle for non- feeding purposes. We investigate and Specify a structural equ- ation for the slaughter supply response production - component here. Theoretically, we postulate that slaughter beef supply is in part a function of current period conditions (such as in- put and output prices, feed availability, weather, insitutional factors, and others); but that current slaughter is, also, in part a function of the producer decisions and commitments in previous periods. In this slaughter supply of beef cattle structural rela- tion the quantity of beef produced for slaughter (QBEEFP) and a farm price of beef cattle (PBEEFF) are specified as jointly determined. and PBEEFF is presumed to reflect current period (output) marketing conditions. The variable specified to ac- count for feeding (input) conditions is price of protein feeds 7 . . . (PPROTEIN). We speley PPROTEIN as an exogenous variable in 7Other variables considered in alternative specifications included a price index of feed grains, available feed grains (ex- cluding government carry—over, both for current and lagged periods), and available high-protein feeds. Some alternative specifications are reported in Appendix A. 68 this study8 (but we do so with some uneasiness; ideally, we would have preferred to incorporate PPROTEIN, and/or other feed economy variables, as endogenous in an expanded system; data availability, increased "computational costs" and other factors precluded our doing so in this analysis.) A major determinant of production capability in any given period, and hence indirectly of slaughter supply, is the level of beef cattle inventories at the beginning of the period. In this study, two aggregate inventory variables are considered; namely, the beginning (January 1) inventory on feed (IBEEFFl) and the beginning inventory not on feed (IBEEFNFl). We can think of IBEEFFl and IBEEFNFl as representing or summarizing the previous behavior of producers, in terms of the resources already committed to current (and future) production. Obviously, the specification of the two components rather than their sum implies a hypothesis that their respective effects on current slaughter beef supplies are not the same; and it seemed reason- able to expect a greater response per 1000 head of IBEEFFl than from IBEEFNFl. We regard the following factors as providing some support for our decision to specify PPROTEIN as an exogenouswvariable in this study: (a) high protein content feeds are used extensively in dairy rations throughout the United States, so PPROTEIN is not solely affected on the demand side by beef cattle and other meat production uses; (b) the impact of international trade in- creases the net elasticity of supply to domestic users; (c) feed grain price support programs have provided a'lower bound" exogenous effect on protein feed prices in most of the postwar period since protein feeds are close substitutes for feed grains; and (d) pro— tein feeds are generally storable and hence can be carried from one period to another. 69 In summary, our Specified slaughter supply of beef cattle relation is as follows: it. Y4: ys. x0. x3. x4. x5 (3) where y4 = PBEEFF, y5 = QBEEFP, x0 = CONSTANT, x3 = IBEEFFl, x4 = IBEEFNFl, and X5 = PPROTEIN. 4. Inventory Demand for Beef Cattle Retained for Feeding at the Farm In the description of the beef cattle production process (see Chapter II), we noted that beef feeding enterprises and cow— calf enterprises are largely separate Operations; and also that the major producing areas for each type of enterprise differ regionally in the United States. Both of these factors led to a consideration of two separate inventory relations in the model. A third factor was that the two inventory components (lagged) are specified separately in the beef supply relation, i.e., rela- tion 3, above. The first of these inventory components to be explained is defined as the number of beef cattle held for feeding on farms at the end of the current period (IBEEFFZ). The relation to be specified is referred to as a demand relation, but it is a de- rnamd relation for an "intermediate" commodity, i.e., a good ‘Which will serve as an input in a future production process. ffheoretically, one would expect to consider factors such as the ;price of the commodity demanded, expected price of the finished 70 product, prices of competing (substitute) commodities, expected costs of resources to be used in the production process, and factors associated with shifts in the demand relation. These theoretical guidelines led to the Specification of the price of beef cattle at the farm (PBEEFF) to represent both the price of feeders and the expected price of "finished" beef. The high correlation between an average price of feeders and PBEEFF (Simple correlation coefficient = .9706) was the main reason for Specifying PBEEFF in this case. Also, the current period PBEEFF was assumed to be a reasonable approximation of an expected price variable.9 Next, an average price of other livestock at the farm (POMEATF) was Specified as representing competing farm enterprises. If, in fact, other livestock prices have influenced beef cattle producers' inventory decisions, then it seemed plausible that the major changes would be made in the IBEEFFZ level, -- Since fed-beef producing enterprises would most likely compete with other livestock producing enterprises for the use of resources, e.g., feed, and possibly labor, capital, and equipment in areas where joint enterprises have been common. (Except for compe- 9 Several alternative specifications were tried in order to separate the effects described; for example, we considered both an average feeder cattle price series and an expected beef cattle price series (from Lerohl, M.: Ph.D. Thesis, Michigan State University, 1965, Expected Prices for U. S. Agricultural Commodities, 1917—62). We had difficulty obtaining statistical significance and plausible results. We believe the final Speci- fication is a meaningful and useful simplication. 71 tition in the use of the feed resource it is believed that a trend toward greater Specialization in livestock production has lessened the direct impact of other livestock prices on fed-beef inventory decisions.) Changes in inventory levels, like slaughter supply (egn 3), are largely influenced by production capability, which in any given year is importantly affected by the beginning level of inventory, IBEEFFl. Or, viewed in a slightly different manner, IBEEFFl reflects the previous period scale of feeding Operations, and the level of IBEEFFZ is expected to be related to this summary measure of the previous behavior of producers. Initially, alternative feed economy variables (e.g., available feed grains in the current period, PPROTEIN, and others) were specified as indicators of expected feeding conditions, but in this particular relation none of the variables considered contributed Significantly (statistically) to the explanation of the specified endogenous mechanism. Thus, no other variables were included in the final Specification. The specified demand for beef cattle to be retained for feeding is summarized as follows: I *1 ; I 4 y4 ye y7 X0 X3 ( ) where y4 = PBEEFF, y6 = IBEEFFZ, y7 = POMEATF, x0 = CONSTANT, and x = IBEEFFl. 3 72 5. Inventory Demand for Beef Cattle Not-Retained for Feeding at the Farm The second inventory equation is in principle quite Similar to the first, i.e., equation 4; however, heavy concen- trations of beef-cow and calf herds in the grassland and range areas of the United States limits, with respect to this relation, the degree of competition for resources between beef cattle and other livestock enterprises. Factors associated with the avail- ability of roughage feeds are also considered to be of greater importance in this equation. With these major differences in mind the number of beef cattle and calves not held for feeding on farms at the end of the current period (IBEEFNFZ) is Specified as being jointly determined with PBEEFF. The PBEEFF variable is believed to reflect both the price of the commodity demanded and an approxi- mate expected price for non-fed beef cattle in a future period. The beginning period inventory (IBEEFNFl) was included to reflect production capability, or scale of Operation in the preceding period. Finally, an average (of August, September, and October) range condition index (ARANGECI) is Specified to indicate the carrying capacity of ranges in the major cow-calf herd producing areas; and also to reflect implicitly the gen- eral availability of roughage feed which is a major input in the cow-calf production process. The economic specification of the inventory demand for 73 beef cattle not-retained for feeding is summarized as follows: y ya:X.x.x (5) 4' 046 where Y4 = PBEEFF, ya = IBEEFNFZ, X0 = CONSTANT X4 = IBEEFNFl, and x6 = ARANGECI. 6. Demand for Other Meat at Retail This relation is specified symmetrically to the demand for beef meat (relation 1). The price of other meat at retail (POMEATR) and the quantity of other meat consumed (QOMEATC) are considered to be jointly determined in this relation, with the price of beef at retail (PBEEFR) specified to reflect the influence of close substitutes, and consumers' income represented by the disposable income variable (DISPY). As before, DISPY also reflects the im- pact of the number of consumers on demand, because the pOpula- tion variable and DISPY were highly correlated over the sample period. The Specified demand for other meat at retail relation is summarized as follows: * . yl' Y3: y9. x0, x1 (6) where y1 = PBEEFRo, y3 = POMEATR, y9 = QOMEATC, x0 = CONSTANT, and x1 = DISPY. 7. Marketing in the Other Livestock-Meat Sector Except for poultry and poultry meat, the marketing seg- ment of the other livestock-meat sector is basically not much 74 different functionally or Operationally from the cattle-beef sector marketing segment. Assuredly, there are important differ- ences but in aggregate studies of this kind it is difficult to account for more than the dominant attributes of the segments involved. Consequently, the same conceptual framework was em- ployed to represent the aggregate behavior of firms in the mar- keting segment of the other livestock-meat sector as was des- cribed above (see relation 2) for the cattle-beef sector. Thus, as one relationship, the endogenous mechanism in- cludes both the price of other meat at retail (POMEATR) and the price of other livestock at the farm (POMEATF) as jointly de- pendent variables; and these variables are further considered to be jointly determined with the quantity of other livestock produced for slaughter (QOMEATP). Disposable income (DISPY) is Specified to reflect shifts in the derived demand for other livestock and also Shifts in the supply of marketing services associated with a given level of other livestock—meat. The cost of marketing meat per pound (CMKTGM) is specified to account for effects of changing costs of marketing on the endogenous mechanism of this relationship. In summary, the Specified marketing behavior relation in the other livestock-meat sector is as follows: * . ' 7 Y3: Y7: ylo, x0. x1 x2 ( ) where y3 = POMEATR, y7 = POMEATF, y10 = QOMEATP, x0 = CONSTANT, x1 = DISPY, and x2 = CMKTGM. 75 8. Supply of Other Livestock at the Farm The theoretical basis for the supply relation postulated here involves a rather straight-forward application of a dis- tributed lag model, such as has been develOped by Nerlove.10 This model will be develOped here both to present the logic underlying the final postulated supply relation, and to specify a relationship which itself has a quite practical usefulness. Let uS assume that current output Qt is a simple function 1* of an expected product price, Pt , and of an expected input price 2* (cost), Pt , so that: 1* 2* . Qt = a + b? + cP . (l) t t Now consider the following assumption about how producers might 9 a i* reasonably form the above price expectations, Pt . Let .* .* i P1 - P1 = Y(Pt_ - P (ii) t t-l l 12']. 1* which is to stay that the current expected price (Pt ) differs ' * from the previous period expected price (P: ) by a constant 11 . proportion (Y) of the difference between the actual preVlous i period price (Pt 1) and the previous period expected price 1* (Pt 1). Rewrite this expression to obtain: 10Nerlove, M.: "Distributed Lags and the Estimation of Long-Run Elasticities of Supply and Demand: Theoretical Consid— erations," Journal of Farm Economics, Vol. 40, May 1958; and also: Distributed Lags and Demand Analysis for Agricultural and Other Commodities, Washington: USDA, Ag. Handbook No. 141, 1958. 11Note that this assumes the same expectation coefficientY for output and input prices. i* i i* i* P = P - P + P t Y‘ t-1 t—l) t-l -— Pi (1 Pi* o o o _ y + -Y) t_l (111) . 1* Substitute Pt from (iii) in (i) to obtain: Q = a +th1 + (l-Y)P1* ] + clyP2 + (l-Y)P2* ] (iv) t t-l t-l t-l t—l Similarly, express Qt 1 as: p b 1* 2* Qt—l = a + Pt-1'+ cPt_l. (v) Now multiply Qt l by (l-Y) and subtract from Qt. The result can easily be shown to simplify to the following 1 2 = a + bP + cP + 1- Qt Y Y t—l Y t-l ( Y)Qt_l d+dPl cap2 a (') = v 1 2 t—l + 3 t-l + 4Qt-1 1 Relation (vi) is identical to the type of function that is Specified in this study. This relation will now be stated in terms of the variables used in this study. The quantity of other livestock produced for slaughter at the farm (QOMEATP) is con- sidered the endogenous (dependent) variable in this relation; and it is specified as a function of the lagged (1 year) price of other livestock at the farm (POMEATFL), the lagged price index of feed grains (PFEEDIDL), and the lagged quantity of other livestock produced for slaughter at the farm (QOMEATPL). The reader might note here that the di (i = 1,...,4) co- efficients are estimated in this study; but from these estimates 77 it is possible to derive estimates of a, b, c, and Y in relation d d d3 (i). i.e., a = -—l———-. b = -—3———-. c = ——————- and Y = l-dy. 1 - _ _ d4 1 d4 1 d4 The di are termed structural form parameters and they indicate the direct effect of their corresponding variables on Qt' In contrast, a, b, and c are coefficients which are assumed to repre- sent the long run influences of the expected prices on current output. Thus, estimates of both the short run and the long run supply response function for other livestock are obtained. (The presentation and analysis of these estimates are discussed in the empirical results chapter). Also, note that only one endogenous variable (QOMEATP) appears in this relation, and consequently,the OLS method of estimation is applicable in this case. In summary, the Specified supply of other livestock at the farm relation is as follows: y* : x . X . X . x (8) 10 O 7 8 9 where ylo = QOMEATP, x0 = CONSTANT, x7 = POMEATFL, X8 = PFEEDIDL, and x = QOMEATPL. 9 9. Other Livestock-Meat Sector Identity In this study the levels of domestic other livestock pro— duction for Slaughter (QOMEATP) and domestic other livestock- meat consumption (QOMEATC) are treated as separate endogenous variables, although both variables are measured in million 78 pounds of carcass weight equivalent. The difference in the levels has been principally due to net shipment of other live- stock commodities out of the U. S. market in the recent past; or, in any case, due to international trading. Also, military supplies are deducted from the total slaughter level prior to estimating the amount consumed by the population eating out of civilian food supplies; and a small part of the difference has been due to changes in commercial storage holdings from one period to the next. To a considerable extent each of these "alternative mar- kets" has been subject to institutional factors which are deter- mined outside of the system being considered. Thus, the differ- ence between QOMEATC and QOMEATP is Specified as being pre- determined; and for Simplicity, defined as net other meat im- ports (NOMIMPORT). Based on the above considerations the following identity is specified: QOMEATC - QOMEATP f NOMIMPORT Of course, no coefficient estimates need be determined in this relation. In the summary notation used previously, this postulated other livestock-meat sector identity is Specified as follows: Y9: Ylo’ x10 (9) Where y9 = QOMEATC, y = QOMEATP, and x = NONIMPORT. How- 10 10 ever, the economic specification includes the assumption that 79 the coefficients are i 1, i.e., such that y9 x ‘ ylo E 10' 10. Cattle—Beef Sector Identity International trading, military consumption and changes in commercial storage stocks are likewise factors which have caused a divergence in the level of beef cattle production for slaughter (QBEEFP) and the level of beef—meat consumption (QBEEFC). Again, international trade has been the dominant component; and, also, the amount of beef movement through these alternative channels has been determined largely by institutional and other conditions outside the system. Consequently, a cattle—beef sector identity is Specified as QBEEFC - QBEEFP I NBIMPORT where NBIMPORT was defined as this difference. In the format thus far used, the cattle-beef sector identity is specified as follows: . ' (10) o I 5 or more Specifically as y2' Y xll y -y5=xll where y2 = QBEEFC, y5 = QBEEFP, and x11 = NBIMPORT. The above 10 relations, taken as a system of relations, complete the Specification of the economic model. Next, the sta- tistical Specifications of the overall model (and of the alterna- tive estimators) are discussed; and the combined economic and statistical Specifications are then summarized in terms of a 80 statistical model. Th§_§tatistigal_Model All the structural relations are specified as linear in the variables and linear in the parameters. That is, each rela- tion, 1 (i = 1,2,...,10), can be represented as follows: ailyl(t) + ... + aigyg(t) + ... + “i,loylo(t) + Bioxo(t) + ... + Bikxk(t) + ... + Bi,llxll(t) + ui(t) = 0 (1) Where dig and Bik are the structural form coefficients to be estimated, yg and xk are the specified observable economic var- iables, and ui(t) is a random disturbance term. From the eco- nomic model the yg and xk that enter a particular equation are known; and for those not specified, the corresponding gig and Bik are assumed to be zero. The above equations are assumed to hold for each period t (t = 1,2,...,T). Since the economic relations are Specified to include only the theoretically most important variables, we do not expect the relations to hold exactly. Thus, the inclusion of %i(t) is required in the statistical specifications in order to Operationalize the estimation procedures. Other prOpertieS regarding the distribution of ui(t) must be specified (or as- sumed) however, and these assumptions are stated below. In matrix and vector notation the overall structural form can be represented aS follows: 81 A §(t) + B §(t) + fi(t) = o (t=1,...,T) (2) where A = (a. ] (i,g=1,...,10), B = [Bik] (k=0,l,...,ll), §(t) lg [y(:2...,y(t)] , x(t) = [xét),...,x(t)] , and fi(t) = [u(:),..., u‘t) 10] Note that (2) refers to only a single joint observation. To write the system in terms of all observations we can define: = [§(l).....§(t).....§r(T)]. (GxT) = fi(l).....§(t),...,§(T)], and (KxT) = Iu(1),....a(t),...,a(T)i,‘“ (GxT) where y(t), x(t) and fi(t) are defined above. With these de- finitions the structural form model, in terms of all T observa— tions can be written compactly as AY + BX + U = 0 (3) where A is of order (GxG)(G 10 in this particular model), y is (GxT) (T = 21), B is (GxK)(K = 12), X is (KxT), and U is (GxT) . At this point it is convenient to derive the reduced form relations, which are derived from the structural form model when the model is complete. Starting with (2) we can write A'lA §(t) + A-lB 2(t) + A'lfi(t) = 0 or I y(t) + I1x(t) + V(t) = 0 (4) where V(t) = [Vl(t),....Vg(t)n...VlO(t)1’ 82 Again this expression represents only a Single joint ob- servation but note the rows represent each y aS a function of only predetermined variables plus a disturbance term vg. Now, to write the system compactly in terms of all observations we can apply the same procedure, such that l 1 1 A'AY+A" Bx+A"U=0 or IY+HX+V=0 (5) where IIiS of order (GxK) and V is (GxT). One can note that the t-th column of (5) is indeed the set (4) above. In a nutshell, the primary objective from this point on was to obtain estimates of the structural form parameters which are implicitly specified in the matrices A and B in (3) above, and estimates of the reduced form parameters in Ilin (4). The struc- tural model is again summarized in Table 3.3 below, but with the emphasis here to note explicitly the structural form coef- ficient parameters which are Specified and estimated (or as— sumed) in this study. The combined economic and statistical Specifications thus far presented can now be conveniently summarized: a) Ay(t) + BS'<(t) + {3(t) = o (t = l,...,T), b) A is nonsingular (assumed), c) Certain elements of A and B are known to be zero, and d) Certain rows of A and B are known, a priori (and the corresponding relations are called identities). 83 a a a: Suaucoou nouuom noomnoauuou .oH H H H: >uaucocn nouoom quZUxOOuno>wA nonuo .m owe moo emu 0mm .7. 5.3m on» us xUOuuo>Hq uonuo no xammam .m use aha one Qfino an mes nouuum use: uxoouno>wq nocuo 0:» ca meauoxud: .h ”we owe coo . an 3o Hanuom as use: Monuo new vanadn .0 9mm emu one an emo Bunk on» an m:«uoo~ nan vocaauom uoz oHuuoo moon uou vcoaon >u0uco>CH .m nvu owe five HI vvo Shah 2.3 an mca000h new vocwnuom oHuunU moon now season aneucowcn .v mma one mme one a- vma aunt or» an cauuuo «own no uaansw nounmaaam .m Hmm awn Own mmo HI awe uouoom woumloHuuuo 0:» ca meauoxum: .~ Ham on mac NHo an Hanuom us moon now ocdavn .H o n v m H 0 OH o m m a:0 an 0% aux on an ax N.x X x x x ~x x x a h m» bu or x v» a N» H% w H N N d .d w .1 I m W _w H ;u M _w d .d nu H mm a mannmsn ... a...“ n... m I m m .a 3 M S m 3 3 a 3 a 3 oarzrnawnmlrrmrnnnann 8 O .c a a a I T. m d «u a Z 8 mmqm I m n; 1 1 I N .L Z QNZHZZNBHQmmm mbozmoonzm ANGO! AdUHBmHadam flue ho hfldZZDm UHBAZflIUm n.n OHQnB 84 Some additional statistical Specifications which will be assumed generally, are the following (see Goldbergerlz): e) f) 9) h) i) E [fi(t)] = 0 (t = 1,...,T), or E [U] = 0, i.e., the random error or disturbance term has an expected value of 0 for each relation i, and for each period t. E [u(t)fi'(t)] = z (t = 1,...,T), where z is a (GxG) nonnegative definite matrix, i.e., the contemporaneous covariance matrix of disturbances in the different equations is the same for all t (but note that Z is not assumed to be diagonal). E Lfi(t)u'(t)] = o (t,t' = l,...,T; t #'t'), i.e., the disturbance factor is temporally uncorrelated, or all lagged covariances between disturbances in the same or different equations are zero. It is assumed that the predetermined variables are generated by a stationary multivariate stochastic process with nonsingular contemporaneous covariance matrix 2 and that any dependence in the process is sufficiently weak so that (taking the variable as deviation from means) -1 T Plim T 22t=l §(t) i'(t) = XXX Further, it is assumed that the process generating the predetermined variables is contemporaneously uncor- related with the process generating the disturbances, So that E [§(t) fi'(t)] = E [2(t)] E [6' (t)] = o, and that any dependence in each of the processes is sufficiently weak such that plim 2 {=1 x(t) fi'(t) = 0, or plim 2 T’1 X'U = o, i.e., plim 23:1 xk(t) ug(t)/T = o for all k and g. This Specification (assumption) captures the idea that the predetermined variables are g9; deter- mined by the system at time t and thus are not dependent on the disturbances at time t. 12Goldberger, A. S.: Econometric Theory, New York: John Wiley and Sons, 1964, pp. 299—306. 85 Goldberger discusses these "generalized" statistical assumptions and one of the main reasons for introducing them is the presence of lagged endogenous variables among the set of predetermined variables. For example, exogenous variables may be distributed independently of all disturbances or simply uncorrelated with the contemporaneous disturbances; but lagged endogenous variables are assumed to be distributed independently of contemporary and succeeding disturbances, which is a stronger assumption than be— ing merely uncorrelated. In any case, the Specification of i) and h) above in terms of stationary stochastic processes is adequately general for denoting the necessary statistical as- sumptions in this study. j) Finally, in each structural equation, the coefficient of one jointly dependent (endogenous) variable may be taken as -l, a priori, i.e., a normalizing variable for each relation i (i = l,...,lO), for which the cor- responding aig* is taken to be -1. The implication of the procedure described in J) is that the coefficients dig and 8i are actually estimated only up to a k factor of prOportionality relative to a'g*7 and by assuming 1 a . 19* = -1. then yg* is in effect explicitly stated as a func- tion of the other endogenous and predetermined variables in the equation. Some Theoretical Comparisons of the Estimators Used in this Study Given the above set of statistical assumptions, i.e., (a),...,(j), one can note some of the theoretical differences 86 between the alternative estimators used in this study. First, consider the structural relations (after normalizing) in the form: Y 19* =zg#g* “is yg + i Bik Xk + ui ' so that on the right—hand Side there are both endogenous (yg) and predetermined (Xk) variables. This form appears Similar to the usual way of denoting a linear regression equation. However, because there are current endogenous variables on the right— hand Side, which are in general not independent of the distur- bance term, OLS coefficients are not even consistent estimates of the structural parameters ( a's and 8's). The ZSLS procedure, in essence, results in replacing the right—hand Side endogenous variables (yg, g#g*) with "apprOp— riate" estimates of y9 which has been shown to establish the consistency of the ZSLS estimators. The ZSLS procedure was develOped by Theil, and also independently by Basmann.l3 Theil has shown, further, that ZSLS is a Special case Of a whole family of (k)-class estimators. The UNK method in this study is one other special case of the (k)- class family of estimators, which has been prOposed by Nagar.l4 The k-value of the UNK estimator has plim (k-l) = 0, and this prOperty establishes, in general, the asymptotic prOperty of consistency for that (k)- 13See Theil, H.: Op.cit., 1961; and, Basmann, R. L.: Op.cit., 1957. 4 Nagar, A. L.: Op.cit., 1959. 87 class estimator. The LISE procedure was develOped prior to the ZSLS and (k)- class procedures by Anderson and Rubin.15 Their approach is an application of the maximum likelihood principle under the speci- fication that the structural disturbances are normally distri- buted and utilizing only restrictions on the structural relation being estimated. Under the normality assumption, estimates are consistent and are also asymptotically normal and efficient. However, Theil has Shown that LISE estimators are members of the (k)-class family, and hence consistent, with or without the nor- mality assumption.17 Finally, the BSLS procedure, as develOped by Zellner and Theil,18 is a system method of estimation, i.e., a "full in— formation" method which makes use of restrictions on the para- meters of the full system in estimating each structural rela- tion; and it is a system method in that all the structural re- lations are estimated Simultaneously. 3SLS is a consistent 15Anderson, T. W. and Rubin, H: Op.cit; see also: Cher- noff, H. and Rubin, H.: "Asymptotic Properties of Limited In- formation Estimates Under Generalized Conditions," in Studies in Econometric Method, W. C. Hood and T. C. KOOpmans, editors, op.cit., 1953, pp. 200-212. 6For definitions of these terms, see, for example: KOOpmans, T. C. and Hood, W. C.: "The Estimation of Simultan- eous Economic Relationships," in Studies in Econometric Method, W. C. Hood and T. C. KOOpmanS, editors, Op.cit., 1953, pp. 128- 131. l7Theil, H.: op.cit., 1961, pp. 231—232, 334—336. 18Zellner, A. and Theil, H.: op.cit., 1962. 88 estimator provided the "starting" estimates are consistent; and Since more information regarding the system is utilized, the 3SLS method is asymptotically efficient relative to the "limited information" procedures described above. This very brief summary of the properties of the alterna- tive estimators is perhaps sufficient to indicate that the prin— cipal theoretical differences are based on asymptotic properties. We know only a limited amount about small sample characteristics of the alternative estimators as indicated primarily from Monte Carlo studies.19 Among the methods employed herein, the 3SLS procedure is presumably the most suited estimation method from the standpoint of asymptotic efficiency. However, one should note that it iS generally believed that the system methods (e.g., BSLS and Full Information Maximum Likelihood) may be more sen- sitive than single-equation methods to Specification errors in the model as a whole. Sample Period and Data Annual time series data for 1936—41, 1949-1963 were used for this study. The main reasons for excluding observations prior to 1936 were non—availability of data series for some variables used in this study (particularly prior to 1930), the 19 For a summary of much of the Monte Carlo studies to date, see: Johnston, J., Op.cit., 1963, Chapter 10, pp. 275— 295. 89 abnormal relationships due to the general economic depression (and drouth) in the early 1930's (including processing taxes levied on meat packers from 1933-1935), and important structural changes (in general, throughout the consumer, marketing and producer segments), many not having occurred until the late 1930's. Observations for the war years, 1942-1946, were ex- cluded because of abnormal relationships (due partly to price controls and rationing in the meat economy); and 1947—1948 observations were also considered to reflect abnormal condi- tions due to adjustment lags, especially in the cattle-beef sector (actually, some 1948 data are used because lagged var- iables are Specified). From a positive standpoint, the sample period is presumed to reflect a "normal" period (generally a period of economic growth with price relationships determined in the marketing system, albeit price supports of some farm feed commodities have prevailed throughout the postwar period). U. S. annual time series (secondary) data were obtained pri- marily from the records of government departments and agencies. The actual data used are presented in Appendix C, where Specific sources for the series used are also cited. The data were ac— cepted as accurate without allowances for errors of observa- tion having been made in the estimation procedures. CHAPTER IV EMPIRICAL RESULTS In the first section of this chapter, the structural form coefficient estimates obtained from the alternative estimators are presented and discussed. In addition, a number of other statistics are presented which are useful for evaluating the fitted relations; namely, estimated standard errors of the co- efficients, k-values, coefficients of determination (R2's), and Durbin—Watson statistics. For all the estimators except OLS, standard errors are based on asymptotic formulas. The Rz's and the Durbin-Watson statistics have been developed for OLS estimation, but the same formulas were used to calculate similar statistics for the Simultaneous equations methods. Since we focus on a particular endogenous variable (due to normalizing) in each relation, there is an intuitive appeal to interpret these statistics in the usual manner; however, in all but the OLS procedure, the reader Should note that the R2'S and the Durbin-Watson statistics are not strictly applicable. Never- theless, it is felt that these statistics do provide additional comparisons among the alternative estimators. The following sections include additional analyses of 90 91 the fitted structural equations (tests of identifiability of the structural relations, the long run slaughter beef supply impli- cations of our estimated producer-segment structural equations, and conditional explanations of the normalizing endogenous var- iables over the sample period); then the implications of the reduced form estimates as forecasting mechanisms are considered; and finally, some comparisons of estimates from this study with related statistics from other studies are discussed. The main purposes of this chapter are to present the main findings of this study and to relate our results to other relevant research results. AS stated in the Introduction, Six alternative estimators were employed: (1) 3SLS, (2) ZSLS, (3) UNK, (4) LISE, (5) OLS, and (6) IBSLS. Zellner and Theil recommend that ZSLS estimates be used as starting estimates for 3SLS (to be referred to as 33LS(2$LS)); however, the only prOperty required of the start- ing estimates is that they be consistent; so, for comparative purposes, the 3SLS procedure is applied using UNK and LISE beginning estimates (and these estimates are referred to, re- spectively, as 3SLS(UNK) and 38LS(LISE). "Converged" I3SLS estimates are presented, but no evaluation is attempted at this time. It is noteworthy that the IBSLS estimates begin- ning with ZSLS, UNK, and LISE estimates did converge in each case to the same values for all coefficients estimated 92 1 (although, relatively faster when started with ZSLS). Structural Form Parameter Estimates For convenience in discussing the results, the 38LS(ZSLS) estimates are generally interpreted in the greatest detail, with comparative statements made regarding the other estimates. Summary tables of the statistics presented are included for each equation on the page immediately following the introduction of the respective equation. A standard table format is used throughout. Namely, the estimated structural coefficients are listed first, and their estimated standard errors are directly beneath; k-values are presented whenever applicable (other- wise denoted by n.a. meaning not applicable); R2 's (coefficients of determination calculated as if the equation had been fit by OLS) and D. W. (Durbin—Watson) statistics complete the informa- tion presented in the tables. The D. W. statistics are gen— erally used to test for autocorrelation (serial correlation) of the disturbances in regressions, but Since the basic assump— tions for applying the Durbin-Watson tables are violated by the lThe IBSLS(ZSLS) procedure was applied for 200 interations (2.83 seconds per iteration) and the coefficient estimates were "converged" (in terms of a maximum absolute change ratio, for an coefficient, from the preceding iteration, to the order of 10‘ ). The IBSLS(UNK) and IBSLS(LISE) procedures were each applied for' 100 iterations and the coefficient estimates were equivalent to the number of decimal places reported (for each of the proce- dures). The estimates were obviously converging to the same limits irrespective of the starting estimates used, i.e., either ZSLS, UNK or LISE. 93 nature of our equations and/or estimation procedures, we do not present any test results, but simply give the statistics them- selves for descriptive or comparative purposes. (It may be noted that a D. W. statistic value less than 2 is an indication of posi- tive serial correlation in the calculated (sample) residuals, while a value greater than 2 is an indication of negative serial correlation.) 1. Demand for Beef at Retail2 Using 3SLS(ZSLS), the estimated coefficient of each var- iable in the demand for beef at retail relation has its expected sign and is statistically significant. The coefficient of QBEEFC is negative (-.00676) thus indicating that increases in the level of beef consumption are associated with lower retail 2 . The Single equation results reported here for this equa- (ZSLS, UNK, LISE) were" computed with NBIMPORT not included (All 3SLS Fion in the set of predetermined variables in the system. gcmputations, however, included all the predetermined variables 11" the system.) The resulting single equation estimates have rIGEarl)? the same asymptotic prOpertieS as would estimates com- plated With NBIMPORT included (in particular, they are consistent, ~Lll): Presumably somewhat less efficient). The ZSLS estimates for 1:‘Ji'iis equation were recomputed with NBIMPORT included (in the set Q 2E predetermined variables in the system), a similar recomputa- ion was also done for a corresponding reason on equation 6, and he resulting 38LS(ZSLS) estimates for _a_ll_ equations were also thained. These results are summarized in Appendix E. In all Q $568 the actual numerical coefficients obtained differ only r3~e<31_-'193|-'J:31y from those reported here. 3An estimated coefficient will be said to be "statistically % ignificant" or "significantly different from zero" when the atio 0f the coefficient to its standard error is 2 or greater. This corresponds roughly to an (asymptotic) significance level <3 If about 5%, 94 .cofluumm on» mo mcflccflmmfl mau um Ummmsomflo mum mHOQamm 0cm umEmOm menses 00m0. Hm.0 H¢00.0 05000. 0N.H mmmm. .m.c Hmom. m0.mm Hum¢.0 h©000.l 0.HI QOMH A: mafia. N0.hm mwmm. m0m00. ©H.H avam. .m.c News. 00.Hm mafia. mm000.l 0.HI Amquvmqmm Am mmmo. vm.h mmoa. 55000. 0H.H vmmm. .m.c wmom. ha.mm mhmv. 05000.I 0.HI AXZDVmAmm Am 0mm0. 0H.m mhaa. 00000. ¢N.H vomm. 0 0Hmm. H0.hm thm. wwhoo.l 0.HI mAO Am Hams. 0m.hHH mNNh.H mmoao. 00.H Nmmo. m©.m omen. v0.0vH mth.HI 0NBH0.I 0.HI MMHA A0 unmo. 0m.m mvma. 00000. hN.H Homm. 0N.H «Ham. mm.mm summ. 0¢500.I 0.HI KZD AU ohmo. 0N.m mfima. 00000. 0N.H momm. H 0Hmm. 0¢.mm hmmm. ¢Vh00.l 0.HI mqmm An NNmo. mm.h mmoa. whooo. ma.H NNmm. .m.: vmom. N0.mm mans. 05000.I 0.HI Amqmmvmqmm Am .3.Q mm M MmmHQ BZ¢BmZOU m8¢m20m 0mmmm0 mmmmmm mmUHBmHadam Qmfiflflmm D24 mmaZH ¢.¢ wHQMB 106 These three components are considered as jointly related pro- ducer segment behavior variables, and the purpose of our approach is to account analytically for such interdependencies. The re- sults for the inventory demand for beef cattle retained for feeding purposes equation are presented next. The signs of the estimated coefficients in this relation are as expected (except for the POMEATF coefficient based on LISE). Two estimated coefficients, that of POMEATF and the CONSTANT, are generally not statistically significant, however. The positive PBEEFF coefficient estimate indicates that increases in the level of ending inventory retained for feeding (IBEEFFZ) are associated with increases in farm prices. It should be noted that PBEEFF was postulated to represent both the cost of feeders and an approximate expected product price (see the Economic Model section of Chapter III). When PBEEFF represents the former, then we would expect a negative assoc- iation with IBEEFFZ; and in contrast, a positive association was expected in the latter case. Assuming that the specifica- tion holds reasonably well, then the coefficient estimate-ob- tained must be interpreted as a net result, i.e., on the average the 925 response to an increase in farm price is an increase in the ending inventory of beef cattle on feed. Based on the 3SLS (ZSLS) procedure, an 6(IBEEFF2/PBEEFF) = + .013 was calcu— lated, i.e., a one per cent increase in the farm price of beef 107 cattle is associated with a .013 per cent direct increase in ending inventory on feed. With regard to POMEATF, the negative coefficient estimate implies that there has been some competition for resources among competing farm enterprises; and €(IBEEFF2/POMEATF) = - .181. Since the underlying coefficient estimate is not sta- tistically significant, we do not place too much reliability on this particular derived elasticity estimate. The beginning inventory (IBEEFFl) was postulated as one measure of current period production capability or previous period scale of Operation and the coefficient estimates obtained indicate its importance; the corresponding e(IBEEFF2/IBEEFF1) = + .922, and the reduced form €T(IBEEFF2/IBEEFF1) = + .886. In actuality, the IBEEFFZ component of total inventory has been largely, if not almost entirely, composed of animals which were classified as IBEEFNFl at the beginning of the period. Thus, it seemed reasonable to expect this variable (IBEEFNFl) to have had an effect on IBEEFFZ. See Appendix A for an alternative specification which included IBEEFNFl as a variable in this relation (fitted by 2SLS). 5. Inventory Demand for Beef Cattle Not Retained for Feeding at the Farm In this relation, the second component of total ending inventory (IBEEFNFZ) is the leading endogenous variable, and 108 hh.mm NmHo. Nb.h©mm m®.m© no.a nmmm. .m.c om.vm oomo.a m®.momoHl HH.N®m O.HI mAmMH A: mm.g¢ memo. mo.©¢mm VH.N> mo.H mmmm. .m.c OH.HB ommo.a Nv.mmmHHI NN.Nmm O.HI Amquvamm Am 0H.m¢ omao. m.mH¢m m>.h© mo.H hmmm. .m.c mm.om m©NO.H b.005NHI Vm.mmm O.HI AXZDVmAmm Am mo.mm mono. H.moav mH.mm no.a mmmm. O mm.mm vmmo.a ¢.mmoaal Ho.hmm O.HI mQO Aw ab.oo mmmo. ®.mm©¢ om.¢m OO.H NNmm. hm.© Hm.¢m mmmo.H m.NNmHHI ma.hmm O.HI mmHA AU hv.mm momo. m.mhag hh.®h h0.H mmmm. mm.a no.hm H¢N0.H H.mmHHHI mm.¢hm O.HI &ZD A0 mv.mm momo. ©.Hhag gh.oh no.H hmmm. a HH.©m mmmo.a N.mMHHHI mm.hhm O.HI mqmm AQ ON.m¢ mmao. m.ma¢m Nh.h© mo.H hmmm. .m.c 00.55 mwmo.H m.v©mNHI m©.mmm O.HI Amflmmvmqmm Am .3.Q mm M HUMGZZH m.¢ magma "Eddm HEB Bfi GZHQmmm 109 we can interpret the estimates in terms of their direct effect on IBEEFNFZ. The coefficient estimates for PBEEFF are positive and statistically significant. Based on BSLS(ZSLS) the cor- responding €(IBEEFNF2/PBEEFF) = + .147. As in the other in- ventory relation, the PBEEFF variable was postulated to repre- sent both the cost of holding beef cattle and an expected product price. Thus, the PBEEFF coefficient estimate, and the correspond— ing elasticity estimate, refer to the net result of these two offsetting factors. The beginning period non—fed inventory variable (IBEEFNFl) coefficient (+1.0263) indicates that absolute changes in IBEEFNFl have, on the average, been associated with even larger absolute changes in IBEEFNFZ. In relative terms, the e(IBEEFNF2/ cT IBEEFNFl) +.989 in the structural relation (and - (IBEEFNFZ/ IBEEFNFl) + .702 based on the reduced form 3SLS(2SLS) coef— ficient estimate). In this relation an average range condition index (ARANGECI) was specified to represent the carrying capacity of the prin- cipal range and grassland areas; and also, indirectly, the gen- eral availability of feedstuffs in the principal cow-calf breed- ing herd regions. An increase in the index value would imply improved range conditions and generally more roughage feedstuffs, so that one might eXpect a positive coefficient on the ARANGECI variable. In this fitted relation the estimated coefficient is 110 positive and "almost" significant based on the 38LS(ZSLS) pro- cedure, i.e., the ratio of the estimated coefficient to the estimated standard error is about 1.8. Both the structural form and the reduced form correspond- ing elasticity estimates for IBEEFNFZ with respect to ARANGECI were estimated as + .128 (based on the 3SLS(28LS) coefficient estimates). The reliability of these estimates is somewhat questionable, the high standard errors being perhaps partly due to the fact that average range conditions over the sample period were not dramatically different from "normal" for any sustained lengths of time. 6. Demand for Other Meat at Retail7 The estimated coefficients in this demand relation have their expected signs and they are all statistically significant for each of the estimation procedures. The LISE estimates are 7The single equation results reported here for this equa- tion (ZSLS, UNK, LISE) were computed with NOMIMPORT not included in the set of predetermined variables in the system. (All 3SLS computations, however, included all the predetermined variables in the system.) The resulting single equation estimates have nearly the same asymptotic prOperties as would estimates com- puted with NOMIMPORT included (in particular, they are consistent, but presumably somewhat less efficient). The ZSLS estimates for this equation were recomputed with NOMIMPORT included (in the set of predetermined variables in the system), a similar recom— putation was also done for a corresponding reason on equation 1, and the resulting 3SLS(ZSLS) estimates for all equations were also obtained. These results are summarized in Appendix E. In all cases the actual numerical coefficients obtained differ only negligibly from those reported here. 111 mmeo. ma.a maeoo. aeoo. om.H omam. .m.o Hmem. ma.om momoo.u mmmo. o.Ha mummH A; omoo. mo.HH maaoo. ommo. em.H Hmam. .m.o mmmm. mm.mm memoo.u mono. o.H- Amquvmumm Am mmmo. mm.o mmaoo. eoeo. mm.a maam. .m.e mmom. om.mm mmmoo.n oaoo. o.Hu szovmqmm Am Hamo. mH.o emaoo. mono. m~.H mmmm. o momm. om.em oomoo.u emom. o.Hu mqo Am omoo. oH.mH nemoo. omma. mv.H mooo. ao.a mmam. mm.oo eoaao.u moan. o.Hu mmHu at maoo. on.HH maaoo. mooo. ee.a oaom. o~.H omom. an.am ammoo.n omao. o.H- x2: Au omoo. mm.aa maaoo. memo. oe.H mmam. H swam. om.om emmoo.u meow. o.H- mqmm in Hamo. ~o.m mmaoo. omoo. em.H Neda. .o.e eamm. om.~m memoo.u ommo. o.Hu Amammvmqmm am .3.o mm x ammHa ezeemzoo oe ( PBEEFR/POMEATR) = + .383; the latter estimate was calculated above in relation 1, i.e., demand for beef at retail). In this demand relation, a negative coefficient estimate for QOMEATC was obtained (as expected), and the corresponding €(POMEATR/QOMEATC) = - 2.277. (Another comparison with the re- tail beef demand relation is that 6(PBEEFR/QBEEFC) = - 1.043. These results are commensurate with stating that the demand for beef is more "price elastic" than the demand for other meat at retail, i.e., based on considering the reciprocals of the above structural form elasticities of prices with respect to quantities as "price elasticities". A price elasticity is the common expression for an elasticity of consumption (quantity) with respect to the price of the good consumed.) Finally, in this relation, the DISPY variable (which is also considered to reflect the effects of population) estimated Similar findings have been reported elsewhere; see, for example: Riley, H. M.: Some Measurements of Consumer Demand for Meats, Ph.D. Thesis, Michigan State University, 1954. 113 coefficient is positive and statistically significant. The corresponding €(POMEATR/DISPY) = + 1.102; and the CT(POMEATR/ DISPY) = + 3.736. While both estimates are positive, the total effect of DISPY, as indicated by the reduced form estimate, is considerably larger than the direct effect of DISPY on POMEATR. (Continuing our comparisons with the retail beef demand equa- tion, we note that e (PBEEFR/DISPY) = + 1.230 and €T(PBEEFR/ DISPY) = + .3.277.) The lower "Rz's" in this equation, rela- tive to the other equations in general, should be noted. Ap- parently, important variables have not been included in this relation based on the "Rz's" as comparative indicators. 7. Marketing in the Other Livestock-Meat Sector The normalizing variable in this relation was POMEATF, and this tends to place the main focus on interpreting this relation as a derived demand for other livestock. The signs for all estimated coefficients are as expected and statistically significant, except for LISE. The LISE estimates are particu— larly unreasonable in this relation. Based on the 38LS(2SLS) coefficient estimates, then for POMEATR, a corresponding e(POMEATF/POMEATR) = + 1.053. We regard this estimate as plaus- ible, but in contrast we note that €(PBEEFF/PBEEFR) = + .419 was derived above in the cattle—beef sector marketing—firm behavior equation. The negative coefficient estimate for QOMEATP was ex- 114 shoe. omao. mm.e mmooo. memo. oo.a mono. .m.c amae.u memo. mo.mm mmaoo.u veem. o.au mummH A: mome.o aom~.H mm.~ee moomo. mmmm.m mo.a mama...m.c ~mmm.a- omao.m «n.amo mmeoo.u mmom.au o.H- amquvmqmm Am mead. mmao. em.e omooo. nemo. oo.H demo. .m.o ammm.u momo. no.em Hmaoo.n mmmm. o.Hu szovmqmm Au Neva. amao. mo.m emooo. ammo. am.a ammo. o oamm.u momo. ee.mm oHHoo.u momm. o.a- mqo Am eHHm.aooH momm.emm mo.omoae ooaaa.o eomo.am Ho.m o.maau mm.m maeo.meu ovoe.a om.aooa oaaaa.u memo.~ o.Hu mqu Au amma. mmao. em.o eeooo. oomo. mm.H memo. om.a enem.u ammo. oe.em Hmaoo.n omem. o.Hu x2: Au omma. mmao. m~.o evooo. oomo. em.H ommo. a meem.n emmo. em.v~ omaoo.u veem. o.Hu mama in mmHH. mmao. mm.e omooo. memo. oo.H memo. .m.o ommm.n eomo. oo.vm omaoo.u momm. o.Hu Amqmmvmqmm .z.o mm x zoemzo wamHn ezeemzoo aeemzoo «Benson maemsoa 5 [HI mUHBmHaflam QMBHA mmmBO Mme 2H UZHBMKm¢S h.v OHQMB 115 pected, insofar as this composite marketing-firm behavior re- lation reflects a derived demand at the farm. The correspond- ing 38LS(ZSLS) €(POMEATF/QOMEATP) = - 1.060. (In comparison, the analogous estimate from the cattle-beef sector marketing relation is €(PBEEFF/QBEEFP) = - 1.755). With regard to the DISPY variable, the positive coeffic- ient estimate implies that shifts in the derived demand for other livestock are positively correlated with consumers in- come (and, in part, other factors such as population or trend). An €(POMEATF/DISPY) = + .460 was calculated (and this estimate is less than the analogous estimate for beef cattle, i.e., €(PBEEFF/DISPY) = + 1.734; which seemed plausible given the apparent shift in beef—meat"consumption relative to other meats). Also we note the reduced form estimate eT(POMEATF/ DISPY) = 4.392. Turning to the cost of marketing meat per pound (CMKTGM) variable, the negative estimated coefficient (and both the structural and reduced form elasticity estimates, i.e., ‘MPOMEATF/CMKTGM) = - .625 and €T(POMEATF/CMKTGM) = - .751) indicate negative effects of increases in CMKTGM on POMEATF. In the structural equation, we expected a negative coefficient estimate, ceteris paribus, i.e., given especially the price of other meat at retail. 116 8. Supply of Other Livestock at the Farm The coefficient estimates have their expected signs and are statistically significant in this supply response relation. Note that the OLS procedure is theoretically applicable, and also that the ZSLS, UNK, and LISE procedures would yield identical single equation estimates. The 3SLS procedure yields different estimates because additional "information" from the estimated 2 in the OLS disturbance covariance matrix is utilized. The R fit indicates that .9732 percent of the variation of the endo- genous (dependent) variable (QOMEATP) is explained by the in- cluded variables. Based on the 38LS(28LS) estimator, the POMEATFL coeffici- ent estimate of +244.89 indicates that current output is dir- ectly associated with changes in previous period prices of other livestock, as expected. The corresponding e:(QOMEATP/ POMEATFL) = + .284, which indicates a relatively inelastic supply response function in the short run. This estimate supports the generally held belief that such farm supply rela- tions are inelastic with respect to price in the short run (1 year in this case). One might note that this elasticity represents both the "direct" and the "total" effects of POMEATFL on QOMEATP since the structural form and the reduced form relations are the same. As expected, the lagged feed grains price index is found 117 Hmeo. om.mH mo.om a.mHmH ma.~ ammo. .m.e amen. am.omH+. mm.oe~ m.am~ma o.H- mummH rm ameo. mm.me ~o.ae H.9ooa em.~ mmeo. .m.e Nome. ma.mmu oo.HmH m.oemo o.H- amququmm at oeeo. ma.ma me.am o.omafl om.~ ammo. .m.e meow. mm.oo- so.e- a.mooo o.H- szsvmqmm Ao ammo. oo.o~ oo.ao n.aomm om.m «mam. o mono. ma.mau no.5ma m.mamm o.Hu moo in Hmeo. em.ma mm.am H.oama om.~ Hana. .m-o mmom. m~.oou om.em~ H.mmom o.H- amqmmcmumm Am .s.o mm x anaemzoo gaHommaa amaemzoa, azeamzoo oeemzoo g mUHBmHB¢Bm 999¢Amm 92¢ mmB¢SHBm9 B29HUH99900 «22¢9 929 B¢ ¥UOBm9>H9 29290 90 mummbm m.¢ OHQMB 118 to be inversely associated with QOMEATP in the current period. Based on the coefficient estimate obtained from the 3SLS(2SLS) procedure, the 6(QOMEATP/PFEEDIDL) = - .662. The current level of production of other livestock for slaughter (QOMEATP) is found to be directly related to recent past behavior of producers. The positive coefficient estimate of QOMEATPL corresponds to an €(QOMEATP/QOMEATPL) = + .784. When this supply equation was specified in the Economic Model section of Chapter III, it was postulated as having been derived from a more basic theoretical relation, i.e., Qt — a + th + opt (1 ) where Pi* = YPi + (1 ~Y)Pi* (i = 1.2) (ii') t t—l t-l i* . and where the P were defined as expected product and input t prices. Further, it was noted that estimates of a, b, c, and Y could be derived from the structural equations coefficient estimates. Let Qt = QOMEATP, Pi* = the expected price of other live- stock at the farm, and P:* = expected price of feed grains, then the estimates of a, b, c, and Y are as follows: a = 51815. E = 1173. 6 = -502. and Y = .1917 119 The corresponding elasticities of QOMEATP with respect 1* to the P t , calculated at the mean values of the actual POMEATF and PFEEDID variables9 are: €(QOMEATP/POMEATF*) = +1.4352, and €(QOMEATP/PFEEDID*) = —3.3825. The long run supply elasticity estimates are approximately five times as large in magnitude as the short run (l—year) estimates. Summary ofggtatistical Tests for the Identifiability of thejgtrugtural Relations In this particular model, all of the behavioral relations, i.e., relations l,..., 8, were "overidentified", a priori, based on the necessary order condition that (g—l)<(K-k). That is, in each relation the number of predetermined variables outside the relation but in the system (K-k) was greater than the number of endogenous variables in the relation less one (g-l). The validity of the a priori exclusion of predetermined variables is subject to uncertainty, and alternative procedures have been developed to test for the identifiability of a structural relation. In the following table (Table 4.9) the results of a test develOped by Hood and KOOpmans10 for the LISE estimator are summarized. The test statistic T loge (i1 92) has an asymptotic 9For the 1936-41, 1949-63 sample period, the mean level of POMEATF was 20.46 (dollars per cwt.) and the mean level of PFEEDID was 112.65 (1957-59 = 100). 10Hood, W. C. and Koopmans, T. C.: Studies in Econometric Method, New York: John Wiley and Sons, Cowles Commission Mono- graph No. 14, 1953, Chap. VI, pp. 183-84. 120 Table 4.9 SUMMARY OF A TEST FOR THE IDENTIFIABILITY OF THE STRUCTURAL RELATIONS (HOOD AND KOOPMANS PROCEDURE) Test Degrees Critical Conclusion: statistic: of value identified or Relation Tloge (1315) freedom x295 not identified 1 62.12 8 15.51 Identified 2 68.13 8 15.51 " 3 104.40 8 15.51 " 4 61.44 9 16.92 " 5 94.59 9 16.92 " 6 39.16 8 15.51 ” 7 53.75 8 15.51 " 8 n.a. - - - Chi—square distribution with (K-k) - g + 2 degrees of freedom, such that if the test statistic is greater than or equal to the corresponding critical value one can conclude that the structural . . . . . . . ll . . relation in question is identified. In every case it is con- cluded that the structural relation is identified at the .05 significance level. One should note that the test is based on an asymptotic distribution, and experimental results suggest that this distribution may not be well approximated in finite 12 sample sizes. Some reservation is therefore placed on the llSee, Ibid., p. 183, for a more complete statement of the hypothesis being tested, and the authors comments that this test is actually a....."test of nonidentifiability rather than of identifiability." 12See, Johnston, J.: Econometric Methods, New York: McGraw— Hill, 1963, pp. 263-64; and Basmann, R. L.: "On Finite Sample Distributions of Generalized Classical Linear Identifiability Test Statistics," Journal of the American Statistical Association, Vol. 55, 1960. 121 reliability of these results. Basmann has prOposed an alternative test for the identifi- ability of structural relations which he considers to be more suited for typically small sample sizes. The test statistic is defined as a function of the least variance ratio (which corre- sponds to )1 in the above test and also to the reported k-value for the LISE procedure); namely, the test statistic is T - K $, (K-k)-g+l minus one (XI—1). Basmann shows that this A Where $ is 11 statistic has an Fa[(K-k)-g+l, T-K] distribution such that for T - K A ¢->-F (K-k)-g+l_ a [(K-k)-g+l, T-K] we would reject the null hypothesis that the "excluded" pre- determined variable coefficients were zero, i.e., H :8 = 0, Where 82 denotes that set of coefficients. The results of the Bassmann test for the identifiability of structural relations in this model are summarized in Table 4.10 (for the LISE estimator). In this case, for relation 5, the test statistic (5.28) is greater than the corresponding F- critical value (3.14) so the null hypothesis (HO:8 = 0) is 2 rejected. All of the other relations are "identified" based 13 on this test. Since the LISE estimator tended to yield ques- tionalbe parameter estimates in our model in general (relative 13 We note that this test is not a strict identifiability test, but rather a test of whether the excluded variable co- efficients can be considered equal to zero (versus non zero). 122 Table 4.10 SUMMARY OF A TEST FOR THE IDENTIFIABILITY OF THE STRUCTURAL RELATIONS (BASMANN PROCEDURE) W Test statistic: Critical value: Conclusion: Relation «p T - K $ F [(K-k)-g+1,T-K] reject H :8 =0 (K-k)-g+l .05 0. 2 not reject l 2.69 2.99 3.02 not reject 2 1.35 1.35 3.18 " 3 2.10 2.10 3.18 " 4 1.98 1.78 3.14 " 5 5.87 5.28 3.14 reject 6 .97 1.08 3.02 not reject 7 1.83 1.83 3.18 " 8 n.a. - - - to the alternative estimators), the results of these tests should probably not be regarded as conclusive. Long Run Beef Supply In this section we explore the "long run slaughter beef supply" implications of the estimated model. That is, what would be the long run response of the producer segment of the model to specified changes in prices of its products (beef and other meat), with "other things" held constant? The producer segment consists of four equations (no.'s 3,4,5 and 8) with six endo— genous variables (QBEEFP, IBEEFFZ, IBEEFNFZ, QOMEATP, POMEATF and PBEEFF). For the purpose of this analysis, two of the six, namely, the two Whose effects we are exploring, are treated as 123 predetermined (in effect, specified or "controlled" by the in- vestigator). The remaining four endogenous variables continue to be treated as endogenous; indeed, it is precisely the effects .gg the remaining endogenous variables (in particular; the effect on the supply of slaughter beef) 2f changes in the "controlled" variables, through the workings of the producer segment structural equations, which we wish to explore. We have, thus, four structural producer—behavior equations, with four endogenous variables, two "controlled" variables and eight predetermined variables. More specifically the predeter- mined variables consist of both lagged endogenous variables (IBEEFFZ, IBEEFNFl and QOMEATPL) and exogenous variables (CONSTANT, POMEATFL, PPROTEIN, ARANGECI and PFEEDIDL). (Actually this analy- sis is relevant only because lagged endogenous variables are present in the producer segment structural equations.) The pro- cedure will be to specify certain initial values for the lagged endogenous variables, certain fixed values for the exogenous variables and a certain set of alternative values for the con- trolled variables, allowing each choice of the latter values to prevail over some specified number of years or ”time horizon", and then to compute the resulting values of the endogenous variables (in particular the supply of slaughter beef) that would be generated by the four structural equations. Further, the lagged endogenous variables (for each period after the first one) 124 take on the computed values of their corresponding endogenous variables from the immediately preceding period (in effect, this allows the endogenous variables to change, in a manner conditioned by the fitted producer-segment structural equations, over the time horizon considered). Computationally, this procedure is readily done by rewriting the four equations in "reduced form" with the four endogenous variables as dependent and including the two controlled variables on the right side as predetermined. For expository purposes this reduced form can be written as follows, with the endogenous var- iables predetermined variables and the estimated reduced form coefficient matrix partitioned as indicated: QBEEFP = 1? IBEEFFl + %2 PCONSTANT-i + £3 POMEATF IBEEFFZ IBEEFNFl POMEATFL PBEEFF IBEEFNF2 QOMEATPL - PPROTEIN (4 X 2) (2 X l) QOMEATP ARANGECI (4 x l) (4 x 3) '(3 x 1) (4 x 5) FFEEDIDL_ (5 x l) or, for convenient reference, as Y1 = '71 x + é} x + 1? X Y2 1 l 2 2 3 3 As initial values for X1 (lagged endogenous) variables we specified their means (for the 1936-41, 1949-63 sample period); the fixed values for the X2 (exogenous) variables were also set at their mean levels; and for the X3 ("controlled") variables, POMEATF was set at its mean and PBEEFF was initially set at $13.00/cwt.. In the meanner described above Y1 and Y2 were 125 estimated for 50 periods. This procedure was repeated, changing only PBEEFF by $.25/cwt. increments (e.g., $13.25, 13.50, 13.75, ...), until PBEEFF was equal to $30.50/cwt.. The estimates of particular interest in this section are Yl (QBEEFP) and the cor- responding "controlled" values of PBEEFF for each time horizon, which together provide our estimates of long run slaughter beef supply response for 50 different yearly time horizons. With these estimates we were able to calculate slaughter beef supply price elasticities for any of the different length of run horizons and for any selected PBEEFF within the range of PBEEFF values indicated. A natural choice for a particular PBEEFF is its mean for the sample period, since all other X1, X and POMEATF variables were specified (only initially, how- 2' ever, for x1) at their means. Some of the elasticities so cal- culated14 are - .1381 for the 1-year horizon (which compares with the 38LS(2$LS) structural equation estimate of -.137), +.1127 for the 3-year horizon and +.3284 for the 5-year horizon. Additional results are presented in Table 4.11. For example, the 3-year horizon estimate was calculated as the inverse of the ratio of a percentage change in PBEEFF (namely, $19.75 - 19.25 = .50 divided by $19.50 which equals an .02564 percent change) to a corresponding percentage change in QBEEFP (namely, 12133 - 12098 = 35 divided by 12116 which equals an .002889 percent change): The ratio (.002889/.02564) = .1127 is our estimate of the point elasticity for PBEEFF = $19.50 and QBEEFC = 12116 . 126 These results are consistent with a priori expectations regard- ing the nature of long run supply relations. The purpose of considering the long run slaughter beef supply for such an extended time horizon and for such a wide range of farm beef prices (PBEEFF) was to investigate other attributes of slaughter beef supply through the workings of the producer—segment structural equations; such as, does the series of long run slaughter supply functions (as derived herein) con- verge to an "equilibrium" long run function; and is there an "equilibrium" PBEEFF through which each of the derived supply relations passes. On the first question, it turns out that there is not a long run supply curve short of an infinitely elastic supply function15 (which we consider a possible weak- ness of the underlying producer—segment fitted structural equa— tions). One possible explanation, since "trend" terms were not 15 To see that this statement is true (and to explicitly show why the long run supply function did not converge) we recog— nized first that once we specified POMEATF as a constant (at its mean level in the above procedure), then the producer-segment other livestock supply equation had none other than a constant (fixed) effect on the beef cattle producer—segment equations. (In essence, an equivalent analysis is a study of only the beef cattle producer-segment structural equations.) Second, while holding PBEEFF at a specified level, each of the inventory equa- tions reduces to a simple first order difference equation of the form: Yt = aYt-l + C (where C is constant). The solution of this equation, starting with some initial value Y is: 0 t 2 t-l Y = a Y + (1 +ta+ a +...+ a )C t 0 127 . . - t Or equivalently [Since (1 + a + 02 +...+ at l) = 1 — a 1’ 1 a Y = atY +l-atc Y O 1 _ a (Note that the solution is convergent if a:=l, divergent if 0 >1”) In particular, let Y1t = QBEEFP, Y2t = IBEEFFZ, Y3t = IBEEFNFZ, a = .9669 and 8: 1.0263, (where the values of<1and Bare the 33LS(25LS) estimated lagged inventory coefficients in Equations (4) and (5) respectively); then, using the 3SLS(ZSLS) estimates, we obtain: From equation (4) t t th = “ Y20 + i_:_2_.(731.67 - 49.330 POMEATF + 36.475 PBEEFF) 1 a From equation (5) 8t t Y3t = Y3o + l—:—%—-(-12564.8 + 77.66 ARANGECI + 358.63 PBEEFF) From equation (3). substituting Y2,t_1 and Y3,t-1 from (4) and (5): Ylt _ 5093.26 t 1 _ at + -6826 “ Yzo + ~6826.______ (731.67 - 49.330 POMEATF + 1 - a 36.475 PBEEFF) + .1364 at y + 1364.l;;JL_ (—12564. 8 + 77. 66 ARANGECI + 30 l ‘ 358. 63 PBEEFF) - 32.27 PPROTEIN - 79.286 PBEEFF which may be rewritten as: Y1t = 5093.26 - 32.27 PPROTEIN t t + a (.6826 Y + B (.1364 Y3O) 20) 128 ,1 t + l—:e%— (.6826)(73l.67 - 49.330 POMEATF) 1 + 1 - 8t 1‘:-§— (.1364)(-12564.8 + 77.66 ARANGECI) t t + [(.6826)(36.475) %_:_§_.+ (.1364)(358.63).%_:_%_ —79.286 PBEEFF] Putting in specified values for Y 20 and Y3 POMEATF and ARANGECI, and designating the various numerical consgants by Ci's for sim- plicity, we obtain the following general form: _ t t Ylt — C0 + cl a + C2 8 + C3(l + a +...+ at'l) + C4(l + B +...+ Bt'l) + [C5(l + a +...+ at-l) + C6(1 + B +...+ B ) C7 ] PBEEFF Now consider the difference: t+1. t t+1 t Y1,t+1 - Ylt — cl ( a - a ) + C2( 8 - B ) t t + C3 a + C4 8 + [c at + c at ] PBEEFF 5 6 Hence, in general, if a, 8 <1, then Y1,t+1 - Yt for a given PBEEFF would converge; but since the estimated<1 = .9669 and B = 1.0263>].the difference diverges. It was thought that a possible reason for the estimated 8 being greater than one might have been that the estimate had partly captured a purely trend effect. However, when this possibility was checked by re-estimating equation 5 including a separate trend term, the result was to increase, rather than decrease, the estimated 8 (see Appendix A). 129 specified in the structural equations, is that average trend effects over the sample period are included in our long run supply estimates (but see comment at end of footnote 15). On the second question, an approximate "equilibrium" PBEEFF was found within a small range of $13.80/cwt.. Another set of slaughter beef sup- ply price elasticity estimates were calculated for PBEEFF cen- tered on $13.75/cwt. (selected estimates are also presented in Table 4.11) and Figure 4.1 illustrates the slaughter beef supply function estimates for selected length of run horizons. Our main interest is in the pattern of elasticity estimates obtained rather than in attempting to draw any conclusions about the validity of any particular function for a possible specific usage; we do consider that this exploration does on the whole strengthen the plausibility of our fitted producer-segment struc- tural equations. Recently a colleague, Michel Petit,l6 reported beef pro- duction (including production for inventories) price elasticity estimates of + .12 for a one—year adjustment period, + .32 for the second year, and + .34 for the third year. His approach was basically a recursive model formulation culminating in a beef production variable as a function of the (estimated) quantities of feed-grains fed to beef cattle, of high-protein l6 . . . . Petit, M. J.: Econometric AnalySis of the Feed-Grain Livestock Economy, Ph.D. Thesis, Michigan State UniverSity, 1964. pp. 174-181. 130 Table 4.11 LONG-RUN BEEF SUPPLY FUNCTIONS: GENERATED DATA AND ESTIMATED SLAUGHTER SUPPLY PRICE ELASTICITIES - QBEEFP (mil. lbsp) - PBEEFF $1/cwt. 1 Year 2 Year 3 Year 5 Year 10 Year 20 Year Hggizon Horizon Horigon Horigpn Horizon Horizon 18.75 '11350 11707 12604 12780 14593 18444 19.00 11330 11705 12081 12835 14745 18810 19.25 11310 11704 12098 12890 14896 19176 19.50 11290 11703 12116 12944 15048 19541 19.75 11270 11701 12133 12999 15200 19907 20.00 11250 11700 12150 13054 15351 20272 20.25 11231 11699 12167 13109 15503 20638 Estimated Supply Price Elasticity (at $19.50) -.1381 -.0100 .1127 .3284 .7878 1.4619 13.25 11786 11737 11686 11576 11255 10402 13.50 11766 11736 11703 11631 11407 10768 13.75 11746 11734 11720 11685 11559 11134 14.00 11726 11733 11737 11740 11711 11499 14.25 11706 11731 11754 11795 11862 11865 14.50 11686 11730 11772 11849 12014 12230 Estimated Supply Price Elasticity (at $13.75) -.1373 -u009549 .08115 .2625 .7255 1.888 1 i “.mmu .JH: _ immwmo soon. So: one... Eon. ones. noon. ooom. ooo. _ oooo. 89m _ 1 3. .1 n. i m. i . om mm \ I/l/zoNHmo: Em» _. / 2323: cam» m / :3ng Eu» m L .833: arm» a. 2033: an...» m .i am pita ...—ma «maid Sang... awhEHhmm _.: mmflwHu. l DOLLHPS/CHT l PBEEFF 132 feeds fed to beef cattle, of labor used in beef production, and the number of non—dairy cattle on farms at the beginning of the year. His model included expected price of beef-cattle vari- ables rather than actual prices, as predetermined in estimating the levels of inputs to be used during the current period. Thus, his price elasticity estimates are based on the recursive im- pact of expected prices on the various input components of the production relation. Nonetheless, his results are comparable, relatively, when considering various adjustment horizons. Fur- ther, his analysis indicated increased inventories given higher expected prices for beef, which implies that the one-year elas- ticity of beef-meat production alone would be lower than + .12. His results are therefore generally consistent with the results of this study. Further Evaluation of the Fitted Structural Model Another way of appraising the structural model estimated relationships is to observe how well the structures obtained explained the normalizing endogenous variables over the sample period. That is, consider each fited structural equation, yg* (t) 9759* O. ig yg(t) + k Bik Xk(t) as if all of the unexplained residuals, ui(t), were in fact random errors in estimating yg*. In other words, assume 0 = a ig ig' Bik Bik (and no errors in obserVing either the 133 Y's or X's), then ui(t) = yg*(t) - yg*(t). When viewed in this manner, the reported "Rz's" are indeed an indication of the relative amount of the variation of the normalizing variables (Yg*) which has been explained by the respective fitted struc- tural equations.17 This type of evaluation has an intuitive appeal since we tend to interpret the estimated structural equ- ations in terms of the effects of the specified variables solely on the normalizing endogenous variable. The following series of figures (Figures 4.2 to 4.9) graph- ically portray the estimated versus the actual series of the normalizing endogenous variables over the sample period (estimated series based on 38LS(2SLS) parameter estimates). We also plot estimates for 1964 as an indication of how the parameter esti- mates "explain" the actual endogenous variables for 1964 (which are observations that were not included in our sample period). For greater facility in observing the nature of the residuals (in the manner described) we also plot the residuals as plus or minus deviations from the actual series. 17Alternatively, we might wish to evaluate the residuals of our estimated linear combination of the endogenous variables in terms of a simultaneous coefficient of determination (pro- vided such a statistic could be calculated — for develOpments along this line see, for example: HOOper, J. W.: "Simultan- eous Equations and Canonical Correlation Theory," Econometrica, Vol. 27, 1959, pp. 245-256; and Theil, H: Economic Forecasts and Polipy Amsterdam: North-Holland, 1961, p. 348. 134 An advantage of graphing the estimated and the actual series of the normalizing endogenous variables is that we can further note how well the mechanisms explain turning-points in the actual series. If there systematic deviations between the estimated and the actual series, then possibly that character- istic would be indicative that a correct specification of the equation (and/or model) had not been achieved. We note, in general, that the figures reflect a reason- ably close fit (which is implicit in the "R2" statistic) be- tween the estimated and actual series of the normalizing vari- ables for each of the structural equations, with the exception of equation 6 (Figure 4.7: Demand for Other Meat at Retail, where the "R2" = .81). While the figures are "self-explanatory", we briefly note in particular the following characteristics, equation by equation. Demand for Beef at Retail (Figure 412). The calculated R2 was .93 (when considering PBEEFR as if it was the sole de- pendent variable). Except for 1955, the estimated PBEEFR moved in the same direction as the actual (observed) series. The larger residuals were for 1941, 1955—57, and 1963. Also, the pattern of the residuals appears somewhat cyclical over the sample period, so one might suspect that some other variab1e(s) should have been specified in this demand relation. Overall, the Specified relation captured fairly well the direction of l CENTS/LB.) PBEEFR l CENTS/LB.) PBEEFR 135 FIGURE H.:"! STRUCTLRFI. ECLHTION l. DEHHD FOR BEEF HT RETHIL H. HCTUHL HND ESTINHTED PBEEFR IDD . ear .0:- 70' bar , .4: SOP 1 _. HOTLHL -..- ESTIHHTED LLLLJL‘LLLLLLLJALLLLLAL] I'qss Iqun I 850 I 955 I‘lbD I was TIME YEHRS B. CORRESPONDING RESIDUHLS N w W WLLA l.LL__1_LL_LLlJL1 11 (Rib IQUD IGD IQSS IQbD l‘bS TIHE YEHRS -D-IIIIICIIII’ 1 U U Y—TTT l CENTS/CHI l PBEEFF l CENTS/CHI l PBEEFF I i: m E'l:3u a nIi:|r m Ulnlzzlr m é a 136 FIGURE U.S STRUCTURHL EOUHTION E. MHRKETINB IN THE CHTTLE-BEEF SECTOR H. HCTUHL HND ESTIMHTED PBEEFF ‘3'.» __ FICTUHL -..- ESTIHFITED l L 1 1 1 LJ_ 1 l J #1. L l _1 1 1__J I‘Bb IRUU i IRSD I‘ISS I‘lbD Icibs TIHE vanes B. CORRESPONDING RESIDUHLS n > 7 WLLLLi LLLLLLLLLLLJ ISISb I‘IUD IHSD ISISS IRbD l 91:35 TIHE YEHRS l CENTS/ONT l PBEEFF I CENTS/ONT I PBEEFF I i: m i'l:Iu u hIl:Ir m Ulnll:lr m ID 136 FIGURE ”.5 STRUCTURHL EOUHTION E. MHRKETINB IN THE BOTTLE-BEEF SECTOR H. HCTUHL HNO ESTIMHTEO PBEEFF 4’ __ FICTUHL -..- ESTIMFITED A||||||filLIlliLIillllJlig I 95b IQUU I qSD I 955 Iqu 191:5 TIME YEHRS B. CORRESPONDING RESIDUHLS W > 7 < Q ng Pi; LJij—LLLLiL LLLJ ISISI: IQUD I‘ISD I‘ISS l‘IbD Iqu TIME YEHRS I MIL. L95.) OBEEFP I MIL. LBS.) QBEEFP I bDDD IUMD IEIIID I DDDD 137 FIGLRE ”.14 STRUCTURE. EOLFITION 5. SLHUBHTER SLPPLY OF BEEF CFITTLE HT THE FORM H. HCTUHL HNO ESTIMHTED QBEEFP T l LlllL‘ llklj 111 111+41LLJ 8 I800 V I850 I855 I880 I885 TIME YEHRS ._$_ ...HCTUHL -“.ESTIMHTED I}. B. CORRESPONDING RESIOUHLS _ DRE h P L- P AiLililjv LJIJLJ 14141414111] (858 I800 I850 I855 I880 I885 TIME YEHRS ‘Tfi U I IDDD HERO I IBEEFFE l IDDD HERD I IBEEFFE -7DD I 38 FIGURE (IS STRUCTURFIL EOLFITION LI. INVENTORY DEMFNJ FDR EEF CHTTLE RETHINEO FDR FEEDING FIT THE FFPM H. HCTURL HNO ESTIMHTEO IBEEFFE ..., __ HCTUFIL --- ESTIMFITED MTL L L l 1 LA L l l l L LLI J L l 1 1 L4 J L J I858 I800 I I850 I855 I880 I885 TIME TEHRS B. CORRESPONDING RESIDUHLS fl w r Lhrl JLL 14 1‘ l l l l l ngiJ l l L_LL 1-] I838 I8u0 V I850 I855 I880 I885 TIME YEHRS I IDDD HERO I IBEEFNFE I IDDD HERD I IBEEFNFE 7DCDD bDDDD SDIIDD IIDDDD SDWD ZSDDD 139 FIGLRE LI.b STRUCTLRFL EQFITIW S. INVENTORY OEMRD FOR BEEF CHTTLE WT-RETHINEO FOR FEEDING FIT TFE FFPM H. HCTUHL RNO ESTIMHTED IBEEFNFB '— l I j 1 P p T _ HGTLflL --- ESTIHHTED 11L1i1~liniliinlilnliiln END I HID I EDD I IIDD I EDD I (DO I'858 I800 I 850 I 855 I880 l 1:5 TIME YEHRS B. CORRESPONDING RESIDUHLS P I- I I I’ r I I firL Ll L 1 1‘ L L l l l l l 1 L1 LLL L “L‘JJ I858 I800 I I850 I855 I880 88; TIME YERRS I CENTS/LBJ POMEIITR I CENTS/LBJ PNEFTR 140 FIGLRE 11.7 STRUCTURE. EDLFITIEN b. OEMFND Fm OTI-ER MEFIT HT RETHIL H. RCTLFIL Rm ESTIMRTEO POIEFI'IR 80 - an - IDI- bOr \ SD ND 50 r .1, .. nc'runt --. ESTIMHTED WLJILLiLLLlILILILI IQSb IROD ISSD ISSS IRSD IQbS T IME I ERRS B . CORRESPONDING RESIDUES V_I I I I I I In I: IN N v I I— r ALLLLLJ.‘LILLALLLIILLLILLLI (858 I800 V I850 I855 I880 I885 TIME IEIIRS I OOLLRRS/CNT I POMEPTF I DOLLHRS/CNT I POMEBTF 25 EN 23 25 2| 2D IS I! I7 It IS 141 FIGLRE U.B STRLETLRFI. EQHTION 7. PWKETING IN THE OTI-ER LIVESTIISK-MERT SECTCF H. RCTURL HND ESTIMRTED POMERTF V r I I T 1 r V r f 1 4| .. MOTLHL ... ESTIMBTED I‘Bb ISUD I‘BD I955 I‘lbD |%5 TIME IERRS B. CORRESPONDING RESIOUHLS /\ /\ m- - \/ NJ 1 .L L LL L L 1 J L L L L L 1 LJ IQSb IQUD I I950 I955 IQbD I‘S TIME IERRS T— V— I’T—firij TV—V—T'V—V F I MIL. LBS.I DOMEHTP I MIL. LBS.I DOMERTP 82000 30000 IBDDD IbDDD IUIIID IEDDD IDDDD RUDD 142 FIGURE U.q STRUCTURHL EDUHTION B. SUPPLY OF OTHER LIVESTOCK HT THE FORM H. HCTUHL HNO ESTIMHTEO OOMEHTP F ./:i I- (’1’ I- f P' (’j " x r- ” " r r .... FICTIJFIL --- ESTIMHTEL~ (III 1 l_I 1 LA . 4 L 1 J...L...L...L_...L__L--L_.l....L...J..--L-l._I I W858 I800 850 I855 I880 I885 TIME YEHRS B. CORRESPONDING RESIDUHLS I275 T l L I\. F I I -808 I/&L_.L__J___,L___L LLLLJLJLLLLILLJLL L...) 295k: IRUD IRSD I t355 IRbD I cTbs TIME YERRS 143 PBEEFR changes over the sample period. Marketipg in the Cattle-Beef Sector (Figure 4.31. A rela- tively closer fit was obtained for PBEEFF than for PBEEFR above, as indicated by R2 = .97. The estimated PBEEFF moved in the same direction as the observed variable except for 1938. The largest estimated errors occurred in 1952, 1958, and 1962. The pattern of the residuals appears reasonably random so that ap- parently systematic changes in PBEEFF have been "explained" by this structural relation. Supp1y of Beef Cattle at the Farm (Figure 4.4). An R2 = .98 was calculated, so in terms of explaining variations in QBEEFP, this relation performed well over the sample period. The esti- mated series missed the direction of the changes in QBEEFP most noticeably in 1939, 1951, and 1954; but otherwise the time path of the estimate was directionally accurate. In absolute terms, the estimates deviated from their actual values most substan- tially in 1950-52, 1956-57. Inventory Demand for Beef Cattle Retained for Feeding at the Farm (Figure 4.5). In 1937, 1953, and 1957, the change in estimated IBEEFF2 was in the Opposite direction from the actual series, and residuals were the highest in 1937, 1957, and 1962. 2 Overall, the R = .97, so the relation was fit reasonably well in terms of IBEEFF2. (Two variables, CONSTANT and POMEATF. 144 were not statistically significant at a high level in this rela- tion, however.) The residuals appear to be somewhat negatively serially correlated, since the residuals oscillate frequently (note that the D. W. statistic is greater than 2, Table 4.4). Ipventopy Demand for Beef Cattle Not-Retained for Feeding at the Farm (Figure 4.6). A very high R2 was obtained for the relation, R2 = .99, so in terms of IBEEFNF2, most of the varia- tion was explained by the specified relation. All turning points in IBEEFNF2 were reflected by the estimated series except for a slight error in 1937. The largest residuals were for 1949, 1956- 57, and 1962, but relatively those residuals represented less than a 2 percent error except for 1949. Demand for Other Meat at Retail (Figure 4.7). According to the calculated R2, this relation was fit the least-well of any: R2 = .81, based on 3SLS(ZSLS). The POMEATR series was quite cyclical over the sample period, and even with the low R2, the estimated series followed the actual series reasonably well. The estimated series missed on direction only in 1950— 51, 1954 and 1960. The residuals appear somewhat cyclical in the postwar period, thus implying that some systematic influ- ences were not adequately accounted for in the specified rela- tion. 145 Marketing in the Other Livestock-Meat Sectorijigure 4.8). Relatively, the cyclical pattern of POMEATF was explained rea- sonably well as indicated by an R2 = .96. The direction of change was estimated incorrectly for 1937, 1951 and 1958. The residuals appear less cyclical in this case than for POMEATR, i.e., more random, as desired. Residuals were relatively large for 1936, 1939, 1941, and 1961. Supp1y of Other Livestock at the Farm (Figure 4.9). The postulated supply relation for other livestock which contained only predetermined explanatory variables seemed to explain a high prOportion of the variation in QOMEATP, as indicated by R2 = .97. Several small directional errors occurred in 1937-38, 1941, 1957 and 1960. The residuals were largest for 1937 and 1956, and they appear non-random, the frequent oscillations indicating negative serial correlation. (Note that the D. W. statistics is about 2.9, Table 4.8. It should be noted also that equations of this type, based on distributed lag expecta- tion models, tend inherently to have disturbances which are negatively serially correlated, under generally plausible as— sumptions.) When the structural form relations are evaluated in the above manner, i.e., focusing upon a particular (normalizing) endogenous variable, then these (3SLS(ZSLS)) fitted relations generally explain a high prOportion of the variations in those 146 variables. Combined with the general plausibility and the statistical significance of the estimated coefficients, then the overall fitted model would appear to represent the aggre- gate behavior of the underlying "behavior units" reasonably well. Reduced Form gptimation and Forecasts The major purpose of this study was to prescribe an eco— nomic (and statistical) model to represent the endogenous mech- anism within the cattle—beef sector and interrelationships with the other livestock-meat sector. Once the underlying structural system was specified and equations estimated then a secondary objective was to translate information pertaining to the struc- tural model equations into forecasting mechanisms. As has al- ready been discussed, given a complete model, one can readily obtain the reduced form of the model, which states each of the current endogenous variables as a function of only the predeter— mined variables in the system (plus a disturbance). The reduced form system is thus in itself a one—period forecasting mechanism. It is instructive to note the reduced form as follows (as previously defined): 1 l 1 A'AY+A'BX+A’U=0 (i) or Y + H X + V = 0 (ii) From (i) it is easily seen that each element of H (reduced form coefficient) is, in general, a function of all the structural 147 coefficients in a row of A.1 and in a column of B; and also that each reduced form disturbance is a linear function of all the con- temporaneous disturbances. Further, each derived reduced form coefficient is, in general, a non-linear function of the struc- tural coefficients. A knowledge of the derivation of the re- duced form coefficients is important because it may commonly be true that even small sampling errors in the individual structural coefficients may build up into substantial sampling errors in the derived reduced form coefficients. Theoretically, it has been established that the estimated U will be consistent if the estimated A and B coefficients are consistent. Unfortunately, this asymptotic property is of limited consolation in typically small sample analyses. Ideally, one would expect a "well-fit" structural model to produce a similarly well-fit reduced form system. Yet in practice, the ideal situation may not be realized. This digres- sion was in part a defense for the structural model estimates obtained above, because the reduced form coefficient estimates did not, in all cases, generate the endogenous variables as closely as was desired, a priori (as indicated by the reduced form equation estimated Rz's; see Appendix B). However, in order to further indicate (in addition to the estimates presented in Appendix B) the possible usefulness of our reduced form parameter estimates, we explore how our fitted 148 model would have performed (as a forecasting tool) over the sample period, 1936-41, 1949-63; given first, some initial values for all thegpredetermined variables, and second, the actual values for each of the exogenous (excludes our lagged endogenous) variables for each period thereafter, i.e., until 1963. (Presumably, if one were to forecast into some future periods, using a statistical model, then he would have to pre- scribe independent values for the exogenous variables. We chose to "forecast", ex post, the sample period fitted so as to utilize observed exogenous variables, and thereby examine the nature of the reduced form mechanism derived from our complete structural model.) The presence of lagged endogenous variables in the re- duced form (also in the structural equations) provided us with a choice; that is, we could either use the observed values at each point in time, and thus get a series of one—year "forecasts" (which is in fact what the reduced form R2's in Appendix B do refer to); or we could instead use the previous period fore- casts of the corresponding endogenous variables as estimates of the "current" period lagged endogenous variables. We chose the latter alternative so as to explore how the reduced form would have generated the endogenous variables assuming only the exogenous factors were "known" (or forecast accurately) over the "forecast" period. 149 This procedure was Operationalized readily by considering the (rewritten) reduced form equations, Y=Hx+v (iii) as a partitioned form, as _ 7 Y [ H1 ”2] X1 -+ V (iv) 1 l 2 2 (V) where Y1 and Y2 are the forecast (endogenous) variables of the system: Xl are the lagged endogenous "estimated" variables, i.e., Xl(t) = Y2(t-l); X2 are the exogenous variables; and H ( H1 and “2) are the appropriately rearranged reduced form coefficient estimates. As indicated above, the initial values for both X1 and X2 were the 1936 actual values; X continued to take on actual values thereafter, and X1 values were succes- sively replaced by the previous period Y2 forecasts. Thus, successive "forecasts" were obtained for 1936,...,1941, 1949, ...,1963.18 The results of this exploration are presented graphically in Figures 4.10 to 4.19. Except for 1936 and 1949 we stress that these "forecasts" are not simply a series of one-year 18Because the 1942 to 1948 observations were excluded from our original sample, we also excluded that period in this sec- tion. Thus, we "restarted" the forecast series beginning in 1949, i.e., X1 and X2 in 1949 are observed predetermined vari— able values. 150 forecasts, but they are successive forecasts which utilize forecast estimates for the included lagged endogenous variables. We also emphasize that this exploration is only one possible way to appraise the reduced form estimated model. In general, the forecast series followed the time—path patterns of the actual series; however, absolute deviations of the estimated series from the actual series were generally sub- stantial. We regard the former characteristic a strength rather than a weakness of the set of forecast mechanisms as a whole; but the latter characteristic negates the usefulness of indi- vidual equations for precise forecasting purposes. Results of this exploration are summarized briefly below for each equation. Price of Beef at Retail (PBEEFR) (Figure 4.10). The abso- lute deviations of the PBEEFR forecasts were particularly large for both the 1936-1941 and 1949-1963 sub—periods. (Since fore- cast values of the lagged endogenous variables were fed-back into the system, then errors in forecasting these variables is another source of error that influences successive forecasts). Other than the fact that this forecast series did not systemati— cally deviate from the general path of the actual PBEEFR series, this forecasting equation did not perform well. Price of Beef Cattle at the Farm (PBEEFF) (Figure 4.11). The characteristics of both the actual and the forecast series for PBEEFF are quite similar to those above for PBEEFR. Devia- I CENTS/LB.) PBEEFR I CENTS/CHI I PBEEFF 151 FIGURE U.ID REDUCED FORM EDUHTION l. PRICE OF BEEF HT RETHIL H. HCTURL ONO ESTIMHTED PBEEFR IDD r 80 . F an t 70 r 80 I )- SD ' ..a V ...... FICTLBL --- ESTIMHTEO IRSb I‘IUD l‘ISD I555 4|“!th 1 1 I‘bS TIME YEHRS FIGURE U.|| REDUCED FORM EOUHTION 3. PRICE OF BEEF CHTTLE HT THE FHRM H. HCTUHL HND ESTIMHTED PBEEFF .rr .... HCTLBL --- ESTIMFITED W1 1L1 LLI LLJLLJLLJ in IQSb I‘IUD ISLSD I955 I‘IbD I%S TIME YERRS 1 MIL. L95.) QBEEFP l IDDD HERD l IBEEFFE 152 FIGURE U.|E REDUCED FORM EOUHTIDN S. OUHNTITY OF BEEF PRODUCED FDR SLHUGHTER B. HCTUHL HND ESTIMHTED QBEEFP lbDDD » |u000 r E I2000 - n0000 F r 3000 P \ f 7000 - ‘“’ ‘ \\ ...;L _ scrum. --- 551100150 ”050 1000 L IIGSE; l 1 11:15er A Anibal J I 1:455 TIME YEHRS FIGURE U.l5 REDUCED FORM EOUHTION U. INVENTORY OF BEEF CHTTLE RETHINED FOR FEEDING H. HCTUHL HND ESTIMHTED IBEEFF2 9000 - 7000 P / ’III”v //,/f;>5/g// 5000 r A_;,w"' A ”’ E, I ‘N 5000 - I .....HCTUHL --- ESTIHHTED I;;111141J11414444114141411 (Asa Iquo V 1050 I055 :000 IBBS TIME YEHRS I I000 HERD I IBEEFNF2 I CENTS/LB.I POMEHTR :53 FIGURE U. I” REDUCED FORM EOLHT ION S. INVENTORY OF BEEF CHTTLE NOT-RETFIINED FER FEEDING H. HCTUHL HND ESTIMHTED IBEEFNF2 70000 ' b0000 I j T I 50000 “0000 I 1 I T 50000 , 25000 ~ ""‘-°--"" 7’ ... HCTLIFIL --- 551100150 fil l l 1 1 L‘ J A L1 1 11 III L1 14 I L] 1'555 mun I 1550 1555 man I $5 TIME YEHRS FIGLRE LI. I5 REDUCED FORM EOLFITION b. PRICE OF OTHER PERT FIT RETHIL H. HCTUHL END ESTIMHTED POMEHTR an 70 V j—j T 1 b0 50 P U0 ’ __.HCTUHL -m.ESTIMBTED 50 P ‘7»- jLL_L_4_J_AL_LJ» J 1 J ELI; 1 L54 1 4.514L 1 1 1 J_J IQSb IBUD l950 IQSS I9b0 IQbS TIME YEHRS I DOLLHRS/CHT l POMEHTF I MIL. LBS.) ODMEHTP 154 FIGURE U.|b REDUCED FORM EOURTIDN 7. PRICE DF DTHER LIVESTOCK HT THE FHRM H. HCTUBL HND ESTIMBTED POMEHTF 00 — 50 P A , P- l\\ ” I an r- \ I \ / I / F \I V 10 r q S 1- ¢#,_ __.0c100L -u.551100150 Ari l_l_l_l JJ J 1444—1 J l_l J41 [A l 14 J 1555 1500 V 1550 1555 1550 1555 28000 30000 I0000 lb000 |U000 l3000 I0000 0000 TIME YERRS FIGURE U.|7 REDUCED FORM EOURTION B. OURNTITY OF OTHER MEHT PRODUCED 0. 0c100L 000 551100150 0005010 / -- " ..J 1- P~~_ J, F I /' J 04"”K . “v / " / r I. I. ‘ V * ...HCTUHL -m.551100150 ”t l l l J l l A 1 J l J 1 _l l J l .1 1__1_l’1_1 J._l W055 1500 V 1550 1555 1550 1555 TIME YEHRS I MIL. LBSJ ONERTC I MIL. L95.) OKEFC 155 FIGURE U.|B REDUCED FORM EOUHTION 9. OUHNTITY OF OTHER MEHT CONSUMED H. FISTLHL 0110 ESTII‘HTED OOI‘EHTC aeuna' 1- emanab lBflflJ“ F ammo ‘ L Hana * 1aun1* L 101110 ‘ 5000 r ...00100L -m.550100150 iiirl 1 l l l l ‘ l J_ J 1 l l l J l l l I l l J l l 1555 151.10 I 1550 1555 1550 15:5 TIME YEHRS FIGURE U.Iq REDUCED FORM EOUHTION ID. OUHNTITY OF BEEF CONSUMED FI. mTLflL HID ESTII‘HTED QBEEFC Hunn - 17uu1» unnn ~ 15uu1' 11un1» I. 5amL I “A 7000 F ~._ T ... 0011.511. --- 551100150 1'555 1500 AV 1550 1555 1550 15.5 TIME YEFIRS 156 tions of the forecasts from the actual series were substantial. This was disappointing, but it is again noteworthy that the forecast series did not systematically deviate from the over-all time—path pattern of PBEEFF. Quantity of Beef Produced for Slaughter (QBEEFP)(Figure 4.12L. A reasonably smooth time—path pattern for QBEEFP was generated with our fitted reduced form mechanism. The cyclical nature of this variable was not explained by the forecasting mechanism, but the general trend was picked up reasonably well. Inventory of Beef Cattle Retained for Feeding IPBEEFFZ) (Figure 4.13L. The forecast series for IBEEFF2 essentially par- alleled the actual series throughout the 1936-41, 1949-63 sample period, with the forecasts generally below the actual values. Inventory of Beef Cattle Not-Retained for Feeding (IBEEFNF2) (Figure 4.14). The forecast series followed the actual series generally well for IBEEFNF2, but again deviations were large on the average. Cyclical characteristics of the IBEEFNF2 actual series were not generally reflected in the forecast series. Price of Other Meat at Retail (POMEATR) jFigure 4.15). This forecast series was severely oscillitory over the sample period, yet the estimates generated followed the pattern of the actual series throughout the sample period. In the 1949- 157 63 sub-period, the oscillations deviated considerably less from the actual series than during the earlier 1936-41 sub-period; Which indicates greater applicability in the more recent past. Price of Other Livestock at the FarmngOMEAT ) (Figure 4.16). The pattern of the forecast series for POMEATF was quite similar to that for POMEATR, with no systematic deviations from the actual series. Also, this estimated series was smoother in the latter part of the sample period. General trends are seem- ingly explained well by this forecasting mechanism. ‘Quantity of Other Meat Produced (QQMEATP)(Figure 4.17). An oscillitory path was generated for QOMEATP; but the forecasts followed the actual series closely throughout the sample period, particularly for the 1949-1963 sub-period. Quantity of Other Meat ConsumedngOMEATC)jFigure 4.18). This forecast series for QOMEATC is actually the same as the above relation for QOMEATP, except for a predetermined amount. Namely, these estimates differ from those for QOMEATP by the amount of NOMIMPORT. Thus, this series has characteristics similar to the above series. .Qpantity_of Beef Meat Consumed (QBEEFC) jFigure 4.19). Like the above relation, no additional information is contained in this forecast series, since QBEEFC differs from QBEEFP by a 158 predetermined value, NBIMPORT. The fact that most of the "forecast" series did not sys- tematically diverge from the actual series over the sample period as a whole seems to be a strength of the mechanism. On the shorter run forecast patterns seem generally inferior to what one might have expected from, for example, simple unrestricted reduced form estimates. A somewhat more straightforward application of reduced form equations is to forecast (conditionally) outside the sample period for periods for which data are available, e.g., all the 1964 data are now available for the variables used in this study. Thus, using the 1964 values of the predetermined variables (and the corresponding BSLS(28LS) reduced form coefficient estimates we obtain "forecasts" for 1964. As another example of how the forecasting mechanism of this study may be expected to perform, the estimated ("forecast") and actual 1964 values (of the endo— genous variables) are presented in the table below (Table 4.12). (These forecasts are still ex pggt since 1964 data are reported; but conditional upon having accurately measured (or estimated) the predetermined explanatory variables prior to 1964, we can regard this "test" as somewhat stronger than using only sample data.) 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H.Hmvh mm.hoa ammo. m.m©¢1 ©O.mOH mhmm.a m.mOHmNI Hm.©©m O.H1 .3.Q mZHE H0m02¢m4 HmzmmmmH BZdBmZOU mmmmmm mmzmmmmH MUHBmHfidfim amadflmm Q24 mmBZH m0 mZOHfidemHummm m>HBZH m0 mZOHB¢UHmH0mmm m>HB4ZmMBQ¢ ¢.¢ OHQMB 182 50.N 00¢H. hhHO. vm.0 00000. hmmo. 50mm. 055N.1 0000. Nh.vH 00000. mamm. 0.H1 00.N 0HNH. 00m0. 05.0 00000. 0000. 0Nvm. 000N.I H000. @0.NH H0000.I M000. 0.HI mH.N mHN. oma. MNO. 0v.h H0000. vao. Hmhm. hH0.I va.l H00.N 05.0 00000.1 0000. 0.H1 .3.Q 0000045 0003mm¢ mZHB ZQBMZU MmmHQ BZHA mmmBO HEB ZH GZHBWMM¢S mo mZOHfidUHmHummm m>HB¢ZMMBA< h.< GHQMB MN.N NmNN. 0Nh. 0000. 0.5N 0NH00. Nm00. 0NNm. 0H00.I oma.N 0HmH. 0.05H 00000.1 hmmv. hm.a 000N. @000. 0.0N 00H00. 0000. mm00. 00N¢.I 000m. 0.0NH 0m000.1 >000. 0.HI @0.H 000. 000H. 0.0H 00H00. mamo. 0H00. M00.H NOHH. 0.0HH Nfimoo.1 0000. 0.HI .ZWQ Zmom mSHB NmmHQ 52090200 UBHeflzmmBA¢ 0.¢ GHQMB 183 00.0 00.00 mama. 00.00 00.00 «.0000 10000 055m. mH.moa «Nae. m0.mm1 mH.0m m.m00HH 0.01 .s.o 0255 0054mzmd 00500050 055HA mmmBO mo Nummbm mo mZOHBdUHmHummm m>HB¢ZMmBA¢ 0.¢ magma APPENDIX B 3SLS(ZSLS) and I3SLS Reduced Form Fitted Equations (and Rz's) The reduced form coefficients (denoted as n in the text, where H is derived from the structural form parameter estimates) for 38LS(ZSLS) and IBSLS procedures are presented in this APPENDIX. Also, we report a coefficient of determination, R2, for each of these equations. The following table contains these estimates. (Note that reduced form equations for QBEEFC and QOMEATC differ from these for QBEEFP and QOMEATP only by a pre- determined variable, i.e., NBIMPORT and NOMIMPORT, respectively. Thus, these equations are not included here.) 184 185 0000.0 0000.0 0000.0 0000.0 0000.0 00.50000 00000 20 0000.0 0000.0 0000.0 0000.0 0000.01 5000.00000000000000 20 0500200 .0 00000.01 000000.01 00000.01 00050.01 00000.0 5000.00 00000 20 00000.0 0000000.01 0000.01 00000.01 0500.0 5000.00 0000000000 20 0500200 .5 005000.01 0000.01 500000.01 00000.01 00000.0 00000.00 00000 20 00000.0 00000.01 000000.01 00000.01 00050.0 00505.01 2000000000 00 0500200 .0 05000.001 0000050 5000.01 0050.5 001 50500.000 050.0000 00000 3 5000.05 00005.0 0000.01 5050.0001 0000.000 00.500010000000000 00 00200000 .0 0000.0 1 500000.01 00000.0 00000.0 0000.0 1 500.0000 00000 00 0000.0 00500.01 05000.0 00000.0 0050.0 1 00000.0000000000000 .0 0000000 .0 00000.00 0000.0 00000.0 5000.00 5505.001 00.50001 00000 00 0000.501 00000.0 ‘ 0000.0 0000.50 000.001 000.5000 0000000000 00 000000 .0 05000.01 00000.01 000000.01 00000.01 00000.0 0005.00 00000 00 50000.0 000000.01 00000.01105000.01 00000.0 500000.5 0000000000 00 000000 .0 00000.01 50000.01 000000.01 50500.01 00000.0 0000.00 00000 00 00500.0 50000.01 00000.01 00000.01 50000.0 5000.01 0000000000 00 000000 .0 20050000 00200000 0000000 205220 00000 52050200 000002 000000m> 000» 0000080000 unmocmmmn Imsvm Am .N 0 0200 020050000 005500 2000 0002000 00000 020 0000000000 H.m wHQMB 186 Hmom.o 0000.0 0000.0 thwh.o mmmm.ONHI mmfim.®vm 0000.0 AQ Hmhm.o 0000.0 0000.0 hmmmom.o hmmmm.®ml hmmm.¢mm 0000.0 Am.m H¢N0.0 mmVNOO.OI QHVOO.OI H00H©OOO.OI momm@.o mmmmm.HI 0000.0 An bOflm.o omNOO.OI Hmvoo.OI m©VOO.OI mmmm.o mmoom.HI 0000.0 Am.h wmwm.OI ®HNOO.OI ohmHHO.OI 00mmoo.OI ov¢V.H avomm.ml 0000.0 AA mmmH.OI omo>OO.OI OQNHO.OI mmoao.OI mHmHN.H mohwm.ml 0000.0 Am.® hmhm.o whon.OI o¢®¢v.OI mmwmm.OI mHNmm.mm mmmm.mOHI 00mm.¢m An mmmm.o mamm.OI Hmmm.OI mmahm.01 Hm©m.Nm Homm.mhl 00000.00 Am.m 0000.0 mfiomo.o m¢mma.o moo©H.o Novb.©ml mmm®.¢m 0000.0 AD mmhm.o mmammoo.o mummma.o mmmoN.o Hmmm.¢ml hmomh.©m 0000.0 Am.v Hmmm.o mo>¢H.o mmomo.o Nmooh.ml Hoooo.o mmvm.ma 0000.0 an Noom.o mNQNH.O momvho.o Vmoooo.o hovma.bl oaah.@a 0000.0 Am.m mmhm.o NNOO.OI MNHOO.OI mNNmOOO.OI mem¢H.o mom0m.OI 0000.0 An hvmm.o mmaoo.on hmmooo.OI hmhooo.OI mmomo.o NBOHN.OI 0000.0 Am.m Hmho.o Nmoao.OI Hoooo.o mvoo.OI hmommh.o ©¢Hw¢.HI 0000.0 an omom.o mmmoao.OI o¢ooo.on mmmmoo.01 Hmmmm.o hmfimv.al 0000.0 Am.H mm BmOmZHmZ BMOQSHEOZ AmefimZOO AQHQmmhm mmfiflmzom vademd 00.0000 0.0 00005 APPENDIX C Data Sources and Data Data Sources The sources of data for each variable used in this study (both in the text and in Appendix A) are indicated here. Two major sources are Agricultural Statistics, annual series; and Livestock and Meat Statistics, periodic series with annual sup- plements. For convenience, we let Statistics refer generally to Agricultural Statistics (1967, 1962, 1964), USDA, Washington: U.S. Government Printing Office. Since summary tables of time series data have been included in these particular publications (except for 1964, which was a source for 1963 data), we note table num- bers for particular variables that correspond with the 1962 pub- lication. Also, we let Livestock and Meat Statistics refer gen— erally refer to: Livestock and Meat Statistics, 1957, USDA, Statistical Bul— letin No. 230, Washington: U. S. Government Printing Office, July 1958: Livestock and Meat Statistics, 1962, USDA, Statistical Bul- letin No° 333, Washington: U. S. Government Printing Office, July 1963; and Livestock and Meat Statistics, Supplement for 1963 land 1964) to Statistical Bulletin No. 333, USDA, Washington: U. S. Government Printing Office. 187 188 We will note table numbers as they appeared in the 1962 pub- lication. PBEEFR QBEEFC POMEATR PBEEFF (and PBEEFFL) QBEEFP IBEEFF2 (and IBEEFFl) POMEATF (and POMEATFL) Retail beef price per pound (estimated weighted average price of retail cuts from choice grade carcass), annual, cents, Livestock and Meat Sta- tics (Table 199). (Non—deflated) Total civilian consumption of beef, annual, mil- lion pounds, Livestock and Meat Statistics (Table 210). Weighted average retail price per pound (weights were QOMEATC components divided by total QOMEATC), cents; PORK: Retail pork price per pound (esti- mated weighted average price of retail cuts), annuals, cents, Livestocks and Meat_§tatistics, (Table 200); VEAL: average annual retail price (estimated as 80 percent of veal cutlet price), selected cities, MonthlyALabor Review, series; LAMB: Retail lamb price per pound (estimated weighted average price of retail cuts from choice grade carcass), annual, cents, Livestock and Meat Statistics (Table 201); CHICKEN (and TURKEY): Average retail price for chickens, U.S., Monthly Labor Review, annual, averages, series and Poultry and Egg Situation, November 1964, (Table 8). (Non-deflated), liveweight, cents, U.S., Agricultural Statistics (Table 616). Non-deflated) Average price of beef cattle received by farmers per 100 pounds, 48 states, dollars, Livestock and Meat Statistics (Table 180). (Non-deflated) Total beef production (slaughter), 48 states, million pounds, Livestock and Meat Statistics, (Table 113). Cattle and calves on feed, 26 states, January 1, 1000 head, Livestock and Meat Statistics (Table 23). Weighted average price (dollars) per cwt. (weights were QOMEATP quantity components divided by total QOMEATP); HOGS: Weighted average price received by farmers, Livestock and Meat Statistics (Table 182); VEAL: Average vealer price, choice grade, St. Louis National Stock Yards, Livestock IBEEFNF2 (and IBEEFNFl) QOMEATC QOMEATP (and QOMEATPL) DISPY CMKTGM PPROTEIN 189 and Meat Statistics (Table 164); SHEEP and LAMBS: Average price (for lambs) received by farmers, per cwt., 48 states, Livestock and Meat Statistics (Table 184); CHICKEN: Average price of commercial broilers, U.S., cents/16, Agricultural Statistics (Table 603; TURKEY: Average price per pound and liveweight cents, Agricultural Statistics (Table 616). (Non- deflated) Total "other" (not kept for milk) cattle and calves (minus IBEEFF2), United States, 1000 head, Livestock and Meat Statistics, (Table 7) Total civilian consumption of pork (Table 212), plus veal (Table 211), plus lamb and mutton (Table 213), in Livestock and Meat Statistics, plus turkey, ready to cook basis, million pounds, Agricultural Statistics (Table 618). Total production of pork, veal, lamb and mutton, chicken and turkey, same sources as for QOMEATC. Disposable personal income, billion dollars, Agricultural Statistics (Table 629). (Non- deflated) Total meat marketing bill divided by total red meat civilian consumption: Marketing Bill for meat products, billions of dollars, annual, Agricultural Statistics (Table 679). All meat total U.S. civilian consumption (includes beef, veal, lamb and mutton), and pork, excluding lard, Agricultural Statistics (Table 533). This series was transformed as defined in the text to arrive at the actual variable used. Price of protein feed in dollars per 1000 pound TPN, calendar year. These data were taken from Feltner, R. L.: "Alternative Models of the Feed Livestock Economy," Ph.D. Thesis, North Carolina State, 1965. A detailed discus- sion of this variable is in Hildreth, C. and Farrett, F. G.: A Statistical Study of Live- stock Production and Marketigg, New York: John Wiley and Sons, 1955, pp. 43-45, (The principal kinds of feeds included are soybean, cottonseed, linseed, and c0pia cakes and meal; dried grains, ARANGECI PFEEDID (PFEEDIDL) NOMIMPORT NBIMPORT POPN PCDISPY AHRWAGE ULABORC AVAILFGl EPBEEFL 190 peanut cake and meal, tankage, fish meal and other by-products). (Non-deflated) Average (of August, September and October) range (first of month) condition, percent of normal, U.S. Agricultural Statistics (Table 404). Price paid (index numbers) by farmers for feed, U.S., 1957-59 = 100, Agricultural Prices, SRS, USDA, May 1962, p. 49. (Non-deflated). QOMEATC-QOMEATP, sources as defined. QBEEFC-QBEEFP, sources as defined. POpulation, number of peOple eating from civilian food supplies, July 1, millions, Agricultural Statistics (Table 794). Per capita disposable income, calculated as DISPY divided by POPN, note sources above. (Non- deflated) Average hourly earnings for marketing farm food products, Index numbers 1957-59 = 100, U.S. Marketing and Transportation Situation, MTS-lSO, USDA, August 1963. (MTS-154, 1964) (Table 7). (Non-deflated) Unit labor costs for marketing farm food products, Index numbers 1957-59 = 100, Marketing and Trans- portation Situation, MTS-150, USDA, August 1963 (also MTS-154, 1964, p. 15) (Table 7). (Non- deflated) Total feed grain production plus other (non- government) carry over, U.S. marketing years (includes October-September year for corn and sorgum grain, July-June year for oats and barley), applies to production up to current year September or June end of marketing year, million tons, Grain and Feed Statistics, USDA, ERS, Statistical Bulletin No. 159, Supplement for 1964, March 1965. Beef price expectations (average price received by farmers), dollars per cwt., in Lerohl, Milbourn: Expected Prices for U.S. Agricultural Commodities, 1917—62, Michigan State University, CPI5759 PPFI5759 Data 191 Ph.D. Thesis, 1965. An estimate for 1963 was made following Lerohl's procedures (Non-deflated) Consumer Prices, all items (U.S. Dept. of Labor), index number 1957-59 = 100, Agricultural Sta- tistics (Table 629). Prices paid by farmers, total including interest, taxes and wages, index numbers 1957—59 = 100, Agricultural Statistics (Table 629). The actual data which were used in this study are presented in the following table. (Note that all monetary variables are presented in their deflated forms.) 1936 1937 1938 1939 1940 1941 1949 1950 1951 1952 1953 192 Table C.1 DATA USED IN THIS STUDY (EXCLUDES DATA FOR VARIABLES INTRODUCED 1! APPENDIX A) PBEEFR QBEEFC POMEATR PBEEFF QBEEFP IBEEFF2 POHEATP IBBEPIFZ QOMEATC Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y3 Y9 cents cents per mil. per mil. 1000 1000 mil. Year pound pounds pound S/cwt pounds 45329 slewt nggg, Apounds 59.21 7742 62.82 13.85 7358 2759 24.72 28486 11018 65.00 7107 64.16 15.56 6798 3336 24.13 27139 11192 58.45 7058 58.00 15.57 6908 3303 21.88 27100 11383 60.95 7159 54.40 17.00 7011 3633 19.03 28254 12501 60.45 7257 49.02 18.00 7175 4065 17.43 30307 13802 61.40 8021 56.10 19.60 8082 4185 23.84 33003 13332 82.41 9439 71.45 23.02 9439 4390 24.77 38118 15289 89.98 9529 70.13 26.48 9534 4534 24.03 42151 15901 97.46 8472 69.06 29.59 8837 4961 24.23 47876 16323 93.30 9548 66.47 24.80 9650 5762 21.94 52558 16859 74.14 12113 67.58 17.16 12407 5370 24.26 54148 16285 73.18 12743 68.11 16.84 12963 5795 23.05 55455 16340 72.35 13313 62.31 16.60 13569 5929 19.59 55762 17391 69.69 14121 57.68 15.68 14462 6122 17.93 53447 18331 72.04 14242 60.54 17.55 14202 5898 19.32 53316 17773 84.37 13786 61.33 21.90 13330 6601 20.03 56013 18037 81.58 14202 54.96 22.16 13580 7173 15.70 58882 19747 78.56 15121 54.58 20.00 14727 7645 16.65 59913 19607 76.01 15873 53.02 19.61 15298 7865 16.02 62587 19991 78.18 16298 53.73 20.29 15296 8941 16.06 66144 20437 75.91 17658 51.57 18.77 16423 8988 14.96 69846 20998 71.97 18984 49.91 16.82 18424 9483 14.71 71000 21361 74.32 11466.76 60.43 .19.53 11288.05 5588.57 20.46 47648.19 16311.29 193 Table C.1 (can't) L n: QOHEATP DISPY CMKTGH IBEEPPl IBEEPNPI PPROTEIN ARANGECI POMEATFL Ylo x1 x2 x3 x4 x5 x6 x7 cents mil. bi1. per 1000 1000 $/1000- % of Year pOunds dollars pound hggg nggd # ton normal Slcwt 1936 11495 137.06 24.84 3202 29193 85.02 72.33 23.67 1937 10901 142.00 25.20 2759 28486 85.56 76.33 24.72 1938 11524 133.81 23.01 3336 27139 76.28 83.66 24.13 1939 12715 145.45 21.90 3303 27100 82.00 73.00 21.88 1940 14178 155.94 20.70 3633 28254 77.98 80.66 19.03 1941 13958 181.29 18.52 4065 30307 87.38 92.33 17.43 1949 15783 228.55 22.53 4540 37020 73.60 81.66 29.04 1950 16330 247.85 22.55 4390 38118 68.31 84.66 24.77 1951 17197 251.38 22.21 4534 42151 66.67 78.66 24.03 1952 17582 258.06 23.68 4961 47876 77.49 74.66 24.23 1953 16615 270.92 29.93 5762 52558 63.13 75.33 21.94 1954 16864 274.47 23.40 5370 54148 71.28 71.00 24.26 1955 17716 294.11 25.19 5795 55455 60.85 78.33 23.05 1956 18747 309.29 24.92 5929 55762 55.44 66.33 19.59 1957 18095 315.10 25.20 6122 53447 51.33 82.33 17.93 1958 18462 315.70 25.22 5898 53316 54.22 83.00 19.32 1959 20092 332.12 25.81 6601 56013 52.76 79.00 20.03 1960 19871 339.38 25.41 7173 58882 48.61 78.66 15.70 1961 20622 349.71 25.43 7645 59915 53.41 78.66 16.65 1962 20799 364.71 25.05 7865 62587 54.78 81.33 16.02 1963 21549 377.32 24.74 8941 66144 54.25 77.33 16.06 1964 21934 399.44 24.24 9433 69671 53.27 75.33 14.99 MEAN 16718£n 258.30 23.78 5324.95 45898.62 66.68 78.54 21.12 1594. Table C.1 (con't) PFEEDIDL QOMEATP NOMIMPORT NBIMPORT CPIS759 PPFIS759 x8 x9 x10 x11 1957-59- mil. mil. mil. 1957-59. 1957-59= Year 100 pounds (pounds pounds 100 100 1936 126.19 9687 -477 384 48.3 42.0 1937 110.57 11495 291 309 50.0 45.0 1938 137.78 10901 -141 150 49.1 42.0 1939 111.90 11524 -241 148 48.4 42.0 1940 111.90 12715 -376 82 48.8 42.0 1941 119.05 14178 -626 - 61 51.3 45.0 1949 140.45 15208 -494 O 83.0 86.0 1950 119.77 15783 -429 - 5 83.8 88.0 1951 119.32 16330 -874 -365 90.5 97.0 1952 121.65 17197 -723 -102 92.5 98.0 1953 128.57 17582 -330 -294 93.2 95.0 1954 120.00 16615 -524 -220 93.6 95.0 1955 118.95 16864 -325 -256 93.3 94.0 1956 112.77 17716 -416 —341 94.7 95.0 1957 108.42 18747 -322 40 98.0 98.0 1958 103.06 18095 -425 456 100.7 100.0 1959 99.00 18462 -345 622 101.5 102.0 1960 98.04 20092 -264 394 103.1 102.0 1961 96.08 19871 —631 575 104.2 103.0 1962 95.15 20622 -362 1002 105.4 105.0 1963 95.24 20799 —551 1235 106.7 106.0 1964 96.26 21555 -573 560 108.1 107.1 MEAN 114.96 16213.48 -407.52 178.71 82.86 82.0 APPENDIX D Simple Correlation Coefficients Between Pairs of Variables The simple correlation coefficients for all the endogenous and predetermined variables in this study (except variables in- troduced in Appendix A) are presented in Table D.l below. 195 196 enhn.o mnem.o mmmm.o nomm.o wNHo.OI mmmm.o thm.o omho.ou mamm.OI oomv.o oomv.o BmOmZHmz nmam.OI omav.OI ommm.0I oomM.OI mmmo.OI ommN.oc momH.OI ovhm.OI h®ma.0l ON®H.OI ONQH4uI9ROmZHzOz momm.o Omh¢.o ohhm.o nvom.o odmm.01 mmvm.o mv~m.o N0nm.0 mHmH.OI mva.o mvH¢.o ama