MSU“ LIBRARIES .—_1—- RETURNING MATERIALS: P1ace in book drop to remove this checkout from your record. §1fl§§_wi11 be charged if book is returned after the date stamped be10w. [J Ufww‘rvigai . 01 .1 L229 .. W 1"”: ' .1 H8 3 Q ‘~"“ ‘4' «J 1:; 13.1} 4 K ' ' AN ECONONETRIC MODEL OF 0.8. LIVESTOCK AND POULTRY SECTOR FOR POLICY ANALYSIS AND LONG-RUN FORECASTING: TESTING OF PARAMETER STABILITY AND STRUCTURAL CHANGE BY Herlinda Dador Inqco A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 1987 Copyright Merlinda D. Ingco 1987 ABSTRACT AN ECONOMETRIC MODEL OF 0.8. LIVESTOCK AND POULTRY SECTOR: FOR POLICY ANALYSIS AND LONG-RUN FORECASTING: TESTING OF PARAMETER STABILITY AND STRUCTURAL CHANGE BY Merlinda Dador Ingco The major problem in empirically tracking changes in demand structure due to changes in consumer preferences is that shifts in the utility function are not directly measurable. Given this problem, empirical attempts to identify structural change in meat demand by ad-hoc procedures and varying-parameter techniques have serious limitations. One criticism pertains to the inability of these procedures to distinguish between structural change and model misspecification. This paper explores the systematic use of several statistical procedures to minimize the problems associated with ad-hoc analysis of structural change. Specifically, the study uses a three-stage approach in investigating Changes in demand structure for beef, pork. broiler, "id “in“! meat. The approach is useful in detecting structural Ch‘nge as well as misspecification in the context of simple IOdels. Heat demand models were constructed in the context of developing an annual forecasting model for 0.8. livestock “‘1 ”“1“? sector. The recursive least squares parameter "unites for beef. pork, and broiler inverse demand models varied over the 1955-1985 period. Two periods with very different patterns are identified: 1961-1976 and 1977- 1985. The average size of the residuals is greater in the second period than in the first period. Second, a tendency to overpredict in the second period is evident. The forward one-step recursive residuals for beef, pork, and broilers deviate from what we expect from the null hypothesis of constant regression parameters. Use of several statistical procedures suggest that structural change in market demand for beef, pork, and broilers occurred about 1976-1977. Health concerns may be the cause but no sound data exists to permit testing this possibility. The three-stage approach is useful in determining the timing of change and pattern of variation in demand parameters. A major conclusion of the study is the inadequacy of a constant parameter formulation for the demand of the three meats. Results indicate an increase in the absolute value 0f own-quantity flexibility for beef and pork. The higher flexibility has implications for price stability and price levels as market structure changes. Government programs on feed grains which indirectly affect livestock quantity, will now have a greater impact on meat prices. To my parents ACKNOWLEDGMENTS Completion of this study would not have been possible without the invaluable intellectual guidance and support of the members of my dissertation and guidance committees. Dr. Lester V. Manderscheid, who served as my major professor during my Ph.D. program, generously gave his time in reviewing the manuscripts and providing insightful comments and suggestions. His interest in my professional develop- ment provided both encouragement and challenges throughout my graduate career. The guidance and support of Dr. James ailker, my thesis supervisor, are also invaluable in the completion of this project. His insights were very useful in answering the many questions and issues I encountered. Dr. John Ferris's assistance and guidance in the construction of the livestock model, particularly the hog sector component were invaluable. His ideas and knowledge about livestock markets were very useful in formulating the model structure. My special thanks also go to Dr. J. Roy Black who provided intellectual challenges and support in the preparation of this project. I am grateful to Dr. Warren Vincent, who .even after his retirement provided continued guidance and support. I also gratefully acknowledge the financial support provided by the Michigan Agricultural Experiment Station and th- ('1 the Department of Agricultural Economics during my graduate program. I thank Chris Wolf, Jeff Anderson, Margaret Beaver, Shayle Shagam, Main-Hui Hsu, Tom Hebert for their technical and computer assistance. Extra special thanks go to my Lord and Savior Jesus Christ for providing many opportunities for growth and special friendships during my stay in the United States. His love provided inspiration and encouragement during the writing of this paper. iv LIST 0? LIST OF CHAPTER 1.7 CHAPTER 2.1 TABLE OF CONTENTS Page TABLES o e eeeeeeeeeee e eeeeee e eeeeeeeeeeeee s eeeeeee x FIGURES eeeeeeeeeee e eeeeeeeeee seseeeoeees eeeeee eeexii l - INTRODUCTION .. ........... . .................. 1 Focus of the Problem . ...... .... ...... . .......... 3 Research Objectives................ .......... .... 5 Hypotheses About Change in the Structure of U.S. Demand for Meat... .......... ... 6 Review of Relevant Research ....... ..... .... ..... 7 Approach in Testing and Estimating Structural Change in Aggregate Demand for Meat .... ..... ............ ................... ll Incorporating Structural Change in Livestock Production in Modeling Livestock Supply Response ....................... 15 Organization of the Study ....................... l7 2 - THEORETICAL FOUNDATIONS OF CONSUMER DEMAND AND DYNAMIC SUPPLY RESPONSE ANALYSIS ......OOOOOCOCOOOOCOCOOO ............ 18 The Static Theory ......... ...... . .............. . 19 2.1.1 Utility Maximization ...................... 20 The Theory of Inverse Demand for Applied Demand Analysis .......................... ....... 24 Theoretical Extensions to Analyze Structural Change in Consumer Demand ............ 31 Demand Irreversibility .................. ..... ... 33 Theoretical Foundations in Dynamic Supply Response Analysis ........... ............ . 35 summary 0000000000 O 0000000000 ......OOOOOOOO ....... 36 v CHAPTER 3 - SPECIFICATION OF CONSTANT PARAMETER BASE MODEL OF 0.8. LIVESTOCK PRODUCTION AND PRICES AND EMPIRICAL RESULTS ...... . ...... 3.1 Structure of the Base Model Page 3.1.1 Livestock and Poultry Production ........... 3.1.1.1 Beef Production Beef Cow Numbers ...... Deef Heifer Replacements ............ Steer Slaugther Weight Heifer Slaugther Weight ....... . ..... . 3.1.1.2 Pork Production ...................... Sow Farrowing in the Fall Sow Farrowing in the Spring ........ .. Pork Production . ...... . ........... .. 3.1.1.3 Poultry Production .................. Broiler Production . ................. Turkey Production. ................... Egg Production .. .................... 3.1.2 Livestock and Poultry Demand .. ...... . ..... 3.1.2.1 Beef Demand ......................... 3.1.2.2 Pork Demand ..... .................... 3.1.2.3 Poultry Demand... .................. .. 3.2 Method of Estimation .................... ........ 3.3 Empirical Results of Base Model Estimation....... 3.3.1 Livestock and Poultry Demand .. ............ 3.3.2 Livestock and Poultry Production........... 3.4 Summary and Conclusions vi 38 39 39 41 43 44 45 46 46 47 47 47 49 50 50 51 53 56 57 59 60 61 76 Page CHAPTER 4 - ANALYSIS OF PARAMETER STABILITY AND 4.5 CHAPTER 5.1 STRUCTURAL CHANGE IN THE U.S. MARKET DMD FORmTOCOOOOOOO0.0000000000000000000087 Definition of Structural Change in Demand Analysis .......... ........... ........... ........ 88 Testing of Structural Change ............. ...... ..88 Conceptual Problems in Testing Structural Change ...... ................ ...... ............... 88 Exploratory Approach of Testing Structural Change ...... ........... . .............. 90 4.4.1 Recursive Estimation ....................... 91 4.4.2 Recursive Residual Analysis ............... 97 4.4.2.1 Significance Tests .................... 99 CUSUM and CUSUMSQ Tests ............. 99 Location Test. ..................... 102 Linear Rank Test ................... 104 Modified Von-Neumann Ratio ......... 106 Heteroscedasticity Test ............. 106 Quandt's Log Likelihood Ratio ....... 107 Runs Test....... ........ ... ......... 108 Specifying Parameter Variation in Demand Models ... ............... . ...................... 109 4.5.1 Time Trend ......OOOOOOOOOOOOOOOOOO ..... .110 4.5.2 Flexible Trend (Spline Functions) ........ 111 4.5.3 Dummy Variables ........................ .. 112 4.5.4 Interaction Variables...... .............. 113 4.5.5 Time Varying Parameter .................. 114 4.5.5.1 Continous Time Varying Parameter Legendre Polynomials ................ 117 Summary ......................................... 121 5 - EMPIRICAL RESULTS OF PARAMETER STABILITY ANALYSIS OF DEMAND FOR MEAT ....... 122 Results of Recursive Estimation and Recursive Residual Analysis........ ............. 122 Page 5.1.1 Beef Demand.. ............................ 125 5.1.2 Pork Demand .............................. 138 5.1.3 Broiler Demand ..................... . ..... 147 5.1.4 Turkey Demand ....... . .................... 157 5.2 Demand Models with Time Trend and Dummy Variables: A Test of Gradual Shift .............. 166 5.2.1 Analysis of Results from Models Without Trend Variables ...... ........... 169 5.2.2 Analysis of Results from Models With Trend Variables ....... ......... .... 176 5.3 Varying Parameter Models Using Legendre Polynomials............. ........................ 183 5.3.1 Beef Demand Model. ....................... 185 5.3.2 Pork Demand Model ........................ 196 5.3.3 Broiler Demand Model... .................. 209 5.4 Summary and Conclusions ......................... 220 CHAPTER 6 - INCORPORATING STRUCTURAL CHANGE IN U.S. PORK PRODUCTION MODEL .................. 226 6.1 Structural Change in U.S. Pork Production ....... 226 6.1.1 Trends in Pork Production ............... 227 6.1.2 Technical Change and Trends in Production Efficiency ................... 228 6.1.3 Trend in Pigs Per Litter ................ 229 6.1.4 Trend in Average Dressed Weights ......... 231 6.1.5 Trend in Death Losses as Percent of Total Pig Crop ........................ 231 6.2 Physical Relationships in Modeling Pork Production ...... ... ........ ..... ........... 233 6.3 Structure of the Pork Supply Model... ........... 238 6.4 Empirical Results..................... .......... 244 6.5 Summary and Conclusions ......................... 263 viii Page CHAPTER 7 - MODEL VALIDATION AND EVALUATION OF EFFECTS OF STRUCTURAL CHANGE ON LIVESTOCK PRODUCTION AND PRICES... .......... 265 Criteria for Selecting Among Alternative Models ........................ .......... ....... 266 7.2 Model Validation ............................... 268 7.2.1 Historical Simulation......... ........... 268 7.3 Discrimination Among Alternative Demand MOde130000............OOOOOOOOOOOO ..... O ........ 273 7.4 Historical Simulation Results... ........ .. ..... . 281 7.5 Projections......... ...... .... .................. 285 7. 5.1 Assumptions on Key Exogenous Variables ...... ..... .................... 286 7. 5. 2 Projections of Endogenous Variables ...... 287 7.6 Summary and Conclusions ......................... 309 CHAPTER 8 - SUMMARY, IMPLICATIONS, AND RECOMMENDATIONS FOR FUTURE RESEARCH ......... 311 8.1 Summary of Methods................... ........... 312 8.2 Summary of Empirical Results .................... 316 8.2.1 Summary of Results of Recursive Estimation and Recursive Residual Analysis.... ......... ............. ........ 316 8.2.2 Summary of Results Of Alternative Specification of Parameter Variation in the Meat Inverse Demand Models ...... ...318 8.3 Conclusions and Implications of the Study ........ 323 8.4 Recommendations for Future Research..............326 BIBLIOGRAPHY .......................... ..... ...... ...... .329 APPENDIX A . ........ ...................... ......... ....A-l ix TABLE 3.1 5.1 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13 LIST OF TABLES PAGE Estimates of Quantity and Income Flexibilities from the Base Demand Models.......... 69 Test Statistics of Parameter Stability Based on One-Step Ahead Recursive Residuals ..... ...126 Beef Inverse Demand Equation: Recursive Parameter Estimates, 1955-1985 ........... ......... 127 Beef Inverse Demand Equation: Recursive Parameter Estimates, 1960-1985 ............ ........ 128 Beef Inverse Demand Equation: Recursive Parameter Estimates, 1970-1985 ....................129 Beef Inverse Demand Equation: Recursive Residual Analysis, k I 1955-1960 ....... ........... 132 Beef Inverse Demand Equation: Recursive Residual Analysis, k - 1960-1970 ....... ..... . ..... 134 Beef Inverse Demand Equation: Recursive Residual Analysis, k 8 1970-1980 ...... . ........... 135 Pork Inverse Demand Equation: Recursive Parameter Estimates, 1955-1985 ............. ..... ..140 Pork Inverse Demand Equation: Recursive Residual Analysis, k - 1955-1960 ........ .......... 144 Broiler Inverse Demand Equation: Recursive Parameter Estimates, 1955-1985 .............. ..... 148 Broiler Inverse Demand Equation: Recursive Residual Analysis, k - 1955-1961 .................154 Turkey Inverse Demand Equation: Recursive Parameter Estimates, 1955-1985 ...................159 Turkey Inverse Demand Equation: Recursive Residual Analysis, k - 1955-1961 .................163 Table 5.14 5.15 7.2 7.6 Page Own Quantity, Cross Quantity and Income Flexibility Estimates from Inverse Demand Models without Trend Variables ...................174 Own Quantity, Cross Quantity and Income Flexibility Estimates from Inverse Demand Models with Trend Variables ....... ... ............ 182 Akaike Information Criterion (AIC) and Posterior Probability Criterion (PPC) of Alternative Inverse Demand Models for Meat . ...... 274 Percent Errors and Accuracy Measures of Simulated Values of Livestock Production, Using PORRSMZ, 1975-1985 .. ...................... 290 Percent Errors and Accuracy Measures of Simulated Values of Meat and Poultry prices, Using PORRSMZ, 1975-1985 ......... ..... . ......... 291 Percent Errors and Accuracy Measures of Simulated Values of PPLF, PPLS, TPC, GRTF, GRTS, Using PORRSMZ .1975-1985 .................... 292 Percent Errors and Accuracy Measures of Simulated Values of SLBG, SS, ADWHG, Using PORRSMZ, l975-1985...... .............. . ..... 293 Percent Errors and Accuracy Measures of Simulated Values of Livestock Production Using Base Model (in Chapter 3), 1975-1985........ 294 Percent Errors and Accuracy Measures of Simulated Values of Livestock Prices Using Base Model, 1975-1985.................. ..... 295 xi FIGURE 3.1 3.2 3.3a 3.3b 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 LIST OF FIGURES PAGE Chart of U.S. Pork, Broiler, Turkey, and Egg Supply and Demand Structure................... 40 Chart of U.S. Beef and Dairy Sector .... .......... 42 Scatter Plot of Beef Quantity and Price .......... 70 Graph of Change in Beef Demand from 1983 to 1984 ......OOOOOOOOOOOO.......O. ....... 0.0.0.0.... 70 CUSUM for Beef Demand and Confidence Boundary at 5 percent Significance Level ............ ...... 136 CUSUMSQ for Beef Demand and Confidence Boundary at 5 percent Significance Level .................. 136 Standardized Recursive Residual of Beef Demand Equation ....................... ........... 137 Quandt's Log Likelihood Ratio of Beef Demand Equation ................. ........ .... ..... 137 Pork Price Equation: Recursive Coefficients on Pork Per Capita Quantity ...................... 141 Pork Price Equation: Recursive Coefficients on Beef Per Capita Quantity.................. ..... 141 Pork Price Equation: Recursive Coefficients on Poultry Per Capita Quantity.................... 142 Pork Price Equation: Recursive Coefficients on Per Capita Real Disposable Income ............. 142 CUSUM for Pork Demand and Confidence Boundary at 5 Percent Significance Level .................. 145 CUSUMSQ for Pork Demand and Confidence Boundary at 5 Percent Significance Level ........ 145 Standardized Recursive Residuals of Pork Demand Equation ............................ 146 xii Figure 5.12 5.14 5.15 5.16 5.17 5.18 5.19 5.20 5.21 5.22 5.23 5.24 5.25 5.26 Page Quandt's Log Likelihood Ratio of Pork Demand Equation ............... ............. 146 Broiler Price Equation: Recursive Coefficients on Broiler Per Capita Quantity ..... 150 Broiler Price Equation: Recursive Coefficients on Turkey Per Capita Quantity ...... 150 Broiler Price Equation: Recursive Coefficients on Beef Per Capita Quantity ........ 151 Broiler Price Equation: Recursive Coefficients on Pork Per Capita Quantity ........ 151 Broiler Price Equation: Recursive Coefficients on Real Disposable Income Per C‘pit. 00.000.00.00.........OOOOOOOO ..... 00.00152 Broiler Price Equation: Standardized Recursive Residuals .................... ......... 152 CUSUM for Broiler Demand and Confidence Boundary at 5 Percent Significance Level . ....... 155 CUSUMSQ for Broiler Demand and Confidence Boundary at 5 Percent Significance level ........ 155 Broiler Price Equation: Quandt's Log Likelihood Ratio ................... ............. 156 Turkey Price Equation: Recursive Coefficients on Turkey Per Capita Quantity ....... 160 Turkey Price Equation: Recursive Coefficients on Broiler Per Capita Quantity ...... 160 Turkey Price Equation: Recursive Coefficients on Beef Per Capita Quantity ........ 161 Equation: Recursive on Pork Per Capita Quantity......... 161 Turkey Price Coefficients Turkey Price Equation: Recursive Coefficients on Real Disposable Income Per c‘pitaOOOOOIOOO......OOOOIOOOOOOO ........... O 162 xiii Figure 5.27 5.28 5.29 5.30 5.31 5.32 5.34 5.35 5.36 5.37 5.38 Page Turkey Price Equation: Standardized Recursive Residuals CUSUM for Turkey Demand and Confidence Boundary at 5 Percent Significance Level ........ . 164 CUSUMSQ for Turkey Demand and Confidence Boundary at 5 Percent Significance Level ........ Turkey Price Equation: Quandt’s Log Likelihood Ratio ..... ....................... 165 Own Quantity Flexibility of Beef Demand Estimated From Model with Quadratic Legendre Polynomial on Beef Quantity. ..................... 189 Own Quantity Flexibility of Beef Demand Estimated From Model with Cubic Legendre Polynomial on Beef Quantity ........... .......... 189 Own Quantity Flexibility of Beef Demand Estimated From Model with Cubic Polynomial on Beef Quantity and Linear Polynomial on Income ......OOOOOOOOOOOO ..... O OOOOOOOOOOOOOOOOOO 192 Income Flexibility of Beef Demand Estimated From Model with Cubic Polynomial on Beef Quantity and Linear Polynomial on Income ............ ....... .... ................... 192 Own Quantity Flexibility of Pork Demand Estimated from Model with Linear Legendre Polynomial on Pork Quantity and Income..... ...... 200 Income Flexibility of Pork Demand Estimated from Model with Linear Legendre Polynomial On Pork Quantity and Income ...... ..... .... ...... 200 Own Quantity Flexibility of Pork Demand Estimated from Model with Quadratic Polynomial on Pork Quantity and Linear Polynomial on Income ..... ...... . ................ 201 Income Flexibility of Pork Demand Estimated from Model with Quadratic Polynomial on Pork Quantity and Linear Polynomial on Income ............................ 201 Figure Page 5.39 5.45 6.1 6.2 6.3 Own Quantity Flexibility of Broiler Demand Estimated from Model with Linear Polynomial on Broiler Quantity ............ ...... 211 Own Quantity Flexibility of Broiler Demand Estimated from Model with Quadratic Polynomial on Broiler Quantity ......... 211 Own Quantity Flexibility of Broiler Demand Estimated from Model with Linear Polynomial on Broiler Quantity and Income ....... .................. ............. 213 Income Flexibility of Broiler Demand Estimated from Model with Linear Polynomial on Broiler Quantity and Income ........... ..... ........ ............... 213 Own Quantity Flexibility of Broiler Demand Estimated From Model with Quadratic Polynomial on Broiler Quantity and Linear Polynomial on Income ...................... 215 Income Flexibility of Broiler Demand Estimated From Model with Quadratic Polynomial on Broiler Quantity and Linear Polynomial on Income .... .............. 215 Own Quantity Flexibility of Broiler Demand Estimated from Model with Cubic Polynomial on Broiler Quantity and Linear Polynomial on Income .. ................ 216 Income Flexibility of Broiler Demand Estimated from Model with Cubic Polynomial on Broiler Quantity and Linear Polynomial on Income .................. 216 Pig Crop, Spring and Fall, 1955-1985 1000 Head ...........OOOOOOOOOOOOOOOOOO 000000000000 23] Average Pigs Per Litter, Spring and Fall, 1955-1985, Numbers ..... ...... ....... ..... ......... 231 Average Dressed Weights of Hogs, 1955-1985, pounds ......OOOOOOOO.......OOOOOOOOOOOOOOOOO ...... 232 XV Figure Page 6.4 Death Losses as Percent of Total Pig Crop 1955-1985' Percent 00...... ...... 0...... ........... 232 6.5 Comparison of Spline Function with Dummy Variable and Time Trend in Spring Pigs Per Litter Equation .................... ........... 255 6.6 Comparison of Spline Function with Dummy Variable and Linear Trend in Fall Pigs Per Litter Equation . ..... ................... ...... 255 6.7 Sow Farrowings in Spring, Actual and Estimated Values from Model with Cubic Spline, 1000 Head ..... ........ .... ........................ 256 6.8 Death Losses as Percent of Total Pig Crop Actual and Estimated Values from Model with Cubic Spline, Percent ....... ..... . ........... 257 6.9 Average Pigs Per Litter in Fall, Actual and Estimated Values from Model with Cubic Spline, Numbers .... ....... ..... ............. 257 6.10 Average Pigs Per Litter in Spring, Actual And Estimated Values from Model with Cubic Spline, Numbers ........ ......... 258 7.1 Beef Inventory, January 1, Actual, Estimated and Forecast Values, 1975-1993, billion head ...... 297 7.2 Fed Beef Production, Actual, Estimated, and Forecast Values, 1975-1993, billion pounds ...................... ...... ................ 297 7.3 Non-Fed Beef Production, Actual, Estimated, and Forecast Values, 1975-1993, billion pounds ............................................ 298 7.4 Choice Steer Price, Omaha, Actual, Estimated, and Forecast Values, S/cwt, 1975-1993.... .......... 298 7.5 Sow Farrowing in Fall, Actual, Estimated, and Forecast Values, million head, 1975-1993 0.0.0.0.0..........OOOOOOOOOOOOOO0.0 ..... 299 7.6 Sow Farrowing in Spring, Actual, Estimated. and Forecast Values, million head, 1975-1993 .... ...... . ...... . ...... .... ............. 299 xvi Figure 7.7 7.8 7.15 7.16 7.17 7.18 7.19 7.20 Pigs Per Litter in Spring, Actual, Estimated, and Forecast Values from Model with Linear Trend, Numbers, Pigs Per Litter in Fall, Actual, Estimated, and Forecast Values from Model with Linear Trend, Numbers, 1975-1993 ................... Total Pig Crop, Actual, Estimated, and Forecast Values, billion head, 1975-1993 ........... Gilts Retained in Fall, Actual, Estimated, and Forecast Values, 1000 head, 1975-1993 ......... Gilts Retained in Spring, Actual, Estimated, and Forecast Values, 1000 head, 1975-1993 Slaughter of Barrows and Gilts, Fall, Actual, Estimated, and Forecast Values million head. 1975-1993 ......OOOOOOOOOO 00000 .000. Slaughter of Barrows and Gilts, Spring Actual, Estimated, and Forecast Values, million head, 1975-1993 .................. Sow Slaughter, Fall, Actual, Estimated, and Forecast Values, million head, 1975-1993 ......OOOOOOOOOOOOOOO...00......00.0.... Sow Slaughter, Spring, Actual, Estimated, and Forecast Values, million head, 1975-1993 ....... ................................. Total Hog Slaughter, Actual, Estimated, and Forecast Values, million head, 1975-1993 0.00.00...0.000.000.0000.000000000000000 Average Dressed Weights, Actual, Estimated, and Forecast Values, pounds, 1975-1993...... ...... Total Pork Production, Actual, Estimated, and Forecast Values, billion pounds, 1975-1993000000000000000 0000000000 O. OOOOOOOOOOOOOO Price of Barrows and Gilts, Actual, Estimated, and Forecast Values. SICWtep 1975-1993 .0.........OOOOOOOOOOOOOOOO ..... Broiler Production, Billion Pounds, Ready-to-Cook, Actual, Estimated, and Forecast Values, 1975-1993 .................... xvii 1975-1993 . ...... . ........... Page 300 300 301 301 302 303 304 304 304 305 305 306 Figure Page 7.21 Turkey Production, Billion Pounds, Ready-to-Cook, Actual, Estimated, and Forecast Values, 1975-1993 .................... 305 7.22 Egg Production, Billion Dozen, Actual, Estimated and Forecast Values, 1975-1993 ...... ...... ........ . ...... . ............ 307 7.23 Broiler Price, Farm, Cents/lb. Real, . Actual, Estimated, and Forecast Values, 1978-1993 ...;... .......... ... .................... 307 7.24 Turkey Price, Farm, Cents/lb. Real, Actual, Estimated, and Forecast Values, 1978-1993 ....... ................................. 308 7.25 Egg Price, Farm, Cents/Dozen, Real Actual, Estimated, and Forecast Values 1978-1993 .......... . ................ .. ........... 308 xviii CHAPTER 1 INTRODUCTION Structural changes in supply and demand relationships have been suspected in the U.S. livestock sector. In particular, structural changes in the U.S. demand for red meat has been suspected to have occurred sometime in the mid to late 1970's. The changes are hypothesized to be the result of the increasing concern of consumers about cholesterol and the change in beef grading starting in the mid-1970s. (Chavas, 1983). A change in the income distribution in the late 1970's is also alleged to have caused the change in the structure of demand for red meat (Unnevehr, 1986). The answers to the question about why and how structural changes take place in the livestock sector and other agricultural subsectors have value in policy formulation and implementation. Knowledge about the structural change process could provide insights on how policies and programs affect the structure of agricultural sectors. This predictive knowledge may be added to the set of information used by policy makers and decision makers in determining what policies have to be formulated to foster a desired structure of agricultural sectors. Current research (Reimund, Martin and Moore, 1981; Hayenga et.al., 1985; Hilker, et.al., 1986) have given some insights about structural change in the U.S. livestock sector. Analysts and model builders, however, are continously challenged to account for the structural changes in the specification of structural models for policy analysis and for forecasting the implications of such changes to the growth prospects of relevant sectors. The Michigan State University Agriculture Model (MSUAM) has recently found it difficult to provide accurate projections of livestock production and prices. Several reasons were given for this difficulty, but foremost was the failure to account for the substantial structural changes that have occurred in the U.S. livestock production and demand for meat. Other forecasting models have been found to exhibit the same deficiency. Braschler (1983) indicated that during the 1960's and through 1973, reasonably accurate projections of both pork and beef prices at the farm and retail levels are provided by econometric models with single equation demand systems. Projection errors were primarily attributed to the errors in projections of supply variables and consumer income. Starting in the early 1970's, however, errors in twice projections were considerably larger than those of the 1360's even under reasonable estimates of supply and 3 consumer income. Tomek and Robinson (1977) likewise observed that projections of beef prices during the early 1970's based on data prior to 1969 were largely underestimated. There is, therefore, a need for forecasting and policy models to accommodate and track structural change. Consideration of structural change in modeling livestock supply and demand is not only crucial to the ability of models to provide accurate forecasts but is also necessary for the structural models to be of continous relevance and value in the important task of analyzing government programs and policies. 1.1 Focus of the Problem Difficulties in developing a model that captures the relationships useful for forecasting and policy analysis in economics have been recognized. One aspect of the problem pertains to the question of ‘how to capture the effects of the unobservable variables which have important effects on the behavior and magnitude of the structural parameters defining the economic relationship of interest. (Rausser, et.al., 1981). In the context of supply and demand analysis, Rausser, et.al. (1981) identified the unobservable variables to include changes in tastes and preferences and evolution 4 of habits, formation of expectations, changes in institutional arrangements, and technological change. These unobservable phenomena are hypothesized to result in structural changes in supply and demand relationships over time. The hypothesis of a change in the structure of demand and supply for meat commodities in the United States is of particular relevance and interest. Whether or not there has been a structural change in the demand for meat products raises important policy questions and poses interesting questions about the choice of an appropriate econometric model for forecasting purposes. If the decline in demand for red meat during the 1970's is strictly due to changes in market variables, then policies that improve meat production and marketing efficiencies will result in lower prices of red meat and will be expected to enhance the quantities of red meat demanded. However, if the observed decline in red meat demand is a result of non-market factors such as preference and habit changes, then a different policy action may be needed to get a desired result. To enhance demand and long- run industry output, policies to upgrade the quality of red meat products (e.g., producing leaner meat) might be required. Furthermore, if the structural change resulted in more inelastic demand or more flexible price for a particular 5 meat, then changes in the available supply of meat will increase the variation in farm prices of meat, ceteris paribus. This has implications regarding the effectiveness of policies designed to influence meat supply and prices after a structural change has occurred. Another important implication of structural change involves the choice of an appropriate econometric model for forecasting. Common econometric procedures require the constancy of parameters.1 This condition of constancy of parameters is usually assumed. If structural change in the demand relationship has occured for U.S. meat products, this assumption is obviously inappropriate and unjustified. Hence, a model specification that considers the likely shifts (e.g., abrupt and/or systematic) in the demand and supply structural parameters would have to be considered. 1.2 Research Objectives The objectives of this study are as follows: a. to detect and test whether structural change has occured in the U.S. demand for beef, pork, broiler, and turkey. ‘ This implies a single parameter vector defining the relationship between endogenous and explanatory variables and constant set of error process. 6 b. to include the structural change in demand in the specification of the livestock demand component of the MSUAM: c. to include some aspects of structural change in livestock production in the specification of the livestock supply component of the MSUAM; d. to estimate the changes in the structural demand parameters over time and determine the implications of such parameter changes on livestock production and prices. 1.3 Hypothesis About Change in the Structure of U.S. Demand for Meg; Several hypotheses have been presented regarding possible causes of structural change in the U.S. demand for meat during the 1970's. The increasing consciousness of consumers about the ill effects of fat and cholesterol and the changes in consumer lifestyle may have resulted in preference shifts away from red meat. The hypothesis of changing preferences in demand for meat has been suggested in some studies. Phlips (1974) considered the possibility of changes in preferences over time in demand analysis. Insights into how changes in preferences might affect demand and what caused such changes are discussed in Green (1978). Green identified three factors which might cause a change in the preferences of 7 consumers. The three factors include the effects of advertising, the effects of choices made by other consumers, and the effects of longer term impact of price changes.3 Another hypothesis pertains to the increase in the opportunity cost of time of the consumer and its negative effect on at-home beef consumption (Chavas, 1986). The change in the structure of households is also alleged to cause the decline in red meat demand. Chavas indicated that the increase in single individual households may result in changes in the structure of demand for meat. 1.4 Review of Relevant Research Efforts to capture and model useful relationships for projection purposes in agricultural economics and other nonexperimental disciplines have been faced with difficult challenges. Starting in the early 1970's, practitioners have been experiencing formidable obstacles in generating reasonably accurate forecasts of prices and supply of agricultural products. Braschler (1983) attributed part of the difficulty to the unprecedented exogenous shocks (e.g., oil embargo and energy shortages) which led the U.S. economy to gradually shift from relative stability to instability during the 1970's. 3 The effects of advertising on consumer demand is empirically tested in Ward and Myers (1979). 8 In the case of the U.S. livestock sector, the challenge in constructing forecasting and policy models arises not only from the concern to consider the potential instabilities due to exogenous shocks, but also from the concern to achieve both ”local” and ”global" approximation accuracy of model structure (Johnson, 1981). The concern to achieve global approximation accuracy has become of more particular relevance especially when there has been a structural change in the sector of interest. In this case, the structural shifts in the economic relationships of interest have to be accommodated and tracked by the policy and forecasting models. Previous empirical attempts to detect structural change in the U.S. meat demand and supply have employed both simple and more complex model specifications and estimation procedures. The results of previous studies provide different conclusions regarding the significance, type, and timing of the hypothesized structural change in meat demand. In particular, time series demand models designed to accommodate structural change by allowing structural parameters to vary over time provided interesting results. Tomek (1965) found some changes in the demand parameters for beef, pork, and chicken between the period 1949-1956 and 1957-1964. Another study conducted using a different time period found only small variations in meat demand between the period 1964-1968 and 1969-1975 (Leuthold, et.al.,1977). 9 This is somewhat supported by a later study which argued that the perceived decline in red meat demand during the 1970's can be attributed to increases in the overall supply of meat substitutes, particularly chicken and turkey and that the tastes and preferences for the three major meats did not change during the post-war period. (Bullock and Trapp, 1980). Using quarterly data from 1965 through 1979, Nyankori and Miller found evidence of structural change in the quarterly demand for beef and chicken during the 1970's, but not in the demand for pork and turkey during the same period. A significant change in the demand parameters for beef was found to have occured in the first quarter of 1976. Nyankori and Miller (1982) used linear spline functions in their analysis, hence, allowing only for abrupt parameter change during the specific point in time. Chavas (1983), by using a Kalman filter specification allowed a more gradual change in the demand parameters of beef, pork, and poultry. Using annual data from 1950 through 1979, significant parameter change in the demand for beef and poultry were detected in the 1970's relative to the 1950-1970 period. Chavas found no structural change in the demand for pork. Moschini and Mielke (1984) tested the hypotheses of structural change in the demand for beef using quarterly data from 1966 through 1981. They found only weak evidence 10 of structural change in beef demand and suggested that the recent decline in beef demand may only be due to changed market conditions and is, therefore, of a reversible nature. Braschler (1983), on the other hand, provided evidence of significant structural change in the demand for both beef and pork. Using a switching regression model that allows abrupt changes in demand parameters, significant shift in the case of pork demand was found to have occured in 1970. In particular, the retail price of pork was found to be less sensitive to changes in the supply of pork, beef and real income, but more sensitive to changes in the supply of broilers during the period 1970-1982 compared to the period 1950-1969. Cornell (1983), on the other hand, rejected a constant parameter formulation for the retail demand of table beef, hamburger beef and broilers. Cornell found evidence of rising direct flexibilities in the case of table beef over the past several years. Frank (1984) used a gradual switching regression model to test structural change in the quarterly demand for beef, chicken, and pork. Using data from the first quarter of 1970 through the third quarter of 1983, the study gave additional evidence of structural change in the retail demand for beef, chicken, and pork. In particular, a significant parameter change was found to have occured in the third quarter of 1975 and continued into the 1980's. Sm para hypc pric 1.5 11 Yeboah and Heady (1984) examined the changes in the structural characteristics and estimates of supply response parameters in U.S. hog production. They tested the hypothesis of a decline in the supply elasticities and its effects on the inter-year fluctuations on pork output and prices. By dividing the period of analysis into two ( 1940- 1959 and 1960-1977), the authors obtained evidence on the magnitudes and directional shifts in the supply elasticities for hogs. 1.5 Approgch in Testing and Estimating Strpctural thpge in the Aggreggte U.S. Demgpd for Meg; The present study extends previous research on structural change in the U.S. demand for meat. In particular, this paper explores the systematic use of several statistical procedures to minimize if not prevent the problems associated with ad hoc analysis of structural change. Specifically, the study uses a three-stage approach in investigating changes in the demand structure for beef, pork, broiler, and turkey meat. The approach is useful in detecting structural change as well as misspecification in the context of simple models. Meat demand models were constructed in the context of developing an annual price forecasting model for livestock and poultry. On an annual basis, quantities of most meats in.the market are predetermined given the lags in livestock 12 production. Given the market level data and the predetermined quantities, the demand models are specified as inverse demand functions.’ That is, real market price is specified as a function of per capita quantity of commodity in question, per capita quantity of substitutes and complements, and real per capita disposable income (prices and income deflated by CPI). The first stage of the analysis involves the estimation of inverse demand functions using recursive least squares‘ for the period 1955-1985. In this stage, the recursive parameter estimates are used as a descriptive tool in determining the effects of individual observation in a sequential updating procedure. The pattern of the recursive estimates of coefficients of the inverse demand models are analyzed, taking note of particular trends and discontinuities. Plots of the recursive coefficients indicate the pattern of variation of individual parameters. Statistical testing of parameter variation and specification errors) constitutes the second stage of the analysis. In this stage, the. statistics based on standardized recursive residuals introduced by Brown, Durbin, and Evans (1975) and those suggested by Dufour ' The theory of inverse demand functions is discussed in Anderson (1980), Salvas-Bronsard (1977), and in Houck (1966). i The details of the recursive least squares are discussed in Harvey (1981). 13 (1981) are used to test parameter variation and departures from the fitted functional form. The third stage of the analysis involve respecifying the model to include the information regarding the timing of the structural break indicated by the recursive residual analysis. Also gradual shifts in demand parameters are tested by augmenting the model with trend shifter variables. Other methods of allowing the parameters to gradually vary over time are also used. This "exploratory approach"° is argued to be more sensitive to a wide variety of instability patterns and capable of providing information on the type and timing of structural change. The procedure is related to the family of approaches that are used to detect departures from the assumption of a model such as the "residual analysis" suggested by Anscombe (1963), Zellner (1975), Belsley, Kuh and Welsch (1980), and the "diagnostic checking" in time series analysis suggested by Box and Jenkins (1969).° Dufour contrasted the exploratory methodology with other approaches which he calls "overfitting" procedures. The latter, which some previous research on structural change have used, involve nesting a model into a more general model by adding parameters and assumptions and 9 See Dufour (1981). ‘ Dufour, J.M., "Recursive Stability Analysis", Journal of Econometrics, 19(1992), PD. 32. 14 testing the significance of the added parameters. This approach is appropriate and powerful when one has a priori information about a specific type of structural change. The power of the tests involved in these procedures, however, depend on the assumptions made regarding the more general model.7 While the latter procedures appear useful in testing structural change against specific alternatives, Dufour argues for procedures that are capable of providing information about the types and timing of the likely changes, without having to make many additional assumptions. In his proposed data analytic approach, which is applied in this study, the recursive residuals are used as the basic instrument for tracking possible points of discontinuity Given the properties of the basic statistics calculated from the recursive estimation process (e.g., standardized recursive residuals, changes in the regression coefficients), structural change are indicated by tendencies to either overpredict or underpredict, heterogeneity in the prediction performance of the model, and trends in the coefficient estimates. While power against a specific alternative is not achieved through this procedure, some power against a broader range of interesting alternatives is facilitated. ' ibid, p.33. 15 For the purposes of this study, these two approaches are considered complementary procedures instead of substitutes. The exploratory approach is used to assess patterns of parameter instability in the linear regression models. Essentially, the model is first placed in jeopardy and formal statistical tests are conducted to assess changes in the regression parameters. The clues and information derived from the significance tests may then be combined with other information to modify the specification of the linear model and explicitly account for the parameter variation. 1.6 IncorporgtingpStructural Change in U.S. Livestock Production in Modeling Livestock Supply Response Significant structural change in U.S. livestock production has been largely due to innovations in mechanical, biological, and organizational technology used in production. There has been a significant trend toward specialized buildings for each phase of production with emphasis on more confinement of the animals and greater environmental control of all aspects of production. These innovations has altered the financial and costs structure of the producing units, increased output per farm, and brought about concentration and greater specialization in livestock 16 production.. The greater specialization in U.S. livestock production has in turn changed the economic relationships and patterns of livestock supply response. To incorporate some aspects of structural change that have occured in U.S. livestock production, the changes in technical and biological factors are considered in specifying livestock supply response. The basic procedure of constraining supply response by a priori information on biological relationships was introduced by Chavas and Johnson (1982) and Okyere (1982). Biological relationships such as birth, culling, replacement, maturing and marketing rates were directly reflected as a priori restrictions for the supply model. These restrictions enter as physical accounting relationships. Ratios are calculated for the flow to flow and flow to stock variables. For instance, data indicated by the physical accounting relationships in hog production were used to estimate ratios between gilts becoming sows, pigs becoming feeder pigs, and feeder pigs becoming slaughter hogs. The trends in the biological ratios are then used to constrain the supply response models.’ ' See Reimund, Martin, and Moore (1981); Hayenga, et. al., (1981); Van Arsdall and Nelson (1984). 9 See Goungetas, B., S.R. Johnson, W. Okyere, A.N, Safyurtlu, "Simultaneous Equations and Unobservable or Proxy Variables," .AAEA Econometrics Refreshers Course Handout, August, 1983. 17 1.7 Organization of the Study Following the introduction is the review of the theoretical foundations of consumer and producer behavior in Chapter 2. Also, the theory of inverse demand functions and supply dynamics relevant in the livestock sector are discussed. Chapter 3 presents the model structure of the constant parameter base model and empirical results. Chapter 4 provides a review of methods of testing structural changes in economic relationships. Simple and more advanced methods of testing and estimating structural change are reviewed. Changes in the model specification to account for possible changes in parameters due to structural change are also presented. The empirical results of the testing of structural change and the reestimation of the base model are presented in Chapter 5. Empirical estimates based on alternative specifications of the model to account for structural change are presented. Chapter 6 presents the specification of U.S. hog supply response model. Selected models are used in simulation analysis to provide intermediate and long-run projections of livestock production and prices. Results of the simulation analysis and model validation are reported in Chapter 7. Summary and conclusions are presented in Chapter 8. CHAPTER 2 THEORETICAL FOUNDATIONS OF CONSUMER DEMAND AND DYNAMIC SUPPLY RESPONSE ANALYSIS The neoclassical theory of consumer and producer behavior provides a general theoretical framework for empirical analysis of commodity demand and supply structures. In the case of applied demand analysis, however, the static theory becomes inadequate as it fails to consider the implications of certain phenomena such as structural change, habit formation and random shocks which may result in changes in the behavioral relationships over time. Since these factors have important implications on the growth prospects and general performance of commodity markets, the theory needs to be extended to facilitate the consideration of such phenomena in empirical applications.‘ This chapter briefly reviews such theoretical foundations. The basic outline is as follows. First, the static theory of consumer demand is briefly reviewed. Second, the theory of inverse demand that is most useful for applied demand analysis is discussed. Specific emphasis is given on the restrictions on inverse demands implied by constrained utility maximization. The duality of inverse and direct demands are shown. The analogue for inverse demands to the concept of income effect for direct demand developed by Anderson (1980) is also briefly reviewed. ¥ ‘ See Pope, R., R. Green, and J. Eales (1980) for mufirical testing of habit formation in U.S. demand for meat. 18 19 2.1 The Static Theory Applied demand analysis over the last 30 years have systematically employed the neoclassical theory of consumer demand. The structure of consumer preferences and utility maximization has important implications on consumer demand. Representing consumer behavior, the structure of the preference function is assumed to possess certain properties, namely, completeness, reflexibity, transitivity, continuity, monotonicity and strict convexity.1 Given these properties, the consumer's preference ordering is represented by a real valued function, viz., the utility function. These properties and the assumption that the consumer chooses that bundle of goods which gives the highest level of satisfaction relative to the other available bundles allows static consumer behavior to be analyzed and modeled within the context of a constrained maximization problem. 1 The meaning and implications of these properties for demand analysis are discussed .in Deaton and Muellbauer (1980), and in other texts of demand theory, viz., Phlips (1974). 20 2.1.1 Utility Maximization Let q: and p: be the quantity and price of good i and q be a vector of goods available to a consumer with some fixed income, Y. Let the consumer's preferences be represented by the function, u(q), which is twice continously differentiable, strictly increasing and strictly quasi- concave (Deaton and Mauellbauer, 1980; Varian, 1978). The consumer's allocation problem is to (2.1) Maximize U = u(q) subject to p x q = Y where p represents the vector of prices corresponding to q. Using the implicit function theorem, the system of first order conditions from (2.1) gives the uncompensated or Marshallian demand functions in vectors as follows (2.2) q = g(p,Y). The direct demands, (2.2), follow the neoclassical restrictions on the nature of the demand relationship, namely, (i) Engel aggregation or adding-up restrictions, (ii) homogeneity of degree zero in p and Y, (iii) symmetry of the matrix of Slutsky substitution effects and (iv) negative semi-definiteness of the matrix of the Slutsky 21 substitution effects. Each of these properties follows from the linearity of the budget constraint. The adding-up restriction require that the total value of each quantity vector must equal the fixed budget. Since the constraint in (2.2) is linear and homogeneous in p and Y, the necessary conditions for a maximum is the same for all multiples of p and Y. Thus, (2.2) is homogeneous of degree zero in p and Y. The above discussion indicates that, in general, the static theory of consumer behavior provides some useful insight for the applied demand analyst. Following the theory, the demand for a commodity may be specified as a function of prices of all goods and income. Also, to achieve theoretical consistency, the demand function should satisfy the theoretical restrictions of homogeneity, symmetry and adding-up. Furthermore, in order for an ad-hoc specification of demand to be consistent with an identifiable utility function, the analyst can impose the theoretical restrictions. The characteristics of the direct demand functions in terms of elasticities also provide useful insights to the applied demand analyst. The price elasticity (uncompensated) can be estimated as follows: (2.3) em = OH (p,Y) (DJ /91 )0 where g1; is the partial derivative of g‘ with respect to PJ- 22 The total expenditure elasticity is estimated as: (2.4) n: = g‘v(p,Y) (Y/g‘), where g1: is the partial derivative of g1 with respect to Y. Following the theoretical restrictions of the demand functions mentioned above, these elasticities possess certain properties, namely,2 (2.5) )2 (em) = -n:, 5 (2.6) Z (w: e11) = -wa. i (2.7) I (w1n1) = 1 i where W1 = pth/Y. Property (2.5) follows from the homogeneity restriction while (2.6) and (2.7) follow from the adding-up restriction. The compensated price elasticities can be derived by specifying the cost function as follows: (2.8) C(p,u) = min (Y I p x q < Y and U(q) > u ). 23 The cost function, C( ), is linearly homogeneous and both continous, nondecreasing and concave in p and increasing in u (Varian, 1978). The first partial derivatives of the cost function with respect to price gives the compensated demand function defined as (2.9) q: = g“ (p,u) = C1(p,u). The Slutsky substitution effects are derived from the : second partial derivatives with respect to price. They are defined as (2.10) c:1(p,u) = gig. The compensated elasticities are then defined as (2.11) ei: = 93* (pJ/g‘*). From the homogeneity restriction, these elasticities follow the condition (2.12) z (eh) = o. 5 The property of concavity of the cost function leads to the negative semidefiniteness characteristic of the Slutsky matrix which in turn, implies the law of demand stated as 811 < O. 24 The compensated elasticities can be defined in terms of uncompensated elasticities based on the Slutsky equation as follows: (2.13) at: = e11 + mm 2.2 The Theory of Inverse Demand for Applied Demapg Analysis2 The discussion on the theory of inverse demand is based on the work of Anderson (1980). The relevance of inverse demand theory in applied demand analysis for some food commodities has been recognized. However, there has been limited applications of the theory in applied work. Examples of empirical studies which specified and estimated demand with prices as functions of quantities are as follows: Salvas-Bronsard, et.al.,(1977); Christiansen and Manser, (1977): Barnett, (1977): Shonkwiler and Taylor (1984): Braschler (1983), Cornell (1983), Dahlgran (1986). This section briefly outlines the theory of inverse demand that is most useful to empirical demand analysis. The theoretical restrictions for inverse demand that are analogous to those of direct demand follow from the standard neoclassical assumptions regarding the structure of the preference function. Inverse demand is specified with 3 See Anderson (1980). Salvas-Bronsard, et. al., (1977) discussed the properties on inverse demand functions in the context of a demand system. 25 price as a function of quantities and total expenditure; that is (2.14) p, = f+1(q,Y) where f’1(q,Y) is linear and homogenous in Y. The "quantity elasticity" or "flexibility" of good i with respect to good j can be defined as follows (2.15) t,, = t;‘(q,Y) (q,/£*’) where fj’ is the partial derivative with respect to qJ. Quantitity elasticity or flexibility is the analogue for inverse demand of price elasticity in direct demand. It indicates the change in the price i necessary to induce a marginal change in consumer's consumption of good j. A relationship between price elasticities and quantity flexibility was first developed by Houck (1965) in the following form (2.16) eH = 1/1:H Houck (1965) showed that under general conditions, the inverse of the direct flexibility is equal to the lower absolute limit of the direct price elasticity. The strength of the cross effects of substitutes and complements will determine the size of the difference between these two 26 values. In particular, if all the cross effects are zero, the reciprocal of the direct price flexibility is equivalent to the direct flexibility. Anderson (1980) developed the analogue of total expenditure elasticities in inverse demands. Within the context of inverse demand analysis, Anderson asked the question: "how much will price i change in response to a proportionate increase in the quantity of all commodities". This question looks at the behavior of prices as the scale of the commodity vector along a ray from the origin is changed. In order to answer this question, Anderson (1980) formalized the notion for marginal increases in the scale of consumption by defining the "scale elasticity" and deriving the restrictions relating "quantity elasticity" and "scale elasticity". The latter was shown to be the analogue of total expenditure elasticity. Following Anderson's notation, the inverse demand function is defined as (2.17) p, = £,( kq‘) = g'( k,q* ) The "scale elasticity" of good i is written as (2.18) s: = g‘o(k,q*) (k/g‘) where gio(k,q*) is the derivative of g1 with respect to k. “i 4. 27 It is also shown by Anderson that the sum of the budget share weighted quantity elasticities with respect to x; is equivalent to the negative of the budget share of good j. This is shown by defining the budget constraint as (2.19) 1 = I f‘ (q)q: 1 By taking the derivative with respect to Q), (2.20) O = 2 £11 q1+ fJ = I f11(QJ/f1)f‘Q1 + qu‘J i i or (2.21) I f1.) W: = -w: (2.21) is the analogue of the Cournot aggregation condition. The analogue to the Engel aggregation is derived by taking the sum of (2.21) as follows (2.22) I W1 1 f11 = - I w; i j j 1, the analogue of restriction Given (2.12) and I w; (2.5) is derived as (2.23) I s: = -1 28 "Scale" and "quantity" elasticities defined above correspond to the concepts of uncompensated elasticities relevant for inverse demands. The compensated "quantity elasticity” is derived from the transformation function which is dual to the cost function. The transformation function, T(q,u), is shown to satisfy the following condition: (2.26) U(q*/T(q*,u*)) = u* for all attainable value of q* and u*. The transformation function indicates how much a certain consumption vector must be divided to bring the consumer on another indifference curve. This function is non-decreasing, linear homogenous and concave in q and decreasing in u. By taking the derivative with respect to goods, the constant utility or "compensated" inverse demand function is derived (2.27) p: = f1*(q,u) = T1(q,u) where T: is the partial derivative with respect to q:. These inverse demand functions indicate the levels of normalized prices that induce consumers to choose a consumption bundle that is along a ray passing through q with an associated utility level u. The second partial 29 derivatives of the transformation function, T, (i.e, the first partial derivative of f1*) provide the Antonelli substitution effects which indicate the amounts normalized prices change as a result of a marginal change in the reference consumption, QJ, while keeping the consumer on the same indifference curve. The constant utility (compensated) "quantity elasticities" or flexibilities can then be defined (2.28) f*1J = fHJ (cu/f“). Since the transformation function is homogenous of degree one in q, f1* is homogenous of degree zero in q. Hence, applying the Euler's theorem to (2.28) gives the following restriction (2.29) I PH: 0 Note that (2.29) is analogous to (2.12). Also, following the properties of the transformation function, the matrix of Antonelli effects is negative semidefinite. This implies (2.30) f*11 < 0 Which define the "law of inverse demand". The understanding of the "implicit compensation scheme" 30 and the derivation of the analogue of the Slutsky equation aids the interpretation of the compensated quantity elasticities in applied demand analysis. To achieve theoretical consistency, specified direct demand equations in a complete system should be homogenous, symmetric and add-up. To achieve this, one could derive the system of demand equations from a specified utility function. This approach results in a loss of generality due to the choice of a particular utility function. On the other hand, any ad-hoc demand structure is assured to correspond to an identifiable utility function if the theoretical restrictions are imposed (Deaton and Muellbauer, 1980). This approach usually requires the use of some sophisticated econometric procedures. When only a number of commodities are of main interest in the demand study, the analyst usually assumes a separable utility function. The condition of strong separability is satisfied if the marginal rate of substitution between goods i and j, which belong to commodity group r and t respectively, is independent of the consumption of commodities in any other group, 1. The separability condition require that the consumers attempts to maximize utility in two stages. In the first stage, the consumer allocates his/her expenditures between 1 separable commodity groups. In the second stage, expenditures in one group are divided among individual commodity expenditures. (George and 31 King, 1971). Since marginal utilities are difficult to estimate in actual practice, the groups of commodities are often arbitrarily selected. DeJanvry's (1966) results indicate that meat could then be considered as one separable group. If structure have changed, meat may no longer be separable. As others have recognized, there remains a gap between theory and empirical analysis of demand. The gap is a result of problems and difficulty in developing and imposing appropriate theoretical restrictions in the context of full market demand systems. For example, the Slutsky condition derived from the individual demand theory does not hold for market demand without assuming strong separability condition (Safyurtlu and Johnson, 1985). 2.3 Theoretical Extensions to Analyze Structural Change in Consumer Demand The basic simplifying assumption in the neoclassical demand theory outlined above is the constancy of preferences of individual consumers. The length of the period in which the utility function is defined is such that it is long enough to allow the consumer to satisfy his(her) preferences regarding certain varieties of goods but not too long so that his(her) tastes 'might change. That is, consumer preferences are assumed to be given in the analysis employing the static theory. Although this assumption makes 32 applied demand analysis manageable, its limiting effect has been recognized. Attempts have been made to consider possible changes in consumer preferences. Phlips (1974) presented a theory of intertemporal utility functions which allows for changing preferences. When consumer preferences are allowed to change in demand analysis, the system of demand will also change. That is, the change in the structure of consumer preferences will lead to a change in the consumer's utility function which in turn lead to a change in the structure of the demand function. Green (1978) identified some factors which might affect preferences of consumers. The effect of such factors as advertising, choices of other consumers and long-run changes in prices on the structure of consumer preferences were discussed. Cornell (1983) discussed the effects of these factors on the consumers' retail demand for meat. The effect of advertising on consumer preferences is based on the notion that the latter is influenced by information available to the consumer. Information on the characteristics of goods influence the choice of an individual consumer (Lancaster, 1966). Another limiting assumption within the context of static demand theory relates to the presumed instantaneous adjustment to new levels of equilibrium when there is a change in prices or income variables. It has been 33 recognized that consumers respond and adjust to such price and income changes in a gradual manner over time due to habit formation and dynamic characteristics of consumer behavior. Attempts have been made to include the effects of habit formation in analyzing consumer demand. The common approaches involve the inclusion of dynamic aSpects into the utility function or directly into the demand functions. The latter approach have been applied more than the former in applied demand analysis. Among the common methods under this approach include the specification of a time trend in the demand equation, use of a distributed lag model, use of a cob-web model, and the use of first differences of variables. Among the different ad-hoc models, the partial adjustment model developed by Houthakker and Taylor (1966) have been employed in empirical, demand analysis. These models specify demand as a function of not only prices and income, but also of lagged values of certain variables. 2.4 Demand Irreversibility Demand irreversibility is based on the notion that consumers' tastes may change in the long-run due to habit formation. An irreversible demand model was first tested by Farrell (1952). The model distinguished between rising and falling stages in the income and price variables. Irreversibility in the demand for beef was tested by 34 Goodwin, et.al., (1968). Possible irreversible behavior in beef demand is a result of the existence of consumption habits, the cyclical pattern in prices and consumption and the identified distinction between short-run and long-run demand response. Habit formation is considered to not only prohibit immediate price-quantity adjustments, but also may affect other patterns of consumption behavior which causes shifts in the parameters associated with other explanatory variables. Pope, et.al. (1980) developed the theoretical basis for possible changes in elasticities due to habit formation. Goodwin, et.al. (1968) provided some empirical evidence on the irreversibility in demand for beef. Their study provided separate estimates of short-run and long-run elasticities for both decreasing and increasing consumption of beef. In the short-run, the direct price elasticities were found to be lower (more inelastic) in periods of declining consumption. This is consistent with the hypothesis that consumers change their consumption level by less during period of increasing price than during the period of declining price. Also, it was found that the income elasticities were larger during periods where prices decline. The stronger response to changes in income during phases of declining prices was considered a result of the existence of a broader range of quantities included in the inelastic portion of the demand curve over time. Another 35 interesting result from the Goodwin study is the tendency of the price and income elasticities to decline over time. This phenomenon was explained to result from the decreasing share of income spent on beef over time as income rises. The coefficient of adjustment was also estimated and estimation results indicated an immediate adjustment of consumption after a decline in price but a lagged adjustment of consumption was found after a price increase. The lagged consumption response after a rise in price was hypothesized to result from the persistence of habits that were formed before the price increase. This phenomena was considered to characterize irreversibility in the demand for beef. 2.5 Theoretical Foundations in Dynamic Supply Re§p0n§g_ Analysis For the purpose of the present study, the distinction made by Cochrane (1955) between supply function and supply response will be adopted. A supply function indicates how the amount of a commodity offered for sale changes with price during a given period under ceteris paribus condition. A supply response indicates how the amount of a commodity offered for sale changes with price when all the other factors are allowed to change. The latter concept is more useful in predicting the impact of changes in price on the quantity offered for sale in the aggregate sector level. 36 The existing theory of supply dynamics has been widely appplied in empirical analysis of supply response of agricultural commodities. Most empirical studies have employed econometric models which attempt to capture the dynamic behavior in supply response. One aspect of the dynamic behavior which has gained attention both in theory and in applied analysis is the price expectations formation of producers and how it affects supply. Also, models usually differentiate between desired and actual levels of output. The adjustment toward the desired output level is estimated using a distributed lag specification. The latter is usually based on Nerlove's formulation of adaptive expectations hypothesis which assumes that in each period, the producer revises his expected price in proportion to the difference between the last period's price and the last period's expected price. In this model, the producer's long-run expected price is specified as a weighted moving average of lagged prices with the weights declining over time (i.e., a geometric distributed lag). 2.6 Summary The neoclassical economic theory provides a general framework for supply and demand analysis. However, the static theory is limited for certain aspects of empirical 37 analysis. Extensions of the theory are needed to analyze habit formation and structural change in demand. The implications of changes in preferences in analyzing consumer demand are considered in extensions in the theory such as in the theory of intertemporal utility functions. Habit formation and other dynamic characteristics of consumer behavior are considered in ad-hoc specifications of demand function such as in Nerlove's partial adjustment model and in stock adjustment model developed by Houthakker and Taylor. The theory of inverse demand provides a useful framework in analyzing demand for meat commodities. The demand parameter measures the responsiveness of a commodity price to a change in quantity supplied. The theoretical restrictions on inverse demand function are shown by Anderson (1980) to be analogous to those of direct demand function implied by constrained utility maximization. Estimated inverse demand function for beef, pork, turkeys, and broilers are presented in the following chapter. The specification of constant price models estimated in the next chapter is based on the theory of inverse demand discussed in this chapter. Estimates of "quantity elasticities" or flexibilities are presented . CHAPTER 3 SPECIFICATION OF CONSTANT PARAMETER (BASE) MODEL OF U.S. LIVESTOCK PRODUCTION AND PRICES AND EMPIRICAL RESULTS The general method employed in the estimation of the constant parameter base model of the U.S. livestock production and prices follows from the approach suggested by and Johnson and Rausser (1977) which involves three major stages. First, the system under consideration is studied and the structural relationships identified and delineated. The second stage involves the representation of the identified relationships in a quantitative framework. This stage includes the specification, estimation, verification, validation, and revision of the model structure. The third stage involves the use of the estimated model in the context of policy analysis and forecasting. Verification‘ involves the evaluation of individual equations based on regression diagnostics and comparison of parameter estimates with previous empirical evidence. The validation stage of the model construction involves the evaluation of both individual equations and blocks of equations. Initial validation of the model is carried out by using the model to simulate the historical period. Separate blocks of equations are simulated in order to locate sources of unstable behavior in the system. The performance of the livestock model as an entire system is 38 39 also evaluated using absolute and relative accuracy performance measures. 3.1 Structure of the Begs Model 3.1.1 Livestock and Poultry Prgguction This section presents the structure of the base livestock supply and demand model. The base model of domestic livestock and poultry consists of 20 behavioral equations and 15 definitional equations covering five major livestock and poultry products: beef, pork, broilers, turkeys and eggs. The structure of the model is presented in Figure 3.1. The livestock and poultry model is an annual model. The annual specification is a result of the underlying objectives of the MSU Agriculture Model to identify the dynamics of adjustment in the longer run and to provide intermediate and long-run projections (of quantities and prices for the commodities included in the model. The specification and design of the model therefore do not measure short-run and seasonal variations within a year. The equations in the model are specified and estimated using aggregate national data. Hence, the model specification does not estimate regional or state differences in production systems such as differences in 40 non. 300:2..— asc= Deacon .0U02 .DCDEOD Uc< bane—m in OLDUE mom .ontah Gazetm .vton Eco—uztm _v): a L— a‘l.lv ‘15:? A .2 -m m U 0010 utnoo ton. m .DOEAO bannm ) brace (..-1v out“. w how-5* m l ....... 00th. CLOU Draco .in. D K >3an {on 0: 00 ton bnnam >045». DSQDO Len. bnnaw Coom DEDEOO DCD banam \AOXLDF u ................. V CO—aODVOLl 4..” Din—DO Lon bannm kin—non 007.1 to:0..m £0.003votl ...—Bum o: 00 ton bunnw vica— Ou..00 Lon. Ennam moom _ 1 007.0 .00rccno 02000 ..on, E bunam « Loo: . A .0002 DCOEOD UCO baaam mEOLO m.3 _ # ofiauo ..01 L bannm u mom :o_uoauotl COSODUDLn. now .......... 00m DCDEOO .uco ban—3m mum UCOEID .uco bannm {on 41 enterprise combinations, size of operations, and relative COBt structures . 3.1.1.1 Beef Production The variables which are endogenous to the beef production model include beef cow inventory, steer and heifer slaughter and cow and bull slaughter. Beef supply is determined in the model by specifying producer decision variables and physical response variables. Producer decision variables include the number of animals to sell, the weight at which an animal is slaughtered and the rate of herd expansion or contraction. Physical response variables are determined mainly by biological factors which are outside the control of the producer. Figure 3.2 shows the structure of the beef model and the linkages between the beef and dairy sectors. Relationships which are estimated based on economic factors are denoted by an asterisk (*). Estimated equations for calving rates, breed-feed-slaughter decisions and the slaughter weights are included. Separate slaughter weight equations are estimated for steers and heifers. The biological parameters specified as independent of producer control include survival rates, the distribution of calves between bulls and heifers and the meat yield per carcass. 42 Figure 3.2 BEEF & DAIRY SECTOR .BEEE 2131 , ................ BEEF i COWS CNMNG CALVES | BULLS m ”E FEREI 'TFEH' m FEEDER HEIFERS mm SEER . DNRYFUJSTEER answer answer fimuxmm( ‘ K aw FED 5m 21 J tom fl PRODUCTION ..... 2 YR LAG 43 Beef cow numbers are estimated as the sum of the cow herd and replacements less the number of culls and deaths. Cull cows and non-fed steers both become part of the non-fed beef category. Non-fed beef production is determined from the number of animals in this category times the slaughter weight per animal. The slaughter weight for non-fed beef is estimated for all non-fed beef and makes no distinction between cows and steers. Dairy cull cows and non-fed dairy steers are also included in the non-fed category. Total commercial meat production is the sum of fed beef steer and heifer production, non-fed beef and dairy production, and dairy fed steer production. Beef Cow Numbers (BFCOWT): BFCOWT I Do + B: * BFCOWT(t-1) + B: * rCVP(t-1) + B: * FCVP(t-2) + 84 * FCVP(t-3) FCVP - Feeder calf prices, S/cwt. BFCOWT 8 Beef cow numbers, January 1, (1000 head) Beef Heifer Replacements (BFHEIF): BFHEIF - Bo + B1* BFHEIF(t-1) + 82* BCP(t-l) + B: * BCP(t-2) where BCP = BFCALP/CPIT 44 BFHEIF I Beef Heifer Replacements, January 1 (1000 head) BFCALF I Beef Calf Price, S/cwt. (Kansas City) CPIT I Consumer Price Index, 1967 I 1.0 Steer Slaughter Weight (STWT): STWT I Bo + 31* TIME + B: * RATIO(t-1) where RATIO(-1) -(FBEFPT/CORNPT)(-1) STWT I Average Steer Slaughter Weight, lbs. TIME I 1983= 83, 1982I82,...etc. FBEFPT I Omaha Choice Steer price, S/cwt. CORNPT I U.S. Average Corn price received by farmers, S/bu. Heifer Slaughter Weight (HFSW): HES" 8 Bo + B:*TIME + 32 * RATIO(t-1) where RATIO I FBEFPT/CPIT HFSW I Average Heifer Slaughter Weight,lbs. TIME I 1983-83, 1982-82,... etc. FBEFPT I Omaha Choice Steer price, S/cwt. CORNPT I U.S. Average Corn price received by farmers, S/bu. 45 3.1.1.2 Pork Production The supply structure for pork is determined largely by the relationship between hog and feed prices. Pork production is determined based on the sows farrowing in the previous fall and sows farrowing in the spring of the current year, last period's pork production and ratio of hog price to corn and soymeal prices. Supply estimation starts with the estimates of spring and fall sows farrowing. The fall farrowing equation is determined by the most recent spring farrowing, corn and soymeal prices and hog price. A variable to represent the closing of the spring farrowing versus fall farrowing levels starting in 1975 is also included. The spring farrowing equation reflects the role of partial adjustment based upon the December 1 inventory of sows and the changes in the profitability of hog production. Variations in pork production is explained in the model by the variations in sow farrowing and the changes in the hog-corn and hog- soybean meal price ratios. 46 Sow Farrowing in the Fall (SOWFFT): SOWFFT I Bo + B: ‘ SOWFST +Bz* PPORK(t-1) + 83 ' CORNP(t-l) + Be * SOYMP(t-l) + Ba*D75*SOWFST where PPORK I PORKPT/CPIT CORNP I CORNPT/CPIT SOYMP I SOYMPT/CPIT SOWFST I Sow farrowing in spring, 1000 head PORKPT I Price of barrows and gilts, 7 markets S/cwt. CORNPT I U.S. Average Corn price received by farmers, S/bu. SOYMPT I U.S. Average Soymeal price received by farmers, S/cwt. CPIT I Consumer price index, 1967 I 1.0 D75*SOWFST I D75 is equal to 60, 61, 62,... for period prior 1975 and equal to 75 for the period starting 1975 to 1984. This accounts for the leveling of fall farrowings with spring farrowings starting in 1975. Sow farrowing in the spring (SOWFST): SOWFST I Do + 81‘ SOWFST(t-1) +Bs* CORNP(trl) + 83‘ CORNP(t-2) +Ba* SOYMP(t-l) + Bs* SOYMP(t-Z) +Be* PPORK(t-1) 47 Pork Production (PORKQT): PORKQT I Do + B:*PORKQT(t-1) +Bs*SOWS + 83 * PKCRR + 84 * PKSMPR where PKCRR I PORKPT(t-1)/CORNPT(t-2) PRSMPR I PORRPT(t-1)/SOYMPT(t-2) . PORKQT I Pork production, million lbs., carcass weight SONS I SOWFFT(t-1) + SOWFST 3.1.1.3 Poultry Production The poultry sector includes separate equations for broilers, turkeys and eggs. This poultry sector is included in the model in order to provide a complete framework for determining feed demand of the entire livestock sector. An annual specification for the poultry sector is inadequate to model poultry production response. Producers frequently make adjustments within a year in response to prices and costs or expectations about future market conditions. It only takes about 8 weeks to produce a batch of broilers while about 2 flocks of turkeys may be grown within one year. Hence a model designed to capture the year- to-year production response is not as clearly applicable for the poultry sector as for the cattle and hog 48 industries. To the extent that within year adjustments may deviate from the year-to-year production patterns, the relationship between average prices in the previous year and the current year's production may be imperfect. The inadequacy of an annual specification for poultry was recognized, yet maintained in the current model specification to achieve consistency in the time period with the rest of the livestock sector. The specification appears reasonable in determining feed demand based on the current characteristics of the industry. The results of the current poultry sector model should, however, be interpreted with caution considering the limitations imposed by time aggregation problems. Future versions of the model might consider a quarterly model specification. Likewise, a procedure to integrate a quarterly model with an annual model would have to be developed. The supply of the poultry commodities is determined in the model by the lagged product and feed prices, lagged production, and a productivity shifter. The latter is represented by the labor efficiency variable as a proxy for a measure of the net effect of technological change. An increase in the average productivity of labor has contributed significantly in the growth of the poultry industry. Man hours required per 1000 broilers has declined from 26 in 1965 to 15 in 1969 as a result of increased 49 mechanization and more efficient layouts (Ensminger, 1980). Due to the high correlation between the labor efficiency time series for broilers, turkeys and eggs, and in order to reduce the number of exogenous variables in the model, the labor efficiency for broilers was used as a proxy for technological change for the three poultry products. Whether labor productivity will continue as an important factor in determining the growth of the poultry industry will depend on the likely share of labor in future poultry production. Mechanical and biological technology and management systems also resulted in better feed conversion, higher production per bird, and reduced mortality. Future model reestimations may need to consider the role of these productivity factors in determining trends in poultry supply. Broiler Production (CHIKQT): CHIKQT I Bo + 81* CHIRQT(t-1) + 82* CHPT(t-1) + 82‘ CORNP(t-l) + 84* SOYMP(t-1) + Bu ‘ LHFW where CHPT I CHIRPT/CPIT LHFW I CHIRLE * FWAGET CHIKQT I broiler production, ready-to-cook, million lbs. CHIKPT I average broiler farm price, live weight, cents/lb. 50 CHIKLE I hours of labor per cwt. of broiler production FWAGET I farm wage rate, S/hr. Turkey Production (TURKQT): TURKQT I Bo + B:*TURKQT(t-1) +B2* TKPT(t-1) + 83* CORNP(t-2) + 84* SOYMP(t-2) + 85 * LHFW where TKPT I TURKPT/ CPIT TURKQT I turkey production, ready-to-cook, million lbs. TURKPT I average turkey farm price, live weight, cents/lb. Egg production (EGGQT): EGGQT I Bo + 81*EGGQT(t-1) +82* EGP(t-1) + 83* CORNP(t-l) + 84* LHFW where EGP I EGGPT/CPIT EGGQT I egg production, million dozen EGGPT I egg average farm price, cents/dozen 51 3.1.2 Livestock and Poultry Demand This section presents the specification of the livestock and poultry demand model. Before the presentation of the model equations, a justification for a price dependent demand model is provided. The structure of the U.S. market for animal products in aggregate provides the justification for a price dependent formulation of the annual demand models estimated in this study. In the case of beef and pork, consumption is determined primarily by the quantities that are marketed. The magnitude of changes in stocks of these animal products is small relative to production; also, exports and imports of these products are small relative to production. Although the decision to feed animals to heavier slaughter weights may be affected by the current price, the decision to produce the animals was made in some previous period. Hence, the quantities of animal products available for consumption are largely predetermined in the current period and prices adjusts to clear the market. It is noted that this specification of demand relationship may not hold for poultry products due to the shorter production cycle involved. However, a similar formulation was applied for poultry in this study in order to achieve consistency in the overall estimation of the annual demand for animal products. The following 52 specification of the U.S. demand for livestock and poultry is therefore adopted in this study: where P(i) I P(i) I 9(1) I 9(5) I g ( 9(1). 9(3). Y. Z ) price of the ith good quantity of the ith good available for consumption, per capita quantity of a substitute good available for consumption, per capita Y I disposable income, per capita z I other shifter variables. 53 3.1.2.1 Beef Inverse Demand The beef demand model includes three equations for Omaha Choice steer prices, commercial cow prices and import demand for non-fed beef. The following equations are formulated for the beef demand model: Choice Steer Price (FBEFPT): (FBEFPT/CPIT) I Bo + 81 * BPPC + 82 * PRPC + 83 * DINC + 84 * DV73ON + Bo * DVT73 + B; * DVBOON + B1 * DVT80 where BFPC I (FBEFQT + NFBFQT + NPBIMT )/POPUS PRPC I (PORRQT + PKIM - PKEX )IPOPUS DINC I DPCIT/CPIT FBEFPT I Choice Steer Price at Omaha, S/cwt. FBEFQT I Steer and Heifer slaughter, carcass weight, million lbs. NFBFQT I Cow and Bull slaughter, carcass weight, million lbs. NFBIMT I Non-fed beef imports, carcass weight, million lbs. PORKQT I Pork production, carcass weight, million lbs. PKIM I Pork imports, million lbs. PKEX I Pork exports, million lbs. CHIRQT I Chicken production, ready-to-cook, million lbs. 54 TURKQT I Turkey production, ready-to-cook, million lbs. POPUS I Total U.S. population, millions CPIT I Consumer Price Index, 1967 I 1.0 DV73ON I 1.0 for Time 1973-1984, 0 otherwise DVT73 I Time * DV73ON DVBOON I 1.0 FOR TIME 1980-1985, 0 otherwise DVT80. I Time * DV800N where Time I 55, 56, 57, ..., 85 The annual average price of choice steers at Omaha was chosen as the proxy variable for the general price level of cattle. This choice is based upon the importance of the Omaha market for cattle, market location relative to production and consistency of price differentials with other markets and availability of consistent time series data. While shifts in per capita production of steer and heifer beef have caused most of the variation in fed cattle prices, other variables are expected to have significant impacts also. Supplies of cow and bull beef including net imports are expected to influence choice_ steer prices. This is because hamburger and other processed beef compete with carcass beef and about a fourth of the steer and heifer carcass is usually used for hamburgers. For similar reasons, supplies of steer and heifer beef is expected to influence cow prices . Also, pork and poultry are considered as competitors for the consumer meat dollar. Likewise, consumer income is 55 expected to influence cattle prices. The consumer price index was chosen as a deflator for both income and the price variables. Commercial Cow Prices (COWP): BFCOHP/CPIT I Bo + B: * QNFB + 82 * QFBEEF + 83 * QNONBF + 84 * DINC + Ba * DV730N + Bo * DVT73 + 81 * DV800N + 89 * DVT80 where COWP I BFCOWP/CPIT QNFB I NFBFQT/POPUS QFBEEF I FBEFQT/POPUS QNONBF I (PORRQT+CHIKQT+TURKQT)/POPUS BFCOWP I Commercial Beef cow price, Omaha. S/cwt. Import Demand for Beef (NFBIMT): Import demand for non-fed beef is determined by the import quotas specified in the counter-cyclical import law. The import law is imposed in order to regulate fluctuations in beef prices. It allows higher imports of beef during period of low domestic supplies and high consumer prices conversely, allowed beef imports are reduced in years of high domestic beef supplies and low prices. The import 56 quota is explicitly included in the structure of the model according to the legislated formula. Since 1980, the level of U.S. beef imports has been determined by applying the counter-cyclical meat import formula defined as follows ( Simpson, 1982). 5-yr.moving average of 3-yr. moving domestic cow Average average of beef Annual annual domestic roduction roduction Quota I imports * IO-yr. average of * g-yr.moving (1968-77) domestic production average of (1968-77) domestic cow beef production In the model, non-fed beef imports are assumed to be equal to the beef import quote as determined by the counter- cyclical meat import formula. This implies that beef export supply of exporting countries is assumed to be completely elastic. That is, exporters are assumed to maximize their profits by exporting beef quantities according to the maximum levels determined through the counter-cyclical meat import law. 3.1.2.2 Pork Inverse Demand The pork demand model include a single equation for the price of barrows and gilts represented by the following equation : 57 Price of Pork (PORRPT): PORKPT/CPIT I Bo + 81 * PKPC + 82 * BFPC + 82 * POULPC + 84 * DINC + 8: * DV73ON + 84 * DVT73 + 81 * DVBOON + 84 * DVT80 where PPORK I PORKPT/CPIT POUL I (CHIKQT+TURKQT)/POPUS The farm price of pork (proxied by the price of barrows and gilts in 7 markets) is determined based on the pork quantity available for consumption, quantities of substitute meats and disposable income. The dummy variable has the same definition as those used in beef price equation. 3.1.2.3 Poultry The poultry demand model include separate equations for broilers, turkeys and eggs. The price equation for each of the poultry products are given as follows: Broiler Price (CHPT): CHIKPT/CPIT I 80 + 8: * POULPC + 82 * 8FPC + 83 * PKPC + 84 * DINC 58 where CHP I CHIRPT/CPIT POULPC I CHIKQT/POPUS Turkey Price (TURKPT): TURKPT/CPIT I 80 + 81 * POULPC + 82 * BFPC + 83 * PKPC + 84 * DINC where TKP I TURKPT/CPIT TURKPT I Turkey price received by farmers, cents/lb. Egg Price (EGGPT): EGGPT/CPIT I Bo + 81 * EGPC + 82 * MEATPC + 83 * DINC + 84 * TIME where EGP I EGGPT/CPIT EGPC I EGGQT/POPUS MEATPC I (PORKQT+PBEFQT+NFBPQT+N88IMT+CHIKQT+TURRQT)/POPUS EGGPT I Price of eggs received by farmers, cents/dozen EGGQT I Egg production, million dozen 59 3.2 Method of Estimation Chapter 2 provided the main theoretical foundations for consumer behavior and how the classical demand theory relates to empirical analysis. It is noted, however, that there exists a gap between theory and applied empirical analysis. Common sense and knowledge of the market of the commodity under consideration provide some basis for determining market demand not only as function of prices and income but of other relevant factors. The present analysis of livestock demand follows a pragmatic approach. That is, a specific utility function is not explicitly imposed and the demand specifications of the demand equations for livestock used in this study deviate from the theoretically derived demand functions. This approach is adopted in order to incorporate in the model specification some dynamic relationships and to account for observed changes in the demand structure of some animal products, particularly beef. Ordinary least squares is employed in estimating the equations in the model. This estimation technique is considered adequate due to the recursive nature of the model specifications. The demand model was estimated using annual observations over the period 1955 through 1984. A long data series was used in order to investigate structural changes in demand for animal products. In the case of the supply 60 model, different sample periods were used in estimating various structural equations. The various periods of time tried to cover at least one complete production cycle for the particular commodities considered. The time periods used for estimation and the lagged specification of supply equations are both relevant considerations in capturing the dynamics of livestock supply structural relationships. 3.3 Em irical Results of U dates and Reestimation of the Base MoaeI Following the design of the systems structure, is the specification and estimation of model equations. After estimation, each equation is verified and evaluated based on regression diagnostics. An essential part of verification involves the evaluation of the plausibility of parameter estimates. This section presents the results of initial specification, estimation and revision. The equations are reported with the estimates of the structural coefficients and statistics describing the accuracy of these estimates. Statistical measures such as coefficient of determination (simple and adjusted), Durbin-Watson statistic, F-value and turning point errors are also reported to provide a general evaluation of each regression equation. A plot of the residuals is also given following each equation. A graph of the fitted values and actual values are also reported. 61 3.3.1 Livestock and Poultry Demand Least squares estimates of the base demand model for beef, pork, chicken, turkey, and eggs are presented in Equation 3.1 through Equation 3.5. With respect to goodness-of-fit measures, the coefficient of determination for each price equation indicated high degrees of explanatory power. Each inverse demand equation has a negative own-quantity coefficient. and exhibited correct signs for the substitute commodities included. The t-values associated with the coefficients suggested, in most cases, the coefficients were significantly different from zero at the .05 level. Estimated income effects on livestock and poultry prices were positive and significant. The estimated mean price and income flexibilities calculated from the price equations are presented in Table 3.1. Ideally, one could draw comparisons of the estimated flexibilities with the results of other studies. However, results from other studies on meat demand are not directly comparable due to differences in model specification ( i.e., use of quantity dependent form demand model), functional forms, and data transformations used. More recent estimates of direct and income flexibilities provide limited areas for comparisons. The estimates of own-quantity flexibilities are all negative as implied by economic theory (Table 3.1). The magnitudes of the estimated flexibilites indicate flexible 62 Equation 3.1 SMPL 1955 - 1965 31 Observations LS // Dependent Variable is F8? VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. 8888888888888888888888:88883388888833888888.8BBSIIIIIIIIICSSSISIIISI C 41.439147 3.1913917 12.964663 0.000 8FPC -0.5053932 0.0457767 -11.040413 0.000 PKPC -0.0603790 0.0605213 -0.9976495 0.329 DINC 0.0157996 0.0020005 7.6960762 0.000 DVT73 -1.1510563 0.1967053 -5.6516691 0.000 DV730N 64.641332 14.793663 5.7213615 0.000 DVT60 -1.3234203 0.3361366 -3.9371461 0.001 DV600N 103.96569 27.100764 3.6370021 0.001 8888888.888888-I...38888888888388.88388888888IIISSIIIIIIIIIIISICIIII. R-squared 0.936546 Mean of dependent var 26.41577 Adjusted R-squared 0.917237 5.0. of dependent var 3.424503 S.E. of regression 0.965179 Sum of squared resid 22.32330 Durbin-Uatson stat 2.173677 F-statistic 46.49737 Log likelihood -36.69757 35 38 15 1955 1969 1965 1979 1975 1999 1985 TIIIE — (ICTIIIIL ------- FITTED 63 Equation 3.2 SMPL 1955 - 1965 31 Observations LS // Dependent Variable is PPORK VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. 388888.88888.88888888838888888888888888838888.SIIIICIIIIIISIIICIIICI C 47.746663 4.3604397 10.949970 0.000 PKPC -0.6797290 0.0607323 -6.4195392 0.000 EFPC -O.2154741 0.0611695 -3.5225764 0.002 POULPC -0.1739415 0.1225566 -1.4192753 0.170 DINC 0.0166523 0.0036654 4.5726642 0.000 DV730N 94.351923 20.666665 4.5166463 0.000 DVT73 -1.2696901 0.2760163 -4.6000544 0.000 DVBOON 74.690653 37.055914 2.0210175 0.056 DVT60 -0.6930645 0.4576674 -1.9505307 0.064 88888-3888888888888888888888838888888888838888.388888888883888.8888. R-squared 0.923445 Mean of dependent var 20.12544 Adjusted R-squared 0.695607 5.0. of dependent var 4.067107 S.E. of regression 1.314060 Sum of squared resid 37.96971 Durbin-Uatson stat 2.270103 F-statistic 33.17166 Log likelihood -47.13666 P099 PRICE 7 IIIIRIIETS, II III. s/cnr (crunL Inn r1111), 19 5-1985 35 39 25 15 19 , . 1955 1989 1965 TIIIE 1979 1975 1989 1985 — (ICTIIIIL ------- FITTED 64 Equation 3.3 SMPL 1957 - 1965 29 Observations - LS // Dependent Variable is CHP VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. 88.3IIIIIBIIIISII.888838888888.8888I..8888888SCISIIIIIICCIIIIIIIIIII C 44.191499 2.6930120 16.409693 0.000 POULPC -0.5674031 0.0679211 -6.6463121 0.000 BFPC -0.2107667 0.0267073 -7.3419269 0.000 PKPC -0.1911915 0.0411179 -4.6496321 0.000 DINC 0.0114666 0.0016121 6.3269647 0.000 ..88-88.88888888888888.888888888888888.888888CISIIBSI-IIIISIIBBIIIBI R-squared 0.944611 Mean of dependent var 14.24397 Adjusted R-squared 0.935360 S.D. of dependent var 3.444026 S.E. of regression 0.675491 Sum of squared resid 16.39563 Durbin-Uatson stat 2.107199 F-statistic 102.3246 Log likelihood -34.54907 “madman!WI.) 1.4mm 25.9 22.5 39.8) 17.14 .. . 15.0) . _ ...... . . 12.5. ' ,. ' 1m. 7.5 1969 1965 1979 1975 1999 1995 I19 — IICTIIIIL FITTED TI 65 Equation 3.4 SMPL 1957 - 1965 29 Observations LS ll Dependent Variable is TKP VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. 888888888.8888888888888888.88888888‘3I.8388883.888888838888888888.8. C 50.469746 5.0525494 9.9669664 0.000 POULPC -0.9569127 0.1274316 -7.5249202 0.000 BFPC -0.2766433 0.0536597 -5.1363654 0.000 PKPC -0.1206139 0.0771443 -1.5634646 0.131 DINC 0.0167542 0.0033996 5.5162919 0.000 8.8.88888.388.IISICICCIIBSCISISIIIS88383883.88383888888888888£883338 R-squared 0.690910 Mean of dependent var 20.72692 Adjusted R-squared 0.672726 S.D. of dependent var 4.604236 S.E. of regression 1.642571 Sum of squared resid 64.75291 Durbin-Uatson stat 2.424243 F-statistic 49.00035 Log likelihood -52.79662 runuzv PRICE RIUEHEIGHT. REAL, csnrsxnn. nc not A) 91112), 1955-1995 3015. 25' . _ - 2w ' - g. a; . 15- ’ . 19 1969 1965 A 1979 1975 1999 1985 TIIIE — ACTUAL ------- FITTED 66 Equation 3.5 SMPL 1957 - 29 Observations LS ll Dependent Variable is EGP 198$ VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. 8.88888SBBIIIIIIIIIIIIBSISBIIS3.8.8.88888888888888888I88888I88888888 C 106.32114 23.117999 4.5990634 0.000 EGPC -0.7279443 0.5666599 -1.2404057 0.227 MEATPC -0.3205765 0.0607950 -3.9676010 0.001 DINC 0.0062666 0.0049966 1.2536619 0.223 DVT77 -1.5166354 0.3720337 -4.0771453 0.000 DV77ON 112.22943 29.926366 3.7501632 0.001 .888888.8838888888888888:28888888888888.888888888838...8888.88.8888. R-squared 0.667944 Mean of dependent var 31.91413 Adjusted R-squared 0.663564 S.D. of dependent var 7.647364 S.E. of regression 2.624523 Sum of squared resid 163.4924 Durbin-Uatson stat 2.356696 F-statistic 36.45077 Log likelihood -67.69994 88-8888.8888888888888888888888338888!88888B8838888833833338338833888 E“ (MIL (11911111): 1511988 " 59 'eee' 35) 381 251 29‘ 15' 1969 1965 1979 TIIIE —- ACTUAL FITTED 1975 1989 1985 67 prices for beef, pork, chicken, turkey, and eggs. This implies that a one percent change in the quantity available for consumption of these commodities will result to more than proportionate change in their price. Interestingly, turkey has the highest own-quantity flexibility relative to the own quantity flexibilities of the other three commodities (in absolute value). Estimated cattle price equation with poultry per capita supply as one explanatory variable showed the latter to be insignificant and has a wrong sign. Equation 3.1 excludes poultry quantity. Other studies, however, indicated that poultry, particulary chickens, has become a strong substitute for beef starting in the late 1970s (Chavas, 1983: Cornell, 1983). The trend variables (DVT73 and DVT80) indicate a decline in real fed beef prices by about $1.16 per year starting in 1973 and by about $1.13 per year starting in 1980. Perhaps, this is a result of the declining demand for beef starting about mid 19703. The estimated income flexibility of beef is significantly positive and is greater than unity. This implies that beef demand is responsive to changes in per capita disposable income. Beef has the largest cross- Quantity effect on pork, broiler and turkey prices as indicated by a higher cross- quantity flexibility on beef relative to pork in the poultry price equations, and relative to poultry in the hog price equation. 68 The significantly negative estimate of cross quantity flexibility of poultry with respect to beef indicate the latter to be a significant substitute for chicken and turkey. The demand relationship for turkeys is represented in the turkey price equation (Equation 3.4). The level of turkey price is associated with the level of poultry, pork and beef production per capita. All coefficients are significant at the .05 level except the pork quantity coefficient. A strong income effect on turkey prices is also indicated by the income flexibility estimate. The demand model for eggs ( Equation 3.5) identifies the relationship between egg price and egg production per capita, livestock and poultry production per capita ( sum of beef, pork and poultry), income and population. Changes in tastes and preferences, as well as the growing dietary concern is proxied by the time variable. The equation indicates a substitution relationship between meat and eggs. The coefficients are significant at the .05 level. Figure 3.3, a scatter plot relating per capita supply to deflated steer prices, shows how the demand for beef has shifted with time. It has been hypothesized by some that the figure implies steadily increasing demand for beef from the 1950's through the 1970's and then appears to shift bll<=kwards in the 1980's. Some explanations include decreasing positive income effects on beef demand, Competition from poultry, and health and diet concerns. Ma‘-wa’ 69 .mcowl 0£a £0 UOafl—aonmo 0L4 mwmfimumnmxouu .mLuunoa Uta JLOQ .wwwn meta—09m awe: mauOk os.~ mv.sn _E.LI meow nw.~ m~.~n vm.ou 64.1: masts» wn.~ oo.~( mm.ou mn._u LoLEotm n~.~ mv.on ss.~I Ns.~) xtoa nn._ ms.ou No.~) comm haw: snoop mmmw mthsaoa xtoa econ now: assume Ema meoocs so «0112 aunmmoammc gown COMLUQ Lea Acomaaeamcou u v m~aaam omenafioo U000~¢0D saw: toe unmemn mammwtmme to ms__wnsxu_u acouc_ new mnmucaae so muaaemumu ~.m «Lamp 70 Figure 3.3 A DEE? DDIAIID 119 1993‘ 99. O 89‘ 79- mmao mamas-u ammo-em ' 9 199 11a 891211 c1111) 1111111 ((111133 (111) Change In Beef Duane Free 1963 to I984 PRICE - Supply (I98: and I964) ’3 D \ \ \ 72 - ' '~ Dmnd 5m: \ Free Inca-e Srowth \ . n \ 7° _ Incas 1‘ ‘I‘Oflt’l \ \ 69 '- \ Steer Prices ‘ \ (simO) “ I 0 \\ 47 144:4: 1 \ . Frei'erenca: \ - \ 46 \ . \I ‘5 - e \ - ; \ 44 P ‘ 63 " ' . QUANTITY 4 a a__ J I L l 1 a l I02 103 I04 105 I06 101 I00 109 .110 III "2 hr 454114 804on 4! In! 144..Cu:444 2419M.) 71 The positive shifts to the right of beef demand appears to have ended around 1972. While beef demand did not appear to be decreasing, it did not increase despite the increase in personal disposable income during the period 1972 to 1979. While this could possibly be explained by a decreasing impact of income effects on beef demand, as other studies (Chavas, 1983) have argued, that would contradict cross-sectional studies indicating continued positive effects of income on beef demand. It is also hard to believe a negative income effect, which would be needed to explain the backward shifts in demand seen in the 1980's. While some decrease in income elasticity is likely, upon inspection, the hypothesis of new factors affecting the demand for beef appears more plausible. The hypothesis in this paper is that there is still a positive response of beef demand to income, but it was being offset by other factors during the mid to late 1970's and overshadowed by other factors in the 1980's. Figure 3.4 (gives a visual example of this hypothesis. Income growth from 1983 to 1984, given the same per capita availability, would have shifted the demand curve to the right enough to increase nominal steer prices about $7/cwt, but other factors, which are labeled tastes and preferences, shifted the demand curve back to the left by about the same amount. I’seal steer prices remained the same as can be seen at the iJltersection of the supply and demand curves, at around 72 $65/cwt. In order to test the hypothesis, several equations were fitted over historical time periods using ordinary least squares. Using Figure 3.3 as a guide, a fairly standard price dependent beef demand equation was fitted over three time periods. Beef inverse demand equation was fitted over the time period 1955-1972, a period of continually growing demand (Equation 3.1.1). As can be seen, the equation with real steer prices as the dependent variable and per capita beef quantity, per capita pork quantity , and per capita real disposable income as the explanatory variables (poultry quantity was insignificant and had the wrong sign and therefore was not used ), has good statistical properties. In particular, the expalanatory variables in. Equation 3.1.1 accounted for 91 percent of the variations in real steer prices. Equation 3.1.2, using a 1955-1979 time period, showed much less explanatory power, 67 percent, even though the same explanatory variables were used, and pork quantity was insignificant. The same specification was estimated for the Period 1955 through 1984 (Equation 3.1.3). Only 18 percent «at the variation in steer prices was explained and none of the variables were significant at the .05 level. The results 3hown in Equation 3.1.1 through 3.1.3 indicate a possible change in the structure of beef demand in the 1970s. Clearly, equation 3.1.3 is missing the effects of other 73 Equation 3.1.1 SMPL 1955 - 1972 16 Observations LS // Dependent Variable is FBP VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. 88888888838888I8.88888888888888888.8888388IIISCISIIIIIISIIII8838.... C 40.506694 2.6026367 15.563352 0.000 BFPC -0.7457245 0.0716460 -10.406167 0.000 PKPC -0.0052252 0.0536104 -0.0971034 0.924 DINC 0.0242690 0.0027044 6.9613467 0.000 I.88883888888888.888888888IIIIISIIBIIICIIICIIIIISS88.388888888888888 R-squared 0.912754 Mean of dependent var 27.40602 Adjusted R-squared 0.694056 S.D. of dependent var 2.071100 S.E. of regression 0.674116 Sum of squared resid 6.362053 Durbin-Uatson stat 2.546642 F-statistic 46.62162 Log likelihood -16.16071 5314?.“ 0'1935'51 ' 2— 1979 25 Observations LS // Dependent Variable is FBP VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. =3888888888888=88888=888888888:3883888888888833833883883883838883888 C 39.546675 5.1247696 7.7166102 0.000 BFPC -0.3919132 0.0611227 -6.4119096 0.000 PKPC 0.0205699 0.0769264 0.2606745 0.797 DINC 0.0100262 0.0016964 5.2625223 0.000 =8888883888838888888888838888833888888888838888888888888883388888888 R-squared 0.675075 Mean of dependent var 27.43773 Adjusted R-squared 0.626657 S.D. of dependent var 2.674293 S.E. of regression 1.629659 Sum of squared resid 55.77154 Durbin-Uatson stat 0.966659 F-statistic 14.54342 Log likelihood -45.50331 8:38:388388888888338=38838883888888888888888388883838338883388888888 Equation 3.1.3 SMPL 1955 - 1965 131 Observations LS // Dependent Variable is FBP VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. =388.88888888888883338888388388888888888888888888388338888888838.838 C 36.206649 9.3696522 3.6643776 0.001 BFPC -0.0057054 0.0763032 -0.0726633 0.942 PKPC -0.0030973 0.1366546 -0.0223360 0.962 DINC -0.0031767 0.0021411 -1.4646017 0.149 ..a3888888838.8888888888888888888838888.88888888888888888888888.838. R‘Squared 0.236076 Mean of dependent var 26.41577 AcIJusted R-squared 0.151196 S.D. of dependent var 3.424503 5'3. of regression 3.155010 Sum of squared resid 266.7604 l)I-ll‘lriin-«Inialtson stat 0.665791 F-statistic 2.761312 L°8 likelihood -77.46450 74 important variables which contributed to the change in the beef demand structure starting in the mid 1970s. An alternative formulation would be to include a proxy for the missing factors. As mentioned, the missing variables are likely to be such factors as changes in tastes and preferences due to the increasing health and diet concerns of consumers. A proxy for the missing variables would be difficult to ~find. However, it is reasonable to expect that changes in preferences occur over a long period of time and will be in the same direction each year. Given this assumption, a time trend was chosen as the proxy. Equation 3.1.4 allows the time trend to enter as a variable starting in 1973, the period hypothesized to be the beginning of the structural change. When to begin to allow the effects of the proxy trend variable was determined by the conclusions reached observing Figure 3.0. Equation 3.1 also includes variables from 1980 on in order to account for the increased effect of the missing variables on beef demand starting in 1980. As shown, this formulation explains 93 :percent of the variation in steer prices over the period and the income coefficient is not only significant but also Quite large. The income flexibility estimated at the means 1J1 equation 3.1.1 (estimated from 1955 to 1972) was 2.2 and the income flexibility in Equation 3.1.4 (estimated from 1955 to 1979) is 1.88. While the income effect on beef Prices has seemed to drop somewhat between the two period, 75 Equation 3.1.4 SMPL 1955 - 1979 25 Observations LS // Dependent Variable is FBP VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. QIIIISIIIIIIUII88.888888838888888.88.88.8888...BIISIIIIIIIIIISIIIIIIS C 41.736133 3.2452105 12.661456 0.000 BFPC -0.5275266 0.0467754 -11.277905 0.000 PKPC -0.0694354 0.0623443 -1.1137411 0.279 DINC 0.0167764 0.0020552 6.1640014 0.000 DV73ON 66.739155 14.516953 5.9750246 0.000 DVT73 -1.1634104 0.1932309 -6.1243337 0.000 838888.88888.888.888.888!!!8.88888888888888838888!!!83888888888.8888 R-squared 0.697543 Mean of dependent var 27.43773 Adjusted R-squared 0.670560 S.D. of dependent var 2.674293 S.E. of regression 0.962077 Sum of squared resid 17.56623 Durbin-Uatson stat ‘ 2.167364 F-statistic 33.26655 Log likelihood -31.07647 ““9999 (1191111)?“191811739“ ' 32.5 ' 35.9 39.9 - 27 .5 - ' ,-"-. 25.9 22.5 29.9 56 59 69 62 64 66 69 79 T2 74 96 99 TI —— ACTIIAL FITTED 76 it is still a very significant factor in the determination of beef demand. The trend variables in Equation 1.1.4 have the expected negative signs and are significant at the .05 level. The magnitude of the structural change in the beef sector is shown by the coefficients of the trend variables. Given all the other variables were held constant, nominal steer prices would drop over S7/cwt. per year due to the shift away from beef approximated by the proxy trend variables. The results imply that beef demand is still responsive to income changes. 3.3.2 Livestock and Poultry Production The empirical results of the supply models as shown in the individual supply equations appear reasonable. Year-to- year changes in the beef cow numbers are explained very well by the lagged beef cow inventory and lagged feeder calf prices (Equation 3.6). The pork supply model (Equation 3.9) showed expected and significant results for all variables. Variation in Dork slaughter is explained by the variation in sows farrowing and the hog-corn price ratio. The ratio between hog and corn prices is a proxy variable to capture the incentive to feed to lighter or heavier slaughter weights. 77 As indicated earlier, the annual specification for the poultry supply model is not appropriate because supply adjustments occur within the year. Hence, the empirical results presented for broilers, turkeys and eggs (Equations 3.10, 3.11, and 3.12, respectively) should be interpreted considering the limitations imposed by the time aggregation problems. In the case of turkeys (Equation 3.11) , the results were encouraging as the signs of all coefficients are as expected and significant at the 5 percent level. The estimated equation for broiler supply is shown in Equation 3.10. The explanatory variables explain year-to-year variation in broiler supply very well. The labor efficiencycoefficient, as well as the product and input price coefficients, have expected signs and are significant at the 5 percent level. The egg supply equation is given in Equation 3.12. The coefficients on corn and egg prices, as well as on labor efficiency are all significant at the .05 level. The empirical results for eggs reflects the weaknesses of an annual specification. However, 74 percent of the year-to- year variation in egg supply is explained by the included explanatory variables. Equation 3.6 SMPL 1961 - 25 Observations LS ll Dependent Variable is BFCO 1985 78 HT Convergence achieved after 2 iterations VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. IIIIIIIIIIIIIII8.8IIIIIIIBIIIIIIIICIIISII8.88.IIIIIIIISIIIIIICIIIOSI C 45.712125 5106.6106 0.0069461 0.993 BFCOUTI-i) 0.6407799 0.1316957 6.3745627 0.000 BCP(-1) 46.291016 31.166336 1.5494607 0.136 BCP(-2) 135.57599 29.169119 4.6447442 0.000 BCP(-3) 25.037726 32.629016 0.7626706 0.455 ARIil 0.6371231 0.2371539 2.6665365 0.015 8888888.8888.88888888888888888888.8388888888888888888888...888.88... R-squared 0.979316 Mean of dependent var 36700.00 Adjusted R-squared 0.973675 S.D. of dependent var 4666.274 S.E. of regression 757.7713 Sum of squared resid 10910131 Durbin-Watson stat 2.107663 F-statistic 179.9345 Log likelihood -197.6025 BEEF COII IIIUEHTOIIU. JANUARY 1. 1999 HEAD 54444 I I I I 62 64 66 69 79 72 74 76 79 .99 92 94 TIIIE — ACTUAL FITTED 79 Equation 3.7 SMPL 1956 - 1965 30 Observations L5 // Dependent Variable is SOUFFT VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. I...88838.8888...88888888888888.8388888888838888888833.8338...88.III C 2375.4936 606.03742 3.9197146 0.001 SOUFST 0.0226916 0.0766093 0.2966116 0.766 PPORK(-i) 41.643534 15.506745 2.6655110 0.013 CORNP(-1) -921.37351 226.14519 -4.0742564 0.000 SOYMP(-1) -32.136261 40.969699 -0.7643910 0.440 SOUFS7 0.0065632 0.0015192 5.6366237 0.000 88888SI8.8888II.88888888888888888888838888838838IIRISIIIISIIIIIICOSC R-squared 0.642666 Mean of dependent var 5926.567 Adjusted R-squared 0.610130 S.D. of dependent var 520.9526 S.E. of regression 227.0003 Sum of squared resid 1236700. Durbin-Watson stat 1.919445 F-statistic 25.74720 Log likelihood -201.9695 sou FAAAOHIHGS FALL 1999 HEAD ACTUAL nun 111111. 1955-1995 75% 1:44 5444 5544 . ' a 2 5. 1 I I (see 1969 1965 1979 1975 1989 1985 TIIIE — ACTUAL ------- FITTED 80 Equation 3.8 SMPL 1962 - 1965 24 Observations LS // Dependent Variable is SOWFST VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. ..888883888888888888.88888888888888888883888888888.8.88.38.83.888888 C -1733.2951 1005.3230 -1.7241176 0.103 SOWFST(-i) 1.1474660 0.1232975 9.3064965 0.000 PPORK(-1) 231.76006 25.402625 9.1242563 0.000 CORNP(-1) -1161.6455 331.27364 -3.5669771 0.002 CORNF(-2) -617.33960 271.53710 -3.0100464 0.006 SOYMP(-i) -103.91999 45.556603 -2.2611162 0.036 SOYMP(-2) -271.16355 62.666096 -4.3255966 0.000 I.8888888888888388I8388888888888888888888838IISBISBBBBISSIISIISIIIUI R-squared 0.690004 Mean of dependent var 6364.667 Adjusted R-squared 0.651162 5.0. of dependent var 601.1179 S.E. of regression 231.6932 Sum of squared resid 914165.7 Durbin-Uatson stat 2.150521 F-statistic 22.92513 Log likelihood -160.6271 0“- 81 Equation 3.9 SMFL 1957 - 1965 29 Observations LS // Dependent Variable is PORKQT VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. 8.88883888888888883888.888888888888888.8888.88888.88.38.888888888888 C -6259.2676 2310.0633 -2.7095506 0.012 PORKOT(-1) 0.6430322 0.0665436 9.7411003 0.000 PKCRR 130.77796 36.646776 3.5664125 0.002 PKSMPR 192.59236 157.00116 1.2266936 0.232 SOUS 0.4067656 0.1409153 2.9007667 0.006 88883888388888:'88I.888888388888888888888888888.88888888888883888888 R-squared 0.676669 Mean of dependent var 12764.63 Adjusted R-squared 0.656660 S.D. of dependent var 1616.732 S.E. of regression 662.9554 Sum of squared resid 11194273 Durbin-Uatson stat 1.715361 F-statistic 43.53305 Log likelihood -227.6717 88.88888888888888888888£8.888.8888888888888888888888828888388883.888 PORK PfiODUCTIOII HILLIOII LBS.9QCARCASS HEIGHT ((21111 11111) 111111). 1951-1 17444 16444 15m 14m 131m 12m 11090 1155559 _" 911m 1969 1965 1979 1975 1999 1985 TIIIE — ACTUAL FITTED 82 Equation 3.10 SMPL 1957 - 1965 29 Observations LS // Dependent Variable is CHIKQT Convergence achieved after 2 iterations VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. 888888888.888.88.888.888888888888.83888888888888.88.83.8888883888888 C 727.52703 791.13939 0.9195940 0.366 CHIKOT(-1) 1.0293666 0.0362775 26.692246 0.000 CMP(-1) 61.243162 35.072626 2.3164133 0.030 CORNP(-1) -576.35295 269.06309 -1.9936656 0.059 SOYMPI-i) -66.521761 54.612015 -1.5642994 0.127 LHFU -1166.7042 624.46563 -1.9003509 0.071 AR(1) -0.4106313 0.1974605 -2.0793507 0.049 8388888-IIIIIIIISSIIS888888838888888888388!8888888888888888888838... R-squared 0.990399 Mean of dependent var 6534.076 Adjusted R-squared 0.967761 S.D. of dependent var 2630.577 S.E. of regression 290.7655 Sum of squared resid 1660237. Durbin-Uatson stat 2.416411 F-statistic 376.2452 Log likelihood -201.6465 SSBBSBSSIIIIUIIISSISS8888838888888888888883888888:388888883883888888 BROILEA PRODUCTION IIILLIOII POUNDS 991991 999 951199I99, 1959-1995 15‘ 125W 1m 75% 5444 25m 1999 1995 ' 1919 ' 1915 ' 1999 1995 TIIIE —- ACTUAL -- ----- FITTED 83 Equation 3.11 SMPL 1956 - 1965 30 Observations LS // Dependent Variable is TURKQT VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. 8888.83.8888.88.888.888.888.8.8888883888888838:88:83.888888888888888 C 135.91260 370.40966 0.3669249 0.717 TURKOT(-i) 0.4056615 0.2175673 1.6643623 0.075 TKPI-i) 19.936796 6.6611095 2.2965725 0.031 CORNP(-1) -274.45966 96.647926 -2.6339260 0.009 SOYMPI-i) -3.4079655 21.155666 -0.1610663 0.673 LHFU 169.22256 257.39062 0.7351566 0.470 T 49.349269 14.122704 3.4943230 0.002 888388388888888888888888888883.888888888883388388888888888883883388: R-squared 0.969940 Mean of dependent var 1619.923 Adjusted R-squared 0.962096 S.D. of dependent var 542.9502 S.E. of regression 105.7036 Sum of squared resid 256966.0 Durbin-Uatson stat 1.906466 F-statistic 123.6667 Log likelihood -176.4016 888888I.88888.8888882288888888888888888888888.888388832882338838888- “111191911919119713925138!“ 3m 9999 25% 2999 1599 1 v. c 599 .. .. 1959 1955 1919 1995 1999 1995 TIME — ACTUAL FITTED 84 Equation 3.12 SMPL 1956 - 1965 30 Observations LS // Dependent Variable is EGGQT VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. =8888388883888888888888823888888888888833838888888883388888888888888 C 362.26046 919.13399 0.4159137 0.661 EGGQT(-1) 0.7666676 0.1445695 5.4546660 0.000 EGP(-1) 25.696192 7.7450515 3.3435791 0.003 CORNP(-1) -299.04249 102.71216 -2.9114614 0.006 LHFU -20.295221 169.37606 -0.1071677 0.916 T 20.299362 7.1752376 2.6290655 0.009 88888888.888888838883838838828888888888888.!888888888888388888888388 R-squared 0.752046 Mean of dependent var 5553.510 Adjusted R-squared 0.700369 S.D. of dependent var 192.1106 S.E. of regression 105.1550 Sum of squared resid 265361.9 Durbin-Uatson stat 1.949571 F-statistic 14.55645 Log likelihood -i76.6641 88838332888888.8888:=88=88888888888888888888838883338888888888888888 sac 9909991199 9111139 9929? ACTUAL 199 11199, 1 55-199 5944 58' 57m 563 5599 54W 53W 52W 51W 1959 1995 ' 1999' ' 1995 1999 1995 1119 — 191191. ------- 911191) 85 3.4 Summary and Conclusions A recursive annual model of U.S. livestock and poultry is specified and estimated to generate intermediate and long-run projections of inventory, production, and prices for beef, pork, broiler, turkey, and eggs. Separate estimates are made for each category. The beef sector models are represented by producer decision variables and biological response variables. Producer decision variables include the number of animals, the weight at which an animal is slaughtered and the rate of herd expansion or contraction. Biological response variables are determined primarily by such factors as death rates and calving rates. The beef sector models estimates beef cow inventory, steer and heifer slaughter. and cow and bull slaughter. The supply structure for pork is determined largely by the relationship between hog and feed prices. Separate equations are used to represent fall and spring farrowings. An inverse demand model is used to represent the null hypothesis of constant parameters in the demand for beef, pork, broiler. and turkey. Preliminary estimations and analysis of scatter plots of per capita beef production and real steer prices suggest a shift in beef demand during mid- 1970s and early 1980s. Estimated price equations using the 1955-1984 period without accounting for these shifts have poor fits and indicate misspecification. The beef and pork 86 price equations fail to include the effects of variables which contributed to the change in red meat demand. The missing variables are hypothesized to be factors affecting the consumers preference function. It is reasonable to expect that changes in preferences occur over a long period of time and will be in the same direction each year.. Given this assumption, time trend shifter variables were chosen as proxy for the missing variables. Based on the scatter plot analysis, trend shifter variables were allowed to enter starting in 1973 and again starting in 1980. The magnitude of the shift in demand is indicated by the coefficients of the trend variables. Nominal steer prices drop over $7/cwt. per year due to the shift away from beef approximated by the proxy trend variables, ceteris paribus. The results imply that beef demand is still responsive to income changes. The results of preliminary analysis of structural change in beef demand carried out in this chapter provide useful insight in further analysis and identification of an appropriate beef demand model. The possibility of parameter variation due to structural change implies that inference based on constant parameter model maybe misleading. Further analysis to identify the timing and pattern of change are essential in identifying more appropriate specifications of parameter variation. The methods to carry out such analysis are discussed in the following chapter. CHAPTER 4 ANALYSIS OF PARAMETER STABILITY AND STRUCTURAL CHANGE IN THE U.S. MARKET DEMAND FOR MEAT 4.1 Definition of Structural Change in Demand Analysis Structural change in demand may be defined as any change in the parameters of the consumer's utility function. Since the utility function itself is not observable, changes in it function are not directly observable. Within the context of the classical demand theory, changes in the parameters or form of the utility function are reflected in the structure of the corresponding demand function. That is, assuming utility maximization by the consumer, any change in the utility function is manifested in the form and parameters of the derived demand relationship. For empirical testing and estimation of structural change, the hypothesis of a change in the utility function is tested by considering changes (systematic and/or random) in the coefficients of the demand equation.1 Moschini and Mielke (1984) defined parameter change to include a) change in functional form, b) change in the quantitative relation- ship between the regressors and dependent variable and c) change in the form of the stochastic process associated 1 Chavas (986) considers this approach as a narrower definition of structural change. He notes that a shift in demand parameters may not necessarily imply structural change and that results may depend on the functional form used. 87 88 with the demand function. 4.2 Testing Structural Change This section provides a brief review of methods that may be used to test whether there has been a structural change in demand relationships. Tests of structural shifts are important in the context of estimating models of economic relationships for policy analysis and forecasting. For most estimation of econometric models used in determini- ng the effects of a policy change, a necessary condition is that of invariant economic structure (i.e., constancy of parameters relating dependent and independent variables, constant functional form and error parameters) with respect to the policy changes of interest. This necessary condition is assumed. When there is structural change this assumption is not justified. Lucas (1976) has shown that changes in policies are likely to induce changes in parameters of structural relationships. Testing possible changes in structural parameters is particularly useful in simulating the likely effects of policy changes. 4.3 Problems in Testing Structural Change Conceptual problems exist in investigating whether structural change has occurred in demand by testing whether demand parameters have varied over time. The problem lies 89 in the fact that parameter variation may arise because of structural change or due to misspecifications in construc- ting the demand models.‘ Rausser, Mundlak, and Johnson (1981) identified types of model misspecifications that result in instability in model parameters. They argued that approximating highly nonlinear ”true" relationships by a simple linear functional form may contribute strongly to the variation of the parameters. Also, they considered the use of aggregate data to contribute to parameter instability. Since the weights used to calculate aggregate data from different smaller units are likely to shift over time (as the relative importance of the individual units to the aggregate measure vary over time), the coefficients corresponding to the aggregate variable in the model vary over time. A third form of misspecification mentioned by Rausser, et.al., (1981) involves the use of proxy variables due to scarcity and absence of data of the "true" variables. They pointed out that the "relationship between the true variable and its proxy can be expected to change over time . . . changes in the true variables which measure the actual economic stimuli induce instability in the estimated parameters for the 3 For details about the relationship between specification errors and parameter instability, see Dufour (1982) and Harvey I Chapter 2, section 7), 1981. 90 proxy variables."a Another cause of parameter instability is the omission of important explanatory variables. The omitted variables are usually the unobservable variables such as preference changes and formation of new consumption habits, changes in institutions and technology and other similar factors. The three-stage approach employed in this study attempts to minimize the above problems by conducting tests to determine departures from the fitted functional form prior to specification of varying parameters. 4.4 Exploratory Approach of Testing Structural Change In the absence of information regarding specific type and timing of structural change, the analyst may have to explore and carefully analyze the available data and detect instability patterns in the estimated parameters of the demand model. Recursive estimation as a method of testing parameter changes in regression relationships was first introduced by Brown, et.al., (1975). Dufour (1982) later extended the approach and presented an exploratory methodology of data analysis to allow the assessment of parameter instability in econometric models. The ' Rausser, G.C., Y. Mundlak, and S.R. Johnson,"Structural Change, Updating, and Forecasting”, lg New Directions in Econometric Modeling and Forecasting in U.S. Agriculture, edited by G.C. Rausser, (New York: Elsevier Science Publishing Co., 1983) pp. 659-666. 91 exploratory approach for testing whether structural change has occurred involves recursive estimation of a given demand model and the analysis of the corresponding standardized prediction errors called "recursive residuals". Dufour differentiated the exploratory approach with those of what he calls ”overfitting" procedures for testing parameter instability over time as done by Chow (1960). Quandt (1960), Farley and Hinich (1970), Cooley and Prescott (1973). These "overfitting" procedures involves "nesting a model into a more general one, by adding parameters and then performing significance tests on the added parameters." In order to detect patterns of parameter instability in the U.S. demand for livestock products, the exploratory approach suggested by Dufour (1982) is used in this study. The patterns of instability of the demand parameters are detected by considering the patterns of the recursive residuals that is revealed by the analysis. 4.4.1 Recursive Estimation‘ This section presents a brief review of the exploratory approach in testing structural change in economic models. The discussion of the theory and procedure draws heavily on the work of Brown, Durbin, and Evans (1975) and Dufour ‘ Recursive estimation is considered a special case of Ralman filtering, a technique used by Chavas (1983) to study structural change in the U.S. demand for meat. 92 (1982). The details of recursive least squares is also discussed in Harvey (1981). Instability patterns in regression coefficients of a demand model maybe detected by performing recursive estima- tion of the demand function. The parameters of a linear demand equation is estimated recursively by using the first R observations to generate an initial estimate of the parameter vector, B. 1 The model is then updated using a recursive updating formula which allows the estimation of Br. I r 8 R+l, ..., T ) parameter estimates. Recursive least squares allows the analyst to track the changes in the estimator over time. Also, under classical assumptions, the procedure allows the estimation of a set of uncorrelated recursive residuals which can be used to test parameter stability. Given T total observations, (T-R) estimates of the vector 8 are generated and correspondingly (T-R-l) one-step ahead recursive residuals are estimated. Given a linear demand function with the following general form, (4.1) Y1 = X't 61 + m t = 1,2,..., T: u “ NIO, 031 I ] where Y: is the observation in the dependent variable at period t, X: is the column vector of observation on R 93 non-stochastic regressors, 81 is a R component vector of regression coefficients (8 is subscripted to indicate the hypothesis of parameter variation over time). u: are ’assumed to be independently and normally distributed with zero mean and variance 0*: The null hypothesis to be tested is (4.2) 11118 Br =Bx11 =...=B'1 =5 Under 3, equation (4.1) follows the classical linear regression model with constant parameters. (4.3) Y 8 X6 + u u ‘ N(O, 021 I I where Y = (yAryzo- o 0' YT ). X' = [x1,x2,. . .,X1] u '-" (U1.uz....,U1)' The ordinary least squares (OLS) estimates based on T observations are given by (4.4) B = (11'x1-1 x-y By recursive estimation, the following sequence of estimates 94 are generated A (4.5) B 3 (X'r Xr )" X'r Yr r 3 K. K+1.. . ..T where X'r = [X1 'e e e' Kr ]' Y'I’ = [ YA 'e e e' Yr] Using subsequent observations, the B coefficients denoted by B: . 83.1 ,. . ..Br are generated without the matrix inversion implied in equation (4.5). Following Harvey's notation, the updating formula has the the following form: (4.6) Br 3 Br-i 4' (X'r Xr)’1 iii-(Yr " X'r br-1)/fr and (4.7) (X'r Xr)" 3 (X'r-i Xr-1)'1 - (X'r-i Xr-i)'1 * Xr X'r(X'r-1 Xr-1)'1/fr where fr 3 1 4‘ X'r (X'r-i Xr-i)‘1 Xr r = K+1....,T Equation (4.6) can be written as (4.8) Br 3 Br-i + (X'r-i )(r-i)’1 Xr Vr /fr where Vr is the one-step ahead prediction error. Hence, Vr 95 is considered to contain all the new information required to update the estimate of the regression parameters. Using the the first R observations, 8: is estimated using equation (4.5). B: is then updated using equation (4.8). Note that the final estimator Br is the same as those estimated by ordinary least squares using the T observations. The sequence of regression estimates provides useful information about the likely instabilities of the parameters over the whole time period. The testing of instabilities in the sequence of regression estimates is facilitated by knowing some information about the behavior of the sequential regression estimates under the null hypothesis and then finding related statistics with already known distributions. To do this, Dufour(1982) starts by generating standardized prediction errors and several steps ahead recursive residuals and then constructing a number of related statistics to assess the significance of the instability patterns identified. The standardized prediction errors are derived by first computing for each r = R + 1, . . . , T, the predicted value of Yr using the estimated 8 from the r-l observations. the corresponding one-step ahead prediction errors are then calculated as follows: (4.9) Vr * Yr " X'r Br r . K+1p e e e p T 96 By doing this the predictive performance of the model is simulated by forecasting each data point in the sample with parameter estimates based on the preceding observations. It can be shown that under the null hypothesis, the forecast error (Vr) has zero mean and variance 03 dzr where dr is a scalar function of the regressors defined as (4.7) dr = [ l + x'r (X'r-1 xr-,)-1 x, ] 1/2 r = K+l, . . . , T The standardized prediction errors are estimated by dividing the estimated forecast error (vr) by the scalar function dr. That is, (4.8) Wr = Vr / dr r = R+l, . . ., T Under Ho . it is shown5 that E( wr Wt ) = O for r # t 5 See A.C. Harvey, Econometric Analysis 9; Timg Series,(New York: John Wiley and Sons, 1981). pp. 55-56. 97 and w:.:, ... W! are independently and normally distribu- ted with zero mean and variance 0: . 4.4.2 Recursive Regidual Analysis Under the null hypothesis of constant parameters, the standardized prediction errors (wr) are independently and normally distributed with mean zero and variance 0‘. Given that parameter variation would disturb the stochastic properties of the recursive residuals, Dufour suggests testing for departures from this null distribution. Before formal significance tests are conducted, Dufour and Brown, et.al., suggest listing and graphing the sequence of statistics derived from the recursive estimation. The statistics include 1) the recursive estimates of regression coefficients, 2) prediction errors (one and several steps ahead), 3) the recursive residuals, 4) standardized first differences of recursive estimates of regression parameters. By graphing the recursive estimates of the regression parameters, the direct effect of each data point on the estimated value of each coefficient as well as the nature of the variations will be apparent. Dufour also suggests the examination of the empirical distribution of each set of coefficients as well as the corresponding variances, and coefficients of variations to determine the importance of 98 the variations. Particular jumps and trends inside the sequences as likely signs of parameter instability. The significance of the variations may be determined by constructing confidence intervals for the recursive parameter estimates. Under the null hypothesis, the recursive residuals are expected to be white noise with zero mean. By graphing the sequence of recursive residuals, parameter instability may be indicated by systematic tendencies to over-predict or under-predict, break points and sudden jumps, as well as runs of over-prediction or under-prediction. The graph of the series of k-steps ahead (k z 2) recursive residuals may also be examined and compared with the one-step ahead recursive residuals to determine the types and timing of structural shifts. Also, the series of backward recursive residuals maybe compared with the forward recursive residuals to test whether there was structural shift at the beginning of the sample period. Under the null hypothesis, the standardized first differences of the recursive estimates are independent and normally distributed with zero mean and variance 0’. Where the recursive residuals are not very revealing of instability patterns, the series of their first differences may show different sign patterns, thereby indicating some possible instabilities and break points in the parameters. ____.————_._~__-_---‘ '— 99 4.4.2.1 Significance Tests Under the null hypothesis of constant regression coefficients, the recursive residuals are normally distribu- ted with zero mean and variance 0’. Thus, if B: is constant up to t - t1 and varying thereafter, the recursive residuals wr, will have zero mean only up to t:, and non-zero mean after period t1. The behavior of the recursive resi- duals are considered to indicate temporal stability or instability of the estimated coefficients. 4.4.2.1.1 CUSUM and CU§UM§QiTests Brown, Durbin, and Evans (1975) developed two signi- ficance tests based on the recursive residuals. The first one, called the CUSUM test, is based on the graph of the following statistic against time, . r (4.9) Wr = (1 / s ) 2 w: t=k+1 where s = I (W: - W )2 / (T-K-l) When there is a structural break, a tendency for a 1 Mm“; .6 100 disproportionate number of the recursive residuals having the same sign will be evident. The cumulative effect of this tendency will be shown in Wr moving away from the horizontal axis. The point at which the structural break occurs is indicated by the beginning of a secular increase or decrease in Wr. That is, under Ho, the E(Wr) - O: the plot of Wr should then be distributed around zero, if the B are stable. To test for the departure from the mean value, the probabilistic bounds for the path of Wr may be estimated. This boundary would be symmetrically above and below the line Wr - 0 , so that the probability of crossing the boundary is a, the required significance level. The equation of the boundary lines is given by Brown, Durbin, and Evans (1975) and Harvey (1981) to be as follows: (4.10) W = t l EMT-R)“2 + 2aIr-R)/(T-K)1’2l where a - 0.948 for 5 percent significance level and 0.85 for 10 percent significance levelIBrown,et.al., p. 154). If Wr crosses the boundary, the null hypothesis of constant parameters is rejected, indicating a structural change. According to Brown,et.al., the CUSUM test is used to detect systematic movements in Br. For haphazard movements in the Br. Brown, et.al., proposed a second test based on the recursive residuals called the CUSUMSQ test. 101 The CUSUHSQ test uses the squared recursive residuals, and is based on the plot of the values for r 2 T 2 (4.11) Sr = 2 wt / I wt t=K+1 T=K+1 The values of Sr lie between zero and one ( Sr = 0 if r < k+1 and Sr 8 1 if r=T). The expected value of Sr , E(Sr ) = (r-k)/(t-k). The null hypothesis of constant parameters is rejected if if the plot of Sr crosses the boundary based on the level of the test. The boundary lines are defined as (4.12) (r-k)/(t-k) i C For a given significance level, a, the value of C is found by entering the table given by Durbin (1969) (Table 1, p.4) at n a 1/2(t-k)-l and 1/2a. According to Dufour, the CUSUM and CUSUMSQ tests are similar to "goodness-of-fit" tests because they are used against a wide variety of alternatives. The plot of Wr can_be expected to cross the probabi- listic boundary when the recursive residuals tend to be positive (or negative) during some sub-periods as a conse- quence of particular large underpredictions (or overpredict- tions). 0n the other hand, the plot of Sr can be expect- 5.— 102 ed to cross the probabilistic boundary during the sub- periods when the recursive residuals are very large. Dufour pointed out some weaknesses of the CUSUM and CUSUMSQ tests. First, Dufour suggested that the periods where the CUSUM plots cross the probabilistic boundaries may not generally coincide with the points of discontinuity in the regression coefficients. Hence, the plot of the recursive residuals may have to be used to complement the analysis of the plot of the CUSUM values. A second weakness involves the approximate nature of the distribution assumed under the null hypothesis. Also, the table given by Brown, et.al., only includes a small number of significance levels, thus, the computation of marginal significance levels can be potentially burdensome. 4.4.2.1.2 Location Tests To test for monotonic type of instability as likely to be indicated by systematic under-prediction (or over- prediction). Dufour suggested testing the null hypothesis E(wr) = 0 versus an alternative hypothesis E(wr) > 0 or E(wr) < 0, r - K+1, . . ., T. The test is a form of a t-test based on the following statistic (4.13) t = (T - K)“8 W/ 8w 103 where T (4.14) W = z Wr / (T-K) and r=R+l 2 _ T - 2 (4.15) sw - I (w - wt) / (T-K-l) r=R+1 Under Ho , the values of t follows a Student -t distribution with (T-R-l) degrees of freedom. The null hypothesis of E(wr) = 0 is rejected if t > c, where the value of c depend on the level of the test. Dufour suggests the t-test as a check against system- atic under-prediction or over prediction. In general, the t-test is based on the average of the expected standardized forecast errors, T (4.17) 21;) = z E(wr) / (T-K) r=R+1 Ho : E(w) = 0 H1 : E(w) is not equal to zero (4.18) If E(wK+1 ) = E(wK+2) = . . . = E(w T) = 0 a t-test based on (4.14) is considered to be uniformly most powerful (one sided test) or uniformly most powerful unbiased (two sided test) among the tests based on the 104 recursive residuals (Dufour, p.60). 4.4.2.1.3 pinear Rank Tests Under the null hypothesis of constant regression coefficients, the recursive residuals are considered to be independent and symmetrically distributed with median equal to zero“. Dufour suggests the use of any test within the family of linear rank tests to test for symmetry around the zero median under Ho. An advantage of the rank test is the fact that it does not require the estimation of the variance 0’. Given the following, (4.19) n = T-K z=w W x+1' " x+2 ' ° ‘ ' ' T a linear rank test for symmetry around zero may be employed using the statistic n . + (4.20) S = til u(zt) an(Rt) where u(.) is an indicator function so that u(z) = 1 if z > 0 = 0 if z < 0 ‘ Under the normality assumption, the mean and median of the recursive residuals are equal. (Dufour, 1982, p. 61). 105 and n ... R = 2 u( Z - Z ) t i=1 t 1 is the rank of 2: when Zi,...,Za are ranked in increasing order. an (.) is a score function used to transform the rank R1’. n (4.21) If a (r) = 1, S = I u(z ) n t t=1 n + (4.22) If a (r) = r, S = SUM u(z ) R n t=l t t In (4.21), S is equal to the number of non-negative Z'cs (Sign Test); while in (4.24) S is the sum of the ranks associated with the non-negative 2'15 (Wilcoxon Test). When the underlying distribution is normal, the Wilcoxon test (based on 4.22) is considered to be relatively powerful. However, in cases where the t-test is optimal, the efficiency of the Wilcoxon test relative to the t-test is about 0.96 (Dufour, 1982, p. 63). Since there is a tendency to overestimate 0‘, the Wilcoxon test is consi- dered to be potentially more powerful against certain alter- natives, due to the fact that it does not require an estimate of ca . 106 Also, Dufour, favors the use of the rank tests because of their robustness to non-normality and the effects of outliers. 4.4.2.1.4 Modified Von Neumann Ratio Test Parameter instability also leads to situations where the means of the cross products 2‘: = WtWt+l, t = R+l,...,T- K (where l s K 5’ T-R-l) is not equal to zero (Dufour, 1982, pp. 52-55). To test for instability in the demand parameters we, therefore, test whether Zr: has a zero mean. For this test, Dufour suggested the modified Von Neumann Ratio (VR) statistic. VR is defined as follows: T-1 -1 (4.23) VR = (n—l) I (w - w ) + n I w t=R+1 t+1 t where nsT-R. VR is considered to be an exact parametric test of the null hypothesis E(w1w1+1) = 0, t8 R+1,...,T-1. (Dufour, 1982). 4.4.2.1.5 Test for Heteroscedasticity Given some information about the possible points of structural break, a test of parameter instability between two subperiods may be tested. Dufour(1982) suggested the 107 test for heteroscedascity for this purpose. Following Dufour's notation, the test involves dividing the recursive residuals into two subperiods 11 and 12. with m: and ma elements and computing the following statistic: (4.24) R = (m1/m2) ( It t I2w”: / 2 Under R., R follows an F distribution with (m2,m1) degrees of freedom. H. is rejected at level a if R 2 F ml: or R s F 1-(a/2) where P[F(ma,m1) 2 Fa] = a for a two sided test. 4.4.2.1.6 Quandt's Log Likelihood Ratio Test If the CUSUM and CUSUMSQ tests led to the rejection of the null hypothesis of constant parameters, the Quandt's log likelihood ratio test may be used to determine the timing of structural change. This ratio is defined by Brown and Durbin (1975). For each r, from r=K+1 to r=T-R-1, the following statistic is calculated: 2 1 2 2 2 (4.25) q = 1/2 r log a + 1/2 (T-r) log s - 1/2 T log s where s31 is the ratio of the residual sum of squares to 4 108 of observation when the regression is fitted to the first r observations, s‘: is the ratio of the residual sum of squares to the number of observations when the regression is fitted to the remaining T-r observations and, 32 is the ratio of the residual sum of squares to the number of observations when the regression is fitted to the whole set of T observations. The timing of the structural break is indicated by the point at which Qr reaches its minimum. Brown, Durbin and Evans indicated that if the plot of qr against time is markedly jagged, the change in the parameters is sharp and discrete. A relatively smooth likelihood surface is considered to indicate an abrupt change. 4.2.2.3.7 Runs Test Given that shifts in the regression parameters tend to be manifested through runs of either under-predictions or over-predictions in the recursive simulation process, a test that considers the sequence of the signs of s(wxii), . . . , s(wr) where s(x) 8 + if x > 0 109 s(x) = - if x ( 0 is suggested. This test first involve counting the number R of runs. A few number of R is taken as an evidence of a few parameter shifts during the time period considered. It is showed that R - 1 “ 81 (N-l, 1/2 ) where N = T- R. Hence, the P[ R < c ] for any c may be computed. The case where there is long run of under-prediction (or over-predictions), an indication of a shift after a given period may also be considered. In this case, the analyst has to determine the length of the longest run (with any sign) in the sequence. The probability of getting at least one run of this length or greater may be computed. If this probability is too low, (smaller than some critical point associated with a particular significance level a, the null hypothesis is rejected. 4.5 Specifying Parameter Variation in Demand Models This section provides a brief review of approaches in specifying structural change in estimating demand models. A more thorough discussion of the econometrics of structural change can be found in Poirier (1976). Most of the applications of these approaches are in the context of quantity-dependent demand models. This study will attempt 110 to incorporate the identified structural change based on the exploratory tests in the previous section in the context of inverse demand models for livestock products. There are several approaches that can be used to incorporate structural change in commodity demand models. Depending on the nature of the structural shift, one approach may be more appropriate than others. This section gives a brief review of approaches that will be used to incorporate structural change in demand for meat. 4.5.1 Use of time trend A time trend variable is often introduced in a demand model to represent the effects of continous change in tastes. There are, however, problems with this particular approach that should be considered. Variables such as prices and income are often highly correlated with time; hence, problems of multicollinearity may prevent the estimation of separate effects of the correlated explana- tory variables. In cases of cyclical fluctuations and sudden changes, the use of time variable in a logarithmic demand specification might be unsatisfactory because inherent in the specification is the assumption that all factors not accounted for by the income and relative price variables are changing at a constant instantaneous percentage rate per unit of time. In a linear demand model, 111 the coefficient of the time variable measures the rate of shift of demand in terms of annual units demanded, given prices and income. In either specification, the shift in demand is approximated by a smooth, steady, monotonic function of time. 4.5.2 g§e of Flexible Trengg Instead of a steady monotonic shift in demand, a flexible trend that allows demand to shift at different rates and at different times may be used.’ The flexible trend may be approximated by a cubic spline. A cubic spline is a special case of piecewise regression consisting of a series of cubic polynomials in time which has continous first and second derivatives. The flexible trend is included in the specification of the demand model as follows: (4.26) P: = Bo + BiQt + 631’: + E(t) 4' e: where P, Q, represents prices and quantities, respectively ' For a discussion of spline functions and its applications to the demand for coffee in the U.S., see Huang, C., J. Siegfried, and F. Zardoshty, ”The Demand for Coffee in the United States, 1963-77," Quarterly Review of Economics and Business, 20 (Summer 1980). PP. 36-50. 112 of a commodity, Y is a measure of income and F(t) is the flexible trend. The trend is specified as a cubic spline by first dividing the time period into subperiods, namely 0 S t 5 k1: k: g kg: and so on. The spline functions is expressed in the form (4.27) E(t) = bo + bit + bat2 + bat8 + Z 01(t-k1)3D1 where the D1 represents dummy variables with value of zero during t < k1 and equals one when t 2 k1. The coefficients may be estimated by ordinary least squares. 4.5.3 Use of Dummy Variables Abrupt or discontinous shifts in supply and demand can be accounted for by introducing dummy variables. These variables are used to represent qualitative information such as qualitative shifts over time or space (e.g., war or peace). Dummy variables take on a value of one for and after the critical year. This approach allows a single displacement of the intercept for the period beginning in the year in which the change occured. The effect of the shift is calculated by adding the coefficient of the dummy variable to the intercept coefficient. 113 Dividing the data set into intervals and the definition of dummy variables to represent the partitions is preferred over procedures which involves dropping some parts of the data set or estimating a function using the whole period without accounting for the interval shift. Suits (1957) indicated that unbiased regression coefficients are generat- ed by the introduction of dummy variables under situation of abrupt or discontinous shifts in the data. Brown (1952) employed a shift variable to represent the structural change which occured after World War II due to disturbances in the habits of consumers, introduction of new products and new technologies and effects of price controls. 4.5.4 Use of Interaction Variable Interaction variables can be introduced if the structu- ral change is believed to have an effect on the magnitude of the slope and shift coefficients. This variable forms a multiplicative term between the slope or shift variable and a dummy or time variable depending on whether the interacti- on involving the slope or shift variable is abrupt or gradual, respectively. 114 4.5.5 Varying Parameter Specification The approaches considered above can be sufficient and appropriate when the structural change produces a discontin- ous effect and that separate regression equations can be estimated for subsets of data to reflect the intercept and slope changes. However, when the structural change have a differential effect on the slope coefficient during the time period or for specific portions of the observations, more complex approaches may be required to account for the structural change in the model specification. Rausser, Mundlak, and Johnson (1981) discussed the justifications for specifying parameter variation in time series regression analysis to capture the changes in the structural relationships between the dependent and the explanatory variables. Variables that cause structural change are often omitted in the specification of equations in classical regression analysis. Rausser, et. al., (1981) note that the excluded variables oftentimes are nonstationa- ry and are correlated with the included variables; hence, the estimated effects of the latter can be expected to vary over time and are biased. The framework for specifying variations in parameter is based on the discussion in Rausser, Mundlak and Johnson (1981). Given a single equation with one explanatory variable, 115 (4.28) Y: B: X: + u: where u ' (O, can ). E(u: X: )"-'-' E(u: B: )= 0 t = 1,2,.... The parameter B: is subscripted to represent variations over time. The changes in B: can be systematic or random. Let (4.29) B: = 80 + L(X:) + Z: a: + e: where e " (0,03. ), E(e: Z: ) = E[e: L(X:)] = 0 The term 2. represent the effect on the coefficient of variables not included in the system while L(X:) represents the effect of the variables in the system. Combining equations (4.28) and (4.29) gives (4.30) Y: -"'- Bo X: +L(X:)X: +ax: Z: +v: where 116 v: 8 X: e: +u: The variable 21 can be a zero-one indicator variable which allows a switch in the regression coefficient. The function L(X:) can be specified in terms of geometric distributed lag as follows (4.31) a. = Bo + 5x{-1 + 5x.-. + ... + 12. + e: with 6 < 1. Multiplying equation (4.31) by 6 and subtracting 5 B:-1 from B:, gives the following equation (4.32) B: = 5 B:-: + (1-5)Bo + 5 X:-: + 6 (Z:- Z:-1) + (e: - 5 e:-:) Note that equation (4.32) follows Rosenberg's specification. Since 5 is between zero and one, the term 6 81-1 indicates a decay process. ‘Note also that equation (4.30) has a heteroscedastic error term. 117 4.5.5.1 Continous Time Varying Parameter: Complex Legendre Polynomial To allow continous variation in the parameters, the parameters may be specified as continous functions of time by using Legendre polynomials.o In a study of structural change in the retail demand for table beef and hamburgers, Cornell (1983) used Legendre polynomials to allow for continous variation in the retail demand parameters. The approach used by Cornell will be applied in this study in testing for continous variation in the parameters of the farm level demand for beef, pork, broilers and turkeys in the U.S. This section briefly reviews the theory and specification of Legendre polynomials applied in estimating farm level demand for meat. The material is based on the presentation in Cornell (1983) and in Manetsch and Park (1981). Legendre polynomials are orthogonal functions used to represent any continous function F(x) or F(t) over the interval (-1,1). For example, a continous function may be represented as ' For a detailed discussion of the theory of Legendre polynomials, see Manetsch, T.J., and Park,G.L., Systems Analysis and Simulation with Application to Economic gpg Social Systems, Part I and II, Department of Electrical Engineering and Systems Science, Michigan State University, East Lansing, 1981. For an application in estimation of retail demand for meat, see Cornell, (1983) 118 (4.32) F(x) = aoP. (x) + a1P1Ix) + + a1P1(x) for -1 < x < 1. The polynomial functions are defines as follows Po(x) 8 1 Plix) - x P2(x) ' 1/2 (3x2 - 1 ) P111 (x) = 1/n+1 [ (2n + 1) x P1(x) -nP1-1(x)] To make the polynomials orthogonal with respect to time, the functions are mapped into 0 ( t ( T. The polynomials are transformed as follows Po'(t) = 1 P1'(t) - 2t/T -1 P2'(t) = 1/2 [ 3(2t/T -1)’ -1 ] Pn+1'(t) = 1/n+1((2n+1)(2t/T -1) Pn'(t) -nPn-1(2t/T-1)] 119 The Legendre polynomials are introduced into the demand models as follows: Given a simple inverse demand model for the ith product: (1) P1: = Bo1+ 811:Q1: + B: Q1: + C1Y: + e: IIMX' j l where P1: is a (nxl) vector of observations on the real price of the ith commodity in time t, Q1: is a (nxl) vector of observation on the own-quantity of meat consumed per person, Q1: is a (nxk) observation on per capita consumption of substitutes commodities, Y: is a (nxl) vector of observation on real per capita disposable income, e: is an (nxl) random vector , serially uncorrelated, and distributed with mean zero and covariance matrix E(e:,e':) = o. Bo1. B111, B1, and c: are the demand parameters to be estimated. Initially, parameter variation is only allowed to occur in the own-quantity per capita consumption, Q1:. The coefficient B11: is generated as follows: (2) 511: 8 A0: 4' A1: Po(t) + A2: P:(t) + ... + An: Pn-1(t) n (2) 5111 ‘ A01 4" I (Ari Pa-i(t)) r81 where Pa-1(t) are the n-l Legendre polynomials. Substitution of (2) into (1) gives: 120 n (3) P1: 3 Bo: + A0: + 2 Ar: Pu-1(t)Q1: + 81 I 911 r=1 + C1Y: + e: where I Ar1 P1-1(t) Q1: is an interaction variable in Q1:. Q1:, and Y: are the substitute and/or complement, and income variables, respectively. Ar: P1-1(t) is a time varying coefficient which can be estimated and tested under standard regression techniques. A demand model with a second degree polynomial in one explanatory variable can be estimated with the following specification: (4) P1: = A0 + A: Po(t) Q1: 4' A2 P1(t) Qit + As P2(t) Q1: n *6: IQJ: +C1Y: +e: i=1 The polynomials may be introduced in any of the explanatory variables that are considered to vary over time. The own-quantity flexibility for the ith commodity corresponding to the linear demand function in equation (4) can be generated as follows: (5) f1: = [A1 Po(t) 4' A: P: (t) + As Pz(t) ] Q1:/P1: As pointed out in Cornell (1983) and in Manetsch and Park (1981), the Legendre polynomials has the important property of finality of coefficients. That is, the addition of a 121 higher degree polynomial in time will not change the coefficients previously estimated using a lower degree polynomial. Also, the polynomial introduced in the variables do not have to be in the same degree. 4.6 Summary Structural change in demand is defined as any change in the parameter of the consumer's utility function. Since the utility function is not observable, empirical analysis of structural change due to change in preferences is carried out in a limited sense. The limited analysis of structural change involves the testing and estimating changes in the parameters of the derived demand function. The analysis of structural change in terms of changes in demand parameters has several important limitations. First, the demand parameters may change not only due to structural change but also because of possible model specification errors. Second, the analysis does not involve explicit investigation of causes of the structural change, actions relevant to the meat industry to affect preferences cannot be adequately addressed. Although there are limitations in the analysis, the testing and estimation of parameter variation in the context of a forecasting model of U.S. livestock and poultry sector offer several benefits. After correcting for potential 122 model misspecification, allowing the parameters to change over time will likely improve the historical fit and forecasting performance of the livestock and poultry model. Second, the analysis allows the determination of effects of observations on the recursive parameter estimates. In addition, one and several steps ahead recursive residuals are instructive tools in identifying the timing and patterns of parameter variation.. The recursive estimation may be used to analyze the patterns of changes in parameters of linear inverse demand models for beef, pork, broiler, and turkey. Estimated one- step ahead recursive residuals may be used in testing the significance of the parameter changes. The identified parameter variation based on the exploratory analysis may be used in respecifying the inverse demand models estimated in chapter 3 to account for the changes. There exist several approaches to specify parameter variation in demand models. For the purposes of the study, approaches that allow abrupt and gradual continous parameter variation are considered. The exploratory analysis and approaches in specifying parameter variation in demand models are applied in the following chapter. ‘llu’3)‘)7)€/ 9~. ,1 --\ A) A ("C/7" (Ml/“(,LU 2 ~ 7 1" (31". L CHAPTER 5 EMPIRICAL RESULTS OF PARAMETER STABILITY ANALYSIS OF FARM LEVEL DEMAND FOR LIVESTOCK AND POULTRY 5.1 Results of Recursive (Sequential) Estimation gnd Recursive Residual Analysis Recursive estimation as discussed in section 4.2.2 was applied to determine the stability over time of the farm level demand parameters for livestock and poultry. The pattern of the recursive estimates of the coefficients of the inverse demand models are analyzed, taking note of particular trends and discontinuities. The recursive parameter estimates are used as a descriptive device in determining the effects of different observations in a sequential updating process. Since the recursive parameter estimates tend to be highly correlated even under the null hypothesis of parameter stability,1 the associated sequences of standardized recursive residuals are used in conducting an exploratory analysis to search for patterns indicative of possible structural shifts. The simple statistical properties of the one-step ahead recursive residuals make them a useful tool in conducting significance tests of parameter instability. As discussed in Chapter four, the statistical properties of the recursive residuals under the 1 Dufour (1982) showed that the recursive estimates follow a heteroscedastic random walk process. 122 123 null hypothesis of parameter stability are similar to the BLUS residuals2 and therefore can be used for descriptive analysis and for the construction of various significance tests. In particular, if the demand parameters are stable over time, the corresponding recursive residuals have a zero mean and a scalar covariance matrix. That is, under the null hypothesis of constant parameters, the recursive residuals have the following properties:3 (1) E(Wr) = 0 (2) E(W’r) = 03 (3) E(wrw1) = 0 r 1‘ s Thus, the recursive residuals under the null hypothesis of constant parameters are a normal white noise series. Structural change in demand is expected to influence the behavior of the corresponding recursive residuals. For instance, an abrupt and sudden shift in the demand parameters at some point r* in the sample period will result in an abrupt increase in the size of the recursive residuals and/or a tendency to overpredict or underpredict prices (dependent variable) for r > r*. A systematic drift in one 3 See Theil (l97l,chapter 5). 3 See Brown, Durbin, and Evans (1975) pp. 151-153; Also see Harvey (1981). PD. 55. 124 or more of the demand parameters often result to a systematic tendency to overpredict or underpredict. In this section, the standardized recursive residuals are used in performing an exploratory analysis to look for patterns which indicate possible structural breaks in the demand for beef, pork, broiler and turkey. For each model considered, the null hypothesis is that of constant parameters. A general alternative hypothesis is that of parameter instability due to structural change in demand. More specific alternative hypothesis such as gradual,abrupt, and/or continous changes in the demand parameters are also tested. For each model considered, the forward recursive estimates of each coefficient, as well as the one-step recursive residuals are reported. The recursive estimates for each coefficient and recursive residuals are plotted. The first two tests applied in the analysis were the BDE's cumulative sum (CUSUM) and cumulative sum of squares (CUSUMSQ) tests which are based on the one-step ahead recursive residuals.‘ With a structural change, the standardized recursive residuals will have a non-zero mean and the CUSUM and CUSUMSQ can be used to test for structural change. The CUSUM and CUSUMSQ statistics for the four commodities are presented graphically with confidence ‘ For applications of the CUSUM and CUSUMSQ test to demand studies, see Martin and Porter (1985): Hassan and Johnson (1979); Moschini and Mielke (1984). 125 boundaries estimated based on a predetermined significance level. If the plot of the CUSUM and CUSUMSQ crosses the confidence boundary, then the null hypothesis of constant parameters is rejected. The nonparametric tests suggested by Dufour (1982a) are also applied in the analysis. Table 5.1 presents the test statistics for the demand model for the four commodities. The forward one-step recursive residuals are used to compute the test statistics. The t-statistic based on the one-step recursive residuals are estimated for each equation to test whether the residuals have a zero mean. The marginal significance levels associated with the test statistics are also reported wherever possible. In discussing the results, the traditional five percent level is used as the benchmark in evaluating the statistical significance of the results. 5.1.1 Beef Demand The recursive parameter estimates for the beef demand equation with k= 1955-1961 are listed in Table 5.2; those based on demand equation with k=1960-1968 and k=1970-79 are listed in Table 5.3 and Table 5.4, respectively. The most striking feature is the declining and increasing trend (in absolute value) in the estimates of coefficients on the beef per capita consumption (BFPC) and poultry (broilers and turkeys) per capita consumption (POULPC), respectively. . -4— 126 .COmfilnlLLOO nlmLIW 0>udQOOC HWleOI #909 DO—mfldllco 05$ 80% Awh91Nv HCmOO OUCOUmkmCUmn ND .38 30~IO Dado Rm 050 COMHQdOLLOO nflmklfl O>ufimfloa $0 4904 oo_aouuaco or» ca tn u an: Lou Ann._u arson cocooamacoan no or» o>ooo no o:_o> a) or» t: 000$ VO—«OUIICO Ila Cm MN .COmHOnOLLOO namkon G>mu«noa unCmoml MIC LO“ Af¢n1nv UCMOQ IOCOOmmeUmn N D .58 30min hm 03—.) fl) OLP * .n.c Amo.ou nm0.00 n00.00 mmN0.~ noow.» m-n.~— rnrr.uw DADA msmomaMOUOOMOLOuOI sa.h.c #s.n.c enm0.00 snm0.00 v~0m.— muck.“ mNum.0 ounN.0 AvomuMUOIV fcocaoz :0) WJWIP OOCOOCOOOD uflwkom .n.c n0000.00 . unru0.00 nmN00.010 nr~n10 un.N mn.NI 0L.Nl eh «on nnN 00.nm 00.00 63m xcoa n.coxoo~«3 .n.c nm0.00 nmNo.ov nm00.ov mmr0.0 onhm.N w—~v.~ mm001n1 u munch comaIOOJ ulna—0 .n.c nm0.00 nm0.00 nm0.00 ~0k~.0 nmNn.0 wmom.0 0«~m.0 omtamau .n.c 1n1C 10.5 .01: rm.0 oh.0 rn.0 00.0 tamau knack A.NDm rN rN mN mN n—onuanom to LOncaz masts» Lessors oar o—aaoo cannaaoum nmoaflmnom ¢>mntaoou UGOfC QOAMIOCD co vonom mum—mnoam LODOCOLOQ #0 homunwanfim finch u.m o~00h 127 Table 5.2 Beef Inverse Desand Equation: Recursive Paraseter Estilates. 1955-1985 1955-62 1955-83 1955-84 1955-85 1955-88 1955-87 1955-88 1955-89 1955-70 1955-71 1955-72 1955-73 1955-74 1955-75 1955-78 1955-77 1955-78 1955-79 1955-80 1955-81 1955-82 1955-83 1955-84 1955-85 Washers in parenthesis are standard errors. 38.3544 38.7371 41.1921 39.8251 37.5811 38.2478 40.8370 40.5859 39.0844 39.4371 40.0990 39.9531 40.4798 39.5013 39.0009 40.3287 37.7177 33.8538 32.8994 30.7820 29.2530 -0.8850 (0.1384) -0.8788 (0.1124) -0.8559 (0.1087) ~0.7588 (0.088) -0.7728 (0.0910) -0.7348 (0.091) -0.7477 (0.0851) -0.7855 (0.0937) -0.7824 (0.090) -0.7218 (0.0843) -0.7441 (0.0745) ~0.8234 (0.0529) -0.8173 (0.0523) -0.8089 (0.0491) -0.8188 (0.0440) *0.8212 (0.0784) -0.5458 (0.0807) -0.3922 (0.0825) -0.3279 (0.0844) -0.2822 (0.0710) -0.2381 (0.0733) -0.2435 (0.0771) -0.1779 (0.0773) -0.1477 (0.0804) °0.0855 (0.1320) '0.0884 (0.1153) -0.0178 (0.1014) 0.0837 (0.074) 0.0884 (0.0781) 0.0255 (0.072) 0.0399 (0.0881) 0.0527 (0.0728) 0.0440 (0.087) 0.0021 (0.0585) -0.0029 (0.0588) 0.0375 (0.0593) 0.0371 (0.0592) 0.0152 (0.0440) 0.0229 (0.0388) 0.0538 (0.0884) 0.0885 (0.0758) 0.0271 (0.0839) -0.0238 (0.0918) “0.0038 (0.1042) -0.0551 (0.1032) '0.0851 (0.1094) -0.0882 (0.1177) 0.1092 (0.1243) -0.1238 (0.1553) -0.1173 (0.1335) -0.0404 (0.1035) 0.0593 (0.0787) 0.0458 (0.0812) 0.0592 (0.0850) 0.0418 (0.0788) 0.0275 (0.0845) 0.0227 (0.0800) 0.0258 (0.0820) 0.0184 (0.0792) 0.0772 (0.0827) 0.0880 (0.0818) 0.0787 (0.0774) 0.0749 (0.0753) 0.1578 (0.1288) 0.1310 (0.1485) -0.0423 (0.1481) -0.1853 (0.1578) -0.3498 (0.1829) -0.4785 (0.1528) -0.5480 (0.1578) -0.5314 (0.1701) -0.5792 (0.1788) 0.0390 (0.0128) 0.0388 (0.0109) 0.0324 (0.0085) 0.0224 (0.0047) 0.0244 (0.0047) 0.0218 (0.0045) 0.0229 (0.0040) 0.0244 (0.0043) 0.0243 (0.0040) 0.0227 (0.0039) 0.0238 (0.0034) 0.0177 (0.0019) 0.0171 (0.0018) 0.0173 (0.0018) 0.0174 (0.0018) 0.0153 (0.0028) 0.0128 (0.0030) 0.0108 (0.0033) 0.0109 (0.0037) 0.0127 (0.0041) 0.0141 (0.0042) 0.0147 (0.0045) 0.0121 (0.0047) 0.0118 (0.0049) 0e 97 0.95 0.95 0.94 0.94 0.92 0.92 0.91 0.91 0.92 0.92 0.91 0.93 0.81 0.74 0.88 0.57 0.48 0.“ 0.45 0.41 0.45 128 Table 5.3 Beei Inverse Deland Equation: Recursive Paraneter Estilates, 1960-1985 Year Constant BFPC PKPC POULPC DINC 9 1960-69 36.8963 -0.7559 0.0691 -0.0261 0.0248 0.83 (0.1925) (0.1325) (0.2865) (0.0075) 1960-70 37.9067 -0.7460 0.0550 -0.0591 0.0248 0.84 (0.1733) (0.1108) (0.2040) (0.0069) 1960-71 40.5897 -0.6712 -0.0027 -0.0795 0.0225 0.83 (0.1391) (0.0789) (0.1962) (0.0061) 1960-72 40.7271 -0.7202 -0.0100 -0.0669 0.0244 0.83 (0.1189) (0.0761) (0.1899) (0.0053) 1960-73 38.2607 -0.5762 0.0179 0.0278 0.0174 0.91 (0.0748) (0.0788) (0.1912) (0.0028) 1960-74 38.7090 -0.5714 0.0158 0.0494 0.0167 0.90 (0.0737) (0.0778) (0.1872) (0.0026) 1960-75 38.9570 -0.5662 0.0068 0.0414 0.0168 0.90 (0.0641) (0.0544) (0.1732) (0.0026) 1960-76 38.8277 -0.5815 0.0250 0.0081 0.0175 0.92 (0.0580) (0.0453) (0.1612) (0.0022) 1960-77 40.0421 -0.6157 0.0500 0.2044 0.0145 0.75 (0.1072) (0.0838) (0.2924) (0.0040) 1960-78 38.5097 -0.5114 0.0744 0.0269 0.0134 0.66 (0.1080) (0.0935) (0.3161) (0.0044) 1960-79 37.6360 -0.3913 0.0651 -0.2941 0.0145 0.66 (0.0729) (0.0967) (0.2365) (0.0045) 1960-80 38.6856 -0.3551 0.0421 -0.4741 0.0162 0.59 (0.0743) (0.1018) (0.2261) (0.0047) 1960-81 36.9255 -0.3446 0.0787 -0.6915 0.0192 0.56 (0.0785) (0.1056) (0.2005) (0.0046) 1960-82 35.1172 -0.3448 0.1140 -0.7813 0.0206 0.59 (0.0778) (0.0959) (0.1678) (0.0043) 1960-83 34.8299 -0.3415 0.1282 -0.8625 0.0216 0.61 (0.0813) (0.1000) (0.1678) (0.0044) 1960-84 32.4587 -0.2742 0.1517 -0.8447 0.0191 0.53 (0.0873) (0.1127) (0.1899) (0.0049) 1960-85 31.6616 -0.2614 0.1735 -0.9114 0.0195 0.57 (0.0918) (0.1184) (0.1969) (0.0052) luabers in parenthesis are standard errors 129 Table 5.4 Beet Inverse Deeand Equation: Recursive Paraneter Estieates, 1970-1985 Year Constant 8FPC PKPC POULPC DINC R 1970-80 97.7432 -0.5440 -0.1346 -0.5093 0.0087 0.74 (0.1495) (0.2061) (0.3279) (0.0084) 1970-81 81.0353 -0.4946 -0.0115 -0.8151 0.0147 0.69 (0.1571) (0.2028) (0.2721) (0.0080) 1970-82 68.8042 -0.4644 0.0717 -0.9246 0.0176 0.72 (0.1459) (0.1581) (0.2142) (0.0065) 1970-83 74.0192 -0.4817 0.0679 -0.9965 0.0179 0.74 (0.1451) (0.1583) (0.2024) (0.0065) 1970-84 90.7640 -0.5225 0.0295 -1.0016 0.0142 0.73 (0.1488) (0.1604) (0.2089) (0.0061) 1970-85 96.3519 -0.4798 0.1195 -1.0104 0.0101 0.83 (0.1541) (0.1980) (0.2058) (0.0071) Nulhers in parenthesis are standard errors 130 The recursive coefficients on pork per capita consumption (PKPC) in the beef demand model appear to be small and were relatively stable over the time period of analysis. However, the signs are contrary to expectations in most years. The recursive estimates of the coefficient on the income variable appear to have slightly declined over the period. From the forward recursive estimates of the coeffi- cient on per capita beef consumption (BFPC) based on the equations estimated beginning 1960, the decline in the absolute value of the coefficient become most evident when the equation is estimated up through 1973. This can be considered a possible discontinuity in the coefficient on BFPC. This coefficient stabilizes at around -.6 starting in 1973 through 1977. It then declined to -.39 in 1979 and then to -.34 and -.27 in 1983 and 1984, respectively. From the equation estimated from 1960 through 1970, the coefficient on BFPC has a value of -.746 (see Table 5.3). The same specification estimated from 1970 to 1984 (see Table 5.4) show a relatively lower magnitude (in absolute values) of -.5225. On the other hand, the coefficient on poultry per capita consumption, POULPC, increased (in absolute value) from -.0591 to -1.0016 during the same period. The recursive estimates of the coefficients on pork per capita consumption,PKPC, stayed very small during the whole 131 time period, with a sign contrary to expectations in most years. The coefficient on real personal disposable income per capita (DINC) averaged around .02 until 1977 when it dropped slightly to .0145 (equation estimated in 1960-77, table 5.3). It increased again to the .02 level starting in 1980 (equation for 1960-80) through 1985 (equation for 1960-85). The recursive residuals for the beef demand model are listed in Tables 5.5 to 5.7. From the one-step ahead recursive residuals based on equation with k=1955-1960 (Table 5.5), a discontinuity is evident starting in 1977 when the residual increased to -8.09 from -O.473 in 1976. Two periods with very different patterns are identified: 1961 to 1976 and 1977 to 1985. They differ in two ways. First, the average size of the residuals is much greater in .the second period than in the first period. The residuals in all the 9 years (1977-85) are more than twice as large in absolute value as the largest residual in the first period: the most "outlying" residual is in 1984 and 1985. Second, there is a tendency to overpredict in the second period (indicated by the negative residuals). Although there are 10 overpredictions in the first period, their average size is relatively small. Statistically, the forward one-step ahead recursive residuals (based on k=1955-1960) deviate from what we expect from the null hypothesis of constant regression 132 www.ml mmm.° mm.nl NO.¢N ho.m~ amm— NNN.mI wmm.o mm.ol mm.hN mo.~N vom— nmm.hl mNm.O NO.DI nm.mN mm.ON mama NO—.ml hmm.o mm.VI Nm.@N VN.NN Nmmm ¢v~.ml mom.o mm.ml ~0.0M nw.mN ummg won.ml ONm.O om.nl mm.Nn m~.hN ommu O—V.VI dom.~ Nm.ml mh.nn m~.~n mumu ~mm.ml DON.O km.nl wn.om mh.mN mum“ O¢O.ml MNm.o vo.nl mN.hN nN.NN humg mNV.OI DNm.o mm.O( MM.MN vm.NN mum— mmn.o mmo.u mw.o NO.NN hw.NN mum— ~OM.~I mmw.o nm.o: m—.mN mv.mN tum— mmN.—I DND.N mm.m1 mh.mm mw.mm mum" nmm.o MNm.O hn.o mm.hN mn.mN thu mn~.—I mvo.— m~.ul mm.NN ON.WN unm— OQD.OI NON.O «v.01 nw.mN VN.DN Ohm— mNO.N —ON.O NV." ov.nN Nm.wN mmmm whn.o mmm.o ND.O NN.DN MN.DN amm— mMN.~I h—o.~ 0N.—I DD.@N mN.DN hwmu awn." nmm.o N~._ MM.DN DV.ON wmmu Nmn.OI m~n.v O¢.NI vm.mN tv.mN Dmmn omn.OI un—.N v~.~l mN.DN N~.VN vom— ~m~.OI omv.— NN.OI mm.m~ ~N.nN mmmu Ohm.o omv.v ~0.m ON.wN ~N.mN Nmmd mv—.OI owm.— mN.OI DD.NN @N.NN «mmq ALSV .u30\n .030\u .&30\fi LOLLw aLfiv unmomLou JMNOULOK LOLLw umMONLou LOLLm Unw£¢ aflamlmco flaumb DwvaLflvcmum mo OOCNMLND JWNUOLOK U>mmLDOOU uwafioc Lam) moms .... .N8_ .32 u .. 68782 n v. mamm~mc¢ uwatmmwa w>mmtaowa "com¢maom ucmewo mew>cu umwm m.m aunmh 133 parameters. The tendency to overpredict beef prices in the latter part of the sample is well pointed out by a run of 10 consecutive negative residuals from 1976 to 1985. The contrast in the size of the recursive residuals is well underscored by the cumulative sum of squares residuals (CUSUMSQ) and the heteroscedasticity tests which are both significant at‘ the 5 percent level (see Table 5.1). The plot of the CUSUMSQ (Figure 5.3) crosses the confidence boundary in 1967 and is outside the boundary until after 1983. Although the CUSUM is not statistically significant at the 5 percent level, the plot of the CUSUM series for beef (Figure 5.1) shows a systematic drift in the residuals starting sometime in 1977. This timing of discontinuity indicated by the recursive residuals is consistent with the timing of structural break indicated by the plot of the Quandt's log-likelihood ratio (Figure 5.4). The latter reaches a global minimum in 1976-1977. Furthermore, the global location tests are all significant at the 5 percent level. This indicates that the expected value of the recursive residuals is not equal to zero, hence violating the required characteristics of the recursive residuals under the null hypothesis of constant parameters. For k=1960-70 (see table 5.6), discontinuities in the size of the recursive residuals occurs in two years: 1976 and 1983. The average size of the residuals for the period 134 ~NV.NI mvm.o ~m.vr mm.NN No.0— mam" www.ml mmo.o —~.ml N—.NN mo.~N vam— ONm.DI umo.o mm.mr um.VN nm.o~ mmmu www.Nl mmm.o w~.NI ow.VN wN.NN Nam" nom.v1 mmm.o mv.v1 mm.hN nv.nN ummu mh~.wl vvo.~ wM.VI mv.~m n—.NN 0mm— Nm—.NI NNV.N mv.nr mm.mm m~.~n mum— om~.nl "hm.o mm.mr mh.om mh.mN mnmu nh0.ml ovw.o h—.DI NV.NN DN.NN unm— omn.on Nvo.— mN.OI on.mN wm.NN wnmu om—.O DNM.~ MN.O vv.hN hm.NN nhmu mNm.~) wwm.o mm.OI NN.mN mm.mN vmmu wom.OI mNm.m mN.nI nh.mm mv.mm mum“ mNm.o vmm.o mm.o mn.n~ mm.mN Num— mvm.OI mmm.~ m—.—I mm.mN on.mN num— ALEV .a30\u .fi30\n .n30\m LOLLm ALDV umaomLou smmumLOu LOLLm JWMOOLOL LOLLm flaws: amumloco ND~ND DNNaDLotcmum we mocamtab ammomtou 03mmtfluflm unnuoc L00) hams.....~um_ ._am~ u L .oam_nomm~ n x mwmmamcc unatmmma w>mmtaomm "comsnzrw UCNEOD mme>c~ umwm m.n a~nmw 135 mmm.su mom.o mm.s- mm.m_ uo.m_ mmms ~m~.vn mmm.o mm.mu mm.v~ mo._~ 4mm— mwm.m- mmm.o mm.~- mm.n~ mm.o~ moms ano.~s ¢n~.s ev.~- mm.v~ v~.- moms ~ao.vu was._ mm.vu m—.m~ n4.m~ some fleas .saoxu .aaoxu .uaoxu Loutw ALUV amaooLou ummooLou LOLLm ammowLou LOLLw tmu£m anmlwco 03~03 uavaLmflcmum $0 wocnmtmb ummooLou U>mmL300u ~03u0¢ Lao) nmm_ ....smms .ommsroum_ mumm~mc¢ umntmmwa w>mMLaoma "comsmaww vCOEwD mew>cH mama n.m U—nmh 136 Figure 5.1 u may amusement)“ 19) 5 . 9 ‘ P---------’-----~-’~‘ ------- ..“s‘\ -5 . ' \‘\ ... \x‘ -10, ...~ \\ -15 "°‘--— «...: 52 54 s: as re 72 74 7: 73 as ea 94 mm Figure 5.2 cusggsg £930 SIGN)?!“ “F nguffvgguurnav 1.5 10') OIS‘ a I a u T o I I I i l I 62 64 66 69 . 79 7 74 76 3IHE 79 99 92 94 137 Figure 5.3 ”(16% (168.1993)“ 2.: 9.9) ~25) 4Lh -L5) '199 _— unnuisunn79300192339435 IHE Figure 5.4 CHOICE SIEER PRICE: 909897'6 LOG 6195619009 99710 \/ 62 64 66 69 IIHE 79 72 79 76 79 138 1960-77 through 1960-85 are more than twice as large in absolute value as the largest residual in the earlier part of the period (1960-70 through 1960-76). The recursive residuals indicate that the beef demand model tends to overpredict in the latter part of the sample. The tendency to overpredict beef prices in the latter part of the period is underscored by a run of 10 consecutive negative residuals from 1977 to 1985. Statistically, the contrast in the size of prediction errors is well pointed out by the CUSUMSQ and heteroscedas- ticity test (both significant at .05 level). The global location tests are significant at .05 level. This again underscores the contrasting behavior and size of predictions between the two subperiods. The foregoing results strongly reject the hypothesis of constant parameters in the beef demand model. They suggest the presence of an important structural break and disconti- nuity sometime between mid and late 19708 and early 19808. 5.1.2 Pork Demand The recursive parameter estimates for the pork demand model are listed in Table 5.9 and plotted in Figures 5.5 to 5.8. The absolute value of the coefficient on pork per capita consumption (PKPC) exhibits an increasing trend from 1965 through 1971, except from 1968-70 where the coefficient 139 slightly declined from -.6693 to -.6479 (see Figure 5.5). A discontinuity beginning in 1971 is apparent, as the coefficient on PKPC started to decline in absolute value, from -.7167 in 1971 to -.5856 in 1978. After a slight increase from 1978 to 1980, the coefficient on PKPC trended downward starting in 1980. The corresponding own—quantity flexibility of demand for pork exhibited the same pattern as the coefficient on PKPC. The coefficient for beef per capita consumption (see Figure 5.6) were relatively stable during the 1965 to 1970 period. Thereafter, it exhibited a declining trend, except from 1973 through 1977, when it slightly increased from 0.2916 to 0.3332. The coefficient on poultry per capita consumption (see Figure 5.7) was relatively constant at around -0.3 during the period 1968 through 1976. A discontinuity is apparent in 1977 when the coefficient declined from -0.2510 in 1976 to -0.l707 in 1977. Starting from this point of discontinuity, the coefficient tended to trend upward, from -0.1707 in 1977 to -0.5254 in 1985. The coefficient on real per capita disposable income (see figure 5.8) exhibits a downward trend starting in 1970. It declined from 0.0284 in 1970 to 0.0139 in 1985. The corresponding income flexibility of pork also exhibits a downward trend starting in the 1970s; however, it has not declined to near zero levels. This indicates that although 140 Table 5.8 Pork Inverse Delano Equation: Recursive Para-eter Estleates, 1955-1985 (0.1020) luebers in parenthesis are standard errors Year Constant PKPC BFPC POULPC DIIIC R 1955-62 66.5140 -0.5750 -0.5410 -0.2370 0.0190 0.62 (0.4280) (0.4490) (0.5040) (0.0410) 1955-63 48.3670 -0.5660 -0.4220 -0.3020 0.0240 0.62 (0.4010) (0.3910) (0.4650) (0.0380) 1955-64 45.4120 -0.5890 -0.4320 -0.3380 0.0270 0.66 (0.3210) (0.3440) (0.3280) (0.0270) 1955-65 46.0670 -0.5720 -0.4150 -0.3210 0.0250 0.73 (0.2000) (0.2370) (0.2120) (0.0120) 1955-66 41.4810 -0.6150 -0.4550 -0.3600 0.0300 0.74 (0.2070) (0.2480) (0.2220) (0.0130) 1955-67 43.1020 -0.6310 -0.4410 -0.3550 0.0290 0.74 (0.1770) (0.2210) (0.2060) (0.0100) 1955-68 47.3050 -0.6690 -0.4060 -0.3080 0.0260 0.73 (0.1610) (0.2080) (0.1870) (0.0090) 1955-69 44.7400 -0.6530 -0.4290 -0.3260 0.0280 0.72 (0.1590) (0.2050) (0.1850) (0.0090) 1955-70 44.3310 -0.6480 -0.4310 -0.3230 0.0280 0.72 (0.1470) (0.1950) (0.1750) (0.0080) 1955-71 48.2530 -0.7171 -0.3640 -0.3180 0.0260 0.75 (0.1230) (0.1780) (0.1730) (0.0080) 1955-72 48.3160 -0.7120 -0.3430 -0.3110 0.0250 0.75 (0.1180) (0.1550) (0.1650) (0.0070) 1955-73 47.6860 -0.6950 -0.2920 -0.2860 0.0220 0.87 (0.1080) (0.0960) (0.1500) (0.0030) 1955-74 47.8340 -0.6950 -0.2890 -0.2820 0.0220 0.88 (0.1040) (0.0920) (0.1440) (0.0030) 1955-75 45.8810 -0.6300 -0.3140 -0.2480 0.0210 0.91 (0.0790) (0.0880) (0.1390) (0.0030) 1955-76 45.6000 -0.6150 -0.3290 -0.2510 0.0220 0.91 (0.0690) (0.0790) (0.1350) (0.0030) 1955-77 46.1100 -0.5860 -0.3330 -0.1710 0.0190 0.86 (0.0850) (0.0980) (0.1650) (0.0030) 1955-78 45.0280 -0.5690 -0.2500 -0.2000 0.0170 0.82 (0.0930) (0.1000) (0.1810) (0.0040) 1955-79 44.6110 -0.6040 -0.1220 -0.3450 0.0150 0.80 (0.0960) (0.0710) (0.1700) (0.0040) 1955-80 44.7580 -0.6100 -0.1150 -0.3580 0.0150 0.81 (0.0910) (0.0640) (0.1570) (0.0040) 1955-81 44.0000 -0.6040 -0.1010 -0.4120 0.0160 0.81 (0.0900) (0.0610) (0.1410) (0.0030) 1955-82 42.2910 -0.5790 -0.0930 -0.4650 0.0160 0.61 (0.0850) (0.0600) (0.1260) (0.0030) 1955-83 41.7680 -0.S730 -0.0820 -0.5040 0.0170 0.80 (0.0860) (0.0610) (0.1240) (0.0030) 1955-84 39.8710 -0.5510 -0.0180 -0.4880 0.0140 0.75 (0.0970) (0.0640) (0.1410) (0.0040) 1955-85 38.6750 -0.5340 -0.0060 -0. 5250 0.0140 0.70 (0.0680) (0.1470) (0.0040) 141 Figure 5.5 remarmwr - '935i-q--q--p-u-f-—-r-—-r-—-r-—-r-r-f-—-$-¢ “697979747679999294 71E Figure 5.6 710)): CIDII 01) MI” W ""3 (9‘69")??pr 142 Figure 5.7 999 7916! mag)“ mum NI MIR! u 4.1: 4.2. 4.3: 14' 4.5. 4.6) Figure 5.8 v 1199 PRICE mIgzmggfmfi 01) 9199099919 9.933 I 9 m7 0 I 9 913' 8 ..HWW “6.7979747679999294 III! 143 the price response to income changes might be weakening starting in the 1970s, income is still a significant factor in determining the future demand for red meat and, hence, the future growth of the meat sector. These results indicate that pork price is about 40 percent less responsive in 1980 than in 1970 ( i.e., decline in the income flexibility of pork from 3.5 in 1970 to around 2.0 in 1980). The recursive residuals for the pork demand model are listed in Table 5.10 and plotted in Figure 5.11. The plot of the recursive residuals shows two periods with quite different patterns: 1965 to 1976 and 1977 to 1985. They differ in two ways. First, the average size of the residuals is much bigger in the second period than in the first period. Second, from the forward one step recursive residuals, there is a tendency to overpredict starting in 1971, reaching the two largest overpredictions in 1977 and 1984. From 1965 to 1971, the recursive residuals tend to fluctuate. A discontinuity is apparent in 1977 when the residuals jumped from -0.921 in 1976 to -7.833 in 1977. Four among nine residuals during the period 1977 to 1985 are nearly twice as large in absolute value as the largest residual prior to 1977. The CUSUM plot for pork (see Figure 5.9) indicate a systematic drift in the recursive residuals starting sometime in 1976. The CUSUMSQ plot indicate discontinuity in the parameters sometime in the mid 1970s and between 144 num.hl wmw.o mm.VI ~m.m~ mm.Mu mmmu mN~.ml mmw.o wN.m( hm.uN ah.nu vmmu mmn.VI $N¢.O mh.Nl vu.m~ mm.n~ mam— DDD.NI kwN.O wm.~l v~.~N m—.m— Nam" vwm.NI mom.o um.~l MN.m— Nm.m~ unm— wON.OI ONm.O no.0) hm.m~ NN.m~ Dam“ mum.MI now." ND.DI mO.WN vn.m— mhmu NNN.wl WON.O mm.v1 ~N.mN Nm.VN chm" mmm.NI MNm.O mm.v: ~D.NN mw.NN hum" uNm.OI DNm.O mh.OI vo.mN mN.nN mum" NDN.—I mmo.~ Nm.~l om.~m mm.mN fitm— mVD.OI mmm.o DM.OI n~.VN mn.mw fum— QVD.OI WND.N nv.~l hm.—n mN.0m mum— vwm.OI MNm.O mm.OI ~m.~N mN._N thu VNQ.—I .mvo.— mm.~l h~.N— ~N.n— mum” vmm.o NON-O MN.O Nm.m— hm.mu Ohm— WND.N ~ON.O Nb." Nm.m— mD.~N mmmm hvn.~l mmm.o nm.—I Dm.m~ Nv.mn Emma NDV.OI N—o.— m¢.OI mm.m— hm.m— hmmn wm~.m Dmm.o h—.m OO.~N N—.VN mwm~ mmo.OI mn~.v NV.OI hm.NN nm.NN Damn owN.o ~D~.N nn.o nm.m~ mv.w~ www— Ovm.— omv.u vN.N mo.v~ Nh.wm nmmu 0kg.“ cwt.? NN.m 0N.mn mn.m— Nmma omn.m omm.~ ow.m DD.N~ n~.m~ ”mm“ atzv .¢30\n .830\u .H30\H LOLLw ALDV ammomtou &mwoaLOL LOLLw £MQONLOK LOLLm umwfic umsmlwcc flauflb flmNmDLanmum to UOCNMLND &m~00LOu fl>mmtaoua ~03£0¢ L00} nmm_....~mms ..mm_ mfimmuacc ~03tmmwa a>mmtaoma t .omm_nnnm_ u x "cosnmaom ocneoo cheeses xtoa m.n «some ms 146 Figure 5.11 “NIB “1'! mm [Ill 5'neefefr-fereer-rfififffiJ 2.51) o e e eeeeeeeeeeeeeee i f 9.94 .mg.. ................ . . . 4L... .................. . . JLSw ................... ‘flhl uuunnrhunwuu mm Figure 5.12 oununr's Loc leznxnoor nnrlo 69 62 64 66 69 79 72 74 76 79 7196 147 1980-1983. The discontinuity in the parameters starting sometime in mid 1970s ~is confirmed by the plot of the Quandt's log likelihood ratio where a global minimum is reached sometime in 1976. The cumulative sum of squares statistic and the heteroscedasticity tests are both significant at the .05 level (see Table 5.1). The tendency to overpredict is indicated in a simple way by observing a run of 15 consecutive negative one step residuals from 1971 to 1985. The probability under the null hypothesis of obtaining at least one run of this length or greater is .00028. The global location tests are signifi- cant at level .05, indicating the rejection of hypothesis of zero mean of the residuals. These results strongly reject the null hypothesis of constant parameters in the pork inverse demand model. The results suggest the presence of an important structural break in the demand for pork starting around 1976-1977. 5.1.3 Demand for Broilers The recursive estimates for the broiler demand model are listed in Table 5.11 and plotted in Figure 5.13- 5.17. The coefficient on per capita broiler consumption exhibits three different patterns. During the first five periods, the coefficient slightly increased (in absolute value) from -1.3241 in 1964 to -1.6512 in 1968. It then declined to 148 Table 5.10 Broiler Inverse Deaand Equation: Recursive Paraseter Estiaates, 1955-1985 Nuabers in parenthesis are standard errors (0.196) (0.073) Tear Constant CHPC TKPC BFPC PKPC 0196 R 1955-62 62.075 -1.515 -0.322 -0.238 -0.075 0.013 0.95 (0.993) (2.383) (0.647) (0.397) (0.046) 1955-63 54.317 -1.300 -0.996 -0.043 -0.037 0.007 0.96 (0.756) (1.628) (0.423) (0.334) (0.038) 1955-64 53.057 -1.324 -0.983 -0.051 -0.047 0.008 0.96 (0.553) (1.398) (0.346) (0.253) (0.025) 1955-65 49.639 -1.463 -0.849 -0.148 -0.120 0.017 0.96 (0.392) (1.238) (0.224) (0.160) (0.012) 1955-66 43.910 -1.569 -0.676 -0.216 -0.163 0.024 0.94 (0.470) (1.492) (0.268) (0.192) (0.013) 1955-67 42.713 -1.609 -0.553 -0.237 -0.150 0.026 0.95 (0.354) (1.129) (0.209) (0.157) (0.010) 1955-68 46.822 -1.651 -0.212 -0.228 -0.185 0.024 0.95 (0.337) (0.977) (0.202) (0.143) (0.009) 1955-69 44.754 -1.488 -0.816 -0.197 -0.178 0.023 0.94 (0.308) (0.827) (0.203) (0.145) (0.009) 1955-70 42.300 -1.336 -1.195 -0.171 -0.145 0.021 0.94 (0.292) (0.793) (0.208) (0.147) (0.010) 1955-71 41.885 -1.338 -1.190 -0.179 -0.138 0.022 0.95 (0.277) (0.754) (0.183) (0.119) (0.009) 1955-72 41.970 -1.329 -1.203 -0.166 -0.136 0.021 0.95 (0.260) (0.717) (0.157) (0.114) (0.007) 1955-73 41.995 -1.335 -1.194 -0.172 -0.137 0.021 0.95 (0.219) (0.663) (0.090) (0.106) (0.003) 1955-74 41.988 -1.335 -1.194 -0.172 -0.137 0.021 0.95 (0.210) (0.639) (0.086) (0.102) (0.003) 1955-75 40.529 -1.350 -1.053 -0.188 -0.097 0.021 0.93 (0.204) (0.577) (0.080) (0.072) (0.003) 1955-76 42.423 -1.276 -1.243 -0.111 -0.174 0.019 0.92 (0.228) (0.649) (0.083) (0.073) (0.003) 1955-77 42.883 -1.212 -1.279 -0.113 -0.160 0.018 0.92 (0.236) (0.680) (0.087) (0.076) (0.003) 1955-78 42.857 -1.213 -1.277 -0.112 -0.159 0.018 0.91 (0.228) (0.659) (0.078) (0.074) (0.003) 1955-79 43.422 -1.058 -1.223 -0.229 -0.128 0.019 0.90 (0.233) (0.713) (0.058) (0.078) (0.003) 1955-80 42.520 -0.983 -1.125 -0.271 -0.095 0.019 0.89 (0.242) (0.749) (0.056) (0.080) (0.003) 1955-81 43.882 -0.883 -1.061 -0.294 -0.105 0.018 0.90 (0.242) (0.775) (0.056) (0.083) (0.003) 1955-82 44.889 -0.835 -1.120 -0.297 -0.118 0.018 0.90 (0.214) (0.751) (0.055) (0.076) (0.003) 1955-83 45.141 -0.817 -1.095 -0.302 -0.121 0.018 0.91 (0.211) (0.743) (0.054) (0.076) (0.003) 1955-84 45.083 -0.807 -1.132 -0.297 -0.119 0.018 0.90 (0.201) (0.707) (0.049) (0.074) (0.003) 1955-85 45.160 -0.828 -0.997 -0.304 -0.123 0.018 0.90 (0.671) (0.047) (0.003) 149 -1.3359 in 1970, then stayed relatively constant at around -1.3 during the six-year period, 1970 to 1975. Starting in 1975, the coefficient exhibits a systematic gradual downward trend from -1.3498 in 1975 to -.8279 in 1975. The coefficient on per capita turkey consumption (Figure 5.14) first declined from -0.983 in 1964 to -0.2125 in 1968. A discontinuity is apparent between 1968 and 1970 when the coefficient sharply increased at -l.l951 in 1970 and stayed relatively constant at that level until 1974. The coefficient exhibits slight fluctuations from 1975 to 1985. The coefficient on beef per capita consumption (see Figure 5.15) show a number of distinct patterns. A slight increase from -0.1485 in 1965 to -0.2371 in 1967 is shown after which the coefficient began to decline to -0.1712 in 1970 and stayed relatively constant around that level until 1974. Another discontinuity is apparent between 1975 and 1976 when the coefficient declined to -0.111. It stayed around that level until 1978 when a third discontinuity is observed. The coefficient exhibited a systematic increasing trend from 1978 through 1983, and then stayed relatively constant at around -0.3 during the last three years. The coefficient on pork per capita consumption (see Figure 5.16) first increased in absolute value from -0.1197 to -0.1848 in 1968 and then declined to about -0.14 in 1970. It then stayed relatively constant at that level through 150 Figure 5.13 km W a" , -..? ea fie e Figure 5.14 9901179 99947109: 191991 09 799991 699911 999 79 r-p-4-q-n-p-u-r-r-r-m-q-m-q-u-q--r-—-r-u 66 69 79 72 74 76 79 99 99 94 7199 151 Figure 5.15 99011.91 WPgmgm WC)” 011 -9.15 ' -9.29* 925‘ . 4 9.39 '9. 35 1W Figure 5.16 911011.711. C11 P99116110)? 1" WWII!” 011 ...m a e 4.100) '9.159* 4.179 ‘ '92“ “697972747679999994 71E '152 Figure 5.17 we mammal "1 .. 9.926 9.925‘ 934‘ 0.023. 9.“- 9J1 9.fl9* 9.919' 9.917 IIIIIIIIIIIIIIIIIII ssssssssssssssss 66 u 79 77 :4 76-79 or a: (4 me Figure 5.18 v v 1 r w ‘U — V ‘ V f V v v v v f ' v-q-w-1-n-1-u-y-w-w-fi-Q'F'fl"F'F'*'T'*'T'* “697972747679999294 71E 153 1974. A decline to -0.0968 in 1975 is shown and then an increase to -0.1743 in 1976. The coefficient then declined starting in 1977 through 1980, after which it slightly increased from -0.1054 in 1981 to -0.1231 in 1985. The coefficient on real per capita disposable income (see Figure 5.17) first slightly increased from 0.0172 in 1965 to 0.0257 in 1967. A slight decline to 0.0211 in 1972 from the 1967 level is shown. The coefficient then stayed at a relatively constant level of 0.0214 during the next three years (1973 to 1975), after which a slight decline occured in 1985 reaching a level of 0.0178. The recursive residuals for the broiler demand model are listed in Table 5.12 and plotted in Figure 5.18. The residuals during the early 19708, say 1971 to mid 708 were small and relatively constant near zero. A discontinuity occured starting in 1976 when the residuals become larger in absolute value. The model underpredicted in 1975 and overpredicted in 1977 and 1978. A run of underpredictions occurs during 1979 through 1983 and in 1985. The CUSUMSQ series for broilers crossed the confidence boundary sometime in the mid 19708, indicating a discontinuity in the demand parameters around that period (Figure 5.20). The plot of the Quandt's log likelihoold ratio (see Figure 5.21) has a global minimum in 1975. The location and serial dependence tests are significant at .05 154 mm.— vmm.o mN.~ wo.m Nn.m 0mm— hm.OI omn.o Nw.OI m~.—~ on.o— vmm— m~.N mNm.o mm.~ ~v.m mn.m nom— MN.~ m~m.o mm.o «m.m om.m Now" $0.? mom.o mN.m oo.h @N.o~ dom— o~.¢ ONm.o nu.m mt.“ mN.~— cam“ mm.m non.— -.D nm.m mm.—~ mum" -.OI o—N.o mo.OI mm.m— um.n~ mum— mo.v1 mNm.o mn.NI ~D.D~ nm.- thu om.v mvm.o ~m.n tn.m nn.m— mum— Nm.Ol OVN.~ v_.—I ww.n— Nm.m— num— No.o mmm.o —o.o vm.v~ nm.v~ whmu no.0 wmm.m n_.o mm.h~ mo.m— mum“ tn.OI NNm.o QN.OI mm.- DN.- Nkmu m~.o nno.~ ON.O m—.- mm.~u unm— Nm.N mmm.o mm.N nm.m mm.~— onm~ 5N.N mmm.o wN.N mm.~— vm.m~ mam— ~n.—I mm_.~ nm.~l m~.m~ mm.m~ mum— wN.o mun.“ ov.o om.N~ om.n~ mom" Nm.m moo.~ mw.m "—.Nn wh.n— wmm~ mm.o N~N.n mm.~ uo.v— hm.n— mom“ mo.o mNm.N ~N.o mo.m~ mN.m— vmm— vm.o me.N mm.— mm.m— Nm.n— mam" m~.— nno.n mN.m mv.m mh.m~ Nmmn ALBV An~.muc00v An—\mucwov An~.m&cwov LOLLw ALUV Jumowtou ammomtou LOLLw #mmomtou LOLLw vmwtm Qwumlmco anumb vamuLmucmem no UOCOMLQD ummowtou 0>Manowa unnuoc L00} name .....mwms .mwms n t ..mmsinmm_ u x mmmm~nc¢ umafiwmma 0>MMLDumm "comumauw vcmewo ame>cH L0—«OLm -.m U~DMF 155 Figure 5.19 mi.i".amui.iaiuiii m -101 '°°”"‘°°°-«......,,,_ 0......“ ... ... ... maOOJ '15 52 54 66 so 79 72 7‘ 76 79 so a: :4 m1 Figure 5.20 C11501159 011 011. 4110 011711) 9011119999 97 5 P CENT S CNIE1999CE 99991 a. a I M ”..."..au 495 auuunqmnnviurzu 156 U11.“ "191(11in “199 fi 3 fi—fiv— r v f 1 r 1 f v— WW “unnuunwuu mm Figure 5.21 9901169 PRICE: 909997'9 LOG 1199119009 94110 '9L3 '1500' -rL5‘ 'fll91 -22631 'flL9 19's: 1964 19%: 19's: 1950 1952 19:4 1976 ms nu: 157 level indicating rejection of the hypothesis that the E(wr) . 0 and E(wrwa) = 0. -This means that the characteristics of the recursive residuals under the null hypothesis of parameter stability are rejected.' The discontinuity in the size of the residuals near 1976 is pointed out by the heteroscedasticity tests which is significant at level .05. The foregoing results strongly reject the null hypothe- sis of constant parameters in the broiler inverse demand model. The results indicate a structural shift sometime in the mid 19708. 5.1.4 Demand for Turkey Recursive estimates for the turkey demand model are listed in Table 5.13 and plotted in Figure 5.22 - 5.26. The coefficient on per capita turkey consumption (see Figure 5.22) averaged around -1.7621 from the period 1955-70 through 1955-72 and then declined slightly to about -1.38 in 1973 and 1974. The coefficient further declined to about -l.06 in 1975 and then increased slightly in 1976 to -1.276. Starting in 1976, the coefficient is relatively constant at about -1.3 until in 1985 when it slightly declined to -l.1356. The recursive coefficient on broiler per capita consumption (see Figure 5.23) showed some fluctuations during the period 1955-66 through 1955-69, averaging around 158 -1.2238. The coefficient during the period 1970 to 1972 stayed relatively constant at around -1.076, a slight lower average than the preceding four years. A discontinuity is evident in 1973 when the coefficient increased in absolute value to -1.3206 and stayed at around -1.3 through 1975. Starting in 1976, the coefficient on broiler per capita consumption systematically declined and then leveled off at around -l.1 starting in 1979 through the rest of the period. The recursive estimates of the coefficients on per capita beef consumption (see Figure 5.24) exhibited a down- ward trend (in absolute values) from 1955-1966 through 1955-1972 period. A discontinuity occurs in 1973 when the coefficient increased in absolute value at around -0.3424 and stayed relatively constant at about -0.33 during the rest of the period, except in 1976 and 1977 when the coefficient slightly declined to about -0.27. The recursive coefficients on per capita pork consumpt- ion exhibits a relatively small variation (Figure 5.25). A slight upward trend (in absolute values) occurs from 1970 through 1974. Except during 1975, the coefficients were relatively constant during the late 19708 through the 19808. The recursive coefficients on real per capita disposa- ble income exhibited a downward trend from 1966 through 1972 (Figure 5.26). A discontinuity occurs in 1973 when the income coefficient increased to 0.0275 from 0.0143 in 1972. The coefficient slightly declined from the 1973 level 159 Table 5.12 Turkey Inverse Delano Equation: Recursive Paraseter Estlaates, 1955-1985 Year Constant TKPC CHPC 9FPC PKPC DINC R 1955-62 55.533 -3.071 -0.294 0.358 0.611 0.031 0.98 (1.661) (0.692) (0.451) (0.277) (0.032) 1955-63 58.559 -2.809 -0.378 0.282 0.597 0.028 0.98 (1.096) (0.509) (0.285) (0.225) (0.026) 1955-64 50.738 -2.731 -0.525 0.232 0.537 0.019 0.98 (0.986) (0.390) (0.244) (0.178) (0.018) 1955-65 34.765 -2.106 -1.173 -0.222 0.198 0.021 0.95 (1.419) (0.450) (0.258) (0.184) (0.014) 1955-66 27.971 -1.901 -i.300 -0.303 0.147 0.030 0.92 (1.736) (0.546) (0.312) (0.223) (0.016) 1955-67 33.937 -2.516 -1.105 -0.200 0.083 0.024 0.93 (1.353) (0.424) (0.251) (0.188) (0.012) 1955-68 48.951 -1.270 -1.262 -0.166 -0.044 0.018 0.89 (1.439) (0.496) (0.298) (0.212) (0.014) 1955-69 45.570 -1.381 -1.231 -0.160 -0.043 0.018 0.90 (1.134) (0.423) (0.279) (0.199) (0.013) 1955-70 46.257 -1.739 -1.087 -0.136 -0.012 0.016 0.90 (1.043) (0.384) (0.273) (0.194) (0.013) 1955-71 48.508 -1.768 -1.074 -0.096 -0.051 0.015 0.91 (0.998) (0.367) (0.242) (0.158) (0.012) 1955-72 49.573 -1.779 -1.068 -0.087 -0.049 0.014 0.92 (0.950) (0.344) (0.208) (0.150) (0.010) 1955-73 49.704 -1.384 -1.321 -0.342 -0.102 0.027 0.91 (0.961) (0.318) (0.131) (0.154) (0.005) 1955-74 51.514 -1.385 -1.258 -0.313 -0.106 0.025 0.89 (1.034) (0.340) (0.139) (0.165) (0.005) 1955-75 48.110 -1.056 -1.291 -0.350 -0.012 0.025 0.88 (0.944) (0.333) (0.131) (0.118) (0.005) 1955-76 50.010 -1.246 -1.218 -0.273 -0.089 0.022 0.87 (0.967) (0.341) (0.124) (0.109) (0.005) 1955-77 50.402 -1.277 -1.162 -0.275 -0.076 0.021 0.87 (0.964) (0.335) (0.123) (0.108) (0.005) 1955-78 50.797 -1.309 -1.143 -0.298 -0.081 0.022 0.87 (0.941) (0.325) (0.112) (0.105) (0.004) 1955-79 50.949 -1.294 -1.101 -0.330 -0.073 0.022 0.87 - (0.919) (0.300) (0.075) (0.101) (0.004) 1955-80 50.953 -1.294 -1.101 -0.330 -0.073 0.022 0.88 (0.894) (0.288) (0.067) (0.095) (0.004) 1955-81 51.170 -1.284 -1.085 . -0.334 -0.075 0.022 0.89 (0.872) (0.272) (0.063) (0.093) (0.004) 1955-82 51.323 -1.293 -1.078 -0.334 -0.077 0.022 0.90 (0.840) (0.240) (0.062) (0.086) (0.004) 1955-83 51.063 -1.320 -1.100 -0.329 -0.074 0.022 0.92 (0.829) (0.235) (0.060) (0.084) (0.004) 1955-84 50.917 -1.412 -1.071 -0.317 -0.071 0.022 0.92 (0.793) (0.225) (0.064) (0.083) (0.003) 1955-85 51.794 -1.136 -1.114 -0.331 -0.078 0.022 0.91 (0.769) (0.225) (0.054) (0.083) (0.003) Rushers in parenthesis are standard errors 160 Figure 5.22 “I811“ “111°18’81”" on WWW— “697979747679999294 1192 Figure 5. 23 m" 11111:)“111‘961991111” °" v ‘v’ r v v .1.‘5. ................... 'lall‘ ' ' ° ' """ .'- .143. .................. ’ . .LZO. ................... .135. . . ............... 4.36 ----------------- '1-35W “697972747679999294 7199 161 Figure 5.24 79111111 ICE 9911471011: C1911 011 4 a 997.9 9111 C991" 8119919 Figure 5.25 11 CE 991191 011: “979191911 011 71191111 901111 991 08 110 9119919 .8” Y ‘ r 162 Figure 5.26 m 1m 1 0mm 0050 O 0&0 I 0.013‘ 0.010 . “607072717610000204 11110 Figure 5.27 111111011 mm m : :rammm mam c10mm u -17-. . fiv~~m~ 163 mom.” vmm.o Om.N wN.N— mm.v~ mama mnv.—I OMN.O mo._l nm.w— om.n~ vam— mDN.NI mNm.O Nv.—I Dm.m— MN.N— mom" vma.o m~m.o Du.o Hm.m~ mm.n~ Nmm~ vvw.o mom.o ND.O mm.m~ n~.v~ www— ~—0.0l ONm.O ~0.0l NN.w~ ~N.@~ ommn m—m.o mom." mm.~ no.0" ~v.m~ mum" Nmn.— O—N.O nN.— mo.—N um.NN mum" Nwm.nl wNm.o MN.NI mm.~N mm.m~ hum— Nm¢.v mvm.o om.n Dm.vu nm.m— mum— hm~.Nl OVN.~ Dw.NI VN.VN mm.—N mum“ moo.wl mmm.o vm.m1 om.NN mm.m— tum" omN.N vnm.N Nh.m mm.—N Oh.mN Mkmg DDN.O! NNm.O ~N.OI mm.h~ Nn.n~ thu m—O.—I nmo.— NO.~I mN.m~ NN.@~ unm— mvm.N mmm.o NN.N ~N.n~ mv.m~ Ohm— NNV.O nmm.o Nv.o wm.m~ O¢.ON mmmu mhh.v1 mn~.— Nm.nl mN.mN hm.m— mam— OmN.~I mmm.— NO.NI Nm.—N ow.m~ www— th.v moo.— om.v mv.m~ mh.nN mmm~ uhm.— N—N.m ~N.m mh.v~ mv.MN mwmu Nmm.o wNm.N mm.— 0N.~N om.NN Yam" mNm.OI mmN.N DN.OI no.WN Nm.vN mam— Owo.o nDO.N Dm.o mv.mm vm.mw Nmmn Asz An~.mucwov An~\macm0v AD~.mucaov LOLLm ALUV &mmowLou &mmowLOu LOLLw fimmomLou LOLLU wacc amamlwco wa—wb UUNMvLflvcmam mo UOCNMLQD umNOwLou 0>MML30wm una&oc mer mom“.....nmm~ .mmm~ u L ._mm~-nmm_ u x mwmm~wc¢ mmaflmmwm w>mmLaomm "comumaow Ocmewo mew>c~ mwaDH m~.n U~DMh 164 165 rum : “WIND “10! 0mm E11110! f ”-1117 1- - - ' fi 205 , , . . .......... I." '2.5‘ 'SI'1 """ 411W “'00‘10'12'1170‘10000204 1111! Figure 5.30 mm mes: mum's LOG mummy mmo 0A0 -205‘ .5.04 .705‘ 'MLO‘ '12-:1 '15J0 19'62 1914 19‘“ 1921 1959 m: 19‘74 1906 1911 m1: 166 reaching 0.0215 in 1977. The coefficient then stabilized. The recursive residuals for the turkey demand model are listed in Table 5.14 and plotted in Figure 5.27. The plot of the residuals does not indicate a systematic pattern. The residuals varied between 5.0 and -5.0 from the period 1955-65 to 1955-68. The variation narrowed to about 2.5 and -2.5 between 1969 and 1973. The recursive residuals then increased (in absolute value) to -6.0 in 1974 and then to 4.5 in 1976. The stability tests based on the one step ahead recursive residuals led to the failure to reject the null hypothesis of constant demand parameters. The location tests are not significant at the 0.05 level. The CUSUM and CUSUMSQ (Figure 5.28 and 5.29) including the heteros- cedasticity tests are also not significant at the 0.05 level indicating a nonsignificant difference in the average size of the one step ahead recursive residuals. The foregoing results indicate that we fail to reject the null hypothesis of stability in the parameters of inverse demand for turkey. 5.2 Demand Models with Time Trend and Dummy Variables: A Test of Gradual and Abrupt Structural Shifts Based on the empirical results of the recursive residual analysis, the null hypothesis of constant parameters of the inverse demand for beef. pork and broilers is rejected against the alternative hypothesis of parameter 167 instability. Information about possible points of discontinuity in the parameters were identified. In this section, the information on the timing of discontinuity in the parameters will be used in specifying the demand models to explicitly account for the changes in the demand parameters for the three commodities. Similar specification will be used in the case of turkey in order to assess whether results similar.to those of constant parameter model will be found. The base model of inverse demand for the four commodities specifies the price of the commodity as a function of the own quantity available for consumption, quantities of substitutes and income. In the specification, the residual term contains the influence of all variables except the quantities and income that affect the price of the product in question, including any changes in tastes or changes in other conditions. It is known that if the residual is correlated with either the quantities or income, regressions of the base model yield biased estimates of the coefficients on the variables correlated' with the error term. For example, if the taste for the commodity is shifting at the same time that income is increasing, the estimated coefficient on income represents the combined effect of the shift in taste and increases in income. To reduced this problem of biased estimates, a time trend variable is introduced as a separate variable. The trend 168 variables are introduced to test for gradual structural shifts in demand due to the hypothesized continous changes in tastes. If the model is linear in the variables, the coefficient on the time trend measures the rate of shift of demand in terms of annual prices, given quantities and income. The shift in demand is approximated by a smooth, steady, monotonic function of time. Several conceptual problems are recognized in the inclusion of a time trend (George and King, 1971). First, the trend variable is often highly correlated with prices and income. Hence, multicollinearity among these variables leads to inaccuracy in the estimates and the variance of the coefficients becomes larger. Second, the time trend is not able to capture possible cyclical changes in demand. It is more realistic to suppose that demand may decline for a while, then recover and increase over another series of years. This situation is considered in the latter part of the study. Inverse demand equation were estimated for beef, pork, broilers and turkeys using time series data for 1955-85. The results were compared with a similar analysis for a more recent period of 1970-85. The demand parameters estimated from these models are compared with those estimated from the models augmented by the trend variables. All the equations were in linear form and were estimated by ordinary least squares. Where serial correlation is indicated, the ARI 169 procedure is used. The flexibilities are estimated at the means of the relevant variables. 5.2.1 Analysis of Results from Modelgiwithout Trend Variables The demand models estimated are specified as follows: n (5.111% '68:. +51 91+}: Bk 0111 +C1Y1+d1DV1+et k=2 where P represents the real price of the commodity, Q's are the quantities available for consumption of the commodity in question and the quantities of substitutes, Y is real disposable income per capita, and DV stands for a shifter variable. DV is an indicator variable to test for abrupt discontinuity and change in demand. Dv700n takes a value of zero before 1970 and one from 1970 to 1985. The models are estimated for the entire period (1955-1985) and then for a more recent time period (1970-85) without the dummy variable for comparative purposes. The statistical results are presented in Equations 5.1-5.8. For beef, the flexibility estimates (see Table 5.15) are generated from Equation 5.1 and 5.2. The own-quantity flexibility (estimated from Equation 5.2) was found to be -1.78344 for the entire time period. For the period 1970- 85, the own-quantity flexibility for beef increased (in absolute value) to -2.3105. A significantly positive income flexibility (1.37118) was estimated from the analysis for 170 Equation 5.1 SNPL 1956 - 1985 30 Observations ‘ LS // Dependent Variable is FBP Convergence achieved after 9 iterations 8......II.IIIIIIIIIIIIIIIICIIIIII888.88.I...IIIIICIIIIIIOICSIIIIIIBD VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. ...-III...I888IIIIIIIIIIIIIIUIIII.88...I.IISIIIIIISSIIICIIII..88...- C 19.399898 171.57740 0.1130679 0.911 BFPC -0.4549013 0.0815863 -5.5757082 0.000 POULPC -0.0659843 0.1825021 -0.3615534 0.721 PKPC -0.0804933 0.0758137 -1.0617251 0.299 DINC 0.0127803 0.0047483 2.6915692 0.013 DV7OON -0.5596941 1.9552618 -0.2862502 0.777 AR(1) 0.9847574 0.0882206 11.162444 0.000 ..88.III...I.II..88....888.I.8.888OCIOIIIIIIIIIIIICIIO.‘IIIIIIIIIIII R-squared ' 0.771114 flean of dependent var 26.34202 Adjusted R-squared 0.711405 S.D. of dependent var 3.457912 S.E. of regression 1.857626 Sum of squared resid 79.38783 Durbin-Watson stat 1.486483 F-statistic 12.91448 Log likelihood -57.16159 Equation 5.2 SHPL 1970 - 1985 16 Observations LS // Dependent Variable is FBP VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. 8888.8...III-8.888.888.88.888..II.I88".IIIIIIIIIIIIIIIIIIIIOI.III-I C 96.943047 27.778306 3.4898833 0.005 BFPC -0.5232701 0.1384182 -3.7803560 0.003 POULPC -1.0276869 0.1957957 -5.2487722 0.000 PKPC 0.0180687 0.1529244 0.1050764 0.918 DINC 0.0136848 0.0058065 2.3568217 0.038 I.8......IIIIII.I'll.88......IIII.I...I..88-I8......lIIIIIIIIIIIIICC R-squared 0.784161 Mean of dependent var 25.38022 Adjusted R-squared 0.705675 S.D. of dependent var 4.083449 S.E. of regression 2.215343 Sum of squared resid 53.98518 Durbin-Uatson stat 2.170348 F-statistic 9.991006 Log likelihood -32.43198 171 Equation 5.3 SHPL 1956 - 1985 30 Observations LS // Dependent Variable is PPORK Convergence achieved after 14 iterations 8888.88.88....-.88....IIIIIOIIOIIIIIIII-lIII33......IIIIIOI.88...... VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. I8.88888I.I.III.IIIIIIIICQIOCDCCIICIIIIIIICOCICCIIIIIIIIIIIIII...... C 64.591304 21.286265 3.0344123 0.006 PKPC -0.6990178 0.0888181 -7.8702181 0.000 BFPC -0.2124539 0.0956387 -2.2214215 0.036 POULPC -0.1142295 0.1976726 -0.5778720 0.569 DINC 0.0088019 0.0049271 1.7864229 0.087 DV700N -0.8570715 2.3531391 -0.3642248 0.719 AR(1) 0.9107558 0.1265517 7.1967098 0.000 a.IIII.IIII-II...IIIIIIIIIIIISISIQII-IIIIIIIIUIIIIC'IIIIIIIIIII.I... R-squared 0.794677 Mean of dependent var 20.06686 Adjusted R-squared 0.741115 S.D. of dependent var 4.123312 S.E. of regression 2.097973 Sum of squared resid 101.2343 Durbin-Watson stat 1.902522 F-statistic 14.83646 Log likelihood ~60.81176 Equation 5.4 SHPL 1970 - 1985 16 Observations LS ll Dependent Variable is PPORK VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. 88II...II.IOIIIIIIIIIIIIII88.88.888.888...IIIIIIIIICCSIIIIOIIIIIIIII c 113.9543o 20.731491 5.4966765 o.ooo PKFC -0.7109559 0.1141305 -6.2293250 0.000 BFPC -0.3465470 0.1033042 -3.3548264 0.006 POULPC -0.7680386 0.1461261 -5.2559979 0.000 DINC 0.0106905 0.0043335 2.4669377 0.031 I88.888.888.888...IIICIIOIIOIOIIIIIII....-..IIISIII.IIIIIII.IIIIII.I R-squared 0.924601 Mean of dependent var 20.55728 Adjusted R-squared 0.897184 S.D. of dependent var 5.156257 S.E. of regression 1.853353 Sun of squared resid 30.06935 Durbin-Watson stat 2.174381 F-statistic 33.72279 Log likelihood -27.75036 ' . 172 Equation 5.5 SHFL 1955 - 1985 31 Observations LS // Dependent Variable is CHP VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. I.II...IIIIIIIII.I...DISC-I'll...-II...........IIIICIICIIIIIIIOIIIIC C 48.795817 5.5574273 8.4203742 0.000 POULPC -0.8490187 0.1051983 -8.0708307 0.000 BFFC -0.3007148 0.0489803 -8.4008859 0.000 PKPC -0.1280398 0.0722948 -1.7434141 0.094 DINC 0.0188088 0.0032847 5.1171910 . 0.000 DV7OON 0.8484291 1.2173922 0.6969234 0.492 II.I...I...I'll-.IIIOIIICIIIIICCIII..........I...IIIIIIIIIIIIIIII.II R-squared 0.911508 Hean of dependent var 15.11533 Adjusted R-squared 0.893809 S.D. of dependent var 4.831722 S.E. of regression 1.574509 Sum of squared resid 81.97895 Durbin-Watson stat 1.308052 F-statistic 51.50218 Log likelihood -54.72511 SNPL 1958 - 1985 30 Observations LS // Dependent Variable is CHP Convergence achieved after 4 iterations I..8.I88.88.8388.ICIIIICIIIIIIIIIIICIIIIIIIIIICIIICICIIIIOIII8.3.8.8 VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. CIIII'8II...-8.UCQIIIIIIIIIIIIIIIIICIIlflflflflilililIII-IIIIIIIIIIIIIII C 42.288713 4.2730581 9.8985920 0.000 POULPC -0.5307903 0.0782188 -8.7859882 0.000 BFPC -0.1864537 0.0353832 -5.2895594 0.000 PKPC -0.1709013 0.0463704 -3.6855666 0.001 DINC 0.0098118 0.0021236 4.8203224 0.000 DV700N 0.0888255 0.9245148 0.0744451 0.941 ARIi) 0.3808222 0.1044957 3.4529888 0.002 I..8888...I...IIIIIIIIIOISSIIIII.8I8888......IIIIIUICIIIIOIIIICIICII R-squared 0.952827 Hean or dependent var 14.57179 Adjusted R-squared 0.940521 S.D. of dependent var 3.830970 S.E. of regression 0.934313 Sum of squared resid 20.07783 Durbin-Hatson stat 2.661718 F-statistic 77.42718 Log likelihood -38.54429 _ Eaaaffafi?v.......-...-........-..........-........................ ean 1970 - 1985 18 Observations LS // Dependent Variable is CHP VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. IIIII3.8.8.8...I.IIOIICIIIIIIIOIIIIIIIIUIIIIIIIIIIIIIIII...88......- C 44.883995 12.710834 3.5311808 0.005 POULPC -0.5638105 0.0895924 -6.2930590 0.000 BFFC -0.2016847 0.0633376 -3.1839667 .0.009 PKPC -0.1812810 0.0699754 -2.5903540 0.025 DINC 0.0103490 0.0026589 3.8950788 0.002 ...I......IIIIIIIII'll-IIIIIIIIISCIII-.33....COUCH-8.83.38.83.33...- R-squared 0.878855 Mean of dependent var 12.24472 Adjusted R-squared 0.831802 S.D. of dependent var 2.471718 S.E. of regression 1.013699 Sum of squared resid 11.30345 Durbin-Hatson stat 2.331382 F-statistic 19.54517 Log likelihood ~19.92317 173 Equation 5.7 SHPL 1955 - 1985 31 Observations LS // Dependent Variable is TKP VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. 38.8888...IltflIICIIISISIIIICIIIIIIIIISCIIICIIIIIIICIIIBCIIIIIIIIIICI C 51.419598 6.4197641 8.0095772 0.000 POULPC -1.1157869 0.1215217 -9.1817879 0.000 BFPC -0.3302287 0.0542702 -8.0849038 0.000 PKRC -0.0783667 0.0835127 -0.9383810 0.357 DINC 0.0221811 0.0037944 5.8404704 0.000 DV700N 0.1688525 1.4082929 0.1200892 0.905 I‘ll...I.8.8.8.8.88.888838888838888...III-888.888.383.3-III-IIIIIIOI R-squared .0.918347 Mean of dependent var 21.88232 Adjusted R-squared 0.902016 S.D. of dependent var 5.810502 S.E. of regression 1.818823 Sum of squared resid 82.70290 Durbin-Watson stat 2.418889 F-statistic 56.23474 Log likelihood -59.19674 Equation 5.8 snPL 1970 - 1985 18 Observations LS // Dependent Variable is TKP VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. I.888.8888...IIIIIOIIIIIIIIIIIIIIII8.88888888888IIBISIIIIIIIIIIDIIII C 58.213024 24.165222 2.3261953 0.040 POULPC -1.0107178 0.1703288 -5.9339216 0.000 BFPC -0.3181829 0.1204143 -2.6424003 0.023 PKPC -0.1360195 0.1330338 -1.0224436 0.329 DINC . 0.0198258 0.0050512 3.8853496 0.003 BIIIOIIIIIIICIC......IICIIIIIOI.IIIIIISIIIIIIIIIIIIIII.IIIIIICIIIIIO R-squared 0.830443 Hean of dependent var 16.18281 Adjusted R-squared 0.788785 S.D. of dependent var 4.007914 S.E. of regression 1.927196 Sum of squared resid 40.85494 ‘ Durbin-Watson stat 2.526591 F-statistic 13.46870 Log likelihood -30.20253 174 mcmwe OLA an Dwamuaouwo 0L0 mwmdmdmnme—m mmvo.m owmn.~ nmmm.s mnnn._ mumm.~ wmmm._ mmm~.~ msnm.s aeoocs nomm.m1 n-6.~1 snm_.~1 whom.~1 oomv.~1 mmmm._n -k~.61 mm-.ou missaoa a n_o~.61 momm.ou nomm.~1 .m.c mmns.ou mmon.oa mmm_.~1 mom—.61 area a monm._1 mnvm.~1 nmmm.su ossm.~1 nwom._1 mmn~._1 Nvmo.sn vmmn._1 comm a Gupta wumLQ wowLQ NOmLQ wopta OOMLQ womLQ NOMLQ masts» 1021016 x106 comm mmxtsh tmsaotm x166 comm moms 1 cums moms 1 mum— eotu maumeaamm mos—«aamwflumwumwcwcwuw wmmuwwuawswwwmueamuwmcwmmmnnm 43.6 m_nmp 175 the entire 1955-85 period. 1 A slightly higher and significant positive income flexibility was estimated for the 1970-85 period. The increase in the income flexibility is in response to a slightly higher coefficient on the income variable and the higher income average and lower average beef price in the 1970-85 period. The cross-flexibility of beef with respect to broilers increased significantly in the second period. This is in support of the hypothesis of increasing substitutability of poultry with beef starting sometime in the 19708 and through the 1980s. The income flexibility of demand for pork slightly increased from 1.23918 in the 1955-85 (Equation 5.3) period to 1.69335 in the 1970-85 period (Equation 5.4). The own- quantity flexibility of demand for pork is almost the same in the two periods. A significant increase in the cross- flexibility of pork with respect to poultry is observed, from -0.27218 in 1955-85 to -2.127135 in 1970-85. For broilers, the income flexibility was also higher in the 1970-85 period than in the entire 1955-85 period. The own-quantity flexibility of demand for broilers likewise increased in 1970-85. A slight increase in the cross- flexibility of broilers with respect to beef and pork was also observed in the 1970-85 period. The income flexibility for turkey was significant and positive during the two time periods. It increased from 176 2.827 in 1955-85 to 3.649 in 1970-85. Likewise, the own- quantity flexibility for turkey increased from -2.430 in 1955-85 to -3.321 in 1970-85. A slight increase in the cross flexibility of turkey with respect to beef is observed. The cross-flexibility with respect to pork slightly increased but was not significant at the 0.05 level. 5.2.2 Analysis of Qemandgnodels with Trend4Yari§ble§ As indicated in the results of the recursive residual analysis, a discontinuity in the demand parameters for beef, pork and broilers occured sometime near late 1970s. In the case of beef, pork, and broilers, the recursive residuals indicate a possible structural shift sometime in 1976-77. Using this information as the timing of the structural change in demand, the base model for each commodity is augmented by two trend variables. One trend variable represents the trend from 1955-76 is labelled T5576, and another to represent the turning point in the trend from 1977 to date.8 The estimated models are presented in Equations 5.9 to 5.16. The associated flexibility estimates are presented ' This procedure is used by Ferris (1985) in a study of demand for meat. 177 in Table 5.16. In contrast to the results from the models without the trend variables, the income flexibility on pork was very close in the two time periods though higher in magnitude in both periods. The own-quantity flexibility of demand for pork increased from -1.8768 in 1955-85 (estimated from equation 5.9) to -2.6041 in 1970-85 (estimated from equation 5.10). These estimates are slightly higher than in Table 5.15. The cross flexibility of pork with respect to beef also increased in the second period and are higher than those estimated without the trend variables. The cross flexibility of pork with respect to poultry increased in 1970-85 but is lower than those estimated in Table 5.15. The lower value of the cross flexibility is due to the correlation between time and quantity of poultry available for consumption. The results indicate an absence of a significant trend before 1976 and a presence of a significant negative trend starting in 1977. The estimates of the own-flexibility of broiler demand remained quite the same between 1955-85 (Equation 5.13) and 1970-85 (Equation 5.14). These estimates were somewhat lower than in Table 5.15, again possibly due to the multicollinearity between the quantities and time. The income flexibility of broiler slightly increased from 2.0165 in 1955-85 to 2.7967 in 1970-85. The estimates of the cross flexibility with respect to beef and pork likewise increased in 1970-85. 178 Equation 5.9 SHPL 1955 - 1985 31 Observations LS // Dependent Variable is FBP VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. 28888888888888.888888838.888883388888888888.888.88.888.8888888888888 C 39.450968 8.6788701 4.5456341 0.000 BFPC -0.5882137 0.0434441 ~13.493517 0.000 PKPC 0.0002278 0.0460524 0.0049460 0.996 POULPC 0.0962027 0.1095527 0.8781406 0.389 DINC 0.0164880 0.0022288 7.3982169 0.000 T5576 -0.0394448 0.1753647 -0.2249299 0.824 T77ON -2.7012587 0.2413120 -11.194049 0.000 3.38888888388888883888888388888838:8888883888888888.338888888883888. R-squared 0.936550 Mean of dependent var 28.41577 Adjusted R-squared 0.920887 S.D. of dependent var 3.424503 S.E. of regression 0.964426 Sum of squared resid 22.32281 Durbin-Watson stat 2.249104 F-statistic 59.04163 Log likelihood -38.89723 8288388388388882823232888:38:8:2888388883888388288832882388:38882888 Equation 5.10 SHPL 1970 - 1985 16 Observations LS // Dependent Variable is FBP VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. 2:388:8:888888888838288883===33888=8===8332:338388888888888838.888888 C 52.407726 17.940135 2.9212560 0.017 BFPC -0.6188976 0.0750484 -8.2468506 0.000 PKPC -0.0814293 0.0919638 -0.8854487 0.399 POULPC 0.0875820 0.2464693 0.3553464 0.731 DINC - 0.0152004 0.0033019 4.8035209 0.001 T5576 ~0.2112829 0.2839251 -0.7441502 0.476 T77ON -2.5589168 0.4828197 -5.2999422 0.000 88888883:888888888888888888888888838888888888333888888!!!83888388838 R-squared 0.950915 Mean of dependent var 25.38022 Adjusted R-squared 0.918191 S.D. of dependent var 4.083449 S.E. of regression 1.167959 Sum of squared resid 12.27715 Durbin-Hatson stat 2.366440 F-statistic 29.05900 Log likelihood -20.58423 179 Equation 5.11 SNPL 1955 - 1985 31 Observations LS // Dependent Variable is FPORK VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG.v ..88.8.IIICIICI...I3.88.33............III-.ilfllIIIBIIICIIIII3......- C 46.498746 13.874786 3.4003272 0.002 PKPC -0.6049325 0.0725620 -8.3367642 0.000 BFPC -0.2851576 0.0684523 -4.1657849 0.000 POULPC -0.0876013 0.1726158 -0.5074931 0.616 DINC ‘0.0168346 0.0035116 4.7940520 0.000 T5576 -0.0030672 0.2763118 -0.0111004 0.991 T77ON -1.7738990 0.3802212 -4.6849139 0.000 I'll......-III.......II-IIIUIIIII.IIII-.......-I.-IIIIIIIICIIIIICIII R-squared 0.888321 Hean of dependent var 20.12544 Adjusted R-squared 0.860401 S.D. of dependent var 4.087107 S.E. of regression 1.519589 Sum of squared resid 55.41963 Durbin-Watson stat 1.772682 F-statistic 31.81896 Log likelihood -52.99177 Equation 5.12 SHPL 1970 - 1985 16 Observations LS // Dependent Variable is PPORK Convergence achieved after 4 iterations VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. I.8.888888III888.888.88.883...I....88I'88IIIIIIIISIIIIIIISI888...... C 111.15304 14.279057 7.7843400 0.000 PKPC -0.8338929 0.0718704 -11.602729 0.000 BFFC -0.5229934 0.0542122 -9.6471562 0.000 POULPC -0.2780987 0.2377967 -1.1694810 0.276 DINC 0.0127085 0.0019573 8.4930272 0.000 T5576 0.0292293 0.2076960 0.1407310 0.892 T77ON . -1.4175877 0.4180584 -3.3909004 0.009 AR(1) -0.7415230 0.2502366 . -2.9632874 0.018 III...II.CIIISIIIIIIIIISIIIIIIII.........IIIIICIIIIIIIIIIIICIIIIIIII R-squared 0.980447 dean of dependent var 20.55728 Adjusted R-squared 0.963338 S.D. of dependent var 5.156257 S.E. of regression 0.987285 Sum of squared resid 7.797859 Durbin-Uatson stat 2.134412 F-statistic 57.30612 Log likelihood -16.95310 180 Equation 5.13 SMPL 1956 - 30 Observations LS // Dependent Variable is CHP Convergence achieved after 4 iterations 1985 VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TA1L SIG. =38888883.8888888888888888888888883388888888888838838838888888888888 C 36.760647 9.9939519 3.6782893 0.001 POULPC -0.4120323 0.1201034 -3.4306468 0.002 BFPC -0.2119077 0.0480934 -4.4061752 0.000 PKPC -0.1798513 0.0464019 -3.8759438 0.001 DINC 0.0107553 0.0025673 4.1893268 0.000 T5576 -0.1115872 0.1976698 -0.5645131 0.576 T77ON -0.3365768 0.2754721 -1.2218181 0.235 AR(1) 0.3831503 0.1012111 3.7856532 0.001 8:88===8888888832:8:888882328388888888888382888833888828828888888883 R-squared 0.955945 Mean of dependent var 14.57179 Adjusted R-squared 0.941927 S.D. of dependent var 3.830970 S.E. of regression 0.923196 Sum of squared resid 18.75042 Durbin-Uatson stat 2.763068 F-statistic 68.19651 Log likelihood -35.51843 =::=======sz:==========3=====::=::=========::======s==========ss==z= Equation 5.14 SMPL 1970 - 1985 16 Observations LS // Dependent Variable is CHP Convergence achieved after 4 iterations 3::=:===88:833=3====388332338383883333833888========8====888838338I: VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. 33==33:===333:83:88:338838888338838838238838832:33883838833388388888 C 38.184611 16.059818 2.3776491 0.045 POULPC -0.2930620 0.2410946 -1.2155480 0.259 BFPC -0.2387859 0.0678345 -3.5201239 0.008 PKPC -0.2361547 0.0837534 -2.8196419 0.023 DINC 0.0105173 0.0027052 3.8878651 0.005 T5576 -0.0930180 0.2385205 -0.3899790 0.707 T77ON -0.6034533 0.4533272 -1.3311648 0.220 AR(1) -0.2411299 0.3641267 -0.6622143 0.526 R-squared Adjusted R-squared S.E. of regression Durbin-Watson stat Log likelihood 0.905967 0.823688 1.037861 2.097844 -17.75243 Mean of dependent var S.D. of dependent var Sum of squared resid F-statistic 12.24472 2.471718 8.617249 11.01095 181 Equation 5.15 SMPL 1955 - 1985 31 Observations LS ll Dependent Variable is TKP VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. 8.88.8888I.888888.888.IIIIIIIIIIIIISIIIIIIII-IIIIIIIICISIBIIIIIICIII C 26.596217 15.842400 1.6787998 0.106 POULPC -0.9039149 0.1999775 -4.5200840 0.000 BFPC -0.3148856 0.0793028 -3.9706738 0.001 PKPC -0.1075442 0.0840640 -1.2793143 0.213 DINC 0.0262593 0.0040682 6.4548013 0.000 T5576 -0.5249419 0.3201105 -1.8398772 0.114 T77ON -0.3743058 0.4404907 -0.8497474 0.404 8.8888.I...I.I8.8.8.88888888IIIIIIIIIII-IIIIIC.8.8.3.8888II3IICICIII R-squared 0.926563 Mean of dependent var 21.68232 Adjusted R-squared 0.908204 S.D. of dependent var 5.810502 S.E. of regression 1.760462 Sum of squared resid 74.38142 Durbin-Watson stat 2.340006 F-statistic 50 46834 Log likelihood -57.55299 . Equation 5.16 SMPL 1970 - 1985 16 Observations LS // Dependent Variable is TKP Convergence achieved after 3 iterations VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. 88888888883888888.888888888888888888888..88.88888888388388.888883338 C 6.8849534 20.860036 0.3300547 0.750 POULPC -0.1090912 0.3396444 -0.3211926 0.756 BFPC -0.3231903 0.0841804 -3.8392565 0.005 PKPC -0.2414971 0.1190202 -2.0290442 0.077 DINC 0.0224392 0.0030271 7.4126696 0.000 T5576 -0.8291894 0.3139213 -2.6413923 0.030 T77ON -1.7511693 0.6092170 -2.8744589 0.021 AR(1) -0.5579115 0.3328708 -1.8760602 0.132 888.8.8IIII8IIIICCIIIIIIIIII88.8.8.888.888.888.388...IIIIIIICIflflllfl. R-squared 0.935839 Mean of dependent var 18.18261 Adjusted R-squared 0.879698 S.D. of dependent var 4.007914 S.E. of regression 1.390127 ' Sum of squared resid 15.45962 Durbin-Watson stat 2.243510 F-statistic 16.88949 Log likelihood -22.42816 182 mcmme mg» no umsm_:o_mo mtm nmmumsanmxm_m vm_o.v mmmk.~ on36.~ comm." -mv.n mmzo.w moan.~ ooms.. meoocm msvm.o1 mwmm.s1 wonk.61 vmm_.o _mmm._1 Naom.~1 kmo~.61 mvk~.o 3162566 e. mmnm.61 smm~.s1 seom.~1 mno~.o1 kmom.61 onvk.o1 mmnm._1 vooo.o 1106 a ommm.~1 mnm2.~1 n_nm.~1 mmmk.~1 moon._1 .nmv.~1 mmmv.s1 ooom.~1 comm a OOMLQ UOMLQ OOMLO momta OOMLQ wuwta wowLQ NOMLQ mmxtap tossotm atom mmmm mmxtap tmsmotm atom mmmm nmms 1 ohms nmmz 1 nmmz mm_mmmtms mamr» rum: mimoo: acmemm mmtm>c~ more mmhmemhmm momsaomxmsm mucosa 6cm mauucmam mmotm .mhmhcmam cam ms.n msnmp 183 With trend factors, the income flexibility of demand for turkeys increased between 1955-85 (Equation 5.15) and 1970-85, (Equation 5.16) and were somewhat higher than those estimated from the model without trend factors. The trend effects are both significant and negative but is highly collinear with the quantity of poultry. The own-quantity flexibility of demand for turkeys declined between the two periods and was lower than those estimated without the trend effects. The cross flexibility of demand for turkeys with respect to beef and pork both increased between the two periods. 5.3 Varying Parameter Models Using Legendre Polynomials Continous variation in the inverse demand parameters for beef, pork and broilers was tested by specifying a varying parameter model with Legendre polynomials. The specification of the inverse demand models follows the equation presented in section 4.5.5.1. The theoretical foundations of the approach was briefly discussed in section 4.5.5. By introducing varying degree Legendre polynomials, the specification allows the demand parameters to vary over time. The models are linear in parameters and were estimated using ordinary least squares. The models are evaluated using standard statistical tests. 184 The empirical results of selected equations for the commodities are presented in Equations 5.17-5.48. Linear, quadratic, and cubic Legendre polynomial specification for the own quantity, quantity of substitutes, and income variables were tested. The corresponding own-quantity, cross, and income flexibilities were estimated and analyzed for each commodity. In general, the results indicate that the null hypothesis of constant parameters of the inverse demand models for the three commodities can be rejected at the .01 level based on the F-tests. It is observed that by specifying the demand coefficients as continous functions of time by introducing Legendre polynomials, serial correlation in all the demand models was reduced. A higher degree polynomial tended to increase the adjusted coefficient of determination and is correlated with the other explanatory variables. Hence, the specification of equations with a high degree polynomial is done with caution. In this study, a sign change or a reduction in a formerly significant coefficient after the introduction of a higher degree polynomial is an indication of potential collinearity of the polynomial with the variable whose coefficient changes sign. In this situation, a lower degree polynomial specification is preferred and chosen for evaluation and further analysis. The own, cross, and income flexibilities over time for the three commodities were estimated using the formula 185 presented in equation 5 in section 4.5.5.1. These estimated flexibilities are presented in tables following each equation. 5.3.1 Beef Demgnd Model with Legendre Polynomial The own quantity flexibilities for beef estimated from the Legendre polynomial models indicate flexible price response to changes in beef quantity available for consumption, other factors constant (Figure 5.31-5.34). The estimated income flexibilities for beef indicate a more than proportionate change in beef prices in response to a one percent change in real disposable income. As expected, the income flexibility estimates are positive. This is because prices move directly with changes or shifts in demand. A higher level of income is associated with a higher demand until a leveling off or saturation is reached where a certain percent increase in income will result in a less than proportionate increase in demand. In contrast with the constant parameter inverse demand model for beef the varying parameter model with cubic Legendre polynomial has better statistical properties. In particular, the Durbin-Watson statistic indicates no serial correlation in the varying parameter model. The fit of the model was materially improved and all the coefficients have signs consistent with theory. 186 The own quantity flexibilities estimated from the models with quadratic and cubic Legendre polynomials exhibit the same general pattern of year to year variation (see Figure 5.31 and 5.32). This is a good indication of the consistency of the estimation and specification of the models. The flexibilities exhibit a slight upward trend (in absolute value) during the whole period. A structural break is indicated by larger fluctuations in the own-quantity flexibilities for beef starting sometime in the mid-19705. The pattern of the estimated own-quantity flexibilities for beef may be related to the pattern of production cycles during the period of analysis. During the period 1964 to 1970, the own-quantity flexibilities varied only slightly. Starting in 1970, they exhibited a slight downward trend until about 1973. With the slight increase in quantities available for consumption and rising prices, the own quantity flexibilities declined during the 1970-73 period. The lower magnitude of the flexibility estimate in 1973 reflect the high beef prices in 1973. The record prices in 1973 is associated with producers decision to withhold animals from slaughter for herd expansion. Due to the slow rate of biological reproduction, beef production can be increased only by withholding animals from current slaughter for further fattening or to increase the size of the breeding herd. Animal slaughter increased thereafter and Equation 5.17 SMPL 1955 - 31 Observations LS // Dependent Variable is FBP 1985 187 VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TA1L SIG. =88888888888888.8888888888888888888888888.888888888888888888888.8888 C 66.450758 11.155087 5.9569915 0.000 BFPC -0.5954262 0.0728896 -8.1688739 0.000 P108 0.0295225 0.0355982 0.8293250 0.415 P208 -0.0836551 0.0114760 -7.2895587 0.000 PKPC -0.0243737 0.0748837 -0.3254876 0.748 POULPC -0.6341983 0.1356594 -4.6749296 0.000 DINC 0.0188678 0.0035981 5.2437780 0.000 =8.8888888888228882288::8:=3=8=88:=88I88883388883383388338.888888888 R-squared 0.845181 Mean of dependent var 26.41577 Adjusted R-squared 0.806476 S.D. of dependent var 3.424503 S.E. of regression 1.506485 Sum of squared resid 54.46792 Durbin-Hatson stat 1.830734 F-statistic 21.83661 Log likelihood -52.72328 83883288888888:88=3====88382888828283388888883283:28:228333388888388 Equation 5.18 SMPL 1955 - 1985 31 Observations LS // Dependent Variable is FBP VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. =88:888888888888883888883838883::8888888888888382888888888888.888888 C 52.973442 8.7947058 6.0233330 0.000 BFPC -0.5812352 0.0541794 -10.727972 0.000 P108 -0.0390648 0.0304362 -i.2834981 0.212 P208 -0.0789738 0.0085783 -9.2062733 0.000 P308 -0.0308378 0.0067971 -4.5369258 0.000 .PKPC -0.0971113 0.0578353 -1.6791005 0.107 POULPC -0.1509152 0.1465644 -1.0296854 0.314 DINC 0.0166589 0.0027141 6.1379071 0.000 8388.8888a8888888888888...IIISCBISBBIBIIBIIISCSSBS'SISIIIIIIIICIIII. R-squared 0.918299 Mean of dependent var 26.41577 Adjusted R-squared 0.893433 S.D. of dependent var 3.424503 S.E. of regression 1.117914 Sum of squared resid 28.74382 Durbin-Hatson stat 1.913656 F-statistic 38.93054 Log likelihood -42.81585 188 beef prices declined. This situation of declining prices and increasing quantity available for consumption is reflected in the upward trend of the own-quantity flexibility estimates starting in 1973 through 1977. Own flexibility estimates subsequently declined until 1979 due to the decline in quantity available for consumption and the increase in real beef prices following liquidation of the breeding herd in earlier period. Beef quantity available for consumption per person was relatively constant thereafter, (1979-1984), while real prices declined. The demand for beef shifted to the left and the own- quantity flexibilities trended upward during this period. During this period of declining demand for beef, large price adjustments are required in response to small changes in quantities: hence, increases in the own- quantity flexibilities for beef. To the extent that an inelastic demand is consistent with a flexible price, these results are consistent with other studies which found the demand for beef becoming more inelastic during the late 1970s (Chavas, 1983; Ferris, 1985). 1 Variation in the price response to income changes (income flexibility) was tested by augmenting the cubic Legendre polynomial model with a linear polynomial on the 189 Figure 5.31 .. ”11111.11 1111111111.. 11m 1...... fit!“ -3051 «.1 ji 1955 19111 1955 1m 1975 1m 1915 1111: Figure 5.32 «810% 01 00 151 [WWI C 0800£q8UflWH1fl1 INHID fr 1915' ' ' 19111 ' ' 1915' 7' 1951' 719775 1 191111 ' ' 1955 13K! Equation 5.19 SMPL 1955 - 31 Observations LS // Dependent Variable is F8? 1985 333383388888388838888338833883=8.883.3888888388838888838388888382338 VARIABLE COEFF1CIENT STD. ERROR T-STAT. 2-TA1L SIG. =383238883888:88....BBIiagttgg888388.3388a8:888:88388888888388883888 C 41.039137 9.6174577 4.2671503 0.000 BFPC -0.6301993 0.0541868 -11.830136 0.000 P108 0.2382349 0.1243361 1.9160562 0.068 P208 -0.0473322 0.0159134 -2.9743586 0.007 P308 -0.0188062 0.0081634 -2.3037241 0.031 PKPC -0.0574429 0.0558993 -1.0276142 0.315 POULPC -0.0940289 0.1369518 -0.6865838 0.500 DlNC 0.0214588 0.0032584 6.5855757 0.000 PiY -0.0113831 0.0049732 -2.2889001 0.032 190 R-squared 0.934013 Mean of dependent var 26.41577 Adjusted R-squared 0.910018 S.D. of dependent var 3.424503 S.E. of regression 1.027250 Sum of squared resid 23.21534 Durbin-Watson stat 1.993359 F-statistic 38.92485 Log likelihood -39.50490 =88:838888.8338388832288828:8888883383838888838833828888283882888==3 Equation 5.20 SMPL 1956 - 1985 30 Observations LS // Dependent Variable is FBP 3:33:8233882::328::28833323383888332838388382888888333238888882.882: VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. 3:23:383283838388:38888883833883338883833=38:888883888288888888888-8 C ' 42.265962 13.300433 3.1777884 0.005 BFPC -0.6111378 0.0737157 -8.2904720 0.000 P108 0.2257077 0.0737580 3.0601117 0.006 P208 -0.0445743 0.0317915 -1.4020823 0.175 PKPC 0.0366801 0.0741156 0.4949031 0.626 PlPK -0.1205698 0.1534445 -0.7857555 0.441 POULPC -0.2345571 0.1885974 -1.2436921 0.227 P1POUL -0.4215605 0.2417844 -1.7435393 0.096 DINC 0.0205081 0.0033496 6.1225593 0.000 33838383388888888888883888888888338333==S:====8=8838888888888883888. R-squared 0.889393 Mean of dependent var 26.34202 Adiusted R-squared 0.847258 S.D. of dependent var 3.457912 S.E. of regression 1.351431 Sum of squared resid 38.35366 Durbin-Uatson stat 1.811524 F-statistic 21.10777 Log likelihood -46.25294 191 income variable (Equation 5.19). Allowing the income coefficient to vary over time contributed materially to the fit of the equation. The Durbin-Watson statistic indicates the further reduction of serial correlation. However, slight changes in the magnitudes of the coefficients of the polynomials and sign change in the coefficient of the linear polynomial on beef quantity are noted. Despite these changes, the own-quantity flexibility estimates from the augmented model exhibit the same pattern of year to year variation as those estimated from the quadratic and cubic models without the polynomial on income. In contrast to the own-quantity flexibility estimates from the latter models, the estimates from the augmented model are slightly larger (in absolute values) prior to 1973 and slightly smaller after 1973. The values of the flexibility estimates from the three models for the 1973 period were very close. The estimates of beef price response to income changes varied over the period (Figure 5.34). Income flexibilities trended upward during 1959 through mid 19603, then trended downward until 1973 and increased again thereafter until 1977. These estimates then sharply declined between 1977 and 1979 and steadily increased during the early 1980s. Starting in mid 1970s, the pattern of income flexibility estimates is positively correlated with changes in per capita real disposable income. That is, declining income flexibility during the period 1977-79 is associated 192 Figure 5.33 “" “11111111111118.0113qu 1.111“ -1.7511 ’21'1’ -ZJB‘ 2.50“ -2J51’ 141130 4.25 .,,..11' e - r r 1.... r 1955 1960 1965 1970 1975 1900 1905 13!! r Figure 5.34 11118111 1181111101111'816‘1'11181111'10'1181111 1L50 1L080 107:” Equation 5.21 SMPL 1955 - 31 Observations LS // Dependent Variable is F8? 1985 193 VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. =88888888.388.IIII88888838882888.8838888888::22883888888888838888888 C 39.649798 8.4671594 4.6827744 0.000 BFPC -0.6094849 0.0465080 -13.104935 0.000 P108 0.1932906 0.0465530 4.1520562 0.000 P208 0.1195201 0.0353293 3.3830325 0.003 PKPC 0.0140194 0.0492183 0.2848405 0.779 PiPK -0.1002526 0.0977747 -1.0253427 0.317 POULPC -0.0282791 0.1264760 -0.2235925 0.825 P1POUL -0.3469288 0.1355049 -2.5602669 0.019 P2POUL -0.3287105 0.0603076 -5.4505630 0.000 DINC 0.0188573 0.0021292 8.8564310 0.000 DV77ON -3.6499762 0.9312053 -3.9196258 0.001 =3=288338888888888838288838388888833888888=8888888888838888888882888 R-squared 0.958826 Mean of dependent var 26.41577 Adiusted R-squared 0.938240 S.D. of dependent var 3.424503 S.E. of regression 0.851044 Sum of squared resid 14.48553 Durbin-Watson stat 2.547486 F-statistic 46.57492 Log likelihood -32.19412 8888888888888388:I:=83388381=8================8============8==8=88833 Equation 5.22 SMPL 1955 - 1985 31 Observations LS // Dependent Variable is FBP 8:8:8:33823::==============:3338282833882:====33322322338383888888": VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. ‘-"--’--‘-====83::83383333833328:8:83::8:======:===:=:==83:3===8==33 C 36.197146 10.928047 3.3123161 0.003 BFPC -0.6002113 0.0602744 -9.9579748 0.000 P108 0.1605926 0.0594330 2.7020766 0.013 P208 0.0615042 0.0416286 1.4774511 0.154 PKPC -0.0188613 0.0629351 -0.2996947 0.767 P1PK -0.2235207 0.1201379 -1.8605340 0.077 POULPC -0.0062436 0.1639632 -0.0380792 0.970 P1POUL -0.1907648 0.1680696 -1.1350345 0.269 P2POUL -0.2668927 0.0755365 -3.5332926 0.002 DINC 0.0194288 0.0027566 7.0482160 0.000 883888888888888888883888883888888388388328288333338888888888883.888! R-squared 0.927198 Mean of dependent var 26.41577 Adjusted R-squared 0.895997 S.D. of dependent var 3.424503 S.E. of regression 1.104383 Sum of squared resid 25.61292 Durbin-Uatson stat 2.092636 F-statistic 29.71711 Log likelihood -4i.02829 194 Equation 5.23 snPL 1956 - 30 Observations LS // Dependent Variable is FBP 1985 VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. =33:88:23838888828838388888888888838883888888:3883888888888888888888 C 38.803168 9.0649098 4.2805906 0.000 BFPC -0.6222738 0.0528662 -11.770738 0.000 P108 0.2389048 0.0953270 2.5061622 0.022 P208 0.1090847 0.0413721 2.6366741 0.017 PKPC 0.0121055 0.0514746 0.2351750 0.817 PlPK -0.0959716 0.1102353 -0.8706068 0.395 POULPC -0.0393886 0.1366064 -0.2883364 0.776 P1POUL -0.2732382 0.2018283 -1.3538152 0.193 P2POUL -0.3039981 0.0836548 -3.6339600 0.002 DINC 0.0198899 0.0028045 7.0920419 0.000 PiY -0.0032447 0.0054117 -0.5995804 0.556 DV77ON -3.4177339 1.0466094 -3.2655297 0.004 23::833:382328=83283333238383288838383888388388828388838828882838888 R-squared 0.959079 Mean of dependent var 26.34202 Adiusted R-squared 0.934072 S.D. of dependent var 3.457912 S.E. of regression 0.887870 Sum of squared resid 14.18963 Durbin-Watson stat 2.482904 F-statistic 38.35211 Log likelihood -31.33786 3:=2:=======:==83=========88=8====8==88=8=8===================888=== Equation 5.24 3MPL 1956 2 1985 30 Observations LS // Dependent Variable is FBP 2:22:8388:88:38:=823388388882388==8=8=388338328====S=883888888888838 VARIABLE COEFFICIENT STD. ERROR T-STA . 2-TAIL SIG. 833:23328:33.88:=88332838888888883888838888==88=88888888383888.888'38 C 39.425885 9.8248780 4.0128625 0.001 BFPC -0.6180008 0.0543541 -11.369905 0.000 P108 0.1048129 0.0611437 1.7142078 0.102 P208 -0.0738255 0.0243903 -3.0268380 0.007 P308 -0.0285492 0.0066093 -4.3195576 0.000 PKPC -0.0392347 0.0573832 -0.6837314 0.502 P1PK -0.2109774 0.1150140 -1.8343630 0.082 POULPC 0.0557089 0.1543932 0.3608245 0.722 P1POUL -0.1159362 0.1917352 -0.6046682 0.552 DINC 0.0181049. 0.0025307 7.1541572 0.000 .83:3:38:838:38838:8283838888888=8888883888.838888S3388838888388I..8 R-squared 0.942778 Mean of dependent var 26.34202 Adiusted R-squared 0.917028 S.D. of dependent var 3.457912 S.E. of regression 0.996048 Sum of squared resid 19.84225 Durbin-Watson stat 2.460136 F-statistic 36.61271 Log likelihood ~36.36740 Equation 5.25 SMPL 1956 r 30 Observations LS // Dependent Variable is FBP 1985 195 Convergence achieved after 3 iterations VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. 88888888383883888883883238:238:3283338888888838888828.888388883888312 C 36.891196 7.9239001 4.6556867 0.000 BFPC -0.6192847 0.0433921 -14.271836 0.000 P108 0.1996924 0.0392639 5.0859069 0.000 P208 0.1231001 0.0329573 3.7351374 0.002 PKPC 0.0255442 0.0458912 0.5566248 0.585 P1PK -0.1077969 0.1002752 -1.0750107 0.297 POULPC -0.0199570 0.1344478 -0.1484366 0.884 P1POUL -0.3702167 0.1495102 -2.4761961 0.023 P2POUL -0.3337640 0.0558393 -5.9772266 0.000 DINC 0.0198173 0.0017990 11.015772 0.000 DV77ON -3.4182330 0.7658849 -4.4631158 0.000 AR(1) -0.3894227 0.2409052 -1.6164978 0.123 38:8:8883333838333=S=8=88:==========8=========8=38382338838383338888 R-squared 0.963326 Mean of dependent var 26.34202 Adiusted R-squared 0.940914 S.D. of dependent var 3.457912 S.E. of regression 0.840535 Sum of squared resid 12.71699 Durbin-Hatson stat 2.346131 F-statistic 42.98280 Log likelihood -29.69428 3288*23:=8:38:8:283:::===:======3=:==:============:======:=====:==:= Equation 5.26 SMPL 1955 - 1985 31 Observations LS // Dependent Variable is FBP :=::===============:=====3:3:======:=============:======:=::====:=:= VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. C 54.332691 11.961568 4.5422716 0.000 BFPC -0.5671045 0.0556908 -10.183093 0.000 P108 ' 0.1617291 0.0551907 2.9303682 0.008 P208 0.1070928 0.0372447 2.8753804 0.009 PKPC -0.0629290 0.0621675 -1.0122490 0.324 POULPC ~0.0318506 0.1467939 -0.2169749 0.830 P10C -0.2366728 0.1268768 -1.8653745 0.077 P20C -0.2308815 0.0712162 -3.2419782 0.004 DINC 0.0146307 0.0029635 4.9370476 0.000 DV730N 105.53152 30.930956 3.4118416 0.003 DVT73 -1.4578048 0.4255210 -3.4259292 0.003 ===3===========83=33=====3333:3:38:332382888338833:3333833888833888: R-squared 0.946659 Mean of dependent var 26.41577 Adjusted R-squared 0.919989 S.D. of dependent var 3.424503 S.E. of regression 0.968662 Sum of squared resid 18.76613 Durbin-Uatson stat 2.465198 F-statistic 35.49485 Log likelihood ~36.20713 196 with declining income during the same period. Thereafter, income flexibility estimates increased as income increased until 1981. Estimates of income flexibility during 1981-82 slightly declined as income declined during that period. During the last three years, income flexibility estimates steadily increased with steady increases in real disposable income. The decline in the income elasticity for beef during the late 1970s was also found in other studies (Braschler, 1983; Chavas, 1983: Ferris, 1985). Except in 1981-82, however, the price response to income changes have steadily increased in the last five years. These results imply that demand for beef is still responsive to income changes. It is observed, however, that the relative magnitude of the income flexibility in the 1980s were lower than those in the 1960s and early 1970s. This supports the hypothesis of a possible decline in the demand response to increases in income in the 19803. 5.3.2 Pork Demand Model with Legendre Polynomial To test for continous variation over time of the demand parameters for pork, the base model for pork demand is augmented by introducing varying degrees of Legendre polynomials on the own quantity, quantity of substitutes, and income variables. The F-test conducted indicate 197 significant contribution of the polynomial on the own quantity and income variables. The pork demand model with linear polynomial on both the per capita pork consumption and income variables is presented in Equation 5.30. The own-quantity flexibility estimated from this model show some variability over the entire period (see Figure 5.37). These estimates are all greater than unity. This implies that a one percent change in the quantity of pork available for consumption will lead to a more than proportionate change in pork prices. In broad terms, a flexible pork price is consistent with the inelastic demand for pork found in quantity dependent demand models. The general pattern of the estimated own-quantity flexibility for pork is the same regardless of the degree of the polynomial introduced. Again this is a good characteristic of the results. The general pattern of variation could be associated with the hog production cycle. For example, the flexibility estimates tended to increase (in absolute values) between 1965. to 1971. During this period, hog prices are declining while quantities available for consumption per person increased. Thereafter, the own flexibility estimates declined to lower levels as pork quantity declined and pork prices increase. From 1975 to 1980, slaughtering increase and pork prices began to fall. This pattern of increased quantities available for Equation 5.28 SMPL 1955 31 Observations 1985 198 LS // Dependent Variable is PPORK VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TA1L SIG. 338.88.88888388.8888883388882‘8SSI88888838.38.838.88:8.883.888.8388: C 55.038745 15.333940 3.5893413 0.001 PKPC -0.6260955 0.0891539 -7.0226343 0.000 P10P -0.0037521 0.0806934 -0.0464983 0.963 P20? -0.0722228 0.0199469 -3.6207617 0.001 BFPC -0.2457646 0.0878952 -2.7961108 0.010 POULPC '0.5357520 0.2095041 -2.5572385 0.017 DINC 0.0195845 0.0044416 4.4092992 0.000 R-squared 0.833152 Mean of dependent var 20.12544 Adjusted R-squared 0.791440 S.D. of dependent var 4.067107 S.E. of regression 1.857380 Sum of squared resid 82.79668 Durbin-Ustson stat 1.714264 F-statistic 19-97394 Log likelihood -59.21431 8888:88888823388:38:33388328888888332=323==3=====3=========838888=8= Equation 5.29 SMPL 1955 - 1985 31 Observations LS // Dependent Variable is PPORK 8:88:83228838888883838889-‘828833832383338:323383388838383388888888838 VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. =38=88.8883388888883888388838888888888388:88838888383.38888888888888 C 44.388120 11.707579 3.7914005 0.001 PKPC -0.7051900 0.0689554 -10.226762 0.000 P10P .-0.1089986 0.0647574 -1.6831838 0.106 P20? -0.0823171 0.0150807 -5.4584549 0.000 P30P -0.0577581 0.0129306 -4.4667624 0.000 BFPC -0.2625655 0.0658096 -3.9897721 0.001 POULPC 0.0471207 0.2038460 0.2311585 0.819 DINC 0.0158996 0.0034211 4.6474941 0.000 888838838888388888.88II888...8.88888.888.88.88.38888888838888888.!88 R-squared 0.910656 Mean of dependent var 20.12544 Adjusted R-squared 0.883464 S.D. of dependent var 4.067107 S.E. of regression 1.388401 Sum of squared resid 44.33612 Durbin-Watson stat 2.108006 F-statistic 33.49028 Log likelihood -49.53319 199 Equation 5.30 SMPL 1955 - 1985 31 Observations LS // Dependent Variable is PPORK VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAlL SIG. 8382888:888888=88888833888838888888388888888388888888888888888883883 C 45.738633 13.207056 3.4631968 0.002 PKPC -0.6884347 0.0866902 -7.9413195 0.000 P10P 0.3395296 0.1171270 2.8988166 0.008 BFPC -0.2054350 0.0707471 -2.9037928 0.008 POULPC -0.5081512 0.1932412 -2.6296208 0.015 DINC 0.0230147 0.0043399 5.3030664 0.000 P1Y -0.0090656 0.0020811 -4.3562105 0.000 888:888338388283883383838838888388388S8888:8888388388388888888888838 R-squared 0.855928 Mean of dependent var 20.12544 Adjusted R-squared 0.819910 S.D. of dependent var 4.067107 S.E. of regression 1.725957 Sum of squared resid 71.49425 Durbin-Watson stat 1.824093 F-statistic 23.76395 Log likelihood -56.93936 Equation 5.31 SMPL 1955 - 1985 31 Observations LS // Dependent Variable is PPORK 2888::=2:23:88:88=33:8:388:383883883883888:8388838333338833883838:=3 VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. C 48.271395 14.915010 3.2 64306 0.004 PKPC -0.6831863 0.0892674 -7.6532550 0.000 P10P 0.2921695 0.1696638 1.7220495 0.098 P20P ~0.0138677 0.0353395 -0.3924149 0.698 BFPC -0.2224032 0.0840106 -2.6473235 0.014 POULPC -0.5182258 0.1984080 -2.6119202 0.016 DINC 0.0226937 0.0044935 5.0502939 0.000 PiY -0.0077492 0.0039677 -1.9530415 0.063 8888888888383388..-9.83888888883823888883333883383838838833888883888888 R-squared 0.856886 Mean of dependent var 20.12544 Adjusted R-squared 0.813330 S.D. of dependent var 4.067107 S.E. of regression 1.757206 Sum of squared resid 71.01877 Durbin-Uatson stat 1.845157 F-statistic 19.67308 Log likelihood -56.83593 200 Figure 5.35 91.1%1101111’11111'11’1111" 11111101011011» 4.91» 19115 "11117111?“11'11'11'11” 7919' '1995 11!! Figure 5.36 mnmmumnm ‘11‘1‘1111‘ 1‘ 4e." 3 311 0 e 3.0' 205‘1 2.01s,. ...,. e1 11.11 1.17.0.,e., .. . ,. .. . 1921 :una 1365 1300 1375 1000 1981 III! . 3.519 201 Figure 5.37 4.1 “11111111 11'11111’1111‘11811‘111‘1‘11‘31111'01'11118‘" -1.'J1 -149. 1955' 1919' ‘ ' 1915‘ ' 1979' ‘ 1915‘ T 19911 ' 1 1915 11111: Figure 5.38 1.18811 1111 131111111 1111011110111'1101‘111111 40"’ 2051' 1"”19'19rflr19‘657' ' 1919“ '1915‘ ”1999' 1995 mm 202 Equation 5.34 SMPL 1955 - 1985 31 Observations LS // Dependent Variable is PPORK VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. 88888888888..I8888888..8888888I88838.88I888888888388.88888888888838. C 49.572497 17.317260 2.8626062 0.009 PKPC -0.6151288 0.0914224 -6.7284275 0.000 P10P 0.1145582 0.1861252 0.6154901 0.544 P20? -0.0302268 0.0627170 -0.4819554 0.634 BFPC -0.2187766 0.0966774 -2.2629556 0.033 POULPC -0.5099620 0.2148393 -2.3736899 0.026 P10C -0.1843767 0.2607386 -0.707i325 0.487 DINC 0.0201962 0.0045712 4.4181131 0.000 3888388SSSBISIISSSSIISSIIIIIIII88888888388888883883888888888.8888888 R-squared 0.836702 Mean of dependent var 20.12544 Adjusted R-squared 0.787003 S.D. of dependent var 4.067107 S.E. of regression 1.877034 Sum of squared resid 81.03492 Durbin-Watson stat 1.674005 F-statistic 16.83530 Log likelihood -58.88094 888:88.8888888833838388888888888888=====3=ISSBE==8833833888388383883 Equation 5.35 SMPL 1955 - 1985 31 Observations LS // Dependent Variable is PPORK =38883:38822:283:83‘63888838888888888888:888:28:38888838238888888888. VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. 88=888888888=8838883888338388888388888338388833383=8=====ISBSISSSIII C 41.806572 12.368614 3.3800531 0.003 PKPC -0.6833989 0.0662472 -10.315887 0.000 P10P -0.0738642 0.1373649 -0.5377224 0.596 P20P 0.1855406 0.0626569 2.9612178 0.007 BFPC -0.2649632 0.0691274 -3.8329671 0.001 POULPC 0.0523399 0.1908318 0.2742724 0.786 P10C -0.0141905 0.1879428 -0.0755046 0.940 P20C -0.3496844 0.0716118 -4.8830537 0.000 DINC 0.0163589 0.0033318 4.9098810 0.000 8288:8888:23833883838388.888888888888388I3388882..8.823388888888882: R-squared 0.921636 Mean of dependent var 20.12544 Adjusted R-squared 0.893140 S.D. of dependent var 4.067107 S.E. of regression 1.329517 Sum of squared resid 38.88753 Durbin-Watson stat 1.963176 F-statistic 32.34253 Log likelihood -47.50073 Equation 5.32 SMPL 1955 - 31 Observations 1985 203 LS // Dependent Variable is PPORK VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. =88883888888888888.8888888.888.88.888.88.88888IISIIIISIICICIISBSSSSB C 37.519970 14.595328 2.5706836 0.017 PKPC -0-6671354 0.0763392 -8.7390892 0.000 P10P -0.1219338 0.1667201 -0.7313681 0.472 P20P -0.0615894 0.0521444 -i.1811310 0.250 BFPC -0.2419288 0.0794624 -3.0445688 0.006 POULPC -0.0144331 0.2257407 -0.0639364 0.950 P10C -0.0039428 0.2196862 -0.0179476 0.986 P200 -0.0624517 0.0178201 -3.5045699 0.002 DINC 0.0178038 0.0038060 4.6778801 0.000 I.888888888888838388888888888888888888888888888883888.88388888888883 R-squared 0.895206 Mean of dependent var 20.12544 Adjusted R-squared 0.857099 S.D. of dependent var 4.067107 S.E. of regression 1.537457 Sum of squared resid 52.00303 Durbin-Watson stat 1.988973 F-statistic 23.49197 Log likelihood -52.00547 3338:88388888888888:33:8888888888888888888838838838:====33383888883: Equation 5.33 SMPL 1955 - 1985 31 Observations LS // Dependent Variable is PPORK =3:=23:88:=888===:====383388332833838:=33:======g==8===332333==3=33: VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. 33338-333333:3=88888823333833883=8====3=8=8=========88==22839-388888: C 66.928769 13.610837 4.9173148 0.000 PKPC -0.6585725 0.0879080 -7.4916124 0.000 PiPK :0.1731339 0.1616020 -1.0713595 0.296 BFPC -0.3594283 0.0779063 -4.6135966 0.000 P108 0.0263708 0.0831489 0.3171511 0.754 POULPC -0.3537566 0.1977638 -1.7887831 0.088 P1POUL 0.2405624 0.2111281 1.1394146 0.267 P2POUL ~0.1840423 0.0610157 -3.0163104 0.007 DINC 0.0169524 0.0038000 4.4611167 0.000 DV77ON -2.4021230 1.5105241 -1.5902580 0.127 338:8:=8:38283:33328=88888883888888388888828283838283838888388328=a: R-squared 0.902182 Mean of dependent var 20.12544 Adjusted R-squared 0.860260 S.D. of dependent var 4.067107 S.E. of regression 1.520356 Sum of squared resid 48.54111 Durbin-Watson stat 2.231285 F-statistic 21.52057 Log likelihood -50.93766 Equation 5.36 SMPL 1955 - 31 Observations 1985 204 LS // Dependent Variable is PPORK 88838888=88:'33....=883888888383.8388888888:88883888.888883888838888 2-TAIL SIG. 0.006 0.000 0.003 0.781 0.012 0.059 0.003 0.024 0.081 VARIABLE COEFFICIENT STD. ERROR T-STAT. 3:388=38888288838338-838838888883883888888883'88388888388338888888888 C 50.486878 16.701532 3.0228890 PKPC -0.6800548 0.0789848 -8.6099422 BFPC -0.2407857 0.0706323 ~3.4090009 POULPC -0.0479862 0.1703030 -0.2817694 P10C 0.4759549 0.1741920 2.7323577 P20C _0.0860287 0.0431787 -1.9923852 DINC 0.0140851 0.0041738 3.3746646 PlY -0.0086530 0.0035479 -2.4389435 DV730N 77.878221 42.542844 1.8305833 DVT73 -1.0179358 0.5853849 -1.7389169 0.097 R-squared 0.930527 Mean of dependent var 20.12544 Adjusted R-squared 0.900753 S.D. of dependent var 4.067107 S.E. of regression 1.281278 Sum of squared resid 34.47513 Durbin-Watson stat 2.518486 F-statistic 31.25305 Log likelihood -45.63398 Equation 5.37 SMPL 1955 - 1985 31 Observations LS // Dependent Variable is PPORK VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. C 47.392850 16.100817 2.9435060 0.008 PKPC -0.7080155 0.0774236 -9.1446999 0.000 BFPC -0.2342120 0.0677657 -3.4562019 0.002 POULPC .0.0740927 0.1782376 0.4156962 0.682 P100 0.3799660 0.1761488 2.1570742 0.043 P20C -0.0500385 0.0464643 -1.0769226 0.294 P300 -0.0308196 0.0181329 -1.6996543 0.105 DINC 0.0138526 0.0040002 3.4629714 0.002 PiY -0.0072179 0.0035016 -2.0612866 0.053 DV730N 83.729206 40.894848 2.0474267 0.054 DVT73 -1.1167388 0.5637168 -1.9810282 0.062 3888=88323:38:88888888888888888882838833338=883383388888888388888838 R-squared 0.939296 Mean of dependent var 20.12544 Adjusted R-squared 0.908943 S.D. of dependent var 4.067107 S.E. of regression 1.227273 Sum of squared resid 30.12398 Durbin-Watson stat 2.661012 F-statistic 30.94655 Log likelihood -43.54278 Equation 5.38 SMPL 1955 - 31 Observations 1985 205 LS // Dependent Variable is PPORK VARIABLE ~COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. =2=========2=2::288888288288888883888:833888888883888838838388883888 C 46.304588 17.122790 2.7042665 0.014 PKPC -0.7226941 0.0840632 -8.5970351 0.000 BFPC -0.2107483 0.0731945 -2.8792930 0.010 POULPC -0.0037392 0.1853704 -0.0201717 0.984 P10C 0.3790290 0.2036861 1.8608484 0.078 P20C -0.0060137 0.0713058 -0.0843363 0.934 DINC 0.0152745 0.0046267 3.3013713 0.004 PiY -0.0066255 0.0038443 -1.7234312 0.101 DV730N 108.01646 48.138959 2.2438470 0.037 DVT73 -1.4493468 0.6682753 -2.1687872 0.043 DV800N 85.157659 61.078517 1.3942326 0.179 DVT80 -1.0441868 0.7580480 -1.3774680 0.184 =2========88=883:88:3383383885'8383828888838:3888888====8s=3==8=88=88 R-squared 0.937705 Mean of dependent var 20.12544 Adjusted R-squared 0.901639 S.D. of dependent var 4.067107 S.E. of regression 1.275548 Sum of squared resid 30.91345 Durbin-Watson stat 2.499419 F-statistic 25.99991 Log likelihood -43.94376 Equation 5.39 SMPL 1956 - 1985 30 Observations LS // Dependent Variable is PPORK Convergence achieved after 7 iterations =================8:883:23:=3:===:===================8.232323323333832 VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. =3=3:=1832:2:====3233:3288:===========23::28:8:38:38:282882382828838: C 57.055375 8.5821963 6.6481088 0.000 PKPC -0.6911711 0.0576891 -11.980972 0.000 P1PK 0.0719286 0.1298762 0.5538242 0.587 BFPC -0.4276840 0.0484328 -8.8304591 0.000 P108 0.3415339 0.0870337 3.9241561 0.001 POULPC -0.3367322 0.1385780 -2.4299119 0.026 P1POUL 0.4084513 0.1630722 2.5047271 0.022 P2POUL -0.0809983 0.0512209 -1.5813509 0.131 DINC 0.0243436 0.0024486 9.9416861 0.000 PiY -0.0216910 0.0046768 -4.6379713 0.000 DV77ON -1.8458681 0.8073581 -2.2863064 0.035 AR(1) -0.5106850 0.2101087 -2.4305753 0.026 =========:=323::2:233:22:=========2======3:28:328:333338233323888322 R-squared 0.956518 Mean of dependent var 20.06686 Adiusted R-squared 0.929945 S.D. of dependent var 4.123312 S.E. of regression 1.091355 Sum of squared resid 21.43902 Durbin-Uatson stat 2.616141 F-statistic 35.99634 Log likelihood -37.52838 206 .MZCUZ NIP FE DUPEJDUJCU UNI MWuPuJumuwau m—@.m hn0.nl QmW.m mmw.~l mmn1nl mmmu 700.“ mmk.ul mmm.n umm.ul «h01Nl Vom— mnn.n NNm.—l Emu.” NV01~1 u~@.Nl ”Emu OTN.N NNf.—l @001N Ofn.ul 0Du1NI NET" 00?.” f0m.~l mnN1m Nmm.ul ffkuNl n00— Qnm.n NON1NI for.” an.Nl Th01Nl 00¢" Tug.” ~NN.~I ”no.” mmw.nl Emu1Nl 0N0“ fnm.N WON.—l Nmf1N ONN.~I Dmf.nl Ohm" uhn.N unf.nl QNN.N Nmn1ul mum.ul thu mmf.N NWN1—l n0f.N OMN1—l mmn.ul Whmu N—u.N NNO.~I Omoufl Ono.«l mwo.nl whmu «VN.N wn@.ul NDN.N 0n0.nl .nn91—I fhmu mmN.N mmN.nl VwN1N NVN1u| amu.ul Mhmu nN—.n r001~l ffu.n «00.nl mN0.«l Nbflu an.f 000.”! 00”.? Nf~.nl k0n1Nl «Nan 00f.n hwnuNl mnm.n TOT.N1 DwO.Nl Ohm— ?00.” «wooNl mun.» ®Ou.Nl 07N1~l @90— ufO.” OfD1Nl huh-n 7001Nl @001Nl Qmmu art.” Quf1Nl MND.D wmf.Nl amm.ul hwmu mrh.N f—0.nl m—D.N Ohm.~l NMf1ul www— mmm.N Nrm.nl 0N0.N ROO.N| fom.nl www— wfm.n Nf01m1 NNT.” 0fu1nl f~n1Nl fwmu nmm.n mmo.ml NON-n nh~1nl ~0N1Nl n00" nmN.n h~N1Nl mar.” G«@.Nl @001Nl Nwmu ~m~.n mnwoNl WON.” NMN.N1 NNm.nl uwmn Mfk.n WNN1nl 000.” fOf.n1 mwnoNl owmn WNN.D rm¢.Nl Nun.n ~N0.nl r«~.Nl mmmu ff@.N mNN1Nl uNN1N fnn1Nl Nmm.«l mmm~ N00.» ufm.Nl uWa.” n¢@.Nl hmn1—l hmmn NWN.” fom.nl $00.” nrw.nl wa.Nl wmmn 00¢.N QVN.NI me.D WW@.NI mN¢.ul mm0— >P~J~D~XNJE )Panmmwau >huJumuXNJu >budumnxm4u )Pudnmumeu mZDUZH >P~PZ¢DGIZIO wZOUZn >FHFZ¢DGI230 )bHFZCDGIZ3D fl¢w> DuhCflOCDG NCNZHJ UnhCMDCDO mmmulmmmu .0u900t uflmEOCJHOQ GLUCOOOJ OMUOLDOOG OED LOGCmJ 6014 oouoemanm iron 104 reason 40 mumsmnuxosu oeoocs pro mausmomxosu mauucoao1cso m~.m ounce 207 .0200: NIP PC DNFCJDUJIU NEE mwuhnanHXMJu NVO.N NW0.MI 0n0.n1 00k.hl ~00.Nl 000u NMN.N NNO.nl 000.01 fkn.nl ffN.Nl T00— 0n0.N nON.MI hkf.hl NmN.nl «0".Nl n00~ «fr.N nur1nl nr~.nl 000.N| 0N0.nl N00— N001N mmu.nl 0001Nl «mN.NI 0u0.—l «00¢ 000.N NN0.NI NOD.Nl unn.Nl 0Nm.nl O00— 0h0.— mnn.Nl 000.Nl nnO.Nl HND.«1 0h0u NnN.N 000.01 0n0.Nl Nu0.Nl N00.u1 0&0“ 0u0.N N00.nl NuN.Ml uuN.nl 0?O.Nl RNO— «nm.N n00.01 00—.nl 00~.nl 00°.Nl 0&0“ N00.N 00N.Nl 0uf.Nl nm¢.Nl n00.~l 0N0— NYO.N N~0.Nl 00N1N1 fun.Nl .nor.ul rk0u 00h.u 00O.Nl 0N0.~l Vf0.~l 00O.ul nh0u DnO.N unm.Nl 00N.Nl fNN.Nl 0nn.nl Nk0u NO~.N m~0.Nl 0n0.Nl 0NM.NI «Tn.~l "N0“ 00n.N NTN.NI nu0.Nl 0N0.Nl 000.") ON0~ #00.N f00.Nl nNn.Nl Nnm.Nl 0MN.ul 000a ~r~.N ~00.Nl f0f1Nl unr.Nl an.ul 000a ff—.N f0r.N| N0n.Nl N0n.Nl 00¢.ul N00u 0uO.N n~n.Nl 0mN1Nl NON.N| ka.nl 000— N00.u nk—.Nl N0u.NI h0u.Nl 000.01 000— nNO.N 00n.Nl HOV.NI u—V.Nl 0VO.~I f00u n00." 00O.Nl 0n~.Nl 0f—.NI 000.01 ”00" 000." 000.~l 0TN.~I 00k.~l ~00.0l N00" 000.u nNN.ul 000.nl NM0.~I 0nh.0| ~00" 0km.~ u0m.~l NNN.~1 NON.ul Nu0.01 000~ 00¢." m0n.nl nnm.ul 00m.«| nN0.0l 000a N0f.~ rhn.nl ffm.~l uN0.n| NOT.Ol 0m0~ "NW." 0~0.ul 0n0.~l 0m0.~l 000.01 N00~ 0Nh.u NNO.ul fN0.ul 00O.Nl n00.0l 000a 000.u f0f.nl 0nk1—l 0~0.ul ~kf.01 000— )PuJumuwau >hHJn0~wau >FHJ~0~XNJK >PHJHOumeu )PHJnmuwau wEDUZH >PHPZEDGIZEO >FHPZEDDIZ3O >FHPZEDGIZ3D }bHPZ0DGIZIO 000) UZuD ZO UCWZ~J 020 0100 20 UanU OmDDU OmOOLDODG LOGEuJ 000—1000" .8—9002 unmeocmuom 8L0C000J OmDOU 090 .OMOOLDQOO .LOOCmJ 6014 00908m9nw 4900 104 090600 40 0&m—mDMXO~u 0800C~ 000 mawuwnmx0~u JAMHCQJGICBO nu.m Quack 208 consumption and falling prices is reflected in the upward trend in the own flexibility during the same period. The own-quantity flexibility estimates then fell between 1980 to 1982 primarily in response to reduced supplies available for consumption following herd liquidation and subsequently rising real prices. During the last three years, the flexibility estimates for pork remained relatively constant. The flexibility estimates for pork is in relatively lower levels during the 1970s and through the 1980s compared to the estimates in earlier periods. Estimates of income flexibilities for pork (Figure 5.36 and 5.38) shows some year to year variation. A constant trend is evident from the beginning of the period until about 1973 when the income flexibility declined to lower levels. This decline is associated with the record prices in 1973 and the slight increase in income in the same year. Since the mid 19703, the income flexibility estimates shows an upward trend, except in 1981 to 1982 when real disposable income per capita slightly declined resulting to a slight decline in the income flexibility. Much of the increase in the price response to income changes is due to relatively stable pork prices and the steadily rising income. 209 5.3.3 Broiler Demand Model with Legendre Polynomidl Continous variation in demand parameters for broilers is tested by introducing varying degree polynomials on the broiler per capita consumption, quantity of substitutes, and income variables. The linear polynomial specification on both the own quantity and income variables appears the best specification. This choice is based on the statistical properties of the model, particularly the resulting Durbin- Watson statistic and the general fit and relative magnitudes of the coefficients. It is observed that the higher degree legendre polynomial models for broilers have a Durbin Watson statistic indicating a tendency toward positive serial correlation. This phenomenon was not encountered in the beef and pork models. The associated own-quantity flexibility estimates for broilers exhibit the same pattern regardless of the degree of the polynomials. The own-quantity flexibility estimates tended to increase (in absolute value) over the entire period of analysis. A discontinuity is apparent sometime in 1973 when the own-quantity flexibility declined in response to a slight decline in the quantity of broilers available for consumption and the subsequent record prices in 1973. After the decline in 1973, a continous upward trend in the own flexibility estimates remained during the late 1970s and through the 1980s. 210 Equation 5.40 SMPL 1955 - 31 Observations LS // Dependent Variable is CHP 1985 VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TA1L SIG. 83I.I888888....I33888I8888388"...8.ICI.388.88.38.833.838...IIIIIUII C 55.570928 5.4914600 10.119518 0.000 POULPC -1.0610717 0.1115154 -9.5150251 0.000 P100 0.1396009 0.0464442 3.0057761 0.006 BFPC -0.1921163 0.0550466 -3.4900681 0.002 PKPC -0.0732316 0.0644123 '1.1369196 0.266 DINC 0.0119930 0.0031783 3.7734445 0.001 R-squared 0.933736 Mean of dependent var 15.11533 Adjusted R-squared 0.920483 S.D. of dependent var 4.831722 S.E. of regression 1.362487 Sum of squared resid 46.40930 Durbin-Watson stat 1.804480 F-statistic 70.45538 Log likelihood -50.24154 8888888828388888==Ss==823838888:88382338888338888828838833328838.8.8 Equation 5.41 SMPL 1955 - 31 Observations LS // Dependent Variable is CHP 1985 VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. =2888828888.....888888888888833.88888888838883888883888888888.888'88 C 55.927127 5.5305528 10.112394 0.000 POULPC -1.0020359 0.1304470 -7.6815531 0.000 P10C 0.1346437 0.0469868 2.8655629 0.009 P20C -0.0122335 0.0138547 -0.8829837 0.386 BFPC -0.1961505 0.0554792 -3.5355675 0.002 PKPC -0.0810235 0.0652971 -1.2408437 0.227 DINC 0.0112073 0.0033140 3.3817664 0.002 888.888883888888888888888833:8883888828838888.8888888888888888888888 R-squared 0.935821 Mean of dependent var 15.11533 Adjusted R-squared 0.919776 S.D. of dependent var 4.831722 S.E. of regression 1.368532 Sum of squared resid 44.94909 Durbin-Watson stat 1.721704 F-statistic 58.32529 Log likelihood -49.74601 211 Figure 5.39 fill IIIOILERS 311M mums! WWW!“ HOD m um -o C.,. eve... T 1955 1950 1965 1m 1975 1900 ms rm: Figure 5.40 on! mnmn or mmm mmm mu mimic mam 9019an noun. 1955"is‘sn"'1925"'is‘:a"rifl?“i9‘so’”fi§s mo: 212 Equation 5.42 SMPL 1955 - 1985 31 Observations LS // Dependent Variable is CHP VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. 2888888888888388888888888883888888888888338388888838888888888388888! C 35.442659 12.671059 2.7971348 0.010 POULPC -0.7961114 0.1702866 -4.6751254 0.000 P10C 0.0010808 0.0875099 0.0123504 0.990 PZQC 0.0675345 0.0379500 1.7795661 0.088 P3QC -0.0320037 0.0173055 -1.8493380 0.077 BFPC -0.1328881 0.0639282 -2.0787076 0.049 PKPC -0.0669035 0.0630364 -1.0613469 0.300 DINC 0.0126094 0.0032702 3.8558524 0.001 88838888838888888::888888888888.38388.88888I88888388838888388883.... R-squared 0.943588 Mean of dependent var 15.11533 Adiusted R-squared 0.926419 S.D. of dependent var 4.831722 S.E. of regression 1.310644 Sum of squared resid 39.50910 Durbin-Watson stat 1.694360 F-statistic 54.95918 Log likelihood -47.74653 Equation 5.43 SMPL 1955 - 1985 31 Observations LS // Dependent Variable is CHP VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. =2=3:2:=:888=888828828883888888888838888888883388888888388.888888888 C 37.693857 5.9564856 6.3282041 0.000 POULPC -0.8647937 0.0974441 -8.8747662 0.000 P10C 0.5429892 0.1011893 5.3660747 0.000 BFPC -0.1813518 0.0424636 -4.2707584 0.000 PKPC -0.1634382 0.0539284 -3.0306502 0.006 DINC 0.0166067 0.0026762 6.2053799 0.000 P1? -0.0096019 0.0022532 -4.2615214 0.000 8888:88838888.888888888388888888888333888888ISIIIIIIISSSIIIIIBCIIIII R-squared 0.962279 Mean of dependent var 15.11533 Adjusted R-squared 0.952849 S.D. of dependent var 4.831722 S.E. of regression 1.049178 Sum of squared resid 26.41860 Durbin-Uatson stat 2.192228 F-statistic 102.0414 Log likelihood -41.50835 213 Figure 5.41 “MI’IIIRmII Illlu‘ifiafiln m" 4.51» -er .34; fiLI' #LS‘ 4.3 . a- 1,5 F... , . -.- e 1955 1960 1965 1970 1975 1900 1905 III! Figure 5.42 m ‘meilfilllkl’luli mam. M” ' “'m 40" Y—fi 19557 ' ’ is'sd ' 192s -. imfi‘ 1955'719'00“ ms III! 214 Equation 5.44 SMPL 1955 - 1985 31 Observations LS // Dependent Variable is CHP VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. 3888883888.88888888.8...888'...’88888888888888888833888888.888888.88 C 44.294775 8.4255545 5.2571941 0.000 POULPC -0.8859170 0.0988811 -8.9594188 0.000 P10C 0.6496148 0.1396280 4.6524684 0.000 PZOC -0.0287300 0.0260517 -1.1028063 0.282 BFPC -0.2096179 0.0494370 -4.2401058 0.000 PKPC -0.1867018 0.0576828 -3.2366968 0.004 DINC 0.0160788 0.0027069 5.9399615 0.000 P1Y -0.0108685 0.0025200 -4.3128331 0.000 88.88388.888888.888888888888888888888888888888888888.888888888888888 R-squared 0.964173 Mean of dependent var 15.11533 Adiusted R-squared 0.953270 S.D. of dependent var 4.831722 S.E. of regression 1.044485 Sum of squared resid 25.09181 Durbin-Watson stat 2.411697 F—statistic 88.42562 Log likelihood -40.70969 Equation 5.45 SMPL 1955 - 1985 31 Observations LS // Dependent Variable is CHP 32:23::8883333882888888838383838I:8338338888328322883888888388883.88 VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. =82282:8883:888338883833888883338383:28:83:3333238888888838888888888 C 32.412370 9.2877055 3.4898146 0.002 POULPC -0.6807427 0.1270180 -5.3594190 0.000 P10C 0.5483235 0.1354103 4.0493483 0.001 PZOC 0.0136247 0.0301342 .0.4521341 0.656 PSOC -0.0292329 0.0126669 -2.3078094 0.031 BFPC -0.1757794 0.0476665 -3.6876953 0.001 PKPC -0.1861745 0.0529208 -3.5179816 0.002 DINC 0.0157545 0.0024874 6.3338161 0.000 P1? -0.0106137 0.0023146 -4.5855201 0.000 838883:3:28:3888888838888888888888882883888888888888888888.888888888 R-squared 0.971156 Mean of dependent var 15.11533 Adiusted R-squared 0.960667 S.D. of dependent var 4.831722 S.E. of regression 0.958248 Sum of squared resid 20.20128 Durbin-Hatson stat 2.319192 F-statistic 92.59086 Log likelihood -37.34935 215 Figure 5.43 CHI tnExIDIIIEZH3§sngglI§§§1a 1‘33 FRO! QflADflIIIC ’105‘ '2.3‘ -2051' .3.'Jl -3031? “LI . ... . . I . ., ... ,s . .. . . 1955 1960 1965 1970 1975 1980 1905 TIME Figure.5.44 .INCONE FLEXIBILITY OF BROILERS 4 5 ESTIHATED IRON QHBDRIIIC LEGEHDRE POLYHOIIAL MODEL 1955"”19‘50' "19'55"i9"mfl"19‘ls 7' is'od ' '1”: mm 216 Figure 5.45 “" “Miollflln‘ffi fill!“ m“ m" '2.ll* -205” -30..1—r.|.r.TI...1fis..lr ...... 1955 1960 1965 1970 1975 1980 1905 13K! Figure 5.46 lacy; , mnmn or mm: 3mm I'llon cum manual: 9019mm. mu. 1955 1960 was 1970 ms 1930 ms we Equation 5.46 SMPL 1956 - 30 Observations LS // Dependent Variable is CHP 1985 217 VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. ==38388888:88:888888888388388888883838888883888383888t88888883888888 C 42.832439 8.4181169 5.0881260 0.000 POULPC -0.7500524 0.1331284 -5.6340515 0.000 P1POUL 0.4034491 0.1461901 2.7597566 0.012 BFPC -0.2284022 0.0490387 -4.6575910 0.000 P108 0.0619824 0.0797234 0.7774676 0.446 PKPC -0.1720619 0.0532616 -3.2305043 0.004 PiPK -0.0009658 0.0789233 -0.0122371 0.990 DINC 0.0149713 0.0027074 5.5297452 0.000 PiY -0.0090175 0.0048084 -1.8753697 0.075 DV77ON -0.9871041 0.9673410 -1.0204303 0.320 883:88=88:283838338888=838888888888338888888838838838388388833'388888 R-squared 0.956908 Mean of dependent var 14.57179 Adiusted R-squared 0.937517 S.D. of dependent var 3.830970 S.E. of regression 0.957613 Sum of squared resid 18.34046 Durbin-Watson stat 2.298371 F-statistic 49.34727 Log likelihood -35.18684 =3==38:===38:83:382:341:33:ng3883:388838883===============38:33-13:33: Equation 5.47 SMPL 1955 - 1985 31 Observations LS // Dependent Variable is CHP ===3:==3:33::===============3======83388833283822332332882288383888: VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. =:2=8:=33:8:::=====3==8========83333:388833338888883383388888888.888 C 36.810086 9.4080861 3.9126009 0.001 POULPC -0.6953465 0.1239671 —5.6091196 0.000 P1POUL 0.4780806 0.1394998 3.4271059 0.003 P2POUL 0.0119967 0.0327994 0.3657590 0.718 P3POUL -0.0404420 0.0153433 -2.6358064 0.016 BFPC -0.1711699 0.0538738 ~3.1772401 0.005 P108 -0.0721226 0.1099385 -0.6560269 0.519 PKPC -0.1732366 ~0.0541349 -3.2000902 0.004 DINC 0.0140059 0.0028948 4.8383786 0.000 P1Y -0.0058901 0.0054699 -1.0768299 0.294 DV77ON -i.7742311 0.9958451 -1.7816336 0.090 =23388333383388888838888888:3:888:83:8833888888833888883838888.8388: R-squared 0.975169 Mean of dependent var 15.11533 Adiusted R-squared 0.962753 S.D. of dependent var 4.831722 S.E. of regression 0.932495 Sum of squared resid 17.39092 Durbin-Watson stat 2.341165 F-statistic 78.54389 Log likelihood -35.02749 Equation 5.48 SMPL 1955 31 Observations LS // Dependent Variable is CHP 1985 218 VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG. C 41.073683 9.2539105 4.4385217 0.000 POULPC -0.8495109 0.1393767 -6.0950698 0.000 P1POUL 0.6213346 0.1251485 4.9647784 0.000 BFPC -0.2343023 0.0540494 -4.3349643 0.000 P108 0.1106309 0.0849958 1.3016033 0.207 PKPC -0.1561360 0.0583071 -2.6778201 0.014 P1PK -0.0147643 0.0868618 -0.1699750 0.867 DINC 0.0171080 0.0028161 6.0749520 0.000 P1Y -0.0142785 0.0047027 -3.0361988 0.006 DV77ON -0.8367400 1.0652544 -0.7854837 0.441 R-squared 0.966511 Mean of dependent var 15.11533 Adiusted R-squared 0.952158 S.D. of dependent var 4.831722 S.E. of regression 1.056834 Sum of squared resid 23.45484 Durbin-Watson stat 2.344333 F-statistic 67.34046 Log likelihood -39.66399 219 To test for continous variation in the price response to income changes, the models are augmented by a linear polynomial on the income variable. The latter is significant based on the F-test at the .05 level. The model with linear polynomial on both the own quantity and income variables has the best statistical properties among the broiler polynomial models. It is observed that the pattern of the own-quantity flexibility estimates after allowing the income coefficient to vary over time remained the same in all the augmented models. However, the relative magnitude of the flexibility estimates from the augmented models seem to be more reasonable compared with those estimated from the models with constant parameters on income variable. Slight year to year variation in the own quantity flexibility of demand for broilers is evident for the entire period of analysis. Similar to the estimates from the three polynomial models, the own quantity flexibility estimated while allowing the coefficient on income to vary over time exhibit an upward trend from the beginning of the period through the early 19708. A discontinuity occurs in 1973 when the own flexibility -declined by about forty percent from its 1972 level. This decline in own flexibility reflects the slight decline in the available quantities of broilers and the record prices in 1973. The flexibility in the mid 1970s through early 19803 trended upward slowly until 1984 when a slight decline in the estimate occured. 220 5.5 Summary and Conclusions In this chapter, recursive least squares and residual analysis were applied to estimate and test parameter change in the U.S. farm level demand for beef, pork, broiler, and turkey. Recursive least squares facilitates the identification of the timing of structural change and measurement of changes in demand parameters. Standardized recursive residuals were estimated and used in performing an exploratory analysis to look for patterns indicative of possible structural breaks in demand for meat. The recursive parameter estimates are used as a descriptive devise in determining the effects of individual observations in a recursive updating procedure. Changes in parameters are indicated by trends and discontinuities in the recursive residuals and a systematic tendency to overpredict or underpredict. The results of the recursive least squares and recursive residual analysis strongly reject the null hypothesis of constant parameters in the inverse demand for beef, pork, and broilers. In particular, the parameters of the linear inverse demand models for beef, pork, and broilers show signs of instability. Forward recursions indicate a tendency to systematically overpredict prices of the three commodities starting in 1976-1977. This period is 221 identified as an important structural break in the demand for the three commodities. No significant parameter instability was found in the inverse demand for turkey. In the case of the beef price model, the most striking feature is the declining and increasing trend (in absolute value) in the estimates of coefficients on the beef per capita consumption and poultry per capita consumption, respectively. The recursive estimates of the coefficient on real per capita disposable income appear to have slightly declined over the period. A discontinuity is evident in beef demand starting in 1977 when the estimated standardized recursive residuals increased (in absolute value) to ~8.09 from 0.595 in 1976. The standardized recursive residuals from 1977 to 1985 are more than twice the absolute value of the largest residual in the 1955-1976 period. Recursive parameter estimates of the pork price model also show signs of instability. The absolute value of the coefficient on pork per capita consumption (PKPC) showed an increasing trend during the 1965-1971 period. A discontinuity is apparent in 1971 when the coefficient on PKPC declined in absolute value until 1978. From the forward one-step recursive residuals, there is a tendency to overpredict pork prices starting in 1971 reaching the two largest overpredictions in 1977 and 1984. The recursive residuals estimated from the broiler demand model indicate a significant structural break 222 starting in 1976. The information on the timing of discontinuity in the demand parameters indicated by the standardized recursive residuals is used in respecifying the demand models to explicitly account for the changes in the demand parameters for the three commodities. The first specific form of parameter variation tested is a gradual structural shift in demand due to the hypothesized continous changes in tastes and health concerns. This is carried out by introducing trend variables. One trend variable representing the trend from 1955-76 and another to represent the turning point in the trend from 1977 to 1985. Since the model is linear in the variables, the coefficient on the time trend represent the rate of shift in demand in terms of annual prices, given quantities and income. Estimated own-quantity flexibility of demand for pork increased (in absolute value) from -1.8768 in 1955-85 to- 2.6041 in 1970-85. The cross flexibility of pork demand with respect to beef and poultry both increased in 1970-85. The estimated ownfquantity flexibility of demand for beef increased in absolute value in the second period (1970- 85). A significantly positive income flexibility was estimated for the period 1955-85. This estimate is found to be slightly higher compared to the income flexibility of beef demand for the period 1970—85. The cross flexibility of beef demand with respect to broilers increased 223 significantly in the second period. This result supports the hypothesis of increasing substitutability of poultry with beef in the 19703 and through the 1980s. In contrast with beef, the estimated own-quantity flexibility of demand for pork is very close in the two periods. However, the cross flexibility of pork demand with respect to poultry and the income flexibility both increased in the second period. In the case of broiler.the own quantity flexibility and cross flexibility with respect to beef and pork both increased in the second period. The price of broilers has become more responsive to income changes in the period 1970- 85. The results from the demand models with trend variables indicate an absence of a significant trend in the demand for beef, pork and broilers before 1976. A significant downward trend was found in the demand for beef starting in 1977. Gradual continous variation in the inverse demand parameter was tested by introducing Legendre polynomials. Linear, quadratic, and cubic Legendre polynomials specification for the own quantity, quantity of substitutes and complements, and income variables were tested. In general, the results imply that the maintained hypothesis of constant parameters of inverse demand for beef, pork, and broiler, can be rejected at the 0.01 level based on F-tests. Flexibility estimates indicate that beef 224 prices are becoming more sensitive to changes in beef supplies over time. The own flexibility of steer price slightly trended upward in absolute value during the 1955- 1985 period. Larger fluctuations in the own quantity flexibility starting in mid 19703 is indicative of a structural break in beef demand staring mid 19703. The analysis of price response to changes in quantities indicate that steer prices is slightly more response to supply changes than are hog prices. Steer price is becoming less sensitive to income changes. The relative magnitude of the income flexibility in the 19803 were slightly lower than those in 19603 and early 19703. Rog prices are becoming less sensitive to changes in pork supplies over time. the own-quantity flexibility estimates for hogs are relatively in lower absolute values during the 19703 and in 19803 compared to estimates in earlier periods. A discontinuity is apparent in the hog price response to income changes during the mid 19703. Income flexibility for hogs exhibited a constant trend from 1955 until 1983. 1 Starting in mid 19703 income flexibility for hog trended upward. The results indicate that broiler prices have become more responsive to changes in broiler supplies over time. The own quantity flexibility estimates tended to increase in absolute value over the 1955-72 period. A discontinuity is evident in 1973 when the own quantity flexibility of broilers declined in absolute value. After the decline in 225 1973, estimates continued to exhibit an upward trend in absolute value. A structural break is apparent in the broiler price response to income changes. Estimates of income flexibility for broilers exhibit an upward trend during the 1955-72 period. The estimate significantly decline from about 4.1 in 1972 to 2.5 in 1973. It then remained in the 2.5 to 3.0 range during the rest of the period. In general, the preceding analysis provides additional evidence that a structural break has occured in the farm level demand for beef, pork, and broilers. Based on the analysis of recursive parameters and recursive residuals for 1955-85, the change began in 1976-1977 and continued into 19803. The structural change resulted in higher own quantity flexibilities for beef, pork, and broilers. Also, the results imply that broiler is becoming a stronger substitute for beef and pork. However, the causes of such change are not investigated in this study. The study only allows the approximation of the effects of structural change on the magnitudes of price and income response parameters. These results are useful in forecasting the growth prospects of the U.S. livestock and poultry sector. CHAPTER 6 INCORPORATING STRUCTURAL CHANGE IN U.S. PORK PRODUCTION IN THE SPECIFICATION OF THE U.S. HOG SUPPLY RESPONSE MODEL 6.1 Structural Changes in U.S. Pork Production Like the rest of the U.S. agricultural sector, pork production has become more concentrated on larger and specialized farms. Varn Arsdall and Nelson (1984)1 indicated that between 1950 and.l980, there was about 80 percent decline in the number of U.S. hog farmers. Average sales per farm increased from 31 in 1950 to almost 200 head in 1980. Moreover, they indicated that in 1980, about 40 percent of all hogs were produced in farms selling 1,000 or more head, which constituted about 3 percent of the total U.S. hog farms. In contrast, only 7 percent of total hog marketings in 1964 were from such large operations. Despite the sharp decline in the number of hog farmers, U.S. hog production remained at relatively stable levels during the last 30 years. However, national average per capita consumption of pork trended downward during this period. Varn Arsdall and Nelson reported that the drop in pork per capita consumption is largely due to the decline in the use of lard. Pork represented about 37 percent of U.S. red meat consumption in 1985, down from about half in 1955. 1 Van Arsdall, R.N., and K.E. Nelson, (1984). 226 227 The shift toward larger and specialized farms brought about some important changes in the structure of hog supply response. This section provides a summary of some important aspects of the structural changes that have occurred in U.S. hog production. These changes are considered in constructing the hog supply response model and in determining the likely future trends in hog production and supply. The summary is based on a number of previous studies on the structural characteristics of the hog industry (Van Arsdall and Nelson, 1984; Hayenga,et.a1., 1985, and USDA statistical reports. 6.1.1 Trends in Pork Production During the early 19503, pork constituted more than half of the total U.S. red meat production, averaging at about 13 billion pounds in carcass weight. Although production of hogs fluctuated cyclically, pork output in the late 19703 stayed at a relatively the same range of 11 to 15 billion pounds in carcass weight. In the early 19803, pork was a third (37 percent) of the total red meat supply. Hog inventory data indicate between 1978 and 1980, the most rapid expansion occurred in the larger hog operations. It is observed that during profitable periods, expansion occurs across all sizes of hog farms. 0n the other hand, small farms reduce their production or drop out during bad 228 times while larger farms tend to stabilize their production. During the mid 19703, hog production and pork per capita consumption were at relatively low levels, while beef cattle production reached a record levels. Per capita disappearance of pork in carcass weight dropped from 75-85 pounds range during the 19503 to about 60-70 pounds in the last 10 years. The decline is partially the result of a reduction in lard consumption which averaged about 14 pounds per capita during the 19503 and about 2 pounds in the late 19703. Market analysts have considered this to be a reflection of a shift in consumers preferences. 6.1.2 Technical Change and Trends in Proguction Efficiency New technologies that have been adopted by hog producers altered the competitive situation in hog production. Van Arsdall (1984) indicated that technological advancements in nutrition and control of diseases of hogs eliminated the necessity of having a large land base in hog production. Also, technical advancements in housing and materials handling equipment permitted the continuous year round production and increases in production per unit of labor. Government policies on research and taxation facilitated the adoption of capital intensive technologies and large size hog enterprises. These technical advances resulted in more intensive use of land for crop production 229 while hog raising become less dependent on land resources. Hog production has become a year round activity with capital intensive systems common in large scale operation. The trends in physical relationships between major inputs used and a unit of output has been indicative of the performance of the hog industry. Since future shifts in hog production will be determined in part by future changes in these physical and biological factors, it is useful to determine the probable future changes of these variables. 6.1.3 Trend in Pigs Per Litter The number of pigs weaned per litter is indicative of the genetic quality of the breeding stock and the quality of attention and care given by the producer. Average pigs per litter increased from about 6.9 in 1955 to about 7.6 in 1985. Litter size has been trending upward except during the period 1968—75, where litter size slightly declined from about 7.3 to about 7.0 pigs (Figure 6.2). Since gilts generally provides a lower number of pigs per litter than mature sows, a lower replacement rate of females results to a higher average litter size. 230 6.1.4 Trends in Avergge Dressed Weights of Hogs Average dressed weight has been trending upward over the last 30 year period (Figure 6.3). From a level of 136 pounds in 1955 to an average of 174 pounds in 1985. Market slaughter weight is largely determined by the hog-corn price ratio and the quality of the stock. During periods when the hog-corn price ratio is low, hog producers usually market slaughter hogs at lower weights. 6.1.5 Trends in Death Losses As Percent of Total Pig Crop Death losses as percent of total pig crop were a little over 10 percent during the mid 19503. A downward trend in percent death loss occurred from 1960 to 1970 (Figure 6.4). From a little above 6 percent in 1970, a slight increase to about 8 percent occurred in 1974. Since 1975, death loss has been fluctuating at a range of 7 to 8 percent of the total pig crop. The trend toward confined housing in hog production has enabled the producer to have greater control of the environment and prevent diseases. 231 Figure 6.1 m filliln‘llllfilI’EIailflolE? I 18861115?” “III 55999 50088 45989 40088 35999.... i955 1959 1965 1970 1975 1989 1985 ... Pcs ....... PCP ”"2 Figure 6.2 “”‘Illizl‘llalfii, “1519198943424“ 7.? 7.6 7.5 7.4 7.3 7.2 7.1 7.8 6.9 6.8 6.? 1955‘ 1m 1965 mm 1975 1999 1995 .... PPLF ....... PPLS 232 Figure 6.3 AVERAGE DRESSED HEIGHTS 0F H008. 1955-05 (pounds) 188 179J 160" 1504 149i 13B 1955 1900 1905 1970 1975 1900 1905 9100 Figure 6.4 0000 100909 09 0000001 or 00101 010 0000 001100 910109, 1955-1903, 9000001 0.11 0.10 0.09 0.00 0.801 90“" 0.05 0.04 . 1905 ' 1900' ' 1905 ' '1970 ' 1905 1990' 9100 233 6.2 Physicsl Relationships in Modeling Pork Supply Johnson, et.al., (1983) hypothesized that biological relationships such as birth, culling, replacement, maturing, and marketing rates can be used as conditioning mechanisms for modeling livestock supply response. Johnson and MacAulay (1980)> and later Okyere (1982) used the physical accounting relationships in the form of stock-flow relationship to restrict a beef supply model. Chavas and Johnson (1982) modeled the sequence of production stages in the U.S. broiler and turkey production, giving particular emphasis on the biological and physical relationships that characterize the structure of supply response. In specifying a farm level pork supply response model Johnson, et.al., (1983) incorporated information on the technical and biological factors in pork production. Pork supply response was hypothesized to be mainly a function of long-term biological, technical and institutional ratios and trends. Any deviation from the long-term trend was explained by changes in relevant economic factors, such as output and input prices. Biological relationships are introduced as restrictions in the hog supply response model. These restrictions enter as physical accounting relationships. 234 Following the notation of Johnson, et.al., the biological relationships between stock and flows are defined as follows: (6.1) CI: + St I CIt-i + IN: where CI: is the closing inventory, S: is the outflow or slaughter and 1N1 is the inflow from one stage to another. This identity is applied to determine the flow of gilts that become sows, baby pigs that become feeder pigs, and feeder pigs that become slaughter hogs. Specifically, the following identities are considered: (6.2) 81111 + $51 I BHIt-1 + ADI-It (6.3) PCi + ABHt I PCt-i + FPt (6.4) FP: + 8081 I FPt-i + FSHt where 931 is the closing inventory of the breeding herd, SS is the outflow or commercial slaughter of sows, ABH is the flow of gilts becoming sows, PC is the closing inventory of the pig crop, FF is the flow of the pig crop to feeder pigs, 868 is the commercial slaughter of barrows and gilts and FSH is the flow of feeder pigs that become slaughter hogs. The number of gilts becoming sows, ABH, is estimated using 6.2. 235 ABR is then substituted in 6.3 to calculate the number of pigs that become feeder pigs. The latter is then used to calculate the number of feeder pigs that become slaughter hogs using 6.4. These physical accounting relations allows a systematic determination of the pork production process and a more coherent analysis of supply response. The next step in the analysis is the calculation of ratios between the flow and stock variables estimated using the identities. For instance, the ratio between gilts becoming sows (ABH) and the baby pigs becoming feeder pigs are estimated. The proportion of slaughter hogs to the total breeding herd and the ratio between the pig crop and the breeding herd with appropriate lags are also calculated. These ratios together with the identities constitute the physical restrictions in the pork supply response model. The trends in these ratios are indicative of the impacts of some of the aspects of structural change occurring in U.S. hog production. In particular, it is observed that the ratio of sow slaughter to the lagged breeding herd has been trending downward overtime. Johnson, et.al., indicated that this could be explained by the improvement in technology in hog production. They hypothesized that control of diseases and improvement in management technology in hog production may have allowed the producers to farrow more litters per sow and hence not to replace sows as often. Furthermore, the ratio of the pig 236 crop to the breeding herd has stabilized in recent years. This stability is explained by the movement of the hog industry towards more large scale operations and more confined hog production. This structural change has tended to give hog producers an increasing ability to control the environment surrounding hog production and lessen the variability in pork output. Johnson,et.al., (1983) used these biological trends as explicit restrictions in their hog model by estimating a trend equation with the following form (6.5) R1 = a: + b1 t DV + C1 DV (1 1,2, 3,4) where R: is a quarterly biological ratio, t is a time variable, DV is a dummy variable which equal one prior to 1975 and zero after and including 1975. a, b, and c are parameters to be estimated. Sow slaughter was then specified as primarily a function of the long term ratios and trends, price of barrows and gilts, price of inputs and cost of money. Specifically sow slaughter is specified as follows (6.6) $5 = fIRATIOS, LAG. 0P. IP, I) where SS represents sow slaughter, RATIOS is the long term biological ratio, 0? is the output price, IP is the input 237 price, I is the cost of money, and LAG is the relevant lagged inventory variable. In this specification, the level of supply is primarily determined by the average biological ratios. Deviations of output from the long term average trend is explained by changes in economic variables such as input and output prices and other relevant costs. Additions to the breeding herd was specified in the same fashion as sow slaughter. Results of the model validation conducted by Johnson et.al., indicated that the general tracking performance is improved by using the trends as restrictions. However, inaccuracies in the simulation results of the additions to the breeding herd variable were encountered. It is noted that this problem stemmed from the potential errors in the data for breeding herd inventories. Unfortunately, their model is specified such that any inaccuracies in the inventory data are carried over to the barrow and gilt slaughter variable. The general method reviewed above offers potential usefulness and relevance in attempts to consider structural change in livestock production in specifying a livestock supply response model. For the present study, long term biological trends and ratios c~ 0>MANCLNH~¢ 40 Aoaav COLLODLLU mamamnmnoua LowLwamoa 0cm nuucv comLmamLU COMJMELOGCH wxmaxm —.n 0—30h mums zs memo 1 memo u meomom mums zs oeum 1 meum n numumm mums za memo 1 memo u mememo mzsm 0 ex» 0 mzsms menu 0 ex» 0 memes memo 0 exp 0 memos c .....w._ n a 010;: meum . ex» 0 meums 275 an- msummms Amzsm .memms .memm .meue .meum .ovu n emo mm- msunnms Amzsm .mesmme .meyes .meue .oeum .msu u memee vnu mslmmms Amzsms ozsm ”memo ”memes meme ”meum ”msu u memee mm: msumnms :Amzsm memo memes mexe meum osu n uemee mm- msnmmms Amuse mzsm meme memmmm memo meoumm meum ”osu u emu mv- msumnms Amzsm meme muse musmme oessme ”meums .oeum ”oou u emu mv: malnmms Aozsm meme mesa muoemm memo meums .meum mvu u emu mvu msumnms sxmzsm .meme .memms .oemm .meums .meum .msu u emu mv- msammms Amzsm .mexe .memms .memm .meums .meum .msu u emu mm: mslmnms *Amzsm .memm .mexe .meums .meum .mvu u emu me: 2188 8sz .memm .meue .meums .meum GK .1. emu on- 918.8 :6sz .mefime .meums .meum GK 0 emu as- malnnms Amzsm .mesmme .meums .oeum .mvu u emu madman! 105:: D2: Educ... . mm- msuoums :Azmousm .mzsm .mesmme .mexe .oeum .msu 0 ex» mm- msuoum— “mouse .mumms .mzsm .mesmme .mexe .meum .mvu 0 es» en: msunnms “zones .menms .mzsm .oessme .oexe .oeum .ovu 0 ex» mommssmxas mos madame zmspmmeusmmem sumo: Aposcmacooo s.e o_nm» nmmslsums Lou _ 6:0 uses v 3 Lou o u zmuusm mesmme . wees u ssmeme messme . shes u same—e meme 0 seem u xese mzsm . shes u >se saseocmsoe streamed animus muss» us need 000;: meum : need 0 meme saseocmsoe misc-mas acumen access as wees 010m: meum s wees 0 meme saseocmsoe cuss-mos corona amuse as shes 010;: meum a shes u ease 276 Amzsm smmewe samese ~41 mmslnnms .messme .xese .xese .meme mmwe ”mm—e meum msun emu “zones: .mzsm ”somewe somese mm: 8762 .oeSme .ueE .mexe .mmNe muse meum .Hmsu emu Aozsm .ssmese or. 8782 .messme .xese .meue .mmNe .mmse .oeum GE 0 emu A>se , mm: mmsumnms .mzsm .mesmme .mexe .mmme .mmwe .mmse .meum .msu u emu n41 mmslmmms Amzsm .messme .meue .mmne .mmme .mese .meum .msu n emu mm- mesannms Amzsm .mesame .meue .meme .mese .oeum .msu u emu meuzDz>ADa waozwwwd IF“: meDDt awhmzcmca wz~>a¢31wtuh maazuhZDo .D mm: mmsummms Amman .meyh .oemms .memo .mexe .meum .msu 0 exp mm- mmslmnms Amzsm .memhs .oeu» .memm .meue .meum .msu 0 exp mm: 8.762 828.. .sz .memm .mev: .meue .oeum._ .meum .msu 0 6: mm- mmslnnm_ Aozsm .memm .oeyp .mexe .oeums .meum .msu 0 ex» 041 mmsumnms Amzsms .ozsm .memos .memo .meue .oeum .mvu u emm ~41 mmslmnm_ Amzsm .memms .memm .mexe .meums .meum .mvu u emm mommasmuss loos moseme zmahmmsuammem sumo: atflncmacouv ~.N Onnmh 277 mm- smu snl mslmnms Azmuusm .mzsm .smmeme .smmese .mesmme .xese .meue .mmse .meum .msu u xemee mm. me: an- mslnmms sxzmuusm .>se .ozsm .smmewe . .smmese .mesmme .uese .mexe .mmse .oeum .mou u semee um- sm1 was mslnnms Amzsm .smmeme .smmese .mesmme .xeme .uese .meue .meum .msu u xemee sun mm- um- mslmmms >se .mzsm .mesmme .xeme .uese .meme .oeum .osu u memee mm- won an. mslnnms A>se .mzsm .mesmme .xese .meue .meum .osu u uemee sul mm: mm- msnmnms Amzsm .mesmme .ueme .uese .mexe .oeum .osu u memee 2935 626 .smmeme .smmese .mesmme on- Nvu on: mslnnms .xese .mexe .mmme .mmse .meum .msu u emu Amzsm .smmese .mesmme mm- m4- mm- mslmmms .uese .meme .mmne .mmme .mmse .oeum .msu u emu “zonesm .>se .mzsm .smmewe .smmese Nu- mvn snl ms1nmms .mesmme .xese .meue .mmme .mmse .meum .osu u emu mommssmmss mee mam loos mmseme zmspmmsusmmem smmmzz ADO-......macoov "K Gun-N... 278 mm: mm- en: 82188 823 .meV: .memo .mese .meum .msu 0 8: men so: mm- momsnmmms Amzsm .mex» .memm .mexe .oeuw .osu u emm mu: sen mm: mmmslmmms Aozsm .oesmme .meme .meum msu u semee smu as- we: nmmsunnms xmzsm .mesmme .oeme .meum .msu u emu sumo: empmmmeme pzmemzmm .m em. on: cs- mmmsnmmms zmeusm .sse .mzsm .smmese .oesmme .xese .mexe .mmse .meum .msu u emm mm: m4- mm: mmmslnnms Azmuesm .>se .mzmm .smmese .mesmme .xese .meue .mmse .meum .msu u emm won me. mm- mmms1mnms Azmeesm .>se .mzsm .smmeme .smmeme .smmese .mesmme .meme .mmse .oeum .msu u emm A>se .mzsm .smmene mm- me. an: nmmsnmnms .smmeNe .smmese .mesmme .oeme .meum .osu u emm A>se .mzsm vn1 mvl s41 nmmsnmnms .smmeme .smmese .mesmme .mexe .mmum .osu u emm sse mzsm mm- m4: .41 mmmslmmms .smmese .oesmme .meye .oeum .msu u emm Amzsm .smmeme smn mm- mvu mmmsumnms .smmeme .smmese .mesmme .mexe .meum .msu n emm Amzsm mm- mm. on- mmmslmnms .smmeNe .smmese .mesmme .meme .meum .osu u emm mm: mm- on: mmmsumnms Amzsm .smmese .mesmme .meme .meum .msu n emm mmmmssmxss mee mse loos mmseme zmshmmsusmmem sumo: finenesscoms s.e «same 279 The results also shows that the value of the log- likelihood function is larger for constant parameter price models which are estimated using more current time series data. Using data during the past 31 years without accounting for parameter variation reduces the value of the log-likelihood function by more than half. Trend variables, T5576 and T770N, were introduced to the constant parameter models to test for shifts in demand beginning 1977, the approximate starting period of parameter change as indicated by the recursive residual analysis. The models were estimated using two time periods: 1955-1985 and 1970-1985. The values of the AIC and PPC criteria of the augmented models indicate significant improvement in the goodness-of-fit and relative parsimony performance relative to the constant parameter price models which do not account for the shifts in demand. Among the alternative specifications to approximate the shifts in demand for meat over time, the continuous varying parameter specification using Legendre polynomials have the best performance based on the AIC and PPC criteria. The model which allows gradual continuous variation in both the own-quantity and cross flexibilities with respect to pork and poultry and shift in the intercept starting in 1977 appear superior among all beef price models as evidenced by values of -42 and -50 for AIC and PPC, respectively. No significant improvement in the values of the AIC and PPC for 280 this beef price model was achieved when the income flexibility was also allowed to change. AIC and PPC values for this models (equation 5.4.5 and 5.4.7) were -43 and -52, respectively. This may be explained by the insignificance of the legendre polynomial introduced in the income variable in the beef price equation after allowing for variations in the own-quantity and cross-quantity flexibilities. Among the pork price model with Legendre polynomials, the model which allows all parameters to change over time and has an intercept shifter beginning in 1977 has the best goodness of fit and relative parsimony performance. The AIC and PPC criteria correspond to values of -49 and -58, respectively. The broiler price model which> allows continuous variation of own-quantity, cross-quantity, and income flexibilities, including a shift in the intercept starting 1977 correspond to the highest values of both AIC and PPC at levels equal to -45 and -52, respectively. In general, the discrimination among the price models based on the goodness of fit and relative parsimony performance measures provided consistent results. That is, the AIC and PPC criteria both indicated superior performance of price models which allow gradual continuous variation of all demand parameters and include a shift beginning in 1977. 281 7.4 Historical Simulation Results Historical simulation involves the estimation of the endogenous variables in the model during the historical period. The purpose of this aspect of validation is to evaluate the ability of the model as a system to replicate the corresponding historical series. This section presents the results of the historical simulation of the U.S. livestock and poultry model. The predictive ability of alternative specifications of parameter variation in the price models (also called inverse demand model) are compared. The tracking performance of the challenger model of hog supply presented in chapter 6 is compared with those of the defender base model of hog supply presented in chapter 3. The challenger model includes the effects of some aspects of structural change in the hog industry. This is carried out by introducing the trends in the physical relationships that are likely to be affected by the identified structural change. The simulation runs from 1975 to 1985. The results of two simulation exercise are presented in this section. The first simulation includes the challenger model of hog supply (presented in chapter 6),the base model of the beef and poultry supply (discussed in chapter 3), and the selected continuous varying parameter models of prices (models with 282 Legendre polynomials selected based on the AIC and PPC criteria). The second simulation uses the defender base model of the hog, beef and poultry supply and price models with trend shifter variables (DVT73,DV730N,DVT80,DV8OON) presented in chapter 3. The results of the simulation are summarized in Table 7.2 to Table 7.6. For each simulation, the values of percent errors of simulated values of endogenous variables are reported for each simulation year. Other measures of relative and absolute accuracy of simulated values are also reported. Johnson and Rausser (1977) indicated some limitations of model validation based on ex-post data for the exogenous or predetermined variables. Since the errors in projecting the latter are not included in the ex-post estimates, the accuracy of tests based on ex-post predictions may be overstated. In this study, the individual equations are estimated using data up to 1985. Hence, ex-post forecasts are not generated. However, projections for 1986 may be compared with the 1986 estimates from USDA statistical reports. The ex-post (historical) performance of the model is evaluated based on relative and absolute accuracy measures for each endogenous variables. In general, the predictive ability of the model is quite good as indicated by the low percent errors of simulated values for almost all endogenous variables. Historical simulation results indicate the price 283 variables to be well predicted by models which accounts for parameter variation over time. Overall, the values of the absolute and relative accuracy measures indicate a better performance of the pork supply model which considers changes in biological and/or physical relationships (presented in Chapter 6, referred as PORKSMZ in the following discussion) over the base model (presented in Chapter 3). Compared with the base price models which only allow abrupt shifts in demand as measured by the trend shifter variables, 'more accurate results of simulated values are given by the price models which allow for gradual continuous variation of the demand flexibilities. A significant improvement in replicating the historical series of hog price and pork production was achieved by using PORKSMZ. This can be seen in the lower percent error of estimated values during each simulation year. The root squared error of simulated values of both variables estimated using PORKSM2 were half of those estimated from the base hog supply model. Also, by using the PORKSM2, the proportion of error in estimated hog prices due to bias was reduced from .218 to .012, representing more than 90 percent reduction. A significant improvement in the accuracy of simulated values of sows farrowing in the fall was also realized by using the PORKSMZ model. The root squared error, for instance, declined from 3400 to 222.9, reducing the 284 proportion of error due to bias from .996 to 0.02. Also, U(2) declined from 6.39 to .381, indicating a superior performance of the PORKSMZ model over a naive no-change model. The mean of the absolute value of the errors decreased from 3000 thousand head to 164 thousand head. In both simulations, the same specification of the beef supply model was used. It is interesting to note that the predictive performance of the beef supply variables is almost the same in both simulations. However, a slight imrovement in the accuracy of simulated values of beef cow numbers, fed-beef supply, and non-fed beef quantity is achieved by using the PORKSMZ model. In the case of the poultry sector variables, no significant improvement in predictive performance was realized by using the continuous varying parameter models. Values of the percent error for each simulation year indicate more accurate predictions in some years and less accurate in others. Overall, the values of both relative and absolute accuracy measures indicate the same performance of the broiler and turkey price models with trend shifters and those with continuous varying parameters. Within the PORKSMZ pork supply model, alternative specification of the pigs per litter equation are evaluated. Simulation results indicate that a linear trend specification of pigs per litter has validation problems, while the flexible trend and dummy variable specifications 285 perform relatively well in tracking the historical series. 7-5 Projections The second stage of model evaluation involves the use of the model as a system in generating ex-post and ex-ante forecasts of endogenous variables. Ex-post forecasts for 1986 are generated using historical values for exogenous variables. The ex-post forecast of endogenous variables are compared to actual data in 1986. Ex-ante forecasts are generated using forecast values of exogenous and predetermined variables and the model is simulated beyond the estimation period. The model is in large part recursive. Supply is predetermined while demand responds to current information, including quantities supplied. To the extent that the model is recursive, single equation bias and inconsistency in parameter estimates are minimized. Simulation of the model is carried out using the GSIM simulation procedure developed in the Department of Agricultural Economics (Wolf,1983). The algorithm follows the Gauss-Siedel method of iteration to obtain a solution to a set of simultaneous equations. Evaluation of the forecasting ability of a model is useful for both predictive purposes and policy analysis. Forecasts may be used to determine and compare the impact of changes in some controllable exogenous variables or the 286 effects of changes in the estimated parameters on the values of the endogenous variables. 7.5.1 Assumptions on Key Exogenous Variables The assumed values of the important exogenous variables during the projection period are given in Table 7.8. Population of the U.S. was projected to increase from 237 million in 1985 to 254 million in 1993. Real per capita disposable income was projected to increase by 2.0 percent from 1985 to 1986 and by 2.5 percent per year in 1987-1993. For the baseline projection, corn and soymeal prices are held constant during the projection years at $2.0 per bushel and $8.8/cwt., respectively. The effects of changes in feed prices may be then be evaluated and compared with the baseline figures. Also, in the baseline projection, the consumer price index is held fixed at its 1985 level (3.22 percent). 287 TABLE 7.8 Projected Values of Exogenous Variables Year Civilian Disposable Interest Population Income Per Rate Person, Real (POPUS) (DPCIT) (INTT) millions $/person percent 1986 239 3710 10.9 1987 241 3800 10.3 1988 243 3890 10.0 1989 245 3990 9.8 1990 248 4090 9.8 1991 250 4190 9.8 1992 252 4300 9.8 1993 254 4410 9.8 7.5.2 Projections of Endogenous Variables The version of the livestock and poultry model which includes PORKSHZ and meat price” models with varying parameters are used in generating projections of U.S. livestock production and prices. As shown in Figure 7.1, beef cow numbers will fall to 33.06 million head in 1987 before increasing to its next peak around 1992 at about 38.461 million head. This next peak level of beef cow numbers is about 16 percent lower than the 1975 reported beef cow numbers. Fed and non-fed beef supply are projected to continue to decline from their 1985 levels up to 1989 and then increase starting in 1990 reaching their next peak 288 levels in 1993. At this next peak, fed beef supply is projected to be about 1.9 percent lower than the previous 1985 peak. The projected 1993 level of non-fed beef supply, on the other hand, is about 12.6 percent lower than the last peak level in 1984. The projections show that the corresponding predictions of per capita beef supply in 1989 will be at its lowest since 1962. Although the projected per capita supply available for consumption of beef and pork are expected to trend down over the next 7 years, total meat per capita supply is expected to stay in the same range due to broiler and turkey per capita supply being projected to continue growing at the same rate observed over the past 20 years. Fed Choice steer prices in constant 1985 dollars are projected to increase up to 1988, reaching a level of a little above $80, as per capita supply of beef decreases during this period. The above projections were estimated under very low assumed real corn and soymeal prices over the entire period, and hence, are maybe on the higher side. Sows farrowings in the spring in 1986 is estimated to be 5424 thousand head, down 2.4 percent from 1985. This is consistent with the projected cutbacks in herd size since 1983 due to the continued poor returns and financial stress beginning in early 1980s. Improvement in producers returns is projected 1987 as indicated by higher hog prices and very low corn prices projected during this period. With the 289 projected increase in producers returns in 1987, spring farrowings are projected to increase from the 1986 level and reach a peak at 6486 thousand head in 1988. Fall farrowings, likewise are projected to increase and reach a peak level of 6716 thousand head in 1988. Pork production is then projected to reach its next peak in 1989, reaching 16.591 billion pounds. The projected 1989 peak level of pork production is up only 1 percent from the last peak in 1980. The resulting price of hogs in 1989 is projected to reach a record low of $39 in constant 1985 dollars. With the projected decline in hog prices and the assumed constant level of corn prices, sows farrowing is projected to continue to decline reaching 5.8 billion head in both spring and fall in 1990, down 8.1 percent from the previous year peak of 6.311 billion head. The decline in spring and fall sows farrowing is projected to continue to 1993 as hog prices continue to remain low during the early 19905. Total commercial pork production is estimated to be 14.128 billion pounds in 1986, down 4 percent from 1985. Commercial hog slaughter is estimated to reach 81.042 billion head, also down 4 percent from 1985. Average dressed weight is estimated at 174 in 1985. These set of estimates of hog supply variables for 1986 are observed to be very close to the 1986 estimates published by USDA in the November, 1986 Livestock and Poultry Situation and Outlook. 290 .mcomuomLummL mm pwmmmuwnm masrucosansot snowmosomn pea saomnmra rum: cosaosuota xLoa so ~wpo¢ one on mtomwt wrmxaoa Nm.0 hm.0 h~.0 mm.0 VN.0 ~Nh.0 Amy: 00.0 No.0 «0.0 No.0 no.0 N—0.0 A—v: mhzmuunuuwou DlJHwa mm.0 wh.0 00.— 00.0 Dh.0 Wk.0 acamm IDDZIU No.0 m~.0 00.0 00.0 WN.0 —N.0 madam Uuhmzmhm>m 0—.0 no.0 00.0 No.0 00.0 v0.0 mcum Oh man zanhaoafiaa om.m—m 00.ahh mm.m0N nm.NNN mm.mmn 0N.000u madam Dwmczam boom 00.NNO@M 00.~010m mm.mm Nm.hmm m~.nn 00.vmuon aommw 2cm: Duncaam mN.m Nm.N N—.~ MN.N -.N on." madam hzmomwa whDADmmm mo zcwz VN.D mm.0I h0.0l 0v.0l 00.0 ~N.0 moamw hzwuama no zmmt 00.n—v 00.vmn 00.nn— 00.?0u 00.DN~ 00.10 moaaw whaaommc no zcwt 00 00g 00.VN~I 00.v~I om.~MI 0N.NI 00.?N acamw zcwt mv.m ND.vI NN.NI m~.hl 00.nl om." amm— ND.— 0N.0 um.0 in.“ NN.N 00.— #00— mm.v 0N.N kn.—I NN.D no.0 ~N.— ”mm— NN.m km.0 "0.0 v0.~l vm.— m—.0l Nmm— no.0 0v.ml mm.0I ”0.0! 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Simulated Values For 1975-1985 and Obsolute and Relative Occuracg of Simulated Values Using Base Model SOHFST SONFFT PORKOT FBEFOT NFBFOT YEOR/ERRORS 294 88382528888 66466666666 T T” 38888838838 flfldflflflfldfiflfl 888888 838888 83 SRONgk 000 If) N1 888888 838 §§8888 ~°° F1 0 I 0; N1") —d 888888 888 KK6J'6 666 Nd v-l NF! 838388 688 ago—{fag 000 NR 88 1 SYSTENOTIC ERROR RONOON ERROR BIOS THEIL-U COEFFICIENTS NEON OF OBSOLUTE PERCENT ERROR PROPORTION DUE TO SOUOREO NEON ERROR NEON OF OBSOLUTE ERROR ROOT SOUOREO ERROR NEON OF PERCENT ERROR NEON ERROR M V on 00 0.0 0.02 0 3 0 67 0.22 0 39 0.01 0.57 U(l) U(2) Base Node! refers to the model presented in chapter 3. 295 .n L0a00£0 cm U0ac0m0L0 _0UOE 05$ 00 0L000L ~0to: 0000 00.0 01.0 kn.o "0.0 10.0 ~1.0 ANVD 00.0 no.0 no.0 00.0 10.0 no.0 nay: 0#20~0n00000 0!A~0I# 00.— 00.0 N0.0 n0.0 00.0 00.0 00000 200200 00.0 ~0.0 ~0.o 00.0 No.0 no.0 00000 0H#020#0>0 00.0 no.0 No.0 00.0 No.0 NN.0 0000 0# 000 20u#000000 00.n “n.~ n0.o 00.~ N0.~ 0n.— 00000 0000000 #000 00.0 —0.0 ~0.0 ~0.0 0N.o 0n.0 00000 200: 0000000 n—.0 ~0.0 00.0 01.0 00.0 nn.0 00000 #200000 0#040000 00 200: 00.~ 0n.— nN.0! 0~.0! N0.N 00.N! 00000 #200000 00 200: 00.N «0.— 00.0 .01.— 00.“ no._ 00000 0#040000 00 200: 10.0 00.0 N—.0! ”—.0! N0.0 n0.0I 00000 2002 00.nn 00.0 0—.0 n0.“ 00.N— 00.0! 000— 0&.N~ an.N 0~.N 0h.0 01.1 N1.NI 100— N0.—! 10.0 00.n! 00.—~! ~0.N! 00.0! n00~ 00.N~! 00.n! N0." 0—.N! "0.1! 00.—~! N00~ 10.nl n0.1 N0.0 01.N— 00.1“ 01.0— ~00~ N0.N! 0N.~ N0.0! 0N.n 00.0 nn.N 000d ~n.~! 0N.N~! n0.N! on.0~! 00.0! 1n.0! 0N0“ on.Nu h0.~! N0.0 ~0.— n0.0 00.0! 0500 HN.0! NN.0 N0.n Nn.o "0.0 1N.N! ~00" ~0.N—! Nn.0! on.N~I 00.0—l nN.n 0n.0 0N0— 00.0 n0.0 10.nl 00.nN 0~.N! 0N.1! 000— #0000 #0¥00# #0¥~IU 030000 #00000 #01000 000000\000> "000: 0000 0:000 003~03 0000—3600 mo 000L3000 0>000~00 0C0 man—omnc 6cm mmmssmsms to» mm:_ms vusmsncam go mtottm scwotoa n.n moan» 296 With the projected decline in sows farrowing beginning in 1989, pork production is predicted to decline in 1990 and stabilize during 1991-93. Pigs per litter in spring and fall 1986 are estimated to be 7.67 and 7.71, respectively. These are slightly above the record 7.64 and 7.67 for spring and fall litter size set in 1985. The increase in pigs per litter in previous years was in part due to the development of cross bred gilts. for the breeding herd and the improvement in management practices and standards in the hog industry. The flexible trend specification of the pigs per litter equation assumes the continuation of these factors, hence, projections generated from this equation shows litter size continually increasing, reaching a level of 8 pigs per litter during the early 19908. The linear trend equation of litter size, however, results in less optimistic projections of pigs per litter. Using this latter specification will result in 7.4 pigs per litter during 1986-1990 and about 7.5 in 1991-1993. Poultry production is expected to continue expanding. Production increases in broilers and turkeys are projected due to high producer returns, expectations of lower red meat supply and the projected continuation of the stronger substitutability of poultry for red meat. Poultry prices are expected to advance as strong demand for poultry BILLION HEAD BILLION POUNDS 297 Figure 7.1 BEEF COW INVENTORY, JAN. ACTUAL. ESTIMATED AND FORECAST VALUES 1 32 f V I V V 1' 1' V l’ V V I ' ' I ' I075 1978 1981 1984 I087 1990 I003 o ACTUAL + EST. a: FORECAST Figure 7.2 FED BEEF PRODUCTION 21 ACTUAL. ESTIMATED a. FORECAST VALUES 20 -1 19 - 1D A‘ I! -4 I7 - I. ' ' I ' ' I ' r I ' ' I ' ' I ' ' 1973 1978 1981 1984 1907 1990 1993 o ACTUAL + EST. 4. FORECAST BILIJON POUNDS 8/ CWT. 298 Figure 7.3 NON FED BEEF PRODUCTION ACTUAL. ESTIMATED dc FORECAST VALUES 3 1975 V I V V I I r j V V r V I r fl 1978 1981 1984 1987 1990 1993 O ACTUAL + EST. I: FORECAST Figure 7.4 CHOICE STEER PRICE, REAL, OMAHA ACTUAL. ESTIMATED a: FORECAST VALUES 32 31 -I 30- 29- 23- 27 26 25- 24- 23-4 22-1 21 - 20- 19- 18- 17 . A V . 1975 r V r r V I f V I V Y r V 1* ' I 1978 1981 1904 1987 1990 1993 O ACTUA. ! EST. 6: FORECAST -..-=3 A ...-1...: J! I {“L_ J MILLION HEAD MILLION HEAD 7.4 2599 Figure 7.5 SOW FARROWING IN FALL ACTUAL. ESTIMATED a; FORECAST 7.2 - '7 .1 0.0 - 0.0 - 0.4 -. 0.2 .1 g .. 5.8 "I 5.0 -' 5.4 -‘ 5.2 1 5 — ... I 1975 7.4 r 1* fi 1' r V 1978 1981 ffir T f f , . . 1984 1907 1990 1993 I: ACTUAL + EST. a. FORECAST Figure 7.6 SOW FARROWING IN SPRING ACTUAL. ESTIMATED d: FORECAST 7.2 ~ 7.1 Edi-1 8.8 -1 604- 5.2 -* B -4 :La«- ans- 504-: 5.2 J 1975 Y r r ' I ' ' I 1978 1981 1904 V V7 I f V I 1987 1990 1993 o ACTUAL + EST. .9. FORECAST NUMBERS NUMBERS 300 Figure 7.7 PIGS PER LITTER IN FALL ACTUAL. ESTIMATED & FORECAST VALUES 7.7 7.6 - 7.5 -I I 7.4 - 7.3 1 7.2 7:! .7 ,7 - .7 , . . e, .eeer , . . , - . 1975 1978 1981 1984 1987 1990 1993 a ACTUAL + EST. a. FORECAST Figure 7.8 PICS PER LITTER IN SPRING 7 7 ACTUAL. ESTIMATED a: FORECAST VALUES 7.5 - 7&5'4 7.4 - 7.3 1 7.2 - 7.1 - 7 1975 V I V V V V 1 V f r 1 V U , . . 1978 1901 1984 1987 1990 1993 O ACTUAL + EST. 0 FORECAST 301 Figure 7.9 TOTAL PIG CROP ‘0‘ ACTUAL. ESTIMATED 8 FORECAST VALUES 102 -I 100 - 90 -1 90 -I ‘ ..- \q 92 -I \ 9O - 88 fl ' 86 -I / a4- BILIJON HEAD so J 78 d 75 -_ 74 1 72 7o T I ' I V f r V v r V W I v V7 j v 1975 1970 1981 1904 1987 1990 1993 a ACTUAL + EST. 4!: FORECAST Figure 7.10 GILTS RETAINED IN FALL ACTUAL. ESTIMATED I: FORECAST VALUES 2.9 - 2.6 -I 2.7 -I 2.6 - 2.5 -I 2.4 - 2.3 1 2.2 J 2.1 THOUSAND HEAD 1.9 1.0 V V f I 1990 1993 1.6f v v T v 1 f . . I . . I . 1975 1978 1981 1984 1907 O ACTUAL + EST. 6: FORECAST 3(12 Figure 7.11 GILTS RETAINED IN SPRING 2 B ACTUAL. ESTIMATED h FORECAST VALUES 2.7 -1 2.0 q 2.5 - 2.. J 2.3 '1 2.2 - 2.1 - 2 - \ 1.9 1.8 - THOUSAND HEAD 1.7-I 1.0-1 ‘.5 r V fiT V f 1’ V V V V l V V 1973 1973 I901 1904 1907 1990 1993 V V I o ACTUAL + EST. 3: FORECAST Figure 7.12 SLAUGHTER OF BARROW AND GILTS. FALL 46 ACTUAL. ESTIMATED dc FORECAST VALUES 4S _ 44 \ 43 42 ‘1 41 4o 39 33 37 33 33 34 33 32 31 so 29~; .7 1 , - 1 Te . . . . . 1973 1973 1931 1934 1937 1990 1993 MILLION HEAD O ACTUAL + EST. & FORECAST 303 Figure 7.13 SLAUGHTER OF BARROWS AND GILTS, SPRING ‘7 ACTUAL. ESTIMATED h FORECAST VALUES 46-1 45-1 44 ..j 42.4 41 - 40-1 39- ‘ I I 38-1 37- 30 . 35 34 33 32 31 MILUON HEAD 3° 1 j 1 T ' ' 1' V V j’ r r V V r V V I 1975 1973 1981 1904 1987 1990 1993 O ACTUAL + EST. I: FORECAST Figure 7.14 SOW SLAUGHTER IN FALL 3 ACTUAL. ESTIMATED I: FORECAST VALUES 2.9 .1 2.. . 7 2J'4 / 7 241- J * \\ za- \_ 3 294- \ 245- 2.2 4 A \/ MILLION HEAD 2.1 .1 2" . 1J1‘l’r 1.3 I 1.7 ‘08 L5 1 . . , . 1973 1973 f f r *V r ' ' T ' 1 ' 1 ' 1901 1984 1907 1990 1993 O ACTUAL + EST. & FORECAST MILLION HEAD MILUON HEAD 2.6 304 Figure 7.15 SOW SLAUGHTER IN SPRING ACTUAL. ESTIMATED 8 FORECAST VALUES 2.3 - 2.4 - 2.3 1 2.2 -1 2.1 -‘ 1.9-1 1.8T 1.7-I .... / \ 1.3- 1.4 A 1973 . , 1 . . , . 1973 I901 1904 1907 1990 a ACTUAL + EST. 3. FORECAST Figure 7.16 TOTAL HOG SLAUGHTER ACTUAL. ESTIMATED l: FORECAST VALUES 1993 90 94-4 92-1 90-1 08-! 85- a4- 82- OO- 73- 76--I 74-1 / 72-1 704 7‘ 33 , 1973 L', i V . , . . 1 . 197C 1901 1984 1987 V l V D ACTUAL + EST. It FORECAST , . I990 1993 BILLION POUNDS S/ CWT. 305 Figure 7.18 TOTAL PORK PRODUCTION ‘7 ACTUAL. ESTIMATED £3 FORECAST VALUES 16--I ”5‘ 14- ' 13-1 12-1 .L r 11 V, ' V7 1 V V T I V jfi V I I V r 1 . 1975 1970 1981 1984 1987 1990 1993 a ACTUAL + EST. 3: FORECAST Figure 7.19 PRICE OF BARROWS & GILTS. REAL ACTUAL. ESTIMATED & FORECAST VALUES a V V I 1— V v v I V v 1 v v ‘— 1 f f 1975 1978 1981 1984 1987 1990 1993 D ACTUAL + EST. 1!: FORECAST 306 Figure 7.20 BROILER PRODUCTION, READY TO COOK ‘9 ACTUAL. ESTIMATED I: FORECAST VALUES 18-1 . 17-1 16-1 ..J 14-1 13- 12‘ BILLION POUNDS 11- 10-1 f . . , . 1975 1978 1981 1904 1987 1990 1993 a ACTUAL + EST. 3. FORECAST Figure 7.21 TURKEY PRODUCTION, READY TO COOK 5 ACTUAL. ESTIMATED dc ACTUAL VALUES 4.8 "I 4.6 .1 4.4 - 4.2 ~ 4 -1 F 3.8 .1 3.8 - 3.4 - Jazl BILLION POUNDS 2.0 -I 2.6 1 2.4 -1 2.2 -< 2 -I L3 . . , . 1973 1973 j’ V V V V! V T ' T T ' 1981 1984 1987 1990 1993 O ACTUAL + EST. It FORECAST BILUON DOZEN CENTS/LB. 5.85 307 Figure 7.22 EGG PRODUCTION ACTUAL. ESTIMATED I: FORECAST VALUES 5.8 -1 3.73 J 3.7 - 3.33 3 3.3 ~ 3.33 .1 3.3 .. 5.45 - 5.4 -‘ [TX V 5.35 j 1975 154 V I V V I r V r r V I V V I V 1978 1901 1984 1987 1990 ACTUAL + EST. 6: FORECAST Figure 7.23 BROILER PRICE, FARM, REAL ACTUAL. ESTIMATED J: FORECAST VALUES V 1993 14 13-4 12—1 11-1 IO-‘ 1978 V V , . . . . j . . , 1901 1984 1906 1990 ACTUAL + EST. 3. FORECAST 1993 CENTS/LB. CENTS/DOZEN 23 24 - 308 ~ Figure 7.24 TURKEY PRICE. FARM, REAL ACTUAL. ESTIMATED I: FORECAST VALUES 1o . , . . , f E , A . , 3 . 1978 1951 1984 1956 1990 1993 u ACTUAL + EST. 3: FORECAST Figure 7.25 11 EGG PRICE, FARM ACTUAL. ESTIMATED G: FORECAST VALUES 1978 I V V I V V I f V r 1981 1984 1986 1990 1993 D ACTUAL + EST. 6: FORECAST 309 continue. However, sizable expansion projected to occur in poultry production will hold prices from increasing rapidly. Projected increase in production through 1987 will hold poultry prices near the projected 1986 levels. 7.6 Summary and Conclusions The first stage of model validation is carried out by simulating the model as an integrated system over the historical period 1955-1985. In the historical simulation, historical values are supplied as initial conditions for the endogenous variables. Exogenous variables also take historical values. Prediction errors result from model misspecification and errors in parameter estimates. Absolute accuracy of simulated values are evaluated using statistical measures describing the differences between the simulated and actual values. Relative accuracy measures compares the simulated/forecast values with values from a naive no change model. The validation exercise is extended to include the ability of the model to simulate turning points in the data series. Another area of model validation is the examination of model's sensitivity to initial period in which the simulation is started and changes in time paths of exogenous variables. Also, the model's ability to respond to stimuli 310 in a way consistent with economic theory and empirical observation is evaluated. Based on yearly and average estimates of percent errors of simulated values, mode12 of pork supply provided more accurate historical estimates. The results indicate more accurate price estimates from price models which allow parameter variation over time. The model of pork supply which include the biological and physical relationships as restriction provided more accurate estimates compared to the base pork supply model. CHAPTER 8 SUMMARY, IMPLICATIONS AND RECOMMENDATIONS FOR FUTURE RESEARCH The construction of policy and forecasting models that accommodate and track structural change in supply and demand relationships has been a challenge to model builders and practitioners. Rausser and Just (1981) pointed out that the ability of commodity models to admit structural change is one of the prerequisite for the achievement of global approximation accuracy. The phenomenon of structural change in the U.S. demand for meat has been given attention by agricultural market analysts. While some rejected the occurrence of significant structural change in demand for meat in the U.S. (Moschini and Mielke. 1984; Hassan and Johnson. 1979). other analysts provided empirical support to the hypothesis of structural change in demand for meat. particularly for beef and poultry. (Braschler, 1983; Nyankori and Miller, 1982; Chavas, 1983; Cornell, 1983; Ferris, 1984; Hilker, et.al.,1985; Unnevehr, 1986). Empirical results from previous studies indicate that structural change in demand for meat began sometime in the mid 1970s. This study extends the testing and analysis of structural change in demand for meat in the context of constructing a long-run forecasting model of U.S. livestock production and prices. The results of the preceding study 311 312 provide further empirical evidence and support to the structural change hypothesis and suggest that such changes have continued into the 1980s. The present chapter highlights the important aspects of the study. First, the methodology employed in testing for structural change is summarized in section 8.1. Section 8.2 provides a summary of the empirical results. Conclusions and implications of the results of the study are discussed in section 8.3. Finally, some recommendations for further research are discussed in 8.4. 8.1 gummary of Methods The difficulties in empirically tracking changes in demand structure due to changes in consumer preferences have been recognized. The major problem is that shifts in the utility function are not directly observable. Given these difficulties, empirical attempts to identify structural change in meat demand by ad hoc procedures and varying parameter techniques have serious limitations. One of the criticisms pertains to the inability of these procedures to distinguish between structural change and model misspecification. That is, an observed shift in the demand parameters implies a structural change only if the model is correctly specified. Hence, an approach that is able to distinguish structural change and specification 313 error is useful in empirical investigations of the hypothesized change in meat demand structure. Another approach is the identification and use of variables that explain shifts in the utility function. While theoretically attractive, severe data limitations usually prevent the application of this approach. This paper explores the systematic use of several statistical procedures to minimize if not prevent the problems associated with ad hoc analysis of structural change. Specifically, the study uses a three-stage approach in investigating changes in the demand structure for beef, pork, broiler, and turkey meat. The approach is useful in detecting structural change as well as misspecifications in the context of simple models. Meat demand models were constructed in the context of developing an annual forecasting model for livestock production and prices. On an annual basis, quantities of most meats in the market are predetermined given the lags in livestock production. Given the market level data and the predetermined quantities, the demand models are specified as inverse demand functions. That is, real market price is specified as a function of per capita quantity of commodity in question, per capita quantity of substitutes and complements, and real per capita disposable income (prices and income deflated by CPI). 314 The first stage of the analysis involves the estimation of inverse demand functions using recursive least squares for the period 1955-1985. In this stage, the recursive parameter estimates are used as a descriptive tool in determining the effects of individual observation in a sequential updating procedure. The pattern of the recursive estimates of coefficients of the inverse demand models are analyzed, taking note of particular trends and discontinuities. Plots of the recursive coefficients indicate the pattern of variation of individual parameters. Statistical testing of parameter variation and specification errors constitutes the second stage of the analysis. In this stage, the statistics based on standardized recursive residuals introduced by Brown, Durbin, and Evans (CUSUM, CUSUMSQ, and Quandt's Log Likelihood Ratio) and those suggested by Dufour (location tests, Von-Neumann Ratio test, heteroscedasticity test) are used to test parameter variation and departures from the fitted functional form. Under the null hypothesis the demand parameters are stable over time and the recursive residuals have a zero mean and a scalar covariance matrix. That is, the recursive residuals are a normal white noise series. A discontinuity in the demand parameters is expected to influence the behavior of the corresponding recursive residuals. For instance, an abrupt and sudden shift in the 315 demand parameters at some point r* in the sample period will result in an abrupt increase in the size of the recursive residuals and/or a tendency to overpredict or underpredict prices (the dependent variable) for r > r*. A systematic shift in one or more of the demand parameters results in a systematic tendency to overpredict or underpredict. The first two tests applied in the analysis were the cumulative sum (CUSUM) and cumulative sum of squares (CUSUMSQ) tests which are based on the one-step ahead recursive residuals. With parameter variation, the standardized recursive residuals will have a non-zero mean and the CUSUM and CUSUMSQ can be used to test for structural change. If the plot of the CUSUM and CUSUMSQ crosses the confidence boundary, then the null hypothesis of constant parameters is rejected at the chosen significance level of 0.05. The non-parametric tests suggested by Dufour (1981) are also applied in the analysis. The third stage of the analysis involve respecifying the model to include the information regarding the timing of the structural break indicated by the recursive residual analysis. Also gradual shifts in demand parameters are tested by augmenting the model with trend shifter variables. Other methods of allowing the parameters to gradually vary over time such as introducing Legendre polynomials are also used. ('f 316 On the supply side, some aspects of structural change in livestock production is considered in respecifying the model of the U.S. beef and pork supply sector. In doing this, hypotheses concerning the likely effects of changes in biological, technical, and management technology on some key biological relationships surrounding hog production are considered. The trends in the physical relationships between stock and flow variables are introduced as restrictions in the specification of the beef and pork supply model. 8.2 ngmgry ofggmpirical Results This section summarizes the major empirical results of the present study. The discussion is divided into three subsections to cover the results of the recursive residual analysis, the results of the alternative specifications of parameter variation in the inverse demand models for meat, and the results from the reestimation of the model of hog supply to capture the structural change in hog production. 8.2.1 Summary of Results of the Recursive Least Squares and Recursive Residual Analysis The main results of the recursive estimation indicate that the parameters of the linear inverse demand model for beef, pork, and broilers show signs of systematic variation 317 starting in 1977. The recursive residuals prior to 1977 in the case of beef and pork are very close to zero. After 1977, the recursive residuals are consistently negative. The results of the significance tests based on the standardized recursive residuals strongly reject the null hypothesis of constant parameters in the beef, pork, and broiler inverse demand models. Forward recursions indicate a tendency to overpredict prices of beef, pork, and broilers starting in 1977. The cumulative effects of the recursive residuals are indicated by the CUSUM plots which shows large overpredictions in the post 1977 period. The year 1977 is identified as the time of an important structural break in the demand for beef, pork, and broilers. No significant parameter variation is found in the inverse demand for turkey. In the case of beef demand model, results of the recursive estimation declining and increasing trend (in absolute value) in the estimates of coefficients on the per capita beef quantity and poultry quantity respectively. The recursive estimates of the coefficient on real per capita disposable income appear to have slightly declined over the period. A discontinuity is evident starting in 1977 in the beef price equation as shown by the values of the standardized recursive residuals before and after 1977. Recursive estimates of the pork demand model also indicate parameter instability. An increasing trend in the 318 absolute value of the coefficient on pork per capita supply was evident during the 1965-1971 period. The coefficient then trended downward in absolute value until 1978. A tendency to overpredict pork prices starting in 1971 was evident in the pork demand model, reaching the two largest overpredictions in 1977 and 1984. The recursive estimates of coefficients of the broiler inverse demand model indicate a structural break in the market demand for broilers starting in 1977. 8.2.2 gummary of Results of Alternative Specifications of Parameter Variation in the Inverse Demand Models The information on the timing of discontinuity in the parameters indicated by the recursive residual analysis is used in specifying the inverse demand models to explicitly account for the changes in demand parameters for the three commodities. The base demand model for each commodity is augmented by trend variables. One trend variable represents the trend from 1955-76 and another represents the turning point in the trend from 1977 to date. The trend variables are introduced to allow for gradual structural shifts in demand due to the hypothesized continous changes in tastes and health concerns. Since the model is linear in the variables, the coefficient on the time trend represents the rate of shift of demand in terms of annual prices given quantities and income. 319 An alternative specification allows for continous variation in the inverse demand parameters for beef, pork, and broilers by introducing Legendre polynomials in each of the parameters. Linear, quadratic, and cubic Legendre polynomial specification for the own quantity, quantity of substitutes, and income variables were- tested. The corresponding own-quantity, cross, and income flexibilities were estimated and analyzed for each commodity. In general, the results indicate that the null hypothesis of constant parameters of the inverse demand models for the three commodities can be rejected at the .01 level based on the F-tests. The own quantity flexibility for beef over time estimated from the Legendre polynomial models indicate flexible price response (i.e., own quantity flexibility is greater than one) to changes in beef quantity available for consumption, other factors held constant. The estimated income flexibilities for beef over time indicate a more than proportionate change in beef prices in response to a one percent change in real disposable income. As expected, the income flexibility estimates are positive. This is because prices move directly with changes or shifts in demand. A higher level of income is associated with a higher demand until a leveling off or saturation is reached where a certain percent increase in income will result in a less than proportionate increase in demand. 320 In contrast with the constant parameter inverse demand models for the three commodities, the varying parameter models with Legendre polynomials have better statistical properties. In particular, the Durbin-Watson statistics in the latter models indicates absence or reduction of serial correlation. The third alternative specification allows for continous variation in each of the demand parameters by introducing Legendre polynomials and also for possible abrupt shifts or discontinuity in demand by using the information indicated by the recursive residuals analysis regarding timing of start of structural change. Discrimination among alternative demand specifications is carried out based on the goodness-of-fit measures and relative parsimony characteristics. The Akaike Information Criterion and the Posterior Probability Criterion are employed to choose the most adequate specification of parameter variation. Based on both criteria, any of the models which allows demand parameters to vary over time is superior to a constant parameter model. The results also show that the value of the log-likelihood function is larger for constant parameter price models which are estimated using more current time series data. Using data for all 31 years to estimate demand without accounting for parameter variation reduces the value of the log-likelihood function by more 321 In contrast with the constant parameter inverse demand models for the three commodities, the varying parameter models with Legendre polynomials have better statistical properties. In particular, the Durbin-Watson statistics in the latter models indicates absence or reduction of serial correlation. The third alternative specification allows for continous variation in each of the demand parameters by introducing Legendre polynomials and also for possible abrupt shifts or discontinuity in demand by using the information indicated by the recursive residuals analysis regarding timing of start of structural change. Discrimination among alternative demand specifications is carried out based on the goodness-of-fit measures and relative parsimony characteristics. The Akaike Information Criterion and the Posterior Probability Criterion are employed to choose the most adequate specification of parameter variation. Based on both criteria, any of the models which allows demand parameters to vary over time is superior to a constant parameter model. The results also show that the value of the log-likelihood function is larger for constant parameter price models which are estimated using more current time series data. Using data for all 31 years to estimate demand without accounting for parameter variation reduces the value of the log-likelihood function by more 322 than half. The discrimination among the price models based on the goodness-of-fit and relative parsimony performance measures indicate superior performance of price models which allow gradual continous variation of the own-quantity and cross flexibilities and at the same time include an abrupt shift in demand sometime in the mid-1970s. The estimated own-quantity flexibilities for beef from models with varying parameters exhibit an upward trend (in absolute value) during the whole period. A structural break is indicated by larger fluctuation in the own-quantity flexibilities for beef starting sometime in 1977. The results indicate a significant positive response of meat prices to income changes. It is observed, however, that the relative magnitude of the income flexibility in the 1980s was lower than in the 1960s and early 1970s. The results also indicate increasing substitutability of poultry for beef as shown by the increase in the estimate of the cross-flexibility of beef with respect to poultry starting in mid-19703. The change in demand for beef appeared to result primarily from the shift in the relation between the price of beef and the consumption of broilers. Broilers has become a stronger substitute for beef beginning sometime in mid 19708. Also, the change in health concerns of consumers as represented by the trend shifters is associated with the 323 decline in beef demand. The own-quantity flexibility estimates for broilers tended to increase (in absolute value) over the entire period. A discontinuity is apparent sometime in 1973 when the own-quantity flexibility declined. After the decline in 1973, a continuous upward trend in the own flexibility estimates remained during the late 19703 and through the 1980s. Prices of broilers has become more responsive to income changes as indicated by estimates of income- flexibility. The price of pork has become more responsive to changes in the supply of broilers and real income starting in mid-1970s. 8.3 Conclusions and Implications of the Study Use of several statistical procedures suggest that structural change occurred about 1976-1977. While we can not be certain, we believe that structural change rather than model misspecification is the relevant explanation. Health concerns may be the cause but no sound data exists to permit testing this possibility. Given the current lack of data to permit analysis of specific causes of structural change, the three-stage approach offers some usefulness in determining the timing of change and pattern of variation in demand parameters. 324 A major conclusion of this study is the inadequacy of a constant parameter formulation for the demand for beef, pork, and broilers. Time varying parameter formulation of demand by using trend shifters and Legendre polynomials made a significant contribution over the constant parameter models. Trends and shifts in the U.S. market demand for meat have important implications for the meat industries. Evidence from the annual inverse demand analysis indicate that the shifts in demand are not only a result of changes in market variables (e.g.,quantities and income) but also due to non-market variables (e.g., changes in consumer attitudes toward meat and increasing diet concerns). Evidence of positive and high estimates of income flexibilities for beef, pork, and broiler imply a strong positive response of real prices to income changes. Future growth in real per capita disposable income can, therefore, be expected to continue to have significant positive effect on market demand for beef, pork, broiler, and turkey. The effects of non-market variables on as proxied by the time trend shifter variables indicate a negative impact of changing attitudes on market demand for beef and pork. Estimation results indicate an increase in the absolute value of own quantity flexibility for beef, pork, and broiler. The higher own quantity flexibility imply a larger percentage change in real prices brought about by a one percent change in quantity supplied. The higher own 325 quantity flexibility for the three meats has implications for price stability and price levels as the market structure change. Also, government programs on feed grains which indirectly affect livestock quantity, will now have a greater impact on meat prices. The use of varying parameter models for analysis and forecasting provided more accurate projections over the sample period than did the base model. This was indicated by both relative and absolute accuracy performance measures. The contribution of varying parameter specification in estimating demand and supply models is substantial and promising. Other causes of structural change, such as changing income distribution and changing demographic characteristics of the population are not explicitly analyzed in this study. However, the results of the study regarding the timing and magnitude of parameter change should prove useful for forecasting livestock production and prices and for policy analysis. By combining the information about the trends in physical and biological relationships in livestock production with economic variables in determining meat quantities, more accurate estimates of inventory and production are generated. 326 8.4 Recommendations for Future Research The inverse demand models in this study are specified and estimated as single equation models. The single equation specification only allowed the imposition of the single inequality restriction which constrains the own- quantity effects on price to be negative. Chavas (1986) points out that there is a strong bias against finding evidence of structural change if it occured by using a single demand equation. The demand system specification may be useful in further reestimation of the livestock model to examine structural change in demand. Under the demand system approach, testing of structural change involves the testing for the symmetry and negative semidefiniteness of the Slutsky matrix at all points. If the consumer preference function is not changing, these restrictions will be met at all points. If they are not satisfied, utility maximization is possible only if the preference function has changed. (Chavas, 1986, p.7). Chavas points out that this procedure has limitations because it assumes that the parametric form of demand correspond to the "true" demand function. The hypothesis being tested is actually a joint one, the theoretical restrictions and the null hypothesis regarding the functional form. The procedure does not allow the 327 differentiation of the two hypothesis. The application of the non-parametric methods suggested by Chavas (1986) and Varian (1982) merit some interest in future examination of structural change. This approach does not involve the ad hoc specification of functional form, and hence one can separate out the hypothesis regarding the consistency of the data with the assumption of utility maximization by testing the symmetry and negative semidefiniteness of the Slutsky matrix. Testing specific hypothesis regarding the cause of structural change offers advantages over the varying- parameter approach and may prove useful in future research in meat demand and reestimation of the livestock model. The present study provided some evidence that structural changes in market demand for meat can be attributed to both market (quantity and income) and non-market (changes in consumer attitudes towards meat and increasing health and diet concerns proxied by time trend shifter variables) factors. However, the time trend as a proxy for the non-market factors has severe limitations. A variable that captures consumers response to information regarding the ill effects of cholesterol may be tested. Combining available data with specific hypotheses about causes of structural change will be useful in understanding the recent changes in meat demand. Likewise, a more meaningful analysis of implications of such changes relevant to the meat industry 328 can be drawn. 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Rausser, ed., NewiDirectiona in Econgmetric Modeling and Forecastiagiin U.S. Agriculture, (New York: Elsevier North-Holland), 1981. “it“ r-"mr V 333 Reimund, D. A., J. Rod Martin, C.V, Moore, Structural Change in Aggicalture: The Experience gorigroileray Fed Cattle and Processing Vegetablgg. Technical Bulletin No. 1648 (April, 1981), ERS, USDA. Schweder, T., ”Some Optimal Methods to Detect Structural Shift or Outliers in Regression", Journal oiithe Americal Statistical Association, Vol. 71, Number 354, June 1976, pp. 491-501. Singh, B., A.L. Nagar, N.K. Choudhry and B. Raj, "On The Estimation of Structural Change: A Generalization of the Random Coefficients Regression Model", international Economic Reviay. Vol. 17, No. 2, June, 1976. Pp. 340-360. Surry, Y. and K. Meilke, "Incorporating Technological Change in the Demand for Formula Feed in France," American Journai of Agricultural Economics,(May,1982), pp. 254- 259. Yeboah, A. and E. Heady, Changes in Structural Characteriatigs and Estimataa oivSapply Responaa Elasticities in U.S. Hog Production, CARD No. 128 (April, 1984), Iowa State University. APPENDIX APPENDIX A Data Used in the Estimations .---------------------------------------------------------C----------------------.---------------------. .-----------COOCO-.----------------.------.-----------.-.-----.------..--.----------. ................... 23513.00 24434.00 25633.00 26589.00 27916.00 29763.00 31909.00 33400.00 33500.00 33770.00 34570.00 35490.00 36689.00 37878.00 38810.00 40932.00 43182.00 45712.00 43901.00 41443.00 38738.00 37062.00 37086.00 38726.00 39319.00 38081.00 37494.00 35370.00 10007.00 9613.000 10025.00 10796.00 11561.00 12470.00 12345.00 13619.00 15002.00 14436.00 15637.00 16591.00 17172.00 17331.60 18201.00 18251.00 18865.00 17532.00 16887.00 17259.60 19932.06 19563.02 19426.74 17895.14 17639.65 18229.98 17952.03 18471.00 18280.00 19098.70 3306.000 2797.000 3166.000 2830.000 2952.000 2809.000 3428.000 4263.000 4057.000 3593.000 3674.000 3795.000 3451.000 3619.000 3516.000 3707.000 4255.000 6413.400 5734.940 5422.980 4563.260 3365.860 3830.350 3830.350 4414.000 4589.000 5100.000 4749.000 A-2 1037.000 1440.000 1677.000 1085.000 942.0000 1204.000 1328.000 1516.000 1640.000 1816.000 1734.000 1960.000 1990.000 1615.000 1758.000 2005.000 1925.000 2322.000 2431.000 2085.000 1761.000 1939.000 1931.000 1823.000 1820.000 10027.00 10284.00 9579.000 9618.000 11131.00 10863.00 10730.00 11129.00 11863.00 12019.00 10736.00 11130.00 12377.00 12867.00 12774.00 13248.00 14606.00 13460.00 12578.00 13683.00 11314.00 12219.00 13051.00 13209.00 15270.00 16431.00 15716.00 14121.00 15117.00 14720.00 14721.00 154.0000 170.0000 177.0000 143.0000 174.0000 164.0000 162.0000 156.0000 242.0000 254.0000 149.0000 158.0000 164.0000 208.0000 260.0000 194.0000 .198.0000 236.0000 279.0000 204.0000 317.0000 421.0000 399.0000 421.0000 448.0000 406.0000 452.0000 365.0000 219.0000 311.0000 266.0000 3572.000 4217.000 4404.000 5005.000 5230.000 5144.000 5749.000 5789.000 6022.000 6195.000 6618.000 7198.000 7379.000 7422.000 7907.000 8465.000 8516.000 8887.000 8761.000 6915.000 8623.000 9751.000 9418.000 10129.00 11219.00 11357.30 11980.90 12174.70 12400.40 13031.70 13597.20 83.14902 86.86643 84.66836 81.42633 '82.41579 65.60237 66.93740 69.72435 95.67115 101.6994 101.0644 106.3167 108.2572 111.4267 112.3295 114.4490 113.6660 115.9670 109.6178 115.7659 117.7506 126.9154 122.1900 116.3009 105.2720 103.4457 103.6390 104.7373 106.6656 106.6935 108.0640 PKPC 60.98175 55.69704 55.51743 62.66590 60.44689 58.75084 60.19665 62.79261 62.94264 56.45307 58.00773 63.67506 65.37423 63.96364 66.05641 71.77062 65.56560 60.55430 64.64330 52.95106 56.26161 59.43997 59.67608 68.07670 72.79187 68.76254 61.91562 66.59560 65.56152 66.32472 POULPC 26.45678 30.63296 31.61922 34.55473 35.72513 34.92536 39.43579 37.97061 36.96070 39.65636 41.65731 45.13635 46.54475 45.00613 46.93675 49.71422 49.54228 51.43500 50.46506 50.67009 49.20522 54.16332 51.94611 54.93162 60.26660 60.52726 63.32244 63.26116 64.18000 67.11939 70.16650 A-3 DINC 2077.307 2121.622 2113.679 2106.545 2162.131 2163.765 2214.266 2279.250 2331.516 2457.461 2577.778 2679.013 2749.000 2626.295 2650.636 2902.637 2965.375 3066.635 3230.954 3159.763 3146.263 3212.317 3286.501 3386.434 3372.125 3254.457 3268.977 3243.514 3340.618 3621.544 3634.472 FBP 28.62843 26.94103 27.47331 31.25886 31.69530 29.19955 27.26563 29.71302 25.71428 24.12271 26.44444 26.45082 25.29000 25.78695 28.82149 25.24506 26.70239 28.55547 33.46356 28.36154 27.67370 22.93842 22.24793 26.78608 31.16375 27.13128 23.43268 22.24144 20.95174 21.06109 18.12733 21.86279 16.83047 20.71174 23.03695 19.19817 16.24577 19.15176 16.56512 16.77208 16.46009 22.55026 24.16667 19.37000 16.41651 21.59361 16.67360 15.21022 21.28492 30.25545 23.77793 29.97519 25.28446 22.62810 24.61576 19.54002 16.22366 16.31552 19.17503 15.96526 15.71061 13.66066 CHP 31.42145 24.07862 22.41993 21.36259 18.44215 19.05299 15.51339 16.77704 15.92148 15.26525 15.67302 15.74074 13.30000 13.62764 13.64335 11.69390 11.37675 11.25299 16.03156 14.55653 16.32134 13.54639 12.94766 13.51075 11.95952 11.26416 10.27749 9.304739 9.765523 10.76527 9.318866 37.65586 33.41523 27.75800 27.59615 27.37686 26.63565 21.09375 23.84106 24.31843 22.60495 23.49207 23.76544 19.60000 19.67370 20.40073 19.43250 16.21929 17.71748 26.70023 18.95735 21.56609 16.65103 19.55923 22.31320 19.41122 16.20746 14.11320 13.66309 12.23190 15.29582 14.86066 23:32:33:=2===:=::=:====:==::===:::=:::=:=:==:2222332322:32:33::=:=:====:=:=:==:=:==2:===:=: 1166.000 1495.000 1294.000 1351.000 1453.000 1515.000 1674.000 1670.000 1611.000 1606.000 1729.000 1772.000 1909.000 1933.000 1921.000 1604.000 2058.500 2023.000 2096.000 2344.300 2425.000 2573.700 2505.500 2633.700 2647.000 3037.000 EGGQT 5463.000 5517.000 5777.000 5680.000 5629.000 5704.000 5606.000 5742.000 5503.000 5466.000 5385.000 5376.000 5408.000 5606.000 5777.000 5606.000 5622.000 5798.000 5655.000 5708.200 5667.100 SOUFST A-4 SOUFFT 5687.000 6126.000 5639.000 5916.000 6096.000 5967.000 5525.000 5006.000 5810.000 5901.000 6130.000 5745.000 6676.000 6339.000 5973.000 5869.000 5476.000 4952.000 5650.000 6009.000 6396.000 7306.000 6629.000 6256.000 5610.000 6176.000 5856.000 5667.000 PPLS TPC 95729.00 176852.0 262066.0 374132.0 496975.0 529296.0 646991.0 748864.0 646504.0 675440.0 666351.0 1051236. 1191664. 1316170. 1330140. 1627424. 1664708. 1630368. 1674337. 1674660. 1494906. 1656690. 1981726. 2124288. 2569600. 2644720. 2534031. 2365292. 2701495. 2597560. 2666166. ====:=:================::==:::====:=:===2=:==::===2333388323833823==332323838233332333238233 BFCALF 21.00000 19.57000 23.36000 31.66000 32.65000 27.88000 27.77000 27.69000 27.02000 22.57000 23.70000 28.38000 26.00000 29.10000 32.89000 36.73000 36.84000 46.54000 59.73000 39.23000 29.48000 36.62000 43.60000 65.63000 97.66000 64.64000 71.69000 66.01000 66.65000 66.57000 70.50000 CHIKLE 1.550000 1.420000 1.310000 1.210000 1.090000 1.000000 0.910000 0.850000 0.770000 0.690000 0.660000 0.590000 0.540000 0.490000 0.430000 0.400000 0.360000 0.290000 0.260000 0.220000 0.200000 0.160000 0.140000 0.137000 0.135000 0.120000 0.120000 0.120000 0.110000 0.110000 0.103000 CORNPT 1.350000 1.290000 1.110000 1.120000 1.040000 1.000000 1.100000 1.120000 1.110000 1.170000 1.160000 1.240000 1.030000 1.060000 1.160000 1.330000 1.080000 1.570000 2.550000 3.020000 2.540000 2.150000 2.020000 2.250000 2.520000 3.110000 2.500000 2.680000 3.250000 2.650000 2.550000 A-5 SUYHPT 2.630000 2.370000 2.670000 2.790000 2.760000 3.030000 3.180000 3.560000 3.550000 3.610000 4.075000 3.940000 3.650000 3.710000 3.920000 3.930000 4.510000 11.45000 7.315000 6.540000 7.390000 9.990000 6.210000 9.500000 9.090000 10.91000 9.120000 9.360000 9.410000 6.500000 9.200000 PDPUS 165.9310 166.9030 171.9840 174.8620 177.8300 180.6710 163.6910 166.5360 189.2420 191.6890 194.3030 196.5600 198.7120 200.7060 202.6770 205.0520 207.6610 209.8960 211.9090 213.6540 215.9730 218.0350 220.2390 222.5650 225.0550 227.7040 229.6490 232.0570 234.2490 236.5740 237.0000 CPIT 0.802000 0.614000 0.643000 0.666000 0.873000 0.887000 0.696000 0.906000 0.917000 0.929000 0.945000 0.972000 1.000000 1.042000 1.098000 1.163000 1.213000 1.253000 1.331000 1.477000 1.612000 1.705000 1.615000 1.954000 2.174000 2.468000 2.724400 2.691000 2.964000 3.110000 3.220000 FWAGET 0.950000 0.970000 0.990000 1.010000 1.050000 1.060000 1.140000 1.230000 1.330000 1.440000 1.550000 1.640000 1.730000 1.640000 2.000000 2.250000 2.430000 2.660000 2.670000 3.090000 3.390000 3.660000 3.930000 4.100000 4.220000 5.470000 5.750000 obs GRTS 2789.000 2975.000 2577.000 2475.000 1946.000 2319.000 2700.000 2242.000 2726.000 2411.000 1557.000 1752.000 2486.000 2093.000 1982.000 GRTF 1684.000 2266.000 1921.000 1662.000 2162.000 1640.000 2128.000 2767.000 2169.000 2553.000 1949.000 2017.000 2020.000 1664.000 1892.000 A-6 SL865 SLBGF 555 55? TSLHG 44055.70 47709.41 2686.000 3157.000 96652.02 41335.68 42219.62 2303.000 2765.000 66946.62 36666.93 41445.62 2239.000 2304.000 85066.71 35646.91 37619.64 2257.000 3316.000 78567.73 36279.67 34460.22 1977.000 1946.000 74661.19 29111.14 32614.23 1505.000 2017.000 65265.42 35468.05 39565.71 2023.000 2212.000 79376.26 38785.32 37930.16 2006.000 2073.000 60503.81 36740.73 43076.42 1965.000 2662.000 66935.36 44675.66 45396.69 2585.000 2670.000 95466.23 45387.96 41505.50 2347.000 2464.000 91554.76 40155.65 37540.60 2176.000 2021.000 61794.63 37873.86 40753.64 1850.000 2742.000 63473.77 42660.98 40799.00 2063.000 2355.000 67954.78 36491.19 38785.60 1916.000 2109.000 60806.23 ADUHG 156.0000 159.0000 164.0000 166.0000 165.0000 166.0000 170.0000 171.0000 172.0000 171.0000 173.0000 173.0000 173.0000 173.0000 174.0000 -1.000000 -0.933333 ~0.866667 -0.600000 -0.733333 -0.666667 -0.600000 -0.533333 -0.466667 -0.400000 -0.333333 -0.266667 -0.200000 -0.133333 -0.066667 0.000000 0.066667 0.133333 0.200000 0.266667 0.333333 0.400000 0.466667 0.533333 0.600000 0.666667 0.733333 0.600000 0.866667 0.933333 1.000000 0.606667 0.626667 0.460000 0.306667 0.166667 0.040000 -0.073333 -0.173333 -0.260000 -0.333333 -0.393333 -0.440000 -O.473333 -0.493333 -0.500000 -0.493333 -0.473333 -0.440000 -0.393333 -0.333333 -0.260000 -0.173333 -0.073333 0.040000 0.166667 0.306667 0.460000 0.626667 0.606667 1.000000 -1.166667 -0.766099 -0.435901 -0.165333 0.046346 0.209676 0.324000 0.395457 0.426986 0.429333 0.401235 0.349432 0.276667 0. 193679 0.099210 0.000000 -0.099210 -0.193679 -0.276667 -0.349432 -0.401235 -0.429333 -0.428968 -0.395457 -0.324000 -0.209876 -0.048346 0.165333 0.435901 0.766099 1.166667 A-7 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 73.00000 74.00000 75.00000 76.00000 77.00000 78.00000 79.00000 60.00000 81.00000 82.00000 63.00000 84.00000 65.00000 0.000000