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This is to certify that the thesis entitled PRICE RELATIONSHIPS AMONG SELECTED WHOLESALE BEEF AND PORK CUTS presented by Duane Hacklander has been accepted towards fulfillment of the requirements for Ph.D. degreein Agr'CU'tura' ECOHOM‘CS Date May 7. 1971 0-7639 ABSTRACT PRICE RELATIONSHIPS AMONG SELECTED WHOLESALE BEEF AND PORK CUTS by Duane Hacklander This study focused on explaining and predicting monthly beef and pork cut price fluctuations at the wholesale level where the storage mechanism is used in conjunction with exports and imports to alleviate short-run supply and demand maladjustments. Several approaches were utilized in analyzing the price variations. The objective of Model 1, consisting of 20 simultaneous equations, was to obtain realistic structural coefficients which explain recent monthly price level fluctuations for the wholesale cuts. An alternative way of examining whole- sale cut price behavior.was to determine the relevant explanatory variables explaining the relative behavioral relationships among the wholesale beef and pork cut prices (Model II). Two ”margin" approaches were used in Model III to analyze the relative relationships between the wholesale cut prices and live steer or hog price. The short-run forecastability of monthly beef and pork wholesale cut prices was also briefly analyzed. As expected, beef quantity was inversely related to the wholesale beef cut prices but the arm chuck price was found to be less flexible to quantity changes than beef loin and rib prices, contrary to expectations. Round price was Duane Hacklander found to be relatively inflexible with respect to ”income" while rib price was the most flexible of the beef cuts. Calculated price flexibilitles with respect to quantity for the wholesale pork cuts were generally slightly more flexible than for the beef cuts. Belly price, in particular, was very responsive to quantity changes indicating its rather limited use as bacon for which substitutes are presently limited. Compared to pork, beef generally appeared to be a more prestigous item which consumers favored purchasing when their ”incomes” increased. The estimated positive quantity coefficients suggested complementarity between belly price and beef quantity and between wholesale pork cut prices and poultry quantity. Beginning pork storage levels were inversely related to pork cut prices while the change in pork storage was gen- erally directly related to pork prices. In the beef supply equation, producers appeared to look at current price levels as a sign of continued future trends. Hog producers appeared to interpret change in live price as a short-run price trend which they expected to continue, and adjusted their marketings accordingly. In the supply equations, the expected shift in response from the heavier weight inventory groups in the quarterly report month to the lighter weight groups by the second month following the quarterly report month was not always found. In the beef wholesale cut price ratio equations, the Duane Hacklander suggested relative price flexibllities with respect to quantity and ”income” were not consistent with the cal- culated flexibilities in the simultaneous equation model. Likewise, the suggested relative price flexibilities in the pork price ratio equationsshowed some inconsistencies with the calculated flexibilities in Model I. Both beef and pork quantity coefficients were signi- ficant in the equations relating beef cut prices to pork cut prices. The ”income" coefficients were generally positive suggesting somewhat higher "income” flexibilities for beef relative to pork, consistent with the Model I results. Relative to the wholesale beef cut prices, the response of steer price to beef quantity levels was proportionally more in the price ratio equations but was less in terms of cents per pound in the price difference equations. Steer price responded proportionally more to changes in the ”income” level than wholesale prices but less in terms of cents per pound. In the equations relating wholesale pork cut prices to live hog prices, the significant responses to the hog quantity variable were similar to the responses between beef quantity and wholesale beef cut prices. Beef quantity levels were a relevant explanatory variable in the pork cut/ hag price ratio equations. The "income” variable was only of limited importance in explaining the differences between wholesale pork cut prices and live hog price. Duane Hacklander A seven month trial forecast period was used to evaluate the usefulness of the forecasting equations in which forecast prices were compared to actual prices. Usefulness of the forecasting equations may have been obscured by the fact that somewhat atypical sharp price fluctuations occurred during the trial period. The mean absolute percentage error ranged from 2% to 8% for the nine forecasting equations. Direction of price change was forecast correctly all seven months for one cut and only missed one month for three others. But, for four cuts the directional price change was correctly forecast only four of the seven months. PRICE RELATIONSHIPS AMONG SELECTED WHOLESALE BEEF AND PORK CUTS it BY lycro': DuanelHacklander A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 1971 ACKNOWLEDGMENTS First and foremost, I am grateful to my wife, Effie, who typed and edited several drafts of the manuscript. The author is indebted to Dr. Marvin Hayenga, chair- man of the thesis committee, for his counsel and guidance throughout the development of this dissertation. I would also like to thank Dr. Harold Riley, my major advisor, and Dr. Lester Manderscheid who read the manuscript and made several helpful suggestions. Appreciation is owed the MED, ERS, USDA for making the transfer to MSU possible to undertake this study while completing necessary coursework. Particular thanks goes to Dr. Richard Crom. The faculty and fellow graduate students at MSU are owed a special thanks for making graduate study a rewarding experience. ii TABLE OF CONTENTS ACKNOWEDGMENTSOOOOCOOOOOOOOOOOOODOOOOOOOOOI0.... " LISTGTABESOOOOOO.OOOOOOIOOOOOOOCOOOOO 000000 .0 v Chapter 1. PURPOSE AND APPROACH 07 STUDY........... 1 Introduction....................... 1 Literature of Related Studies...... 2 PrOb'emOOOOOOOOOOOOO00.000.000.000. 11 ApproachOOOOOOOOOOOOOOOO0.0.0.0000. 12 II. ANALYTICAL PRmEDUREOOCCCCOOOO0.000....C 1? Model I - Simultaneous Equations... 17 Model 11 - Cut/Cut Price Ratio Equations....................... 30 Model III - Wholesale Level to Live Level Equations............ 33 Forecasting Equations.............. 35 Estimation Procedures and Data Sources......................... 35 ~/III. ESTIMATED COEFFICIENTS FOR THE SIMULTANEOUS EQUATIONS (Model I)..... 43 Wholesale Demand Equations......... 43 BeefCOCIOOOCOCOOCOOOOCOCCCCO.... 43 Pork...........O'COOCCCCCOCOCOO. 52 supp'y Equat'onSOeeeeeeeeeeeeeeeeee 59 Change in Pork Storage Equations... 67 summaryOOOCOC0.0COOOICCOCCOOOQ..C.. 69 IV. FACTORS AFFECTING RELATIVE BEEF AND PORK WHOLESALE PRICES (Model II)..... 74 Beef/Beef Wholesale Cut Price Ratios 7S Pork/Pork Wholesale Cut Price Ratios 84 Beef/Pork Wholesale Cut Price Ratios 98 SummarYCCOOOOOOOOOCODOOO0.000000... 107 iii V. RELATIONSHIPS BETWEEN WHOLESALE AND LIVE PRICE LEVELS FOR BEEF AND PORK (Model III) 111 Wholesale Beef Cut Prices Relative to Live Steer Price.................. 112 Wholesale Pork Cut Prices Relative to Live Hog Prices................... 120 Summary... ....... ........... ............ 127 VI. FORECASTING EQUATIONS............. ........... 129 RoundSOOOOO...000......OOOOOOOQOOOOOOOOO 13“ Arm ChUCRseooeeeeeeeeeeoeeeeeeeoeeeeeeee 1)“ Beef 'o'nseoeeeeeeoeeeeeoeeeoeeeoeeeeeee 136 RibsOOOOOOOOOOOOOOO.OOOOOOOOOOOOOOOOOOOO 1}? Hams...IOOOOOOOOOOOOO.OOOOOOOOOOOOOOOOOO 137 Be.I'eBOOOOOCOOOOOOOOOOOOOOOOOO...COO... ‘39 Pork lolns.............................. 139 P'cn'C80000000COOOOOOOOIOOOOOOOO00...... 14‘ BUtt800000OOOOCOOOOOOOOOOOOOOOOOOI.00... ‘41 summarYCOOO000.000.00.000...0.0.0.000... ‘44 VII. CONCLUSIONSOOOOOOOOOOOOOOOOOOOOOOOOO0000O... 1A5 LITERATURE CITEDOOOOOOOOOOOOOIOOOOOOOOOO00.00.000.000. 149 iv LIST CF TABLES Table Page 1. Estimated coefficients, coefficients] standard error,"R2", asymptotic Durbin- Watson Statistic for the Model I Equations normalized on wholesale prices........... 46-47 2. Price flexibllities with respect to quantity and ”income" for beef and pork wholesale CUts.OO0.000000000000000...00.00.000.000. 48 3. Estimated coefficientg, coefficients/ standard errors, ”R ”, asympotic Durbin- Watson test for the Model I normalized SUDDIY equations......................... 61-62 4. Estimated coefficientg, coefficients/ standard errors, "R ", asymptotic Durbin- Watson tests for the Model I equations normalized on change in pork storage..... 68 5. Ordinary least-squares estimated coeffi- cients and related statistics for the beef and pork forecasting equations...... 131-132 6. Forecast and actual round prices, actual and percentage errors, June - December, 1%90000COCO...0.0.000...0.00.00.00.00... 135 7. Forecast and actual arm chuck prices, actual and percentage errors, June - DECEMDGI‘,1969.............o............. 135 8. Forecast and Actual beef loin prices, actual and percentage errors, June - December,1969.....OOOOOOOOOOOOOOIOOOOOOO 138 9. Forecast and actual rib prices, actual and percentage errors, June - December, 1969. 138 10. Forecast and actual ham prices, actual and percentage errors, June - December, 1969 140 11. Forecast and actual belly prices, actual percentage errors, June - December, 1969 1&0 12. 13. 14. 15. Forecast and actual pork loin prices, actual and percentage errors, June - December, Forecast and actual butt prices, actual and percentage error, June - December, 1969........ Number of correct forecasts of direction of change for the wholesale price estimates, the probability of getting as many or more correct forecasts by chance alone, and the mean absolute percentage errors, June 1969 - December 1969........................ vi 1969... Forecast and actual picnic prices, actual and percentage errors, June - December, 1969....... 142 142 1A3 143 CHAPTER I PURPOSE AND APPROACH OF STUDY n r ct on Meat plays an important role in the United States economy. The amount of a consumer's food dollar spent on meat typically ranges between 20 and 25 percent. Consumer groups protesting high food prices usually single out meat prices, especially beef, for special criticism. Likewise, livestock production plays a major part in the agricultural sector. In 1969, cash receipts from the sales of cattle and calves amounted to 12.5 billion dollars or 26.5 percent of the cash receipts from all farm marketings.' The 4.7 billion dollars receipts from the sale of hogs accounted for 9.9fi of farm cash receipts. Fluctuations in meat prices are a major concern to producers, meat packers and processors, retailers, and consumers. The explanation and anticipation of the price levels, as well as the relative differences among farm, wholesale, and retail price levels, have a pro- nounced impact on the profits and competitive position of the participants in the meat industry. Concern expressed over changes in meat prices is evidenced by 1 Obtained from the Farm Income Estimates Section, Economic and Statistical Analysis Division, ERS, USDA. -1- an influx of inquiries to the U.S. Department of Agri- culture about the cause of the change. Responses to the inquiries are usually made in terms of the live to retail price spread, or in terms of the recent changes in the retail price relative to the changes in the live price. This study was designed to focus on monthly wholesale price levels for beef and pork and their relationship to supply levels and live prices. The U.S. Department of Agriculture could use results of this study in their ongoing price spread analysis. Further, the results would be helpful in policy analysis, such as the effect that beef import changes would have on beef prices. The results of this study may be useful to relatively small wholesalers, packers, or retailers who don't have access to a research department. It may pro- vide guidelines to the relative effects of the different market factors on wholesale price levels which they can expect. In addition, other analysts of the market for meat products may find it informative. r R l d Studie Analyses of wholesale meat price behavior are practically non-existent in the literature. An exception to.this vacuum is a bulletin by Maki titled, Egnggagglgg c l n P r - . (so)1 Maki 1 Numbers in brackets refer to References Cited, pp 149 -3- used the wholesale market as the central level in price determination. The results of his analysis indicated that beef quantity had a significant effect on the beef wholesale price variable while pork quantity, disposable income, and linear trend coefficients were not signifi- cantly different from zero at the .01 level. For the wholesale pork price equation both beef and pork quantities, as well as disposable income, appeared to have a signifi- cant effect. Recently several theses dealing with beef and pork prices using monthly data have been completed. A master's thesis by George H. Hoffman dealt with a short run price forecasting model for beef (14325). Hoffman dealt pri- marily with the live level but he did devote a small section to looking at wholesale prices. In a table showing the two month predictive equations for a five market wholesale price of beef it was evidenced that the only predictive variable used was a lagged price variable in all months except November, where an index of prices received for feed grains and hay in the U.S. was also used. A lagged 5 market wholesale price was the most prevalent of these lagged price variables. The R2 for these equations varied from .23 in September to .85 in November. Another master's thesis dealing with farm level demand for slaughter cattle using monthly data was done by Prato (22:23). Prato's statistical model consisted of four equations--demand, supply, and stock holding relations and a market clearing condition. Again, as in the previous study, equations were fitted for each month. Two-stage least-squares techniques were used to estimate the monthly demand fuctions in the model. In order to minimize the number of variables in the equations, all data were adjusted by population and the price level prior to the computational analysis. After adjustment for population, the demand relations were expressed as the price received by farmers as a function of per capita volume of slaughter cattle, per capita cold storage holdings of beef, and per capita income. In the actual variate form of the model the quantity coefficients were significantly different from zero at the .01 level of probability, the personal income variable was significant at the .05 level, except for January, while the cold storage holdings of beef coeffi- cient was significant for only six months (February-June and August). Using a model of eight behaviorial equations and two identity relationships, Myers, Haviicek, and Henderson analyzed the monthly structure of the hog-pork sector (21).1 1 Based on L. H. Myers Ph. D. thesis at Purdue. -5- The normalized dependent variables for the equations included monthly supplies of live hogs and cattle for slaughter, farm-retail margins for beef and pork, monthly supply of pork for consumption, and monthly demands for pork, beef, and broilers for consumption. With ten jointly determined variables in the model, the two-stage least-squares method of estimation was used. For the live hog supply for slaughter equation, live hog price was found to have a negative, but signi- ficann, influence. The other explanatory variables included in the equation were an inventory of live hogs on farm, interest rate, price of corn, a measure of cyclical production patterns in hogs, and a linear trend variable plus eleven monthly dummy variables. The coeffi- cients of the interest rate and cyclical production patterns variables were smaller than their standard error. Similar variables were included in the live cattle supply for slaughter. Again, the negative relationship was found for live cattle prices. These negative relationships led the authors to conclude that in short-term decisions the response to expected prices was greater than to current prices since current prices are a component of expected future prices. The equations for retail pork and beef demand equated per capita consumption of pork and beef with the retail prices of beef, pork, and chicken, disposable income and eleven monthly dummy variables. The only insigni- ficant coefficient resulted for the price of chicken variable in the retail beef demand equation. The signs of the coefficients were consistent with a prion! expectations. Another recent thesis by Bullock included a monthly price forecasting model for slaughter cattle. (3) ,Since the emphasis was on forecasting, the model was set up with some structural simplications and fitted by ordinary least squares. The model was concerned with the price forecasts by months up to 12 months in advance for 900-1100 pound Choice grade slaughter steers at El Centro, California. Slaughter cattle price was fitted as a function of projected marketings of fed cattle for flee regions and lagged slaughter cattle prices. Leuthold shortened the time period for analysis to a daily basis (17:18). He found that daily prices offered for slaughter hogs responded very little to daily changes in quantity. Quantity supplied was a factor though in influencing prices for three consecutive days. Wholesale prices of pork cuts from the previous day affected the buyers' bid price for live hogs. The price was also in- fluenced by the day of the week. The terminal market supply of hogs was found to be extremely responsive to the change in live price. The day of the week was also found to influence the producers' marketing decisions. -7- In a study utilizing retail price cut data, Riley utilized consumer panel data of weekly prices and quan- tities from July 1951 to June 1953, to obtain some measurements of consumer demand for meats (24). He found that, during a period of rapidly declining prices, the price elasticities of demand were inelastic for ground beef, slightly elastic for beef roasts, and highly elastic for steaks. For selected pork cuts the demand for pork chops and ham was found to be elastic while the demand foo bacon was slightly inelastic. Also it was found that the demand for some of the fat pork cuts may shift considerably from winter to summer. The lagged response of selected pork cuts was studied by Snell (28). He concluded that there was no lag be- tween farm and wholesale prices on a weekly basis. For farm to retail a one week lag was evidenced. These con- clusions were drawn from fitting, individually, wholesale loin and butt prices and retail pork chops and pork roast prices as a function of live hog price and beef and pork quantities. Then the explanatory variables were lagged up to three months. For the wholesale cut prices the best fit in terms of variance explained (R2) occurred in the same time period. For the retail prices the best fit occurred in the 't-i' time period. Snell found no dif- ference between an upward or a downward price movement. The related lagged price response of retail prices to changes in price direction at the live level on a monthly basis has been reported in two USDA bulletins dealing with price spreads for beef and pork (2:4). The lag was observed for periods of increasing and decreasing prices as well as for both the beginning and end of a period. The lag of the retail beef prices to a change in direction of live steer price for the beginning of a period of increasing prices (or end of a period of de- creasing prices) averaged out to be .9 months. The leg for the end of a period of increasing prices (or beginning of a period of decreasing prices) was .6-.7 months. For pork the retail lag averaged about .9 months for both the beginning and the end of the periods. Probably the most influencing factors on this study were prior analyses done by Hayenga and Hacklander. These analyses incorporated many of the ideas brought forth from the review of related studies. The prior analyses con- sisted of two parts, the first being primarily concerned with forecasting techniques by months for live steers and bags (12) while the second part was concerned more from a structural viewpoint with possible simultaneous effects between supply and price for steers and hogs at the live level (11). The forecasting part was completed first. Variables chosen for the forecasting equations were included not only -9- on their ability to improve the forecast but also because of their reasonableness. Consequently the variables used in the forecasting equations were also incorporated into the behavioral model used in the second part of the study. The review of the study shall be focused primarily on the second part. A behavioral model of the live level for beef and pork consisting of five equations was developed and fitted using two-stage least-squares techniques. The endogeneous variables in the model were the live prices of steers and hogs, changes in pork storage levels and commerical beef and pork production. Steer and hog prices were negatively responsive to their own supply levels and positively responsive to per capita income levels. Choice grade steer prices were also affected by the quality composition of the supply as well as the competittveusunply level of pork. Hog prices were influenced by both the absolute level of pork storage and the change that occurred in the amount of pork stored during the month. The effect of beef production on hog prices resulted in an unexpected positive relationship. This result may have been a spurious statistical result or might conceivably be attributed to consumers' desire to maintain some variety in their meat purchases with high levels of beef consumption. Change in pork storage (beef storage was a very minor item) levels were found to be influenced by the storage level at the beginning of the month, the quantity of pork produced, and the live hog price. Slaughter levels of beef and pork were fairly well explained by cattle and hog inventories on farms by weight categories plus recent price behavior. Live price monthly changes appeared to affect the cattle and hog producers' expectation of future price changes differently. Hog producers appeared to expect an upward price movement to continue for some finite period; thus, they held back their production from the market. Cattle producers appeared to view an upward price movement in this month as an indication that it would fall during the next period; thus, the quantity they supplied for slaughter increased. Several other studies provided a good background framework to the development of demand and supply analysis for livestock. These included: Ihg Analysig of Qemgng fgr Egcm Products by Karl A. Fox (7), A Statistical Study of Liyestogk Pgoggction and Mggkgting by Hildreth and Jarrett, (13) nggnd for Meg; by Elmer J. Working (42), m n n P fo Me -F c o nfluen n Th fligtggicg! ngelogmgn; by Harold Breimyer (1), Eagtgrg Affecting the Pnigg and Suggly of Hogs by Arthur A. Harlow (10), and nggnd and Price Analysis by Fred Waugh (41). All of these studies were somewhat peripheral to this study because they focused at either the live or retail levels and used annual data. -11- Pcoblgm The related literature pointed up the gap in published research between the live and retail levels for monthly beef and pork prices. Literature has recently been forthcoming dealing with monthly demand and supply relationships at the live and retail levels, but not at wholesale level. Another gap found was the lack of studies dealing with behavioral relationships for beef and pork prices on a cut or primal basis, especially using time series data. The problem focus of this study is to fill, to some degree, these gaps at the wholesale level. Objectiyeg This study focuses on explaining and predicting monthly beef and pork price fluctuations at the wholesale level where the storage mechanism is used in conjunction with exports and imports to alleviate short run supply and demand maladjustments. This study endeavors to broaden the usual scope by focusing on individual wholesale beef and pork cut prices instead of average prices for all beef or pork wholesale cuts. Relationships among in- dividual cuts as well as the live and wholesale cut price levels will be analyzed. More specifically the objectives of this study are to: 1. Determine factors affecting monthly demand and supply for selected wholesale cuts of beef and pork. 2. Estimate selected monthly beef and pork wholesale cut demand and supply relation- ships. }. Analyze monthly price relationships among the selected wholesale cuts. 4. Analyze monthly live-wholesale price relationships. 5. Tentatively assess the forecastability of prices of selected cuts of wholesale beef and pork for several months in advance. AEEFOQCH Monthly wholesale price levels over a recent time period, January 1962 ~ May 1969, are graphically presented for selected beef and pork cuts in Figures 1 and 2. A wholesale price analyst must not only concern himself with explaining and forecasting the monthly fluctuations but also must consider the divergence between cut prices as well as between price levels. The general price patterns of the wholesale pork cuts were similar, but there were differences in the price change magnitude and the month when changes began. Sometimes, during short-run periods, prices of cuts actually moved in opposite directions, for example, from July to December 1968 pork loin price fell while the price of hams rose. The wholesale beef cut price patterns showed slight divergences between cut prices. With a general price pattern of increasing prices, the higher- price beef cuts increased at a faster rate than the lower- price cuts. -13- ._ 0&4...“le St . .3: _ S: . .2: _ 13: _ it _ 3t . as: . >_r_——______p______'P_._._..._.._...p..L.._.r_L__....»._L_.LL|»_._—C_~_.FLFF._.__...L_L_LF MN: m a so. s so up . w e p r p p e r be r Perm r? r1 p pp ' p meow e P e r, p v» pp p or u w.. a up; bbhu or» b b ’9 D p w e vhm a\ D pp 31540 fit 9 w who uh ’ D D P + S + ++ ++ r ++ .+ o o r +0 + + + + + 1 e o $++ a .« +r+ ++++ + + + .a ..+o. + + +4 a ++ . o. + + + b * + + + 0 ++ I + + O O. + 00 I O 0. ”0+ m + ++ ++ . .. . ++ + +1 ++ O 0 O C + H. O 9) ++ I? e 0 find.“ we 0 a O O / If 0+ 0 0' a 0" O O O. ,0. It a e 00 a so 0 J.M e e e e e l 7 O O O ‘“ x e K K O x xx .. a K x K x X X Xx In» A x I xx ‘ V“ K x e «A K x X {X x xx x XX X ‘ x . (lies/x Xi (it! X X XX x X 1% (4.. 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TM“ r. «x p pp e .- o p it“. . a. .. x . . xxx x ’. 0 O X e pwx (x xxx e p» or o p w. haunt . .. n. 13.. n e xx u. x at» e a . x. . xx u 1 o XX 0 e a ‘ co § 0 X .4 4) IX XO 00 O X *X * ’ * ‘ O ‘*4‘. f‘ e f X 0 ‘0 ’ ‘ O / so a e C ‘ ‘ 4 ‘ lhn 00 x e K . + + 4 e I e + + + ‘ l x . x . + + + 4 7 C O O *+ + ++ 1* fl ‘ O 1’. o . + . x ¢¢4( + + ++ ++ + 4 . . + to as. 4 . x .4 < 4 a 1.4 . «+13. ‘ + so + ‘ + 4 3.. { + + o o Liar} 4+++ « C «3.4+... c 4 x . x x x .r 4 L. « + + + +.+ fife o +4.»... < 1 + d 1.3.. +4 + ‘ 4. *‘ + C +‘ ‘ ‘ ‘ ‘ + * .X to +4. ‘. e 4 L. + x1. 1. 25 4 4 1 L. luh ( +4 Weld ll+ 1 T3 I... -15- To fill the gap in the lack of published research analyzing beef and pork wholesale prices, the problem is approached in several ways. A simultaneous equation model will be formulated containing the behavioral whole- sale demand and supply relationships envisioned for beef and pork. An alternative analysis of wholesale cut prices focuses on the relative relationships among the wholesale cuts. Relationships between the live and wholesale cut price levels are also examined. Finally, the feasibility of forecasting wholesale cut prices will be tentatively assessed by estimating, by least squares, the wholesale cut price equations in the simultaneous equations model, and using the resulting coefficients in forecasting prices for the next seven months. By comparing actual and fore- cast prices the usefulness of these forecasting equations can be tentatively assessed. The following chapters are organized for reporting the procedures used and the results obtained to the dif- ferent approaches. Chapter II will be concerned with the presentation of the analytical procedures used for the selection of the relevant variables and the construction of the behavioral relationships in the study. A brief description of the criteria used for the selection of the major wholesale cut prices and their price fluctuations over the period covered in this study will also be included in Chapter II. The estimated coefficients, and their -15- implications, of the simultaneous model will be reported in Chapter III. The behavioral relationships among the wholesale cuts will be presented in Chapter IV, while Chapter V will contain the estimated coefficients of the relationships between the wholesale cuts and the live price levels. Comparisons of forecasting results with actual prices over a short-run time span will be under- taken in Chapter VI. Chapter VII, a ”Conclusions" chapter, will draw together the major findings of the study relative to what has been found in prior analyses and also point out possible further research areas. CHAPTER II ANALYTICAL PROCEDURE Several approaches are utilized in analyzing the price variations for the wholesale beef and pork cuts. Since the focus of these approaches varies, the following discussion is broken down accordingly to deal with: i) explaining monthly beef and pork wholesale cut price behavior--Model I, 2) explaining changes in relative wholesale cut prices--Model II, 3) explaining live and wholesale price ratios and differences-~Model III, 4) equations for short-run forecasting, and 5) estimation procedures and data sources. M - mult n ous a ns The objective of Model I is to obtain realistic structural coefficients which explain recent monthly price level fluctuations for the wholesale cuts. The supply and demand structure thought to be the basic underlying cause of observed price behavior was care- fully studied, and the variables which were quantifiable and consistent with the expected underlying structure are incorporated into the model. Model I utilizes live and wholesale cut prices, commercial production, and change in storage levels of pork cuts as endogenous variables. Referral to the functional description of Model I on pages 27-29 may aid in following the upcoming -17- -18- discussion of the relevant behavioral relationships. Seemingly, prices which wholesalers offer for beef and pork cuts would be strongly influenced by the current commercial production of that cut.1 Total commercial production is used to represent these quantity factors since published production data for each out were not available. Substitution of total production variables for individual wholesale cut production variables was done under the assumption that the carcass proportions and cutout procedures remained approximately the same over the period studied. Because the number of days, weekends, and holidays differ between months, the monthly commercial production figures are divided by the number of packer workdays in each month. Commercial production divided by workdays for each month provides a more standardized index of the quantity pressure affecting wholesale cut prices during each month. The particular workday variable selected resulted from looking at data for daily volume of federally in- spected beef and pork slaughter for the region including 1 Commercial indicates that both federally and non-federally inspected production are included. Production, used here, indicates that the data are in terms of carcass weight and not live weight. -19- Chicago from July, 1966-January, 1967.1 The average percentage of slaughter being done on each weekday was similar for both beef and pork. Variation between the days from Monday through Friday was minor, so these week- days were simply assigned equal weights of 1 unless a holiday occurred.2 Slaughter occurring on Saturday appeared to be about one-third that of the other weekdays and thus was weighted 1/3, unless a holiday. The influence of holidays was noted by assigning a weight of 1/2 to that day when it fell on Monday through Friday, since it appeared that there was a slight slaughter increase on the other days during a week with a holiday. When the holiday fell on Saturday no slaughter increase during that week was noted. Consequently, Saturday received zero weight when a holiday. The price quoted for aiaingle grade of beef, Choice, is used for this analysis, therefore another factor to consider is the substitutability among the different grades of beef. Since total beef production includes all grades 1 Actually three different versions of the weighting procedure were tried at the live levgl and it was found that the explan- atory power, in terms of R , of the selected version was better than the version which did not weight holidays and differed only slightly from the most difficult version to compute using the actual average percentages. 2 Holidays: January 1, May 30, July 4, Labor Day, Thanksgiving, December 25. of beef, a modifying variable is incorporated into the normalized equations for beef prices to account for monthly variations in the quality composition of the total beef production variable. The variable incorporated is the percent of the total federally inspected beef numbers consisting of cows. One would expect that an increase in the percentage of total slaughter made up of cows would reduce the relative supply of beef which most strongly competes with and affects the price of Choice grade beef. The positive relationship between Choice grade beef prices and percent cows is expected to be stronger for the higher- price cuts relative to those cute more competitive with lower quality beef products. Beef and pork production may be placed into storage for later consumption if price increases are expected. Storage data are published for individual wholesale cuts for pork, but only on an aggregate basis for beef. During the period, 1962-1969, only a small amount of beef was frozen or cured and stored. The corresponding small storage volume variation from month to month of individual beef cuts probably has had little impact on beef cut prices. Because of its presumed insignificant impact, storage variables are not incorporated into the wholesale beef equations. Pork products were stored in greater volume than beef and exhibited substantial variations among months. Pork -21- storage volume is reported for each wholesale cut at the end of each month, or conversely, the beginning of the next month. Both the volume of a particular pork cut stored at the beginning of a month and the change in storage during the month are expected to influence whole- sale pork prices. If the quantity stored of a particular pork cut is relatively high at the beginning of the month, the relative wholesale price of that cut would probably be depressed because of the threat (or actual movement) of this quantity moving onto the market. If storage levels are low, wholesale pork prices probably are relatively higher because of the demand to increase the storage levels and the lack of threat from high storage levels. Changes in storage levels during the month influence wholesale pork prices by affecting the total quantity of pork moving in or out of the wholesale distribution channel. Changes in storage levels during the month may also be a reflection of anticipated prices which in turn are related to current prices. Two other variables which would affect quantity directly are imports and exports. Here again data were reported by species, but not by cuts. Neither pork imports nor exports influenced total pork production much in recent years. The percentage of pork production imported in 1969 was 3 per cent while the percentage of production exported was 2 per cent. (35) Further, these flows remained fairly -22- constant throughout the years under consideration. Since pork export and import variations seemed to be of minor importance in the pork supply picture, they were eliminated from consideration in the wholesale pork price equations. Beef exports were a very minor factor in relation to commercial production (1969 beef exports/1969 commercial beef production a .004) and remained fairly constant through- out the recent years. Thus, beef exports were eliminated from further consideration in the wholesale beef price equations. Beef imports appeared to be somewhat more prominent in the supply picture (1969 beef imports/1969 commercial beef production - .08). Also there tended to be more month to month variation within a year than was evidenced for beef exports and pork imports and exports. Thus, beef imports are included in the beef price equations to assess their impact on wholesale beef prices. The supply of substitutable commodities is another major factor expected to affect the price offered for wholesale beef and pork cuts. Competition between beef and pork would be expected to be important as they are the major red meats consumed in the U.S. Thus, both beef and pork production per workday are included in each whole- sale beef and pork price equation. Poultry consumption and production has increased in recent years to a point where it might have a fairly strong competitive impact on both beef and pork; thus, a poultry production variable is -23- included in the wholesale price equations. The main components of poultry production are turkey and chicken. Since chicken production may have an impact different from the more seasonal turkey production, both chicken and turkey production variables are included in wholesale beef and pork price equations. The primary factors expected to influence the demand for each wholesale cut are prices of closely competitive products. Reality and theoretical considerations dictate that the wholesale price of one individual cut is deter- mined simultaneously with the prices of other cuts of that species and cuts from closely competing species. A case might also be made for simultaneity between poultry prices and wholesale beef and pork prices since poultry production has been suggested as a likely explanatory factor affecting beef and pork prices and vice versa. However, it was assumed that the current beef-pork influence on monthly poultry prices is small relative to other factors; therefore it was ignored. Other factors expected to influence the demand for meat at the retail and, correspondingly, the wholesale level are population and per capita income. These two variables are very highly correlated. Thus, the per capita income variable is included as a proxy for both population and per capita income, as well as any other closely related factors. Monthly dummy variables are used to pick up otherwise -24- unquantified variations normally associated with each month. Potentially important variables which are not quantified include weather, buyers' expectations, seasonal demand patterns related to temperature, menu pattern vari- ations due to holidays and religious observance, or other recurring seasonal or institutional factors affecting demand. Commercial production per workday would seemingly be affected by the relative level of prices. In periods of low prices when the producers expect prices to rise in the near future they would hold their livestock off the market and feed to heavier weights. Where as in periods of high prices with an expectation of declining prices producers probably sell their livestock at lighter weights and thus presumably somewhat earlier than originally anticipated. Livestock prices have already been hypothesized as being responsive to total production levels. The other explanatory variables included in the production equations are the quarterly inventory data published by weight groups of the number of steers and heifers on feed and the number of hogs and pigs on farms. Quarterly dummy variables, corresponding to the three months following the month in which the inventory data are published, are in- cluded in the beef and pork commercial production equations to account for unspecified normal quarterly differences. Factors which could potentially cause such seasonal vari- -25- ations are seasonal temperature or feeder cattle acquisition patterns and corresponding feeding and selling patterns in different seasons of the year. Livestock producers are probably more responsive to live prices than wholesale prices. Consequently, the supplies of hogs and steers for slaughter, represented by commercial production of beef and pork per workday, are related to live prices rather than wholesale prices. Live prices, in turn, are related directly to their respective beef and pork wholesale prices. Such a relationship be- tween live and wholesale prices seemed theoretically con- sistent and is supported by Snell's findings that the timing and magnitudes of price changes at the live and wholesale levels coincided on a monthly basis. (28) Price changes at the retail level have been found to lag about a month after changes at the live and wholesale levels have occurred and the magnitude of changes differed in that retailers tended to even out their price fluctuations relative to the live and wholesale levels. (2:4) Theoretical considerations also suggest that the change in the storage of wholesale pork cuts during the current Inonth is also an endogenous variable. Once hogs are slaugh- tered the pork can go rather quickly to the final consumer: otherwise it must be stored. The amount of pork quantity Inoving into storage or the amount of pork stored moving into the wholesale market is affected by current price and vice -25- versa. The explanatory variables included in the change in storage equations are two endogenous variables--the wholesale pork cut price and the current pork quantity, a predetermined variable--storage level at the beginning of the month, and monthly dummy variables to capture the effects of regular, but otherwise unquantified factors affecting storage behavior. The simultaneity between other relevant explanatory variables and the wholesale prices is assumed sufficiently low that these variables could be considered predetermined or exogenous. The income variable is considered exogenous, realizing that the wholesale beef and pork prices have a minor influence on per capita personal income. Pork storage at the beginning of the month is obviously a predetermined variable. The modifying beef supply variable, percentage of cows slaughtered, is assumed to be predetermined. This assumption was based on the feeling that cows were sent to market based upon considerations related to short-run grass availability, stage of their productive life, and longer run expectations about beef prices. Because of the short pro- duction cycle for chickens and turkeys, changes in current beef and pork prices are probably a minor factor in determining the current month's chicken and turkey production. Similarly, because a monthly time period was involved, current beef imports are assumed to be predetermined by previous market behavior and price expectations. The preceding discussion of Model I is summarized into functional form below. -27- Model I 1) Rounds* - f(QE*, QHf’I, PERCOW, MPORT, TKPD, CKPD, M.D., u1) 2) Armchks* s f( " u2) 3) BLoins* . f( " u3l 4) Ribs* . f( " uA) 5)‘Hams* . r(qc*, qHs, CHAMST', HAMST, I, TKPD, CKPD, M.D., us) 6) Bellies“ - f( n csELSTs, BELST, ' u6) 7) PLoins* . f( " CLOINST*, LOINST, " u?) 8) Picnics* . f( " CPICNST“, PICNST, " "8’ 9) Butts* - f( ~ CBUTST*, BUTST, " u9) 10) see - f(CSteerP*, Ich, Q.D., u10) 11) OH11 = f(CHogP*, INVH, 0.0., U1.) 12) SteerP* - f(Rounds*, Armchks*, BLoins', Ribs“, M.D. u12) 13) HogP* - f(Hams*, Bellies*, PLoins*, Picnics', Butts*, M.D., u13) 14) CHAMST* . f(Hams*, qHs, HAMST, M.D., u,,) 15) CBELST‘ . f(Bellies*, QH*, BELST, M.D., u15) 16) CLOINST’ - f(PLoins*, QH*, LOINST, M.D., u16) 17) CPICNST* . f(Picnics*, QH*, PICNST, M.D., u17) 18) CBUTST* = f(Butts*, QH*, BUTST, M.D., "18) 19) Identity: CSteerP*, a SteerPg - SteerPt_1 20) Identity : CHogP* - HogPt* - HogPt-1 Where: * denotes jointly determined variables and Rounds = wholesale price of beef rounds, cents/lb. Armchks a wholesale price of beef arm chucks, cents/lb. BLoins - wholesale price of beef loins, cents/lb. -28- Ribs a wholesale price of beef ribs, cents/lb. Hams - ' pork hams, " Bellies c " pork bellies, " PLoins " pork loins ” Picnics " pork picnics, " Butts " pork Boston " butts, QC 2 Commercial beef production, 48 states, million lbs. divided by the number of industry workdays for the month QH = Commercial hog production, 48 states, million lbs. divided by the number of industry workdays for the month SteerP = Average price of 900-1100 Choice steers at Chicago, 3/cwt. HogP 3 Average price of U.S. 1-2,1 hogs at Chicago, S/cwt. ZOO-220 lb. I a U.S. per capita personal income, seasonally adjusted, at annual rates, thousand 8 PERCOW a number of cows as a percent of the total federally inspected beef numbers MPORT - beef imports, carcass weight, million lbs. TKPD a turkey certified as wholesome in federally inspected plants, ready to consume, million lbs. 1 Used price quotation for U.S. 1 and 2, 200 to 220 lbs. hogs until July 1, 1968 when hog grading system was changed. U.S. 2-3, 200-220 lbs. hogs, a closely comparable quotation, was used after that. -29- CKPD = chicken certified as wholesome in federally inspected plants, ready to consumer, million lbs. INVc - quarterly cattle on feed inventory groupings, 1000 head INV a quarterly hogs and pigs on farm inventory groupings, 1000 head HAMST 2 Frozen ham: cold storage holdings, beginning of month, 100,000 lbs. BELST 3 Frozen pork bellies: cold storage holdings, beginning of month, 100,000 lbs. LOINST -Frozen pork loins: cold storage holdings, beginning of month, 100,000 lbs. PICNST aFrozen picnics: cold storage holdings, beginning of month, 100,000 lbs. BUTST = Frozen Boston butts: cold storage holdings. beginning of month, 100,000 lbs. C s before pork storage variables refers to change in storage (t + i - t) M.D. - Monthly dummies, January a base Q.D. - quarterly dummies, (base defined in text) u's a stochastic disturbance terms -30- Model 1; - Cut/Cut Price Ratio Equations An alternative way of examining wholesale cut price behavior is to determine the relevant explanatory vari- ables explaining the relative behavioral relationships among the wholesale beef and pork cut prices. The relative relationships are expressed as ratios between paired wholesale cut prices. Relative relationships between high and low price cuts and cross relationships between beef and pork primals are of special interest. This model could conceivably be used as a method of forecasting other whole- sale cut prices if one wholesale cut price was determined by some other means. Ratios between the wholesale cut prices are influenced by quantity levels because of different price flexibilities with respect to quantity. Commercial beef production per workday is used as the main quantity variable for beef/beef price ratios while commercial pork production per workday represents the competitive situation. For pork/pork price ratios, pork production per workday represents the main quantity variable while beef production represents the competitive situation. When wholesale pork prices are involved in the ratios, i.e. either pork/pork or beef/pork, the storage figures for those cuts are included in the equations. When the dependent variable involves a ratio of two pork cut prices, the most relevant explanatory storage variable is the storage ratio of those two cuts. The relative -31- effect on wholesale cut prices, of the other quantity variables hypothesized as being relevant explanatory variables in Model I, is assumed similar for each cut. Consequently, when a ratio of wholesale prices is used as the dependent variable, the effect of the other quantity variables tend to cancel out and become of minor importance as explanatory variables. Per capita income, again acting as a proxy for population and any other closely related factors, is included to see if a differential income effect was a factor causing changes in relative price movements over time. Monthly dummy variables are included in the equations to pick up the effects of otherwise unquantified factors associated with each month. Wholesale prices and certain supply variables were hypothesized as being jointly determined in Model I. How- ever, wholesale price ratios would seem to be relatively unimportant as explanatory variables for determining supply. Consequently, Model II is specified as a series of one equation models. For simplicity these equations are con- sidered as sub-models under Model II and are not given individual numbers. The functional forms of the three types of equations in Model II are summarized below. -32- p e Bi/PBJ - f(Qc, OH, I, M.D., u.) p e Pi/P : r(qc, OH, §I§§l I, M.D., u Pj ST j , 2) p * BI/PpJ = f(Qc, QH’ STORJ’ I, M.De’ ”3) where: PBi/PBJ refers to the different combinations of the wholesale beef prices such that l i J PPi/PBJ refers to the different combinations of the wholesale pork prices such that 1141 3%ggfi refers to a combination of the pork storage data corresponding to the Pi and PJ of the pork price ratio Psi/Pp refers to the ratio of the i th whole- J sale beef prices with the j th wholesale pork prices STORj refers to the storage of the Pj pork cut in the beef/pork price ratio. * denotes endogenous variables The other variables are the same as defined in Model I, -33- Model III - Wholesale Level to Live Level Equations Attention by producers, packers and processors, and consumers alike has been focused on price relationships among market levels. Primary focus has been on the live to retail spread. Model III endeavors to explain a smaller portion of this spread, namely the wholesale to live spread. Meat packers and processors are concerned with this spread because of its impact on their profit picture. Because of the availability of adequate price forecasting equations at the live level, Model III also could be envisioned as a means to convert these live level forecasts into corres- ponding wholesale forecasts by cuts. Two "margin" approaches are used to analyze the relative relationships between wholesale prices and live prices. One approach uses wholesale cut/live price patios, expressed as a fraction, as the dependent variables similar to those used in Model II. The other approach involves wholesale cut-live price diffepenpep as the dependent variables. The calculations of the wholesale to live price ratios and price differences in this study involves taking whole- sale beef cut prices relative to live steer price and whole- sale pork cut prices relative to live hog price. The price differences in this study are not directly comparable to the price spreads published by the U.S. Department of Agriculture. This study's price differences compare wholesale cut prices with the live level while the USDA's wholesale to live spread -34- relates an aggregate wholesale price with the live level. Also, in this study, the price differences are not con- verted to an equivalent weight basis.1 The main reason for not converting the live price to an equivalent wholesale weight basis was the unavailability of live prices for cuts. Another reason is that the conversion factor varies among companies and probably even within a given company. The relevant variables for explaining the ratios and differences between wholesale and live prices are essen- tially the same as those used in Model II, for the cut/cut price ratio equations. Commercial beef and pork production per workday are included. Pork storage is also included in the pork equations. Per capita income is included again in its role as a proxy for other closely related factors, such as population. In addition to these variables, average weekly earnings for each month in meat packing plants are included. This variable is included as representative of the "services" portion of the difference between the whole- sale price and the live price. The explanatory power of the wage variable is weakened because it is only an index of the labor cost of each unit of service, but is not a measure of the changes in the capital/labor mix in the 1 Equivalent weight refers to the fact that a pound of Choice grade steer yields only about .6 lb. of carcass beef while a pound of 200-220, No. 2-3 hog yields about .5 lb. of wholesale cuts. (6) -35- functions performed between the wholesale and live market levels. As in Model II, the simultaneity between the explanatory variables and the dependent variable is assumed to be minimal. Thus, Model III consists of a series of one equation sub-models. The functional forms of the four types of equations involved in Model III are presented below. 1. fig-'- 3 f‘Qc’ QH’ I, W, M.D., U1) C (PBI - SteerP). B f(QC’ QH’ I, W, M.D., U2) p e .52 = f(Qc9 QH’ STORJ, I, W, M.D., U3) H Where: PBi - the wholesale beef cut prices, is Rounds, Armchks, BLoins, Ribs PPj - the wholesale pork cut prices, j- Hams, Bellies, PLoins, Picnics, Butts W - average weekly earnings for each month in meat packing plants, 3 * refers to endogeneous variables. The other variables are the same as defined in Model I and Model II (pages 27-29 and 32). -35- Fopecasting Eguations During periods of rapidly rising or falling beef or pork prices the USDA receives many inquires questioning the reasons behind the recent price changes and asking what can be expected in the near future. The preceding three models are focused at determining the reasons for recent price changes. However, they can also be adapted to price forecasting. Model I normalized wholesale cut price equations in reduced-form could be used for forecasting. Any one of the reduced-form wholesale cut price equations could be used to project to some desired future time period. Then, the relative cut to cut relationships found in Model II could be used to determine the other wholesale cut prices. Similarly, by some other means, live cattle and hog prices could be forecast and converted to wholesale prices using Model III wholesale to live relationships. Forecasting equations used in this study are the normalized wholesale price equations in Model I which are each fitted by ordinary least-squares. The use of derived reduced-form equations from Model I for forecasting was considered, but no adequate statistical routine was available to handle the number of variables involved in Model I. tim ion Procedu es nd 0 Sourc s The time period chosen for analysis, January 1962- May 1969 is relatively short. Hopefully, the relationships -37- will also be reasonably representative of the factors affecting current and possible future price relationships. A related consideration in the choice of this particular time period was that this study may become part of a broader overall systems approach to the meat industry which might include consideration of price relationships at the retail level. The USDA continuing study from which the retail beef and pork cuts prices would probably be drawn did not start compiling adequate monthly price data until January, 1962. Even by starting the time period as recently as January, 1962 a problem was encountered in Model I concerning the quarterly hogs on farms inventory data. Hog inventory data were not published on a quarterly basis prior to March, 1963. Thus, rather than try to extrapolate the quarterly hog inventory data back to the beginning of 1962, the time period for Model I was shortened to March, 1963-May, 1969. Numerous daily Chicago wholesale beef and pork cut prices are published in Th Nation l Pro i ion r, (30) a trade magazine for the meat processing, purveying, 1 packing, and rendering industries. From the daily wholesale 1 These prices are taken from The Ngtipnai Proyipionp: Daily Market Sprvicg, which is commonly referred to as the ”ye low sheet”. -38- cut prices published, average monthly prices were cal- culated for several weight classes of nine major primal cuts of beef and pork. These thirty price series were then plotted for the period January 1962-May 1969. The relationships among the price series within each wholesale cut grouping were analyzed and found to be fairly consistent. Thus, the most heavily traded weight class for each whole- sale cut was selected for more intensive analysis. The beef cuts selected are the U.S. Choice grade: a) rounds, 70-90 lbs., b) arm chuck, 80-110 lbs., c) loins, 50-70 lbs, d) ribs, 25-35 lbs. Pork cuts are: a) hams, 12-14 lbs., b) loins, 12-16 lbs., c) bellies, 10-12 lbs., d) picnics, 6-8 lbs., e) Boston butts, 4-8 lbs. Linear functional forms are used for the equations under the assumption that they reasonably reflect the likely behavioral patterns at the wholesale level. The functional forms are linear both from a typical economist's point of view as the variables enter in a linear fashion and from a statistician's viewpoint in that the parameters enter in a linear fashion. The variables are used in form of actual variates without any deflation or indexing. As a comparison against the linear functional form, the use of a log-log functional form was considered because of the ease of obtaining price flexibilities. Since the change in pork storage variable was expected to involve some negative values, the log-log form was not used. -39- The slopes of the demand and supply functions are assumed approximately constant over time. Consequently, the Models are estimated for the whole year instead of estimating each month separately. Although the slopes are assumed to be approximately equal, the level of the functions are permitted to differ among months by in- corporating monthly dummy intercept shifters. Logan and Boles analyzed quarterly retail meat price fluctuations and found that the slopes of the demand functions for selected meats were constant by seasons within the year but that the level of the demand function varied among seasons of the year.(19l. Of the estimation techniques available to obtain unbiased coefficients for the simultaneous equations in Model I, two-stage least-squares was selected. The two- stage least-squares estimation technique yields asymptotic unbiased, asymptotic efficient, and consistent coefficients under the assumptions of serial independence, finite and constant variance, and identification (15, pp 258-260, 275). Normality is also assumed in order to test whether the estimated coefficients are statistically different from zero.by using readily available statistical tables. All the stochastic equations in Model I are over- identified. The assumption of serial independence is tested by an approximate Durbin-Watson test because the variance formula is asymptotic. The time period from March 1963 to -40- May 1969 covered in the analysis of Model I is fairly short, hopefully maintaining a fairly constant variance. Unlike Model I, the cut/cut price ratio and wholesale to live equations in Models II and III are assumed to have only one endogenous variable per equation. Assuming serial independence, finite and constant variance, and normality, estimation by ordinary least squares yields best, linear, unbiased, consistent, and sufficient parameters (15, pp 106-115). The assumption of normality in Models II and III as well as in Model I is acknowledged as being inconsistent. If u1 and u2 are normally distributed in Model I, then the ratio equations in Models II and III have essentially :1 as the disturbance term which is clearly non-normal. “2 Obviously, the assumption of normality for Models I, II, and III cannot be simultaneously true. But, in each case uncertainity exists as to the exact degree of compliance with the assumption. No good method for determining com- pliance is available since the error terms are unobservable and the estimated error terms are dependent upon the estimation procedure. As was previously mentioned, the normalized wholesale cut price equations in Model I are fitted by ordinary least- squares for forecasting purposes. The estimated coefficients are biased and statistically inconsistent because there is -41- more than one endogenous variable in each equation (27; 15, pp 232-334). But, the relevant concern for forecasting is that the estimated value of the normalized endogenous variable is efficient and unbiased. D t ources With the exception of the wholesale beef and pork prices, data for this study were obtained from published government reports. As was previously mentioned, the wholesale prices came from The National Provigiongr. (30) Per capita income data were obtained from the urve of Cuprent Businesg published by the Department of Commerce. (39) The monthly per capita income figure was derived by dividing seasonally adjusted monthly U.S. total personal income at annual rate by total population as of that month. Wage data were published in the Employment and Earnings report of the Department of Labor. (40) Other data were obtained from various reports published by the USDA. The monthly beef and pork data, excluding wholesale prices, were obtained on a current basis from tttggtpg§t_flggtt_gggt Mgpket News (36) and the Livestock gnd Meat Situation. (33) A more historical source of this data would be the Liyeptock and Meat Statistics (35) published annually since 1957. The quarterly inventory data were obtained from the Cattlg on £32; (31) report and the Hogs and P1g§ (32) report, which prior to June 1968 was titled Pig Cpop Report. The poultry production data were obtained from the monthly report -42- entitled, Poultry Slaughtered under Federal Inspgction and Poulttx Used in Further ngcessing (38). CHAPTER III ESTIMATED COEFFICIENTS FOR THE SIMULTANEOUS EQUATIONS (Model I) The estimated coefficients of the eighteen stochastic equations in Model I are presented in four major sections-- 1) behavioral demand equations normalized on wholesale cut prices, 2) relation of normalized live prices to wholesale prices, 3) behavioral supply equations normalized on com- mercial production per workday of beef and pork, and 4) normalized change in pork storage equations. Wholesale Damand §guations Baa: -- The estimated coefficients for the demand equations, normalized on wholesale beef and pork prices are presented in Table 1. As expected, wholesale beef cut prices were inversely related to the quantity of beef. However, price-quantity relationships differed among the beef cuts. The price flexibilities with respect to quantity found in the first column of Table 2 were cal- culated using mean values for the period under study. The relative positioning of the various flexibilities was somewhat contrary to expectations. The price of arm chucks 1 was expected to be the most flexible. with respect to 1 Discussion of relative flexibilities will be in absolute terms throughout. .4}- -44- quantity because of its being a more standard item, with fewer alternative uses, in consumers' meat purchases as roasts, low-priced steaks, and ground beef or chuck. Also, arm chucks had the lowest average price of the four beef cuts studied and probably serves as a buffer when prices change. During price decreases, consumers probably tend to shift to more luxury meat items such as rib roasts, sirloin and round steaks tending to keep the prices of those cuts higher relative to arm chucks whose price would have to decrease even more in order to be purchased in greater amounts by the consumers. During price increases, the relative increase of arm chuck price may be more than for the three higher-price beef cuts as consumers shift some of their demand from these cuts to arm chucks. The price flexibilities with respect to quantity for rounds, ribs, and beef loins were expected to be less flexible than arm chuck prices because of their variety of uses and the relative ease of substituting pork roasts or chops, poultry, as well as lower-price arm chuck for them when their relative prices are high. All the beef wholesale cut prices were directly related to the per capita personal income variable. As was pre- viously stressed, the income variable is really a proxy for per capita income, population, trend, and other unspecified closely correlated factors. Thus, in looking at the dif- ferences in response to this income variable, income will be -45- denoted in quotes. Price flexibilities with respect to "income", presented in column 2 of Table 2, were calculated using the mean values of the beef prices and "income". Beef rib price was the most flexible with respect to "income" indicating that as "incomes" increase the proportional price change of ribs was more than the proportional changes in the other beef cut prices. The ”income" flexibilities of arm chuck and loin prices were slightly less. Again, as was found with respect to quantity, round price was the least flexible of the four beef cuts. The relatively high "income” flexibilities of beef rib and loin prices were consistent with prior expectations because of the high status roasts and steaks sold from these cuts at retail. Three of the wholesale beef cut prices were inversely related to the quantity of pork. Only the pork quantity coefficient in the arm chuck equation was even slightly larger than its standard error. Thus, none of the coefficients for pork production in the wholesale beef price equations were significantly different from zero at the .05 level according to the asymptotic approximation of the "t-test” (coefficient/standard error).1 The positive relationship 1 Significance in this chapter refers to statistical signi- ficance with an asymptotic approximation of a t-value judged against a critical .05 probability of a larger value of t, sign ignored, of approximately 2.0 with 75 degrees of freedom, forntegting the hypothesis that the coefficients a 0. (29, p. 33 -oom.- -n-m.- -m.m- -om.m- -meo.- .eem.- moo. o-o. oeo. omo. moo.u m-o.u cage .oe.m- -oop.- .mw.m- -mm.- -o-m.- -mne.- mmo. -o. >no.1 ~mo.1 moo.1 soo.i ooxo Ae-.- Ae-.- -ne.- Aooe.- m-o:. o-ox. n-o. eoo. 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Nsmm: 00. 0..0 00: 00.- 0..- 000 00... 0.... 00: 00.0- 0..0- 000 00.0 00.0 .0: 00.0- .0.0- .00 .00.0. .00... 0.0. 000. 0: 00 .00... .000.. 000. 000. 00 00 .00... .00... 000. 000. 00 00 .00... .000.. .00.0. .00... 000.- 000.- 0.0 00 000. 000. ..0 00 .000.. .000.. .00... .000.. 000. .00. 00. 00 000. .00. 0 I 00 I; s: 0.1.. Illa-3.222% :20 i um 00.00.00> 0300000000 00n..0500z 00.00.00) 0000000.0xm 00m0_ucmu n qu<» -53- ficantly different from zero. Current price levels may signal conflicting messages to producers. For example, a high price level may encourage producers to sell now and take the assured price and presumably good profit or it could encourage producers to hold off in expectation of even higher prices and profits. The negative coefficient would signify the latter of these two responses which is in conflict with the prior finding of the positive relatbonship to changes in steer price. When both current price and change in price were included in the same equation the signs of the coefficients were the same as those found when the variables were included individually leading to confusion as to the appropriate interpretation. From the criteria of reasonableness the change in price alternative appeared to be the most appropriate for the beef supply equation. The confusion was increased even further by the fact that the estimated coefficients for the different pork price alternatives had opposite signs from the comparable beef coefficients, as seen in equations 3 and 4. A possi- ble explanation for the inverse relationship between change in hog price and pork quantity found in equation 3 is that hog producers expect short-run price trends to continue. During rising trends this would imply that producers would hold their pigs off the market in expectation of higher prices forthcoming. The opposite response would be expected -54- during downward trends with producers marketing their pigs early because of expected further drops in live hog price. The expected direct price relationship was obtained when current hog price was included in equation 4. However, the hog price coefficient was not significant. When both price alternatives were incorporated in the same equation the directional responses were the same as when they were included individually. The results of the alternative supply equations leave unresolved the question of whether producers are more responsive to short-run price expectations, current live price levels, or a combination of the two. Over the period studied the supply of beef produced was more responsive to live steer price while the supply of pork produced was more responsive to change in live hog price. The on feed and on farm quarterly inventories by weight groups included in the supply equations were selected as being the relevant weight groups affecting marketings up to two months following the month in which the quarterly report was issued. The two months following the quarterly report month (01) were distinguished from each other by the use of dummy variables, 02 and 03. The purpose of dis- tinguishing between these months was to allow for marketing shifts among the weight and sex groupings as the lag from the quarterly reporting month increased. The expected shift -55- in response from the heavier weights in the quarterly report month (Di) to the lighter weights by the second month (03) following the quarterly report month was not always found. The impact of the 900-1100 pound steers on feed decreased from the quarterly report month to the second month following the report month, as expected. The coefficients for the heifer inventory variables had mixed signs resulting in uncertainity as to their impact. The coefficients for the hogs on farm inventory variables also had mixed signs. The expected heavy supply impact of the 180-219 pound hog class in the quarterly report month and of the 60-119 pound class in the second month following the quarterly report month were found. A probably explan- ation for the lack of a consistent shift from heavier to lighter weights being marketed, as the time following the quarterly report month increased, was that the different cattle on feed and hogs on farm weight groupings were highly correlated (=.9 or above) for both hags and cattle. Consequently, the estimated coefficients for the weight groupings during the same time period were probably subject to large standard errors and a clear distinction of the effects of each weight group was not possible. Given the other variables, the quarterly dummy shifters indicated that commercial beef production per work day was lower in the other three quarters relative to the base quarter of August, September, and October. Marketings of -55- grass fed cattle off the range in the fall might be a partial explanation for this finding. The rates of gain during the base quarter might be better than during the preceding hot months and following cold months. The base quarter for the dummy shifters in the commercial hog pro- duction per work day was July, August, and September. This base quarter differs from beef because of a one month difference in the timing of the quarterly inventory reports. The supply of hogs, relative to the base quarter was higher for the other three quarterly periods. Hot weather, slower growth rates, and expectations of price declines during the hot summer months may cause hogs to be marketed at lower weights during this period of the year. The portion of variance explained by the coefficients for the supply equations containing the different price alternatives varied only slightly from each other. For the beef supply equations, the amount ranged from .87 for the equation containing change in price to .89 for current price and for the combination of the price alternatives. For hog supply the range was from .78 for the supply equation incorporating current hog price to .91 for the change in price and combination of price alternatives equations. -57- Change in pork storage eguations The estimated coefficients and related statistics for these equations are found in Table 4. For the most part higher wholesale pork cut prices were associated with reductions in storage levels. Only the coefficient for ham price was positive, although statistically insignificant. With high prices one would expect movements out of storage and back into the market channels. With one exception, the response to pork quantity was positive. The exception this time was the insignificant coefficient obtained for the change in picnic storage equation. Generally, as pork quantity increased the amount in storage increased. Larger beginning of the month storage stocks resulted in an out- movement of storage stocks during the month. Smaller be- ginning storage stocks typically were associated with supply moving into storage during the month, probably as a safe- guard against the fluctuating and uncertain supply picture or because of an improved outlook for storage profits. The pattern for the change in monthly storage intercept shifters for hams showed peaks in January, April, and October relative to the rest of the months. These high points might have resulted from the expectation of or replenishing after the more traditional ham eating holiday seasons of Thanks- giving-Christmas and Easter. 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