Disaggregated Analysis of Short-run Beef Supply Response Enrique Ospina and C. Richard Shumway Conceptual problems in model specification of beef supply response studies are investigated and a simultaneous equation model is formulated to estimate annual U.S. carcass supply, demand, and inventories of beef. Three basic issues are addressed: (a) disaggregation, (b) simultaneity, and (c) differentiation between current and expected price effects. Empirical results indicate positive supply response of each quality type of steers and heifers, and negative supply response of cows to current own-price changes. The derived aggregate supply elasticity is positive. The effects of grain price changes on beef price, supply and composition are also evaluated. Nelson and Spreen recently refocused at- tention on the controversy surrounding proper specification of the short run supply relationship for slaughter cattle. A variety of models have been developed and fitted re- sulting frequently in zero or negative elas- ticities of supply with respect to cattle prices.' The variability in short run slaughter supply elasticities derived with different models is great, varying both with the time interval defined as short run and with model specification. Among annual models these elasticities range from -. 17 [Reutlinger] to +.16 [Langemeier and Thompson] for all beef, from 0 [Freebairn and Rausser] to + .23 [Langemeier and Thompson] for fed beef, and from -. 97 [Shuib and Menkhaus] to +.61 [Freebairn and Rausser] for non-fed beef. Supply elasticity estimates with respect to feed prices also have been unstable. These Enrique Ospina is an agricultural economist, Winrock International. He is a former research associate and C. Richard Shumway is an associate professor of agricultural economics, Texas A&M University. Texas Agricultural Experiment Station Technical Article No. 14532. This paper is a result of research contributing to Western Regional Project W-145. The authors ac- knowledge with gratitude the constructive comments on earlier drafts by Bruce Beattie, James Richardson, Bruce Gardner, Calvin Boykin, Peter Barry, Dale Menkhaus, and an anonymous reviewer. findings, a product of nearly two additional decades of econometric modeling, further validate Knight's 1961 observation that "re- search workers have probably had more diffi- culty deriving meaningful and realistic supply-price elasticities for beef than for any of the other commodities" (p. 82). The frequently estimated negative supply elasticities seem contrary on the surface to economic reasoning for a marketed commod- ity. Explanation has been sought in the fact that cattle are both consumption goods and capital goods. Slaughter and inventory deci- sions are made simultaneously [Reutlinger; Jarvis; Nelson and Spreen]. Further, because gestation lasts 9 months and cows typically bear only one offspring at a time, the ratio of breeding herd inventory to animal slaughter is large and much greater than for either hogs or poultry. Consequently, it is reasoned that the difference between current and expected future prices should be extremely important in explaining current cattle slaughter [Elam; Nelson and Spreen]. Further, beef is a heterogeneous product consisting of carcasses from steers, heifers, and culled members of the breeding herd. 'A zero elasticity is typically the result of deleting the price variable prior to final estimation of the beef sup- ply equation because the initial parameter estimate was negative, not significant, or both. 43
Conceptual problems in model specification of beef supply response studies areinvestigated and a simultaneous equation model is formulated to estimate annual U.S.carcass supply, demand, and inventories of beef. Three basic issues are addressed: (a)disaggregation, (b) simultaneity, and (c) differentiation between current and expectedprice effects. Empirical results indicate positive supply response of each quality type ofsteers and heifers, and negative supply response of cows to current own-price changes.The derived aggregate supply elasticity is positive. The effects of grain price changes onbeef price, supply and composition are also evaluated.
Nelson and Spreen recently refocused at-tention on the controversy surroundingproper specification of the short run supplyrelationship for slaughter cattle. A variety ofmodels have been developed and fitted re-sulting frequently in zero or negative elas-ticities of supply with respect to cattleprices.' The variability in short run slaughtersupply elasticities derived with differentmodels is great, varying both with the timeinterval defined as short run and with modelspecification. Among annual models theseelasticities range from -. 17 [Reutlinger] to+.16 [Langemeier and Thompson] for allbeef, from 0 [Freebairn and Rausser] to + .23[Langemeier and Thompson] for fed beef,and from -. 97 [Shuib and Menkhaus] to+.61 [Freebairn and Rausser] for non-fedbeef. Supply elasticity estimates with respectto feed prices also have been unstable. These
Enrique Ospina is an agricultural economist, WinrockInternational. He is a former research associate and C.Richard Shumway is an associate professor of agriculturaleconomics, Texas A&M University.
Texas Agricultural Experiment Station Technical ArticleNo. 14532. This paper is a result of research contributingto Western Regional Project W-145. The authors ac-knowledge with gratitude the constructive comments onearlier drafts by Bruce Beattie, James Richardson, BruceGardner, Calvin Boykin, Peter Barry, Dale Menkhaus,and an anonymous reviewer.
findings, a product of nearly two additionaldecades of econometric modeling, furthervalidate Knight's 1961 observation that "re-search workers have probably had more diffi-culty deriving meaningful and realisticsupply-price elasticities for beef than for anyof the other commodities" (p. 82).
The frequently estimated negative supplyelasticities seem contrary on the surface toeconomic reasoning for a marketed commod-ity. Explanation has been sought in the factthat cattle are both consumption goods andcapital goods. Slaughter and inventory deci-sions are made simultaneously [Reutlinger;Jarvis; Nelson and Spreen]. Further, becausegestation lasts 9 months and cows typicallybear only one offspring at a time, the ratio ofbreeding herd inventory to animal slaughteris large and much greater than for either hogsor poultry. Consequently, it is reasoned thatthe difference between current and expectedfuture prices should be extremely importantin explaining current cattle slaughter [Elam;Nelson and Spreen].
Further, beef is a heterogeneous productconsisting of carcasses from steers, heifers,and culled members of the breeding herd.
'A zero elasticity is typically the result of deleting theprice variable prior to final estimation of the beef sup-ply equation because the initial parameter estimate wasnegative, not significant, or both.
43
Western Journal of Agricultural Economics
Carcass quality for consumption varies sub-stantially depending on age and productionpractices employed. It is reasoned that theclass and quality composition of carcass beefundoubtedly changes in response to pricechanges. This expectation has beendocumented previously in the form of supplyresponse differences between fed and non-fed beef [Langemeier and Thompson;Freebairn and Rausser] and between steers,heifers, and cows [Reutlinger].
Objectives
The model specified here incorporatesthese three important conceptual issues plussimultaneity in supply and demand for beef.In addition, carcass beef is disaggregated intomore homogeneous groupings than in priorstudies with the goal of generating more reli-able estimates of supply responsiveness bothof beef components and of the entire beefindustry. The specific objectives of this studyare (a) to formulate a disaggregated, annual,simultaneous equation model of the U.S.livestock sector that differentiates betweencurrent and expected price effects in order toestimate beef supply, demand, and inventoryresponse (b) to obtain elasticity estimates forthe components and for the aggregate, and (c)to assess the impact of feed price changes onbeef prices, supply and composition. Theperiod of analysis is 1956-1975.
Economic Model
Carcass beef is disaggregated into steer,heifer, and breeding herd cull classes.2 In-stead of disaggregating by quality into fedand non-fed beef components as in previousstudies, USDA grade standards are used to
2In the empirical model, bulls and standard grade steersand heifers are included with cow slaughter supply.Although standard grade steer and heifer beef is mar-keted in quite different ways than cull cow and bullbeef, it represents a very small proportion of total beef.Since these animals typically are not fed appreciableamounts of grain, they are grouped in this study withbreeding herd culls because of production similaritiesrather than with good grade steers and heifers. Thiscategory is referred to as cow slaughter.
44
define three quality categories: choice-prime(choice), good, standard and lower (utility).Three basic explanatory relationships arespecified from neoclassical theory: carcassslaughter supplies are defined as functions ofcurrent prices, inventories as functions of ex-pected prices, and carcass demand asfunctions of current prices and income. De-mand, supply, and inventories are simulta-neously determined within the model.
Competition in the use of resources,mainly feed grains, and in consumption war-rant the incorporation of hog and broiler sub-sector decisions in the model. Feed grainsupplies are considered predetermined out-side the beef industry in the short run.Linear functions are specified to explain: (a)slaughter supply of two defined qualitycategories (choice and good) of steers and ofheifers; (b) supply of slaughter cows, beefimports, pork, and broilers; (c) feeder cattleinventory formation; (d) breeding herd in-ventory formation for beef and pork; and (e)demand for pork, broilers and three definedtypes of beef (choice, good, and utility).
Steer Supply
Slaughter steers are a primary product ofthe beef industry. Total slaughter is deter-mined by number of animals slaughtered andtheir average weight. Although number ofanimals slaughtered within a year is largelypredetermined by prior decisions governingsize of the breeding herd, weight per animalcan be affected by length of feeding and so isexpected to be related to current prices. Forany quality type, supply of slaughter steers (intotal weight) during the year is specified as afunction of current product and variable inputprices and fixed input level (i.e., inventories).In linear form, this relationship is:
(1) SSt = a10 + aiPSt + al2PAt +
al3PCNt + al 4IFCt
where SSt is current steer slaughter in weight;PSt, PAt, PCNt are current own-price, closestproduction alternative (i.e., other quality)price, and major variable input (corn) price,
December 1979
Ospina and Shumway
respectively; IFCt is current January 1 feedercattle inventory for steers and heifers 500pounds and over.
From neoclassical theory of the firm, re-sponse to own-price changes is expected to bepositive. The closest production alternative isdefined as the next lower or upper qualitycategory to which production can be switchedby simply varying the amount of grain fed;thus, the response to alternative productprice is expected to be negative. Choice steersupply is expected to respond negatively tovariable input (i.e., corn) price. Good steersupply, on the other hand, is expected tomove in the same direction as corn price sincean increase in grain price mainly reduces theamount of grain fed per animal rather than thenumber of animals fed. Fewer steers (andheifers) are fed enough grain to grade choice,but they still grade higher than standard. Thequantity of beef slaughtered during the yearin each class is expected to be positively re-lated to the number of animals available forslaughter at the beginning of the year (i.e., thefixed input level.) Expected signs are a1l,a14>0; a12<0; a13<0 for choice grade; a13>0for the good grade equation.
Feeder Cattle Inventory
Inventories of feeder cattle are a conse-quence of past adjustments in the breedingherd, number of calves born, number ofcalves slaughtered, and death losses. Becausewidespread weather inclemencies and diseaseare rare, death losses change little from yearto year [Ehrich]. However, since the optionexists to slaughter young calves for veal, thetheory of the firm implies that vealer price,feed input price, expected cattle slaughterprice, and competitive enterprise priceshould be relevant in determining the num-ber of calves that are retained for later slaugh-ter. This functional relationship can be ex-pressed linearly as:
(2) IFCt = a2o + a21PSH* +
a22PPK* + a23PCN* + a24PVtl +
a25IBHt 1
where PSH*, PPK*, PCN* are expectedprices for own-product (slaughter steer andheifer), competitive product (pork), and input(corn), respectively; the subscript indicatesthe expectation is for year t given conditionsprevailing in and prior to year t- 1 when thefeeder cattle inventory decision was made; PVis price ofvealers and reflects incentive for calfslaughter; IBH_ 1 is January 1 breeding herdinventory in the prior year and is a measure ofthe potential supply of feeder cattle. Ex-pected signs are a21, a25>0; a22, a23, a24<0.
Breeding Herd Inventory
Heifers and cows serve a dual purpose asboth capital goods and consumption goods[Reutlinger; Jarvis; Nelson and Spreen]. As aconsequence, their slaughter supply equa-tions must take into account current demandfor breeding herd inventories. 3 FollowingReutlinger (pp. 910-13), the number ofheifersand cows slaughtered can be viewed withinthis context simply as the difference betweenavailable heifers and cows in a given year anddemand for breeding herd inventory in thesame year:
(3) Nt = At - DIBHt
where N is number of slaughter heifers andcows, A is total available heifers and cows, andDIBH is demand for change in the breedingherd inventory, all in animal numbers. Breed-ing herd inventory demand is thus treated as aconceptual (although not necessarily tempor-al) antecedent to cow and heifer slaughtersupply. It is defined as the difference in inven-tories between two subsequent years:
(4) DIBHt - IBHt+i - IBHt'
3Both Jarvis and Reutlinger develop models of beefsupply that derive slaughter supply equations from in-ventory demand relationships. While Jarvis' develop-ment is more inclusive and also more elegant in dem-onstrating the logical chain of implication, both modelsare derivable directly from the neoclassical theory ofthe firm. Our conceptualization of breeding herd in-ventory demand and slaughter supply departs from thesimpler Reutlinger model.
45
Beef Supply Response
Western Journal of Agricultural Economics
Identity (4) represents net changes (positiveor negative) in inventory numbers whichoccur by changes in either heifer or cowslaughter.
To explain inventory changes, desired in-ventories are defined as functions of expectedprices of output and variable inputs, and fixedinput levels. Expected revenue from andcosts of producing offspring from these ani-mals thus create the incentive to increase ordecrease breeding herd inventory. In linearform this relationship is expressed as:
(5) IBH*+1 = ao3 + a3 1PSH*+2 +
a32PCN*+2 + a33RX*+ 1
where IBH* represents desired breedingherd inventory, RX* is expected range condi-tions representing expected level of the majorfixed input to the breeding herd, and the sub-script indicates the year of expectation givenconditions prevailing in and prior to yeart-1.4 Sign expectations are a31, a3 3>0;
a32<0.Desired inventory as specified by equation
(5) is not an observable variable. However,the difference between actual inventories inyears t and t + 1 frequently is assumed to be aconstant proportion of the difference betweenactual inventory in year t and desired inven-tory in year t + 1 (Griliches):
(6) IBHt+ 1 - IBHt = c(IBH*+ 1 -
IBHt)
where 0<c<1.Substituting equations (5) and (6) into (4)
leads to the expression for inventory demand:
(7) DIBHt = ca3o + ca 31PSH*+2
+ ca 32PCN*+2 + ca3 3RX*+l -
cIBHt.
4It takes nearly three years from the time a decision to
modify inventories is made before the impact of its
offspring on steer and heifer slaughter is realized(Bentley, Waters, and Shumway).
46
With the exceptions of the expected rangecondition variable and inclusion of prices inlinear rather than ratio form, this equation isthe same as Reutlinger's equation (6).5
Heifer Supply
Slaughter heifer supply can now be de-fined. Available heifers in a given year are aproportion of feeder cattle inventories:
(8) AHt = dlIFCt
where AH is total available heifers and d1 isthe proportion of heifers in feeder cattle in-ventory.6 The value of d1 is expected to bequite stable near 0.5. Following equation (3)yields:
(9) NHt = dlIFCt - d2IBHt -
d3DIBHt
where NH is number of slaughter heifers, d2
is the normal replacement rate, and d3 is theproportion of breeding herd inventorychanges satisfied by modifications in heiferslaughter. For simplicity d2 and d3 areassumed constant [Reutlinger, equations (11)and (13)]. 7 The first term on the right side of(9) is available heifers; the other two termstogether depict heifer demand for the breed-
5It is also consistent with Tryfos' inventory demand
equation. Only two differences exist between our equa-
tion and his equation (4): (a) he uses current prices as
proxies for expected prices, and (b) we include ex-
pected range condition as an independent variable.
6If equation (2) were substituted for IFC in (8), we
would obtain a relation similar to Reutlinger's equation(10).
7Although some heifers in the feeder cattle inventory on
January 1 remain in the inventory after December 31,most either enter the breeding herd or are slaughteredduring the year. Thus, Reutlinger's term for heifer in-ventory demand is not included in this equation. Fur-ther, Reutlinger's heifer inventory demand is specified
as a function of the same variables as number of heifers
available (except IBH is unlagged). Since IBH t andIBHt_1 are highly correlated, he dropped IBHt from
his estimation equation. Consequently, our estimation
equation does not differ from his in this respect.
December 1979
Ospina and Shumway
ing herd inventory, both for replacement andchange in breeding herd size.
Total slaughter supply of heifers is equal tothe number of heifers slaughtered multipliedby their average weight. Following thereasoning for equation (1), weight is expectedto be related to current prices. Thus, heiferslaughter supply of a given quality type isspecified as a function of current own andalternative product prices, variable inputprice, and the fixed input level (NH):
(10) SHt = a40 + a4 iPHt + a42PAt +
a43PCNt + fiNHt
= a40 + a4iPHt + a42PAt +
a43PCNt + a44IFCt + a45IBHt
+ a4 6DIBHt
where SH is slaughter heifer supply inweight, PH is own-price, and other variablesare as previously defined. The last three termsrepresent the parameter f1 multiplied byequation (9). Since d1, d2, and d3 are all posi-tive, sign expectations are a4 1, a44>0; a42, a45,a46<0; a43 <0 for choice grade; a43>0 for thegood grade equation.
This equation differs from Reutlinger's heif-er supply equation (15) in that the theoreticaleffects of current and expected prices areseparated. Expected price changes provideincentive to increase or decrease breedingherd inventory while current price changesprovide direct incentive to alter slaughtersupplies. Only as they might affect expectedprices do current prices impact on inventorydemand. In contrast to Reutlinger's model,the sign of the own-price variable in the heifersupply equation can be clearly hypothesized apriori.
Cow Supply
The supply equation for slaughter cows canbe derived similarly. Total available cows in agiven year are:
(11) ACWt = d4IBHt + d5IDHt
where ACW is available cows; IDH is a prede-termined variable - dairy breeding herd in-ventory; d4 and d5 are normal culling rates forbeef and dairy breeding herds, respectively,and are assumed to be constants (with d4being d2 minus breeding herd death rate).Following equation (3), number of slaughtercows is:
(12) NCWt = d4IBHt + d5IDHt -
d6DIBHt
where d6 is the proportion of breeding herdinventory demand satisfied by variations inthe culling rate (i.e., 1 - d3). By the same logicas used for equation (10), cow slaughter sup-ply is formulated as:
(13) SCWt = a5o + as1PCWt + f2NCWt
= a5 0 + a51PCWt + a52IBHt
+ as3IDHt + a54DIBHt
where SCW is cow slaughter in weight andPCW is utility slaughter cow price. Grain andalternative product quality prices are not in-cluded in this equation because cull cowstypically grade less than standard and are notfed significant quantities of grain prior toslaughter. Because d4, d5 , and d6 are positive,expected signs are a51 , a52, a53>0; a54 <0.
These equations for slaughter heifers andcows account for simultaneity in inventoryformation and slaughter decisions. Inventor-ies are endogenous to the model. Effects ofboth current and expected prices are recog-nized and separated. A few previous models[Freebairn and Rausser; Folwell and Sha-pouri; Tryfos] had endogenously determinedinventories. However, Freebairn and Raus-ser did not include current inventories as ex-planatory variables in the supply equations,and current prices were deleted from the fedbeef supply equations. Neither Folwell andShapouri nor Tryfos included prices in thesupply equations.
47
Beef Supply Response
Western Journal of Agricultural Economics
Other Relationships
The remaining linear equations will be dis-cussed only in implicit form (for a completedevelopment see Ospina and Shumway 1980).Beef import supply is specified as a function ofcurrent U.S. utility grade beef price and dum-my variables to account for the impact of the1964 Meat Import Bill on slope and intercept.
Slaughter pork supply is a function of cur-rent pork and corn prices, inventory of breed-ing sows, and a shift variable - pigs raised perlitter [Freebairn and Rausser]. Breeding sowinventory is a function of expected prices forpork, beef and corn, and lagged sow inven-tories.
Slaughter broiler supply is a function of pastbroiler and corn prices and a shift variablelabor productivity in the broiler industry.Broiler supplies are not expected to be highlydependent on prior inventories. Less than ayear is required between broiler planning de-cisions and slaughter, and no significant re-sponse of supplies to current prices wasobserved in prior studies [Freebairn andRausser].
Carcass demand functions for the threequality types of beef (choice, good, and util-ity), for pork, and for broilers are explained bycurrent own and alternative meat prices, dis-posable personal income, and the wholesaleprice index.
Aggregate Elasticity
An extension of Allen's elasticity formula (p.252) is made to derive the short-run elasticityof aggregate beef supply with respect to cur-rent cattle prices from the elasticity of thecomponents:
E = kieijii
where ki is the proportion of component i tototal slaughter and eij is the supply elasticity ofcomponent i with respect to price j. This for-mula presumes that all beef quality priceschange proportionately. The sign of E cannotbe theoretically deduced from the compo-
48
nents since eii are expected to be positive andeij i are expected to be negative. However, itis empirically hypothesized that prior nega-tive estimates of E were due to model misspe-cification and the true short-run elasticity ofaggregate beef supply with respect to currentprice is positive.
Data and Estimators
Based on production characteristics andmarket structure of the U. S. beef industry,this study develops a disaggregation schemefor slaughter beef among class (steers, heif-ers, and cows) and quality (choice, good, andutility) components. Even though there areno national data series which classify allslaughter beef into class and quality compo-nents, considerable information is available.With a generally plausible set of assump-tions, proxy data series are constructed to ac-commodate the needs of the model.
Class Disaggregation
The USDA publishes beef slaughter datacategorized among steers, heifers, cows,bulls and stags. These data relate to federallyinspected beef slaughter and are reported inanimal numbers. Beef slaughtered in non-federally inspected plants is not reported bycomponents. However, it appears reasonableto assume that the same percent breakdownamong class components applies for non-federally as for federally inspected beefslaughter [Ospina and Shumway 1978]. Theanimal number estimates thus derived aremultiplied by average dressed weights, re-ported annually by class [USDA, Livestockand Meat Statistics], to yield class slaughterestimates in total weight.
Quality Disaggregation
Between 1956 and 1975, the period underinvestigation, 43 to 65 percent of all beef car-casses were graded by USDA (Livestock,Meat, Wool Market News). USDA defineseight grades: prime, choice, good, standard,commercial, utility, canner, and cutter. This
December 1979
Beef Supply Response
study defines three grade equivalents: choice(which includes choice and prime), good, andutility (which includes standard and lower).Two underlying assumptions are made inorder to estimate grade equivalents for allbeef based on actually graded beef: (a) Be-cause producers want the higher prices as-sociated with higher grades, it is likely thatmost of the prime and choice steer and heiferbeef produced is graded by USDA. Thus, it isassumed that the USDA-reported prime andchoice figures cover all the higher qualitysteer and heifer beef produced. (b) Virtuallyall cows slaughtered classify as USDAcommercial-or-lower grades (Williams,Bowen, and Genovese). The USDA-reportedstandard grade, consequently, is composedmainly of steer and heifer carcasses. It is thenassumed that non-graded standard beef is thesame percent of nongraded beef as gradedstandard beef is of graded beef.
These two assumptions permit allocation ofnon-graded beef among the two definedlower grades. By further assuming the samesex distribution within the two higher grades,the data series thus developed are treated ascrude approximations of class and qualityslaughter beef quantities. These data areavailable on request from the authors.
Other Data
Data on beef and dairy breeding herd in-ventories are published by the USDA inLivestock and Meat Statistics. Feeder cattleinventory is composed of steers and heifers(beef and other) 500 pounds and over, as re-ported in Livestock and Meat Statistics. Be-fore 1970 the cattle inventory series wereclassified by class and age. Beginning in 1970the classification was changed to its currentform, by class and weight. The series arepublished in both classifications for theperiod 1965 to 1970, from which a conversionfactor was derived to transform all previousdata to the current classification. The under-lying assumption is that the relationship be-tween inventories in the old and newclassifications remained constant.
The remaining USDA data for beef and
pork are published in Livestock and MeatStatistics and in Agricultural Statistics.Broiler data are reported in Poultry and EggSituation. Income, population, and price in-dexes appear in Business Statistics and inSurvey of Current Business.
Price indexes across sexes are calculatedfor each grade and used in the steer andheifer slaughter supply equations in place ofthe individual steer and heifer prices. Thecorrelation coefficient between contem-poraneous feeder cattle inventory and beefbreeding herd inventory variables is .984.Since estimation of the separate effects of in-dividual inventory variables is not an objec-tive here, the breeding herd inventory vari-able is deleted from the heifer slaughter sup-ply equations in order to reduce collinearityproblems. The combined effects of the pro-portion of heifers in the feeder cattle in-ventory less withdrawals for normal replace-ment should thus be reflected in the esti-mated feeder cattle inventory parameter ofeach slaughter heifer supply equation.
To conserve degrees of freedom, expectedsteer-corn and hog-corn price ratios are usedin place of separate variables in the feedercattle and breeding sow inventory equations.
Estimation
The model is specified as block recursivewith two blocks. One contains a single equa-tion with only the supply of slaughter broilersas an endogenous variable. Due to autocorre-lation in the error term, it is estimated bygeneralized least squares. The other blockcontains the remaining fifteen simultaneousstochastic equations and is estimated bythree stage least squares. The estimatedmodel consists of 16 equations and sevenidentities. Twenty-three variables areendogenous and 19 are predetermined.
Price Expectations
The relevant price, current or expected,which motivates a particular type of decisionis clearly distinguished in the economic
49
Ospina and Shumway
Western Journal of Agricultural Economics
model. Slaughter supplies are judged to re-spond most directly to current prices whileinventories (or the assets required for futureslaughter supplies) respond to expectedprices. Since an increase in one quantity im-plies a decrease in the other, both decisionsare affected indirectly by both sets of prices.
While current prices are observable, ex-pected prices are not. The only representa-tion of expected price provided by the mar-ketplace is futures price [Gardner]. Two prob-lems, however, preclude the general use offutures prices in this study: (a) futures marketsfor cattle and hogs are of recent origin, and(b) futures prices are not provided far enoughinto the future for the breeding herd in-ventory demand equation. Consequently,the unobservable expected price must be de-fined by the economist.
A number of alternative proxies for ex-pected prices have been used in previousbeef supply studies. In one way or another allhave used current or past prices, or a combi-nation of both. Most commonly used hasbeen lagged price. However, since livestockprices generally are quite cyclical, the arbi-trary use of lagged price seems unnecessarilynaive. Although the average producer maynot formulate price expectations as accuratelyas some econometric forecasting models, helikely considers the cycle. Thus, the ap-proach taken here is to define expected pricesas those predicted by a polynomial distributedlag model [Almon] of annual own-prices priorto the year of decisionmaking. Although thisautoregressive model may not predict actualprice as well as an econometric forecastingmodel [Leuthold, et al.], it does account forcyclical effects.
Alternative polynomial degrees rangingfrom 1 to 4 and lag lengths from 4 to 5 yearswere considered. The final choice was basedon R2's and ratios of coefficients to standarderrors. In the feeder cattle and breeding sowinventory equations, expected steer slaugh-ter prices are used in place of expected aver-age steer-heifer slaughter prices since theyare highly correlated; a quadratic polynomialwith lag of 4 years was chosen. For expected
50
pork prices the polynomial is quadratic with alag of 5 years. For expected corn prices acubic polynomial with a 5-year lag was used.R2 's are .83, .77, and .78, respectively.
The polynomial lag functions for steerslaughter price and corn price in year t+2yielded very low R2's, and were dominatedby annual prices in the year prior to de-cisionmaking. In addition, steer slaughterprices in year t+2 were more highly corre-lated with lagged feeder steer prices thanwith lagged steer slaughter prices. Con-sequently, lagged feeder steer and cornprices are used as proxies for expectedsteer-heifer slaughter and corn prices in yeart+2 in the breeding herd inventory demandequation.
Empirical Results
Estimated relationships for beef supply,imports and inventory appear in Table 1.Ninety-one percent of the estimated param-eters have hypothesized signs, and 85 per-cent of the coefficient to standard error ratiosare greater than 1.0.8
Domestic Supply
Of current prices, the estimated param-eters on alternative price in the good steersupply equation and own-price in the cowslaughter supply equation are contrary to ex-pectations. All other coefficients are as ex-pected.
Increases in feeder cattle inventory are as-sociated with increases in supplies of choicesteers and choice and good heifers, and de-creases in good steer slaughter; only the lastsign is inconsistent with expectations. An in-crease of one animal in feeder cattle in-ventory is associated with increases of 598,312, and 57 pounds in choice steer, choiceheifer, and good heifer supply, respectively,and a decrease of 39 pounds in good steersupply. Combined heifer slaughter supplyresponse to feeder cattle inventory is lower
8For small samples, the test statistic does not have a tdistribution in simultaneous equation methods; the tratio is regarded only as a guide [Kmenta, p. 584].
December 1979
Ospina and Shumway Beef Supply Response
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Western Journal of Agricultural Economics
than steer supply response (a) because heifercarcasses typically weigh less than steer car-casses and (b) because a substantial portion ofheifers are withdrawn from feeder cattle in-ventory for normal breeding herd replace-ment.
Increases in demand for breeding herd in-ventory changes are associated with de-creases in slaughter supplies of cows andchoice and good heifers, as hypothesized.The magnitudes of these coefficients suggestthat about one-third of the variation in breed-ing herd inventory demand occurs by alter-ing the replacement-heifer retention rate,and the remaining two-thirds by varying thecow culling rate. The absolute sum of thesethree coefficients is 539, which exceeds aver-age carcass weight of slaughter cows, 491pounds, but is less than that of slaughterheifers, 556 pounds.
The coefficients on the beef and dairybreeding herd inventories (IBH and IDH)are larger than average carcass weight mul-tiplied by typical replacement rates. Assum-ing replacement rates of 14 percent and 25percent for beef and dairy, respectively [Os-pina and Shumway 1978, p. 148], the abovemultiples would be 69 and 123. The esti-mated coefficients are substantially greaterthan these figures, implying that either re-placement rates are actually higher (i.e.,about 26 percent and 34 percent) or cowsslaughtered (not slaughtered) due to in-creases (decreases) in breeding herd in-ventory are heavier than average.
Inventories
As hypothesized, feeder cattle inventoriesrespond positively to the expected steer-cornprice ratio and negatively to the expectedpork-corn price ratio and to vealer price. Thecoefficient of lagged breeding herd inventory,.77, is a reasonable approximation of percentcalf crop.
Demand for changes in breeding herd in-ventory responds positively to expectedfeeder steer prices and range conditions, andnegatively to expected corn prices, as
52
hypothesized. The magnitude of the partialadjustment coefficient, c (i.e., the negative ofthe beef breeding herd inventory param-eter), is smaller than would be expected. Itindicates a very long mean lag in adjusting todesired inventory, (l-c)/c = 25 years. Thisfigure is not consistent with previous findingsabout beef cycles [Freebair and Rausser].
Import Supply
Supplies of beef imports respond positivelyto current cow prices. In 1964, the Meat Im-port Bill introduced a system of quotas onbeef imports. Although quotas have beenbinding for only a few years [USDA, Live-stock and Meat Situation, February 1975],their presence has contributed to shifting outthe intercept (DQUO) and increasing theslope (DUP) of the estimated import supplyequation. The responsiveness of imports todomestic beef price changes was reduced bynearly two-thirds.
Supply Elasticities
Estimated supply elasticities are presentedin Table 2 along with estimates derived fromprevious studies. Elasticities for heifers aregreater than for steers. This finding is consis-tent with Jarvis' argument that the slaughterelasticity of females is normally greater sincethere is an alternative market for heifers, thatis, for breeding stock (pp. 501-2). The crosselasticities with respect to corn price indicatethat as corn price increases, producers re-duce the amount of grain fed. This decreasesboth the total amount of slaughter beef andits average quality since fewer animals attainthe choice grade and more are slaughtered atthe good grade. With the negative relation-ship between current cow price and slaugh-ter supply, it is inferred that current cowprice movements are strong indicators of fu-ture slaughter prices and that the consequentdemand for inventory change dominates theresponse.
The derived aggregate supply elasticity ispositive, thus consistent with our empirical
December 1979
Ospina and Shumway
TABLE 2. Domestic Slaughter Beef Supply Elasticities with Respect to Current Year Prices,Computed at Mean Price Levels
Elasticity with Respect to the Price of
Beef Category Choice Beef Good Beef Utility Beef Corn All Beef
2.63.00
3.16- .85
-2.50.12
-2.681.34
-. 18
-. 65.31
-1.03.02
- .25 .14
Fed Beef Non-Fed Beef All Beef
Other studies:
ReutlingeraSteersHeifersCowsAll Beef
Langemeier and ThompsonFed BeefNon-fed BeefAll Beef
Tryfos
Freebairn and RaussercFed BeefNon-fed BeefAll Beef
Folwell and ShapouriSteer-HeiferOther BeefAll Beef
Shuib & Menkhaus e
Fed BeefNon-fed Beef
.23- .55
.61
.06
.04
.14- .97
aSupply elasticities are with respect to prices lagged one year.blncludes import supply.CAt 1970 prices.dNeither current nor one-year lagged beef prices are included in these supply equations.eSupply of number of federally inspected steers.
hypothesis. 9 The elasticity of supply with re-spect to corn price is higher in absolute valuethan the own price elasticity. This resultsuggests that grain price manipulation may
90ne third of the product price parameters are statisti-cally weak. However, treating those parameters as zerowithout re-estimating the remaining parameters stillyields a positive aggregate supply elasticity, 0.19.
be a more effective policy tool than beef pricemanipulation for altering beef output in theshort run.
Pork and Broiler Supply
Pork and broiler supply and breeding sowinventory equations are presented in Table 3.The signs of the pork and corn price coeffi-
cients in the pork supply equation are con-trary to theoretical reasoning, but consistentwith prior empirical findings [Freebairn andRausser; Tryfos]. Breeding sow inventoriesrespond positively to the expected pork-cornprice ratio. The sign of the expected steer-corn price ratio coefficient is contrary to ex-pectation; thus, it does not support the no-tion of competition among beef and porkproduction suggested by the estimatedfeeder cattle inventory equation.
All coefficients in the broiler supply equa-tion have the expected signs. This equationrepresents the recursive block of the model.
Demand
Table 4 presents the estimated demandequations for all three qualities of beef, forpork, and for broilers. Negative response ofper capita demand to own-price changes andpositive response to income changes are ob-served in all demand equations except goodbeef demand. While it may be reasonable toinfer that good beef is the inferior good ratherthan utility beef (see Freebairn and Rausser;Langemeier and Thompson; Shuib and Menk-
haus for evidence of a negative income elastic-ity for non-fed beef), serious consideration ofgood beef as a "Giffen" good seems logicallyuntenable [Ospina and Shumway 1980].At this point, the empirical finding of a nega-tive income coefficient for good beef demandis viewed as a hypothesis in need of furthertesting. The positive own-price coefficient isalso not ignored in the subsequent aggrega-tion since it has a small standard error; how-ever, it is viewed more as an empirical anom-aly due to data limitations than as a serioushypothesis. The coefficient on the wholesaleprice index in this equation also is contrary toexpectations.
Estimated beef demand elasticities arepresented in Table 5 along with estimates de-rived from previous studies. The cross pricecoefficients indicate complementarity amongcertain qualities of beef (e.g., choice andgood, good and utility) and among a particu-lar beef quality (choice, good) and othermeats. Similar results have been reported inprevious studies. Freebairn and Rausser(1975) argue that while this is possibly due tospurious relations, it also could be explainedby consumer preference for a varied meatmenu.
TABLE 3. Estimated Stochastic Equations, Supply and Inventory, Pork, and Broilers
aRetail level.bAt 1973 levels.CAt farm level, George and King's elasticity estimate is -. 42.
Short-Run Impact of CornPrice Changes - Policy Implication
Because major policy instruments are fre-quently invoked to alter free market grainprices, the short run impacts of a change incorn price on beef prices, supply and compo-sition will be examined briefly. To evaluatesuch impacts, the reduced form model wasderived by the procedure outlined byGoldberger (pp. 365-388).10 The reducedform coefficients (impact multipliers) de-scribe the current period effect of a change in
'Two operating assumptions were imposed to permitthe derivation: (a) weights used to calculate beef andother meat price variables were treated as constants,and (b) the per capita operator was treated as constantfor each period and was used to specify demandequations in total quantities. Thus, the nonlinear iden-tities were transformed into linear form.
56
the exogenous variable (in this case cornprice) on the endogenous variables (beefsupplies and prices) after taking into accountthe interdependencies among currentendogenous variables [Goldberger, p. 369].
The estimated short-run impacts of a $1.00per bushel increase in corn price are re-ported in Table 6. Signs of the beef supplyand price multiplier estimates are consistentwith those of the structural model. The esti-mated magnitudes imply that a $1.00 perbushel increase in corn price decreases cur-rent slaughter supply by 1.7 billion pounds;choice beef supply decreases 2.9 billionpounds, and good beef supply increases 1.2billion pounds. Choice beef price increases$8.80 per cwt; good beef price increases$6.30 per cwt.
Based on 1976 supply and price levels, theimpact multipliers indicate that a $1.00 per
December 1979
Ospina and Shumway
bushel increase in corn price (45 percent of1976 price) would result in a substantial de-crease (25 percent) in choice beef suppliesand a marked increase (13 percent) in goodbeef supplies in the same year. Choice beefprice increases 15 percent and good beefprice increases 11 percent. The choice-goodquantity ratio decreases from 1.32 to .88 (seeTable 6), while the choice-good price ratioincreases from 1.05 to 1.08. Estimatedchanges in the composition of slaughter beefsupply are also presented in Table 6. Majordecreases are in choice steer and heifer sup-ply. The most important increase is in goodsteer supply.
Conclusions
This study has focused on conceptual prob-lems and empirical estimation in modelingslaughter beef supply. Three basic issueswere addressed in model specification: dis-aggregation according to animal class and
quality components, differentiation betweencurrent and expected price effects on slaugh-ter supplies, and simultaneity in slaughtersupply, demand, and inventory accumulationdecisions. An econometric model was de-veloped to estimate supply, inventory, anddemand relations for slaughter beef in theU.S. for the period 1956 to 1975.
Although some are statistically weak, mostestimated beef supply and inventory param-eters have the expected signs. Positive own-price and negative alternative price coeffi-cients are estimated for choice steer andheifer supply. Supply of choice beef is nega-tively related and supply of good beef posi-tively related to corn price. Price parameterscontrary to expectations are estimated onown-price in the cow slaughter supply equa-tion and alternative price in the good steerequation. Aggregate short-run beef supplyelasticity derived at mean prices from thecomponent estimates is positive and consis-tent with our empirical hypothesis. It is near
TABLE 6. Estimated Effects of a $1.00 per Bushel Increase in the Price of Corn on Beef Supply,Composition, and Price
Variable Levels,
Predicted LevelsMultiplier, Actual Levels, Following Corn
the upper limit of prior estimates. Composi-tion of slaughter beef supply is highly depen-dent on beef and grain prices. The corn priceelasticity of supply for all beef is higher inabsolute value than the own-price elasticity.Both the corn price elasticities derived fromthe structural model and the estimated re-duced form impact of a change in corn pricedocument the sensitivity of beef supply,composition, and prices to free market and/orpolicy-induced changes in corn price.
On the demand side, all own-price incomecoefficients show the expected signs except inthe good beef demand equation. Most crossprice coefficients do not support the notion ofsubstitutability among beef types and be-tween beef and other meats.
In drawing these empirical conclusions,several limitations, which are important can-didates for further evaluation, must be noted:
(a) Although pragmatically defensible, thedisaggregation procedures are basedon rules that are at least partially arbi-trary. Equal justification could perhapsbe found for alternative rules. Existingdata pose a serious limit on the confi-dence that can be placed in any beefsupply response estimate.
(b) The process by which producers for-mulate price expectations is not clearlyunderstood. Because no historical dataseries exists for expected beef prices,such variables must be constructed bythe economist and consequently aresubject to non-unique definitions. Thespecification for expected prices likelycould be substantially improved overthat used here. Certainly, the justifica-tion is weak for excluding current pricefrom the expected price specificationfor the breeding herd inventory de-mand equation.
(c) Since some of the questions posed hereare dynamic in nature, further valida-tion of the dynamic attributes of themodel is an important priority for fu-ture work.
(d) The model is derived and estimated as-
58
suming perfect competition. The ef-fects of risk on beef supply responsewere not evaluated.
References
Allen, R. G. D. Mathematical Analysis for Economists.New York: St. Martin's Press, 1960.
Almon, S. "The Distributed Lag Between Capital Ap-propriations and Expenditures." Econometrica 33(1965): 178-96.
Bentley, E., J. R. Waters, and C. R. Shumway. "De-termining Optimal Replacement Age of Beef Cows inthe Presence of Stochastic Elements." S. J. Agr.Econ. 8 no. 2 (1976):13-18.
Ehrich, R. L. Economic Analysis of the U.S. Beef CattleCycle. Wyoming Agr. Exp. Sta. Science Monograph 1,1966.
Elam, T. E. "Canadian Supply Functions of Livestockand Meat: Comment." Amer. J. Agr. Econ. 57
(1975):364-65.
Folwell, R. J. and H. Shapouri. An EconometricAnalysis of the U.S. Beef Sector. Washington StateUniv. Tech. Bul. 89, 1977.
Freebairn, J. W. and G. C. Rausser. "Effects ofChanges in the Level of U.S. Beef Imports." Amer. J.Agr. Econ. 57 (1975):676-88.
Gardner, B. L. "Futures Prices in Supply Analysis."Amer. J. Agr. Econ. 58 (1976):81-84.
George, P. S. and G. A. King. Consumer Demand forFood Commodities in the United States withProjections to 1980. Giannini Foundation Monograph26, 1971.
Griliches, Z. "The Role of Capital in InvestmentFunctions." Measurement in Economics. ed. C. K.Christ, Palo Alto: Stanford University Press, 1963.
Goldberger, A. S. Econometric Theory. New York:Wiley & Sons, 1964.
Jarvis, L. S. "Cattle as Capital Goods and Ranchers asPortfolio Managers: An Application to the ArgentineCattle Sector." J. Polit. Econ. 82 (1974):489-520.
Kmenta, Jan. Elements of Econometrics. New York:MacMillan Company, 1971.
December 1979
Ospina and Shumway
Knight, D. A. "Evaluation of Time Series Data for Es-timating Supply Parameters."Agricultural SupplyFunctions. ed. E. O. Heady, et al. pp. 74-104. Ames:Iowa University Press, 1961.
Langemeier, L. N. and R. G. Thompson. "Demand,Supply, and Price Relationships for the Beef Sector,Post-World War II Period." J. Farm Econ. 49(1967):169-83.
Leuthold, R. M., A. J. A. MacCormick, A. Schmitz andD. G. Watts. "Forecasting Daily Hog Prices andQuantities: A Study of Alternative Forecasting Tech-niques."J. Amer. Statistical Assn. 65(1970):90-107.
Nelson, G. and T. H. Spreen. "Monthly Steer andHeifer Supply." Amer. J. Agr. Econ. 60 (1978):117-25.
Ospina, E. and C. R. Shumway. "Possible Implication ofVoids in USDA Cattle Slaughter Data: Comment."Amer. J. Agr. Econ. 60 (1978):148-50.
Ospina, E. and C. R. Shumway. "Disaggregated Econ-ometric Analysis of U.S. Slaughter Beef Supply."Texas Agr. Exp. Sta. Technical Monograph 9, 1980(forthcoming).
Reutlinger, S. "Short Run Beef Supply Response." J.Farm Econ. 48 (1966):909-19.
Tryfos, P. "Canadian Supply Functions of Livestock andMeat." Amer. J. Agr. Econ. 56 (1974):107-113.
U.S. Department of Commerce. Business Statistics.Washington: U.S. Government Printing Office, 1971.
U.S. Department of Commerce. Survey of CurrentBusiness. BLS, Washington, bimonthly series, 1971-1976.
Williams, W. F., E. K. Bowen, and F. C. Genovese.Economic Effects of U.S. Grades for Beef. USDAMktg. Res. Rep. 298, Washington: U.S. GovernmentPrinting Office, 1959.
Shuib, A. B. and D. J. Menkhaus. "An EconometricAnalysis of the Beef-Feed Grain Economy." W. J.Agr. Econ. 1 (1977):152-156.
