Steer and Heifer Price Differences in Live...

Steer and Heifer Price Differences inthe Live Cattle and

Carcass Markets

Robert W. Schultz and John M. Marsh

A dynamic model is used to estimate quarterly price differences between steers and heifersin the feeder, slaughter, and carcass markets. For cattle within the same weight and graderange, their price differences are hypothesized to be influenced by seasonal, economic, andstochastic factors. The effect of stochastic factors is large in the carcass and fed cattle markets,partly reflecting time changes in evaluation of steer and heifer quality in the live cattle anddressed meat trades. Stochastic factors are less prevalent at the feeder level, although risk ofplacing pregnant heifers in feedlots and weather are important. Steer and heifer inventories,slaughter prices, cost of gain, and margins explained most of the variation in feeder steer andheifer price differences.

Price premiums and discounts betweensteers and heifers typically vary over timeand space. For example, periodically,young heifers may sell at a smaller pricediscount during the rapid growth stage ofthe cattle cycle compared to the deceler-ation stage since they are in greater de-mand for herd replacement (Hasbargenand Egertson). The opposite may run trueduring the herd liquidation period of thecycle. Also, across regions of the U.S., somefeedlots (or packers feeding cattle) de-mand relatively more heifers since thenumber of days on feed is shorter; that is,heifers mature at lighter finishing weightsthan steers. However, some large com-mercial cattle feeders may demand rela-tively more steers because the cost is higherif they must handle large numbers of non-open heifers (BEEF Magazine).

This paper analyzes price differencesbetween steer and heifer cattle at thefeeder, slaughter, and wholesale levels of

Robert W. Schultz and John M. Marsh are formerGraduate Student and Research Assistant and Pro-fessor, respectively, of the Department of Agricul-tural Economics and Economics, Montana State Uni-versity.

Montana Agricultural Experiment Station No. J-1713.

Western Journal of Agricultural Economics, 10(1): 77-92© 1985 by the Western Agricultural Economics Association

the market (the latter restricted to carcassprices). These price differences are re-stricted to cattle within the same weightrange and grade categories. Some produc-ers feel that the magnitude of sex pricedifferences for cattle of the same weightand grade are not justifiable and that thereis a bias against heifers. An example isheifers that are placed in feedlots at a $10-$12 per cwt. discount to steers, but whenfinished as fed heifers, they sell at only a$2-$3 per cwt. discount to fed steers. Thus,if the magnitude of this price spread isunwarranted (too large), returns from sell-ing feeder steers and heifers (to feedlots)are unjustifiably low.

To test sex price behavior, a quarterlyeconometric model was formulated, di-rectly estimating steer and heifer pricesand their price differences based uponseasonal and economic variables. Price be-havior is hypothesized to be a dynamicadjustment process, attributed to biologi-cal factors and economic expectations inthe market. For example, if feedlot costof grain increased, feedlot operators'change in demand for steers versus heifers(i.e., adjustments in their price differ-ences) would take into account expectedbiological performance, feed efficiency,

Western Journal of Agricultural Economics

and the perception of how permanent theincrease in the cost of gain might be.

Historical data show that, at all threemarket levels, prices of steers are consis-tently higher than prices of heifers withinthe same weight and grade categories. Thegreatest difference occurs at the feederlevel, with considerably smaller pricespreads at the slaughter and carcass levels.Also, the largest variations in steer andheifer price differences occur in the feed-er market. At the feeder level, Boggs andMerkel attribute these price differences tophysiological and growth factors in steersversus heifers and to the costs of handlingpregnant heifers in feedlots. More recent-ly, increased usage of abortifacients hasreduced the pregnancy problem. At theslaughter level, meat packers generallyconsider steer carcasses to be of betterquality than heifer carcasses since theytend to have better marbling characteris-tics (Riley). Since, in addition, the averageweights of heifer carcasses are less thanthose of steer carcasses, per unit process-ing costs for heifers are higher. Given thesefactors, there has been a relatively higherdemand for steers.

Previous Work

The literature is meager regarding steer-heifer price premiums and discounts atdifferent levels of the market. Most of thework has been done at the stocker-feederlevel. Buccola and Jessee (1979) investi-gated feeder price differences by sex andanalyzed their variations over time andspace. Feeder steer and heifer price dif-ferences were a function of differentbackgrounding and finishing costs perpound of gain, expected future feederprice, price differences between slaughtersteers and heifers, and inventories of steersand heifers. Results also showed that feed-er sex price differences varied accordingto feeding regions, reflected in the pro-portion of steers to total cattle on feed andin the differences between slaughter prices

of steers and heifers. Buccola (1980)showed that breakeven analysis could beused to analyze price premiums and dis-counts between different lots of feedercattle. The results indicated that the vari-ables that impact individual feeder pricesalso determine price differences betweenclasses of feeder cattle. Feeder cattle price-weight slopes were estimated as a functionof expected slaughter cattle prices, feedprices, soil moisture conditions, and in-ventory adjustments. Lambert et al. de-termined the effect of management andmarketing factors on the prices of calvesand yearlings of both gender. Though em-phasis was on price differences acrossweight categories, the results also mea-sured discounts on steer and heifer pricesemanating from the traits of health, bodycondition, frame, and grade. The statisti-cal results revealed that steer price-weightdiscounts exceeded those for heifers whenthese traits deviated (negatively) fromnormal levels for both sexes. Folwell andRehberg utilized cross section data to es-timate prices of individual lots of calvesand stocker-feeders in eastern Washing-ton. The results revealed that premiumsand discounts were sensitive to sex, weight,grade, breed, lot size, and general ap-pearance of cattle.

Model and Methodology

Our structural model tests for system-atic and stochastic behavior in prices andprice differences for steers and heifers viadistributed lags. Distributed lags are hy-pothesized since, on a quarterly basis, theimpacts of certain economic variables areexpected to extend beyond one time pe-riod. The model also provides the neces-sary link between the carcass, slaughter,and feeder levels of the market. Theselinks, as seen below, are accomplished asprices from the higher market levels feedinto the lower market levels. The latter isnecessary since, on a short term basis,feeder prices depend upon prices in the

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Steer-Heifer Price Differences

slaughter and dressed meat trade (Bresterand Marsh; Crom; Cromarty). Thus, it ishypothesized that prices for steer andheifer carcasses and their premium-dis-count relationship directly impact slaugh-ter steer and heifer price differences(USDA). The slaughter market, in turn,partly determines steer and heifer pricesat the feeder level. Gender price differ-ences at each market level are also uniquein that they are characterized by certaineconomic variables specific to only thatlevel. An example is feedlot cost of gainat the feeder level and the value of by-products at the slaughter level.

The following equations represent theprice relations for steers and heifers at thethree market levels:

[PSCt, PHC,, PSC - PHC,; D, QSHCQ_, QPKPYtj,BPVC,t_, Y,_j, MCRt-,, E(DEPt-,), U,] (1)

[PSSt, PSH, PSSt - PSHt; D, QFStj, QNFStj,PSCt_j, BPVFt_,, E(DEP,_), U2t] (2)

[PFS4-5,, PFH4-5t, PFS4-5t - PFH4-5,; D, PSSt_,,QFSj,, QFH,_,, MFCj,, PCtj, E(DEPt), U3t ] (3)

[PFS6-7t, PFH6-7t, PFS6-7t - PFH6-7t; D, PSStj,QFStj, QFHtj, MFCtj, PCt_,, E(DEPt_), U4J] (4)

iBj

Table 1 presents the definitions of thevariables. All variables are stated in nom-inal terms, however, in the regression pro-gram the price and income variables aredeflated by the Consumer Price Index(1972 = 100) and the quantity variablesare deflated by population. Quarterly datafrom 1971 through 1982 are used, gath-ered from the USDA's Livestock, Meat,and Wool Statistics and Livestock andMeat Statistics reports. All variables to theleft of the semicolons are the dependentvariables, while all variables to the rightof the semicolons are the independentvariables. A total of 12 price equations arespecified, eight consist of individual steerand heifer prices and four consist of theirprice differences. For each market level,the same set of regressors is specified inthe price premium equations as in the in-dividual price equations, since the former

are determined by similar economic andtechnical factors (i.e., cost of gain and in-ventory levels).

The specification of each function isbased on theoretical precepts and priorknowledge of the industry. At the carcasslevel (equation 1), steer and heifer pricesare hypothesized to be a function ofwholesale production (QSHC, QPKPY),carcass by-product value (BPVC), a retaildemand factor (Y), and carcass-retailmarketing cost (MCR). Beef carcass pro-duction and pork and poultry productionmeasure the effects of direct and compet-itive meat supplies on price. By-productsextracted from carcasses are usually soldby packers for edible and inedible pur-poses. Thus, changes in their values areexpected to affect the value (price) of steerand heifer carcasses. Income is specifiedto measure changes in retail demand thatfilter back to the wholesale level. Thus, ifconsumer demand changes because of ex-ogenous shifts in disposable income, thisshould have a noticeable impact on thedressed meat trade. The margin variableis included to measure the impact ofchanges in processing and distributioncosts on carcass prices. Increases in suchcosts, ceteris paribus, would decrease car-cass prices as retailers would decrease theiroffer (buying) price.

At the slaughter level (equation 2), steerand heifer prices are hypothesized to re-flect changes in production (QFS andQNFS), slaughter by-product values(BPVF), and steer carcass price (PSC). Thevariables QFS and QNFS are numbers offed cattle and nonfed cattle slaughtered,respectively, where the latter represents alower quality grade of beef. Changes inthe value of edible and inedible slaughterby-products are hypothesized to affectslaughter price since they usually pay forslaughter costs and profits (Doane). Final-ly, the inclusion of steer carcass price (PSC)is to act as a proxy for the direct effect ofchanges in the wholesale market on thelive slaughter market. For example, since

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TABLE 1. Definitions of the Variables for the Steer and Heifer Price Premium Model.

PSC = price of Choice, yield grade #3 steer carcasses, 600-700 Ibs., Omaha ($/cwt.) (en-dogenous).

PHC = price of Choice, yield grade #3 heifer carcasses, 600-700 Ibs., Omaha ($/cwt.) (en-dogenous).

PSC - PHS = the difference between steer and heifer carcass prices ($/cwt.) (endogenous).QSHC = quantity of steer and heifer carcasses (billions of Ibs.) (exogenous).

QPKPY = quantity of commercial pork and young chicken supplied (billions of Ibs.) (exogenous).BPVC = by-product value for Choice, yield grade #3 beef carcasses (cents/lb.) (exogenous).

Y = per capita disposable personal income (dollars) (exogenous).MCR = beef carcass-to-retail margin (cents/lb.) (endogenous).

D = seasonal dummy variables specific to three calendar quarters with the January throughMarch period omitted.

E(DEPt_,) = the ith lag on the expected value of the dependent variable (applies to all price equa-tions).

PSS = price of Choice, yield grade #3 slaughter steers, 900-1,100 Ibs., Iowa ($/cwt.) (endog-enous).

PSH = price of Choice, yield grade #3 slaughter heifers, 900-1,100 Ibs., Iowa ($/cwt.) (en-dogenous).

PSS - PSH = the difference between slaughter steer and heifer prices ($/cwt.) (endogenous).QFS = quantity of commercial fed steer and heifer slaughter (millions of head) (exogenous).

QNFS = quantity of commercial cattle slaughter, nonfed steer and heifers (millions of head)(exogenous).

BPVF = by-product value for Choice, yield grade #3 slaughter steers (cents/lb.) (exogenous).PFS4-5 = price of medium frame #1 steer calves, 400-500 Ibs., Kansas City ($/cwt.) (endoge-

nous).PFH4-5 = price of medium frame #1 heifer calves, 400-500 Ibs., Kansas City ($/cwt.) (endoge-

nous).PFS6-7 = price of medium frame #1 feeder steers, 600-700 Ibs., Kansas City ($/cwt.) (endoge-

nous).PFH6-7 = price of medium frame #1 feeder heifers, 600-700 Ibs., Kansas City ($/cwt.) (endog-

enous).PFS4-5 - PFH4-5 = the difference between steer and heifer calf prices ($/cwt.) (endogenous).PFS6-7 - PFH6-7 = the difference between feeder steer and heifer yearling prices ($/cwt.) (endogenous).

QFS = number of steers on feed, 13 states, millions of head (endogenous).QFH = number of heifers on feed, 13 states, millions of head (endogenous).MFC = farm-to-carcass marketing margin (cents/lb.) (endogenous).

PC = price of #2 yellow corn, Omaha ($/bu.) (exogenous).U = random disturbance terms (numbered for each equation). Each is assumed to have

zero mean, constant variance, and serial independence.

carcass price represents an output price topackers, an exogenous increase in carcassprice would cause packers to bid higherprices for existing supplies of slaughtercattle.

Calf and yearling steer and heifer prices(equations 3 and 4) directly affect the wel-fare of cow-calf and yearling producers.These prices are hypothesized to be afunction of steer price in the fed slaughtermarket (PSS), inventories of feeder steersand heifers (QFS, QFH), cost of gain inthe feedlot (PC), and a marketing cost be-

tween the rancher and the packer (MFC).A priori, the effect of a change in slaugh-ter market price would be expected to ex-ert a strong influence on feeder prices sincethe former represents the output price tothe cattle feeder (thus, affecting the de-rived demand for feeder cattle inputs).Steer and heifer inventories reflect feedercattle supplies. It is expected that changesin the supply of one gender relative toanother would change their price differ-ence. The cost of gain, represented by theprice of corn, would be expected to influ-

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ence feeder steer and heifer prices be-cause of its effect on cattle feeding mar-gins. Coupled with the fact that feedconversion of heifers is not as efficient asthat for steers, changes in feed costs wouldbe expected to change the relative place-ment demands between steers and heifers.Also, feeder prices for each weight cate-gory may not respond equally to changesin feed costs because of different risks in-volved in raising calves and yearlings tofinishing maturity. Margins were includedto capture the effect of marketing costs onthe derived demand for feeders. Ceterisparibus, larger marketing charges trans-late into reduced derived demand, hencelower feeder cattle prices.

All the equations above are treated asreduced form relations, estimated by ra-tional distributed lags. Rational lags havebeen shown to have a flexible generatingfunction which can approximate most lagforms (Jorgenson). Sims also shows that es-timating unknown lag coefficients by ra-tional lags may yield tighter approxima-tion properties, i.e., a more preciseestimate of the true lag structure, thanthose of other dynamic regression meth-ods. Each equation is specified as a differ-ence equation; however, the lagged ex-pectations of the dependent variable areused rather than the lagged observed val-ues. This procedure allows the systematicpart of each equation to be strictly exog-enous when the disturbance term is au-tocorrelated (Marsh). For any price equa-tion, the application of Jorgenson's rationallag is:

Pt = W(L)Z, (5)

and

W(L) = (6)X(L)'

where Zt is a vector of independent vari-ables; W(L) is a rational generating func-tion expressed as the ratio of two polyno-mials (with no characteristic roots incommon); the numerator f(L) is an mth

order polynomial in the lag operator L,and the denominator X(L) is an nth orderpolynomial in the lag operator L. 1 Thefunction W(L) is constrained to all of Zt,thus, the denominator X(L) is imposedacross all the independent variables. Thisimplies, for example, that if X(L) implieda first order difference equation, then thedependent variable would decline geo-metrically over time in response to achange in any independent variable (Gri-liches). If we arbitrarily let m = 1 and n= 2, apply the concept of nonstochasticdifference equations as given in Marsh andRucker et al., and add a disturbance term,equation (5) is reduced to:

P, = f0 + ,Zt, + f2Z,_I + XE(P,_,)+ \2E(P,_2) + u,.

Equation (7) is a second order differenceequation and the error term is an autore-gressive structure of ut = put- +. +

pqut-q + ct, where E, is white noise. Thelagged expectations of the dependent vari-able are purely predetermined, therefore theestimated parameters of the systematicportion of the equation are uncorrelatedin the limit with the estimated parametersof the error structure. In models of thisnature where there may be an autocor-related error structure and/or lagged ex-pectations of the dependent variable, non-linearities in the parameters occur. Thus,least squares estimates of the model wereobtained by a consistent maximum like-lihood estimator developed from a modi-fied marquardt nonlinear least squares al-gorithm. To handle potential problems of

1In the rational lag formulation, its application inour model was that f(L) determined the order oflags on the independent variables and X(L) deter-mined the order of lags on the dependent variables.Initially, they were set at a lag of two quarters. Theerror structure was initially estimated as second or-der autoregressive, the same order as the differenceequation. However, based on asymptotic t ratios,the higher order f, X, and p coefficients were trun-cated if not significant. Thus, in the final set, therewas a variation among the equations as to the orderof lags.

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(7)


TABLE 2. Statistical Results of Quarterly Steer and Heifer Carcass Prices and Price Differ-ence.

Variablesa

Equation Constant D2 D3 D4 QSHC QSHC- 1

PSCc -11.478 -. 559 -1.606 -2.004 -13.638 10.943(-1.630) (-.681) (-2.378) (-2.394) (-5.124) (3.215)

PHC -7.893 -. 995 -2.257 -2.051 -14.150 10.979(-1.095) (-1.189) (-3.420) (-2.522) (-5.452) (3.267)

PSC - PHC -1.157 .150 .477 .278 .899 -(-.984) (.657) (2.095) (1.220) (1.653)

a The asymptotic t ratios are given in parentheses below each coefficient. The critical boundary is 2.030 for a95 percent probability level (degrees of freedom are 35).

b Represents the expected value of the lagged dependent variable.c Regression results for PSC are: adjusted multiple R-squared statistic (R2) = .955, standard error of estimate

(SY) = 1.185, and Durbin-Watson statistic (DW) = 2.039. For PHC: R2 = .955, SY = 1.164, and DW = 1.944.For PSC - PHC: R2 = .074, SY = .546, and DW = 1.703.

simultaneity, all right hand side variablessuspected as jointly endogenous (see Table1) were estimated as instrumental vari-ables, permitting consistent and asymp-totically efficient estimates (Hanssens andLiu).2

Empirical Results

Tables 2 through 9 present the regres-sion results of the steer and heifer pricesand their estimated price flexibility coef-ficients. The latter are estimated for se-lected time periods, based upon the dis-tributed lag behavior of the dependentvariables. 3 All the ensuing equations rep-resent, statistically, the best estimates sincemodel tests revealed no superior specifi-cation of distributed lags and order of au-tocorrelation.

2 In Table 1 all the independent variables consideredas endogenous were estimated as instrumental vari-ables from a set of reduced form equations. Theo-retically, their predicted values (used as the instru-ments) are uncorrelated in the limit with disturbanceterms in the structural equations.

3A mathematical algorithm using a recursion for-mula was used to calculate the partial derivativesof the dependent variables with respect to changesin the independent variables. These time paths ofthe endogenous variables, or their distributed lagbehavior, served as the basis to estimate the variouslength of run price flexibilities presented in the ap-propriate tables.

Steer and Heifer Carcass Prices

Steer and heifer carcass prices are esti-mated as geometric distributed lags (i.e.,first order difference equations). First or-der serial correlation was not significant.Table 2 presents the statistical results ofthe regression equations. Table 3 presentsthe price flexibility coefficients for differ-ent time periods. All asymptotic t values(except those of the intercepts) indicatethe coefficient estimates are significantlydifferent from zero at the 95 percentprobability level. The geometric lag ef-fects of the independent variables declinerelatively slowly because of the large es-timated coefficients on the lagged depen-dent variables (0.96 and 0.94).

The coefficient estimate of the pork andpoultry production variable, QPKPY, hasa positive sign. This result appears con-trary to theoretical reasoning since a neg-ative effect would be expected with com-petitive meat supplies. Brester and Marshshowed such substitutes to be significantwith the correct sign in a retail beef priceequation. However, Freebairn and Rausserand Hayenga and Hacklander encoun-tered sign problems with substitutes in re-tail beef demand equations. They attrib-uted such results to consumer preferencefor variety in diet menu. Since the colli-nearity of QPKPY with other variables is

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TABLE 2. Extended.

Variablesa

QPKPY BPVC BPVC- 1 Y Y- 1 MCR E(DEP- 1)b

1.978 11.572 -7.417 .023 -. 016 -. 442 .959(7.676) (4.210) (-2.657) (4.805) (-3.608) (-4.838) (14.441)1.813 13.055 -8.613 .021 -. 015 -. 382 .942(6.967) (4.920) (-3.128) (4.407) (-3.402) (-4.231) (13.704)

not serious, we conclude that this varietypreference may be reflected back to thewholesale market.

Steer and heifer carcass production(QSHC) is specified to measure the effectof wholesale beef production on steer andheifer carcass prices. For each equation,the sum of the regression coefficients forperiods t and t - 1 is negative, which isin agreement with a negative relationshipbetween prices and quantities.4 In Table3 the price flexibilities reflect a slow geo-metric adjustment rate. Through the firsteight quarters it appears that heifer pricemay be slightly more sensitive to produc-tion changes than steer price. Estimatesfor the long-run indicate the opposite(based only upon arithmetic differences inthe price flexibilities). It also can be seenthat the price flexibilities increase withtime, indicating that carcass prices morecompletely adjust to changes in supplyconditions in the market. The effects arecumulative, that is, a one time change insupply has its largest impact in the firsttime period, and then increases at a de-creasing geometric rate. Some of the con-straints that may cause this behavior in-clude short-term price agreements orcontracts between packers and retailers,fixed (short-term) processing and storage

4 Quantities of steer carcass production and heifercarcass production were tested as separate regres-sors. However, their high collinearity precludedsignificant asymptotic t ratios, and, also, producedcoefficient signs inconsistent with theoretical rea-soning.

capacity, and perhaps incomplete marketinformation.5

The value of carcass by-products ishighly significant in affecting short- andlong-run steer and heifer carcass prices.The positive correlation is expected sinceincreases in the value of by-products in-crease the per unit values of steer andheifer carcasses. The heifer carcass priceappears to be more sensitive in the short-run while the steer price appears moresensitive in the long-run (based on arith-metic differences of the price flexibilitycoefficients). For a period of one quarter,a 10 percent increase in the value of by-products leads to an increase in steer andheifer prices by 3.0 and 3.5 percent, re-spectively. Over the long-run, the same 10percent increase produces a 26.2 and 20.7percent increase in the respective carcassprices.

Real disposable income is a shifter ofprimary demand, reflecting changes inconsumer purchasing power. These in-come changes are reflected back to thesteer and heifer carcass market throughpurchases by retailers. The results reveala positive income effect. For example,

5 Such short term constraints are not explicitly mod-eled because of data limitations. However, one vir-tue of the difference equation approach is that thelagged dependent variable captures short term ri-gidities in the market. In the carcass price equa-tions, the large difference equation coefficients sug-gest that sufficient time is required to overcome thementioned constraints. This is not surprising due tothe time involved in beef demand changes and inadjusting plant size and technology.

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TABLE 3. Partial Derivatives and Price Flexibilities of the Distributed Lags in the Steer andHeifer Carcass Market.

Quartersa

Equation 1 2 4 8 Long-run

PSC/QSHC -13.638 -15.769 -19.769 -26.822 -65.105(-.700) (-.809) (-1.014) (-1.376) (-3.340)

PHC/QSHC -14.150 -16.506 -20.820 -28.054 -55.081(-.744) (-.868) (-1.094) (-1.475) (-2.895)

PSC/BPVC 11.572 15.249 22.151 34.324 100.39(.302) (.399) (.579) (.897) (2.624)

PHC/BPVC 13.055 16.746 23.502 34.832 77.163(.350) (.448) (.629) (.933) (2.066)

PSC/Y .023 .030 .042 .063 .178(1.770) (2.308) (3.231) (4.847) (13.695)

PHC/Y .021 .026 .035 .051 .109(1.655) (2.049) (2.759) (4.020) (8.592)

PSC/MCR -. 442 -. 866 -1.661 -3.064 -10.676(-.330) (-.647) (-1.241) (-2.289) (-7.975)

PHC/MCR -. 382 -. 741 -1.400 -2.504 -6.629(-.292) (-.567) (-1.071) (-1.916) (-5.073)

PSC - PHC/QSHCb .899 -(1.928)

a The top figures represent the partial derivatives and the figures below in parentheses are the price flexibilitycoefficients (calculated at the mean values of the variables). Each figure represents the cumulative effects overthe indicated quarterly periods.

b Carcass price difference equations were estimated as static models; therefore, partial derivatives and priceflexibilities were calculated for the first quarter only.

within a period of one quarter, a $100increase in income will lead to an increasein steer carcass price by 2.3 cents perpound and heifer carcass price by 2.1 centsper pound. The estimated income flexi-bility coefficients are highly significant,showing values greater than unity for alltime periods.

The carcass-to-retail marketing marginvariable is specified to capture the effectof changes in per unit processing and dis-tribution costs on the prices of steer andheifer carcasses. The absolute values of theprice flexibility coefficients are less thanunity for a time period of less than oneyear, but are "flexible" (>1.0) for a periodof one year or more. This suggests that ifthere is an increase in distribution costs,in the shorter term, retailers may absorbmore of the cost increase (or pass it on toconsumers) since they may be temporarilylocked in on purchase price agreements

with packers. 6 Over time, however, retail-ers can adjust their purchase price offers(on wholesale meat) in accordance withchanges in costs they face.

The directly estimated difference be-tween steer and heifer carcass prices(PSC - PHC) is reported in Table 2. Theregression results reveal that the only sig-nificant exogenous variable (at the 90 per-cent level) to influence steer price pre-miums is the production of steer and heifercarcasses. The positive regression coeffi-cient is consistent with the results of the

6 Usually these arrangements are through "negoti-ated" transactions or "formula pricing." For ex-ample, under the former if a packer agrees to shipa certain quantity and quality of meat to a retailerin 60 days, the price is negotiated at the time ofthe agreement. Under formula pricing, if a packeragrees to ship a certain quantity and quality ofmeat in 60 days, the price agreed upon is the onethat would be listed on the Yellow Sheet near theday of delivery.

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Schultz and Marsh

individual carcass price equations. That is,increases in carcass production decreaseboth steer and heifer carcass prices, butheifer prices relatively more. For exam-ple, in Table 3 the price flexibility coeffi-cients show that, for a period of one quar-ter, a 10 percent increase in carcassproduction reduces steer carcass prices by7.0 percent and heifer carcass prices by7.4 percent. The difference relates to thegender component of slaughter. The sam-ple data show that significant increases incarcass production stems from increasedslaughter numbers and/or dressed weightsof steers and heifers. Often when there isan increase in slaughter numbers relative-ly more heifers enter slaughter, particu-larly in the deceleration stage of the cattlecycle (the years 1971-77 in the sampledata). Since the distribution of weights be-tween steer and heifer carcasses changeslittle, the additional heifer slaughter yieldsrelatively more total heifer carcass weightthan steer carcass weight.

The adjusted R2 is extremely low, in-dicating that the effects of seasonality andproduction on steer-heifer carcass pricedifferences are quite minimal. This leavesa large impact due to the stochastic errorterm, which may be attributed to severalfactors. One may be variation in quality,as heifer carcasses (even within the sameyield grade) are not always as well mar-bled, showing more fat deposits on theoutside of the meat. Another may reflecthigher per unit processing costs for heiferssince heifer carcasses average lighter inweight than steer carcasses. Also, overtime, there may be random errors due tovariations in the grading (quality andyield) of steer and heifer carcasses.

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TABLE 5. Partial Derivatives and Price Flexi-bilities in the Slaughter Steer andHeifer Market.

Variablesa

Equation PSC BPVF QFS QNFS

PSS .540 .483 -. 698 -1.719(.847) (.126) (-.076) (-.026)

PSH .493 .487 -. 849 -2.127(.797) (.131) (-.095) (-.033)

PSS - PSH .038 - -(1.969)

a The top figures represent partial derivatives and thefigures in parentheses are the price flexibility coeffi-cients (calculated at the mean values of the vari-ables). Each figure is representative of a first quartereffect of an independent variable on a dependentvariable.

products are performed by the same firm.Cattle buying is highly influenced bychanges in wholesale prices; thus, ratherquick adjustments in slaughter priceswould be expected. The independentvariables include the contemporaneousprice of steer carcasses, by-product values,and the quantities of fed and nonfedslaughter. The price of steer carcasses en-ters the slaughter price equations as aninstrumental variable due to its endoge-nous nature in the model. Table 4 givesthe statistical results for steer and heiferslaughter prices while Table 5 presents theestimated price flexibilities.

The market prices of beef carcasses andby-products (meat packer output) play amajor role in the pricing of slaughter steersand heifers. This is confirmed by positivecoefficients that have highly significantasymptotic t ratios. A 10 percent increasein the price of steer carcasses results in an8.5 percent increase in the slaughter steerprice and an 8.0 percent increase in theslaughter heifer price. These results indi-cate that an increase in the market valueof carcasses increases the derived demandfor slaughter inputs, hence slaughterprices.

By-product values in the slaughter sec-tor reflect the prices of hide and offalproducts and usually pay for slaughter

86

costs and profit margins (since carcass val-ue is usually less than live animal value).Consequently, when their values increase,the overall value of the live animal in-creases. This hypothesis is supported bythe positive sign of the coefficient esti-mate. The price flexibility coefficientshows that a 10 percent increase in thevalue of by-products increases steer andheifer slaughter prices by 1.3 percent.

The quantities of fed and nonfedslaughter are specified to account for sup-plies of steers and heifers marketed fromfeedlots and ranches, respectively. Theirnegative coefficient signs are consistentwith economic theory.7 Based on the priceflexibility coefficients, the results show thatfed slaughter has a greater direct impacton steer and heifer prices than does nonfedslaughter (i.e., about three times as great).This is expected since nonfed cattleslaughter, which consists of cull stock andrange fed steers and heifers, competes withfed slaughter and is considered to be oflower quality (Osprina and Shumway).

The equation specification for theslaughter steer and heifer price difference(PSS - PSH) initially included the sameset of exogenous variables as did the in-dividual equations. However, the price ofsteer carcasses was found to be the onlystatistically significant variable (prices ofsteer and heifer carcasses were specifiedas separate independent variables, how-ever, high collinearity precluded their in-dividual statistical significance). The steercarcass price variable, PSC, is positivelycorrelated with the steer-heifer price dif-ference. The reason for its positive effectis based on the relationship between thecarcass and live slaughter markets. Tomeat packers, variables influencing theoutput market (i.e., carcass and boxed beefsales) directly impact the input market

7 Commercial slaughter of steers and commercialslaughter of heifers were also specified as separateregressors in the slaughter price equations. How-ever, strong collinearity among those variablesyielded insignificant asymptotic t ratios.

July 1985


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(purchases of slaughter cattle) since profitmargins are affected. Thus, for example,if retailers were bidding higher for steercarcasses, to meet that demand packerswould demand more live steers (relativeto heifers) for slaughter.

The adjusted R2 is small at .33, how-ever, larger than found in the steer-heifercarcass price difference equation. Thoughthe systematic portion of the equation in-dicates that increasing levels of steer meatprices tend to increase the slaughter steer-heifer price difference, random factors stillexplain the greatest proportion of thevariation in the dependent variable. Someof these factors may include variations inpreferences by packers for steers versusheifers, changes in beef grades, and vari-ations in judging quality differences be-tween steers and heifers when they arepurchased from feedlots and ranches.

Feeder Market

The statistical results for the 400-500pound and 600-700 pound feeder steerand heifer price equations are presentedin Table 6. All models were estimated asfirst order difference equations with pos-itive first order serial correlation. The sizesof the coefficients on the lagged depen-dent variables are relatively small, indi-cating that the rates of geometric decline(or the distributed lag effects of the in-dependent variables) are relatively rapid.

Slaughter steer price (PSS) is crucial indetermining the prices of feeder steers andheifers in both weight categories. Therationale is that this variable represents thevalue of output to feedlots; thus, its changeaffects placement demand for feeders.There appears to be a noticeable, but notmajor, difference in the effect of slaughterprice on feeder steer and heifer pricesacross weight categories. That is, the re-gression coefficients (and price flexibili-ties) show that the prices of feeder steersand heifers in the 400-500 lb. weightrange to be more highly impacted than

88

the prices of steers and heifers in the 600-700 lb. weight range. The difference mayrelate to minimizing feeder purchase costs.Other variables constant, when slaughterprice increases it becomes more econom-ical for feedlot operators to buy relativelylighter weight cattle. Thus, prices of light-er cattle increase relatively more thanthose for heavier cattle, a result also en-countered by Buccola.

The price of corn serves as a proxy forcost of gain in the feedlot. Work by Buc-cola and Jessee (1979) and Marsh (1983)have shown corn prices to significantly in-fluence derived demand, hence, prices offeeder cattle. Results of this study showthe correct signs (negative) but not partic-ularly large asymptotic t ratios, particu-larly with respect to the price of 600-700pound feeder steers. The price flexibilitiesreveal that, for a period of four quarters,a 10 percent increase in corn price de-creases light cattle prices (for both sexes)about 1.7 percent, heavier steers .8 per-cent, and heavier heifers 1.2 percent.These results reflect rational adjustmentsby cattle feeders to keep the cost of gainin feedlots at near minimum levels whengrain prices change. That is, when feedcosts increase, relatively heavier cattle arefed since time on feed is shorter, thoughdemand for both feeder weight classes de-clines. Also, since feed conversion is lessefficient for heifers, relatively more steers(compared to heifers) are placed on feed.These results are consistent with Buccola'smeasurement of the effect of the cost offeed on cattle price-weight slopes.

The negative effect of the marketingmargin (MFC) is consistent with theoret-ical precepts, since an increase in market-ing costs reduces the derived demand forsteers and heifers. Its impact is not muchdifferent on steer prices than on heiferprices. That is, for a period of one quarter,a 10 percent increase in the margin showsan approximate three percent decrease inprices for light and heavy cattle of bothsexes. Over time, the long-run price flex-

July 1985


TABLE 7. Partial Derivatives and Price Flexibilities of the Distributed Lags in the Feeder Steerand Heifer Market, 400-500 Ibs.

Quartersa


PFS4-5/PSS 1.039 1.548 1.922 2.034 2.040(.885) (1.318) (1.637) (1.732) (1.737)

PFH4-5/PSS .859 1.277 1.580 1.669 1.675(.869) (1.292) (1.599) (1.689) (1.695)

PFS4-5/PC -1.911 -2.849 -3.536 -3.742 -3.754(-.085) (-.127) (-.157) (-.166) (-.167)

PFH4-5/PC -1.833 -2.726 -3.373 -3.563 -3.575(-.097) (-.144) (-.178) (-.188) (-.189)

PFS4-5/MFC -1.958 -2.919 -3.623 -3.833 -3.846(-.295) (-.440) (-.546) (-.577) (-.579)

PFH4-5/MFC -1.765 -2.625 -3.248 -3.431 -3.441(-.316) (-.470) (-.581) (-.614) (-.616)


ibilities become less inflexible, yet less thanunity.

The respective steers and heifers on feedvariables, QFS and QFH, are included tomeasure the effect of relative inventorysupplies. Statistical results indicate they arepositively correlated with the dependentprice variables (for each sex and weightcategory), which conflicts with theoreticalexpectations of negative price and quan-tity relationships. It is suspected that strongjoint dependency exists between cattle onfeed and feeder prices. An effort to elim-inate joint dependency included estimat-ing QFS and QFH as instrumental vari-ables; however, it was unsuccessful.

The regression fits of feeder steer andheifer price differences (PFS4-5 - PFH4-5 and PFS6-7 - PFH6-7) are significant-ly greater than found at the other marketlevels (Table 6). The statistical results alsoshow that the price differences are char-acterized by geometric distributed lags asevidenced in the individual price equa-tions. All parameter signs meet a prioriexpectations.

The effect of a change in the price ofslaughter steers is similar to that found inthe individual price equations. That is, an

increase in slaughter steer price leads toan increase in the derived demands (henceprices) for both steer and heifer feederinputs; however, there is a relativelygreater increase in demand for feedersteers. With a 10 percent increase inslaughter steer price, over a period of fourquarters, feeder steer and heifer price dif-ferences for both weight categories in-crease about 17 percent (Table 9). Suchbehavior is traceable to the nature of thevertical relationship between the slaugh-ter and feeder sectors in the livestock mar-ket channel. If packers demand relativelymore slaughter steers (compared to heif-ers), this yields a price signal to cattlefeeders which results in rational purchas-ing behavior. That is, to increase finishingreturns, feeders would demand relativelymore feeder steers for placement, increas-ing the price spread.

The supply variables demonstrate aninverse relationship between prices andquantities. Logically one would expect thatan increase in the number of steers on feedwould decrease the steer-heifer pricespread, while an increase in the numberof heifers on feed would increase it. Theprice flexibilities in Table 9 support this

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Schultz and Marsh


TABLE 8. Partial Derivatives and Price Flexibilities of the Distributed Lags in the Feeder Steerand Heifer Market, 600-700 Ibs.

Quarters"Equation 1 2 4 8 Long-run

PFS6-7/PSS .939 1.299 1.490 1.522 1.523(.882) (1.221) (1.400) (1.430) (1.431)

PFH6-7/PSS .809 1.120 1.285 1.313 1.314(.860) (1.190) (1.366) (1.396) (1.397)

PFS6-7/PC -1.064 -1.472 -1.688 -1.725 -1.726(-.052) (-.072) (-.083) (-.084) (-.085)

PFH6-7/PC -1.310 -1.813 -2.082 -2.127 -2.128(-.073) (-.101) (-.116) (-.118) (-.118)

PFS6-7/MFC -1.624 -2.247 -2.577 -2.633 -2.634(-.270) (-.374) (-.428) (-.438) (-.439)

PFH6-7/MFC -1.685 -2.333 -2.678 -2.736 -2.738(-.317) (-.439) (-.504) (-.514) (-.515)


hypothesis for both weight categories. Suchresults are also consistent with work byBuccola and Jessee on regional steer-heif-er price differences, where larger steer toheifer inventory ratios in cattle feedingregions decreased the steer price premi-um.

Interestingly, the cost of gain variable(PC) is not significant in the light cattleprice difference equation and is only mar-ginally significant in the heavier cattleprice difference equation. The coefficientsigns are consistent with the effects of feedprices found by Buccola and Jessee, butthe statistical significance here is consid-erably less. Such might be the case in thismodel since the data averages across allregions. Price flexibility estimates showthat a 10 percent increase in corn priceincreases the price spread between 600-700 lb. steers and heifers by only 1.4 per-cent over a period of four quarters. Theseresults suggest that cattle feeders may notbe very sensitive to steer-heifer feed con-version differences when cost of gainchanges. That is, when feed costs increase,price reductions for both steers and heif-ers are nearly equal. One reason may bethat even though heifers require more feed

90

per pound of gain, finishing weights arelighter, thus, they are on feed a smallernumber of days (than steers). Another rea-son may be that feed conversion differ-ences are not overly large, ranging fromseven to 10 percent between steers andheifers, depending upon weights andgrades (SBCN).

Concluding Remarks

Some producers in the cattle industryfeel that heifer price discounts (particu-larly at the feeder level) are too large, andtherefore are economically unwarranted.Perhaps on a local basis some cattle feed-ers and stocker operators may have cer-tain preferences against heifers. Since thedynamic model used time series data thataverages across all firms and regions, suchallegations are difficult to prove. How-ever, the geometric adjustments of feedersteer and heifer price differences mayprovide some information. First, the mod-el revealed that 75 and 80 percent of thevariations in sex price differences forcalves and yearlings, respectively, wereexplained by seasonal and economic vari-ables. These factors would not constitute

July 1985


TABLE 9. Partial Derivatives and Price Flexibilities of the Distributed Lags for the Price Dif-ferences in Feeder Steers and Heifers, 400-500 Ibs. and 600-700 Ibs.

Quarters,


PFS - PFH4-5/PSS .176 .256 .310 .324 .325(.946) (1.376) (1.666) (1.741) (1.747)

PFS - PFH4-5/QFS -. 745 -1.087 -1.316 -1.374 -1.377(-.452) (-.660) (-.799) (-.834) (-.836)

PFS - PFH4-5/QFH 2.364 3.448 4.175 4.360 4.368(.674) (.983) (1.190) (1.243) (1.245)

PFS - PFH6-7/PSS .136 .184 .206 .209 .209(1.103) (1.492) (1.671) (1.695) (1.695)

PFS - PFH6-7/QFS -. 447 -. 603 -. 676 -. 686 -. 686(-.409) (-.552) (-.619) (-.628) (-.628)

PFS - PFH6-7/QFH 1.017 1.371 1.538 1.560 1.561(.437) (.590) (.662) (.671) (.671)

PFS - PFH6-7/PC .211 .284 .319 .323 .324(.089) (.120) (.135) (.137) (.137)


economically unwarranted price differ-ences unless, however, one was suspiciousof the steer-heifer carcass and slaughterprice spreads. Second, the dynamics of themodel indicate that, given shifts in the ex-ogenous variables, feeder steer and heiferprice differences stabilize, or approachequilibrium levels rather quickly.

The effect of the remaining 20 to 25percent unexplained variation is open tospeculation. However, two importantcharacteristics of the beef industry couldplay a role here. One is risk of placingpregnant heifers in a feedlot, the other iscompetition from heifers placed in thebreeding herd. The risk of placing non-open heifers in feedlots may vary amongcattle feeders since knowledge about theirpregnancy status is not uniform (i.e., somefeeders may or may not pregnancy test),and use of abortifacients is not uniform.Thus, in the aggregate, adjusting a heiferprice discount to account for this problemmay be random. Heifer retention for thebreeding herd could also fit in the errorstructure because of weather conditionsand different financial constraints amongproduction units. Thus, over time, deci-

sions about heifer replacement rates willvary because of these factors, i.e., reducedherd replacements in areas of drought andin periods of financial stress. Such actionsaffect the feeder steer-heifer price spreadbecause of the relative changes in demandfor breeding heifers.

Finally, with the explanatory power ofthe residuals larger than one would pre-fer, there is always suspicion of temporaryeconomically unwarranted price differ-ences between steers and heifers. In thevery short term, such anomalies might oc-cur. However, as time increases, it wouldbe difficult for unwarranted price differ-ences to persist. The profit motive wouldcause, through competition, firms at eachmarket level and buyers and sellers in thevertical market channel to bring steer-heifer price spreads into equilibrium.

References

BEEF Magazine. "Pregnant Heifers are a Fiasco inthe Feedlot" and "Integrated Florida Feedlot-Packer Opens Retail Stores." Volume 20, No. 9,May 1984.

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Boggs, D. L. and R. A. Merkel. Live Animal CarcassEvaluation and Selection Manual. Kendall-HuntPublishing Co., Dubuque, 1979, pp. 69-79.

Brester, Gary W. and John M. Marsh. "A StatisticalModel of the Primary and Derived Market Levelsin the U.S. Beef Industry." Western Journal ofAgricultural Economics, 8/1(1983): 34-49.

Buccola, S. T. "An Approach to the Analysis of Feed-er Cattle Price Differentials." American Journalof Agricultural Economics, 62(August 1980): 574-80.

Buccola, S. T. and D. L. Jessee, "An U.S. RegionalModel of Feeder Steer-Heifer Price Differentials."Southern Journal of Agricultural Economics,11(July 1979): 61-5.

Crom, R. A. "A Dynamic Price-Output Model of theBeef and Pork Sectors." Department of Agricul-ture ERS Technical Bulletin 1426, Washington,D.C., 1970.

Cromarty, William A. "An Econometric Model forU.S. Agriculture." Journal of the American Sta-tistics Association, 54(1959): 445-74.

Doane Agricultural Service. Profit Marketing. Doane-Western, St. Louis, 1975.

Folwell, Raymond J. and Wallace A. Rehberg. "ThePricing of Calves and Stockers-Feeders in EasternWashington." Agricultural Experiment StationBulletin Number 83, Washington State University,1976.

Freebairn, J. W. and G. C. Rausser. "Effects ofChanges in the Level of U.S. Beef Imports." Amer-ican Journal of Agricultural Economics, 57(1975):678-88.

Griliches, Zvi. "Distributed Lags: A Survey." Econ-ometrica, 35(1967): 16-46.

Hanssens, D. M. and Lon-Mu Liu. "Lag Specificationin Rational Distributed Lag Structural Models."Journal of Business, Economics and Statistics,1(October 1983): 316-25.

Hasbargen, P. R. and K. E. Egertson. "Beef Cycles:A Clue to the Current Cattle Outlook." MinnesotaAgricultural Economist No. 579, Agricultural Ex-tension Service, University of Minnesota, May 1976.

Hayenga, Marvin L. and Duane Hacklander."Monthly Supply-Demand Relationships for FedCattle and Hogs." American Journal of Agricul-tural Economics, 52(1970): 535-44.

Jorgenson, Dale W. "Rational Distributed Lag Func-tions." Econometrica, 32(1966): 135-49.

Lambert, C., L. Corah, and 0. Grunewald. "FactorsAffecting Prices of Calves and Yearlings in Kan-sas." Agricultural Fact Sheet MF-667, Kansas StateUniversity, November 1981.

Marsh, J. M. "A Rational Distributed Lag Model ofQuarterly Live Cattle Prices." American Journalof Agricultural Economics, 65(August 1983): 539-47.

Osprina, Enrique and R. C. Shumway. "Disaggre-gated Econometric Analysis of U.S. Beef SlaughterSupply." Technical Monograph 9, Texas Agricul-tural Experiment Station, Texas A&M University,1979.

Riley, J. "A Look at Ways to Handle Pregnancy inthe Feedlot." BEEF, April 1983.

Rucker, R. R., 0. R. Burt, and J. T. LaFrance. "AnEconometric Model of Cattle Inventories." Amer-ican Journal of Agricultural Economics, 66(1984):131-44.

Sims, C. A. "The Role of Approximate Prior Restric-tions in Distributed Lag Estimation." Journal ofthe American Statistical Association, 67(1972):169-75.

Subcommittee on Beef Cattle Nutrition. (SBCN).Nutrient Requirements of Beef Cattle. Washing-ton, D.C.: National Academy Press, 1984.

United States Department of Agriculture. "BeefPricing Report." Agricultural Marketing Service,Packers and Stockyards Program, December 1978.

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