VERTICAL INTEGRATION IN THE CHICKEN BROILER INDUSTRY

Transcription

1 Libraries Cnference n Applied Statistics in Agriculture th Annual Cnference Prceedings VERTICAL INTEGRATION IN THE CHICKEN BROILER INDUSTRY Juana Sanchez Fllw this and additinal wrks at: Part f the Agriculture Cmmns, and the Applied Statistics Cmmns This wrk is licensed under a Creative Cmmns Attributin-Nncmmercial-N Derivative Wrks 4.0 License. Recmmended Citatin Sanchez, Juana (1994). "VERTICAL INTEGRATION IN THE CHICKEN BROILER INDUSTRY," Cnference n Applied Statistics in Agriculture. This is brught t yu fr free and pen access by the Cnferences at. It has been accepted fr inclusin in Cnference n Applied Statistics in Agriculture by an authrized administratr f. Fr mre infrmatin, please cntact cads@k-state.edu.

2 30 Vertical Integratin in the Chicken Briler Industry Juana Sanchez Department f Ecnmics University f Missuri Rlla, MO Abstract This paper analyzes three hyptheses cncerning supply in the U.S. chicken briler industry: (a) there has been a cycle in the industry f apprximately mnths length; (b) the seasnal and ther peridic cmpnents, as well as relatins between variables, have changed as a result f vertical integratin in the industry; (c) the effects f vertical integratin in the industry were cunteracted in the early seventies by such frces external t the industry as dmestic and internatinal ecnmic cnditins. The hyptheses are analyzed using new mnthly, nn-seasnally adjusted time series data fr chick placement, whlesale briler prices, chicks hatched and net returns. Explratry analysis using three different spectrum analysis methds, shws that there is evidence t cnfirm thse hyptheses. Using that infrmatin, frecasting mdels are cnstructed, and their perfrmance is cmpared t the perfrmance f the standard distributed-lag mdels used by analysts f the industry. The paper then ffers rbusts results cncerning hyptheses that have ccupied the interest f analysts f the industry fr a very lng time. These results indicate that as vertical integratin reached maturity, briler suppliers tended t becme sales maximizers. Key Wrds: peridgram, autregressive spectrum, Bayesian, demdulatin, frecasting, distributed-lag, vertical integratin, sales maximizatin. 1 Intrductin Brilers are yung chickens 7 t 10 weeks f age. Since the fifties, the briler industry has been ne f the mst rapidly changing agricultural subsectrs, gradually passing frm being characterized by many small, independent farm flcks and small prcessrs scattered acrss the cuntry t being a highly vertically and hrizntally integrated, efficient industry lcated in a relatively few cunties ([2], [8]). This evlutin has been illustrated

3 Applied Statistics in Agriculture 31 by descriptive trend analyses in [34], [8], [2], by the cmmn practice f reestimating every year (t accunt fr the changes) the distributed-lag ecnmetric mdels used fr plicy analysis, and by traditinal spectral methds [33]. Prductin decisins in the industry can be investigated at fur stages. First, "placements" refers t the intrductin f chicks r pults int the prductin prcess. The United States Department f Agriculture (USDA) reprts the briler placements (number f chicks placed) in hatchery supply flcks. Secnd, "testing" refers t the testing' fr pullrum-typhid disease undertaken by state agencies, which reprt the number f briler-type chickens in the tested flck. Testing is perfrmed abut five mnths after chickens are placed in the hatchery supply flck. The third stage f prductin is "hatching" f eggs frm the hatchery supply flck. The USDA reprts the number f eggs hatched in cmmercial hatcheries. After hatching, apprximately eight weeks are required t prduce a 3.8 pund liveweight briler. The USDA publishes the "prductin" f brilers, r chicks hatched, the furth stage. Placements and chicks hatched are tw variables ften used in studies f the respnse f prductin t ther variables. Analysts f the industry are interested in determining whether there are any predictable relatins between any f thse variables mentined abve, whether there are sme regularities in each f them that can be used fr predictin, and hw the variables depend n ther independent cvariates, such as briler price, vertical integratin, returns and( r) csts, in particular feed cst, the mst imprtant ne in the industry. Obtaining reliable answers t these questins helps design structural mdels f prductin with gd frecasting perfrmance, which in turn allws fr a mre effective planning and plicy in the industry. In additin t that, the answers t thse questins allw reaching cnclusins abut the bjective functin f briler suppliers. In rder t make the results f this paper cmparable t earliei; studies, I investigate the same questins abut prductin decisins at the "placement" and "hatched" level, with new data and methds. T update the results f earlier studies, particularly thse f [33], with new data, I analyze three hyptheses cncerning prductin. (1) There is a cycle in sme time series f the industry f apprximately mnths length ([4], [40], [33]); (2) The seasnal and ther cmpnents, as well as relatins between variables, have changed as a result f vertical integratin in the industry ([33], [38], [39], [20], [8]); (3) The effect f vertical integratin has been cunteracted by such frces external t the industry as dmestic and internatinal ecnmic cnditins ([35]). Hypthesis (1) was very imprtant in the pre-vertical integratin perid f the industry. By the nature f pultry prductin there was a lag between the time at which the prductin decisin was made and the time at which the prduct was sld. Being the market the crdinating mechanism, prices and quantity supplied varied widely, as in all ther agricultural subsectrs. This led sme researchers t claim that the industry exhibited a pattern f cyclical fluctuatins (Bluestne [4], Tbin and Arthur [40]), namely a 30 mnths cycle (the time it tk t cmplete a cycle f prductin). Such cycle was fund significant by [4] and [40]. Rausser and Cargill [33] fund that a cycle f that length

4 32 during the fifties and sixties was significant nly fr price, nt fr quantity. The existence f this cycle is still questined, and is relevant t determine whether stabilizatin plicies shuld be based n the existence f fixed peridic cycles. Hypthesis (2) is widely accepted ([8], [2]). With the advent f vertical integratin in the fifties, Tbin and Arthur [40] expected a dampening f the cyclical cmpnents in the price and utput series. Henry and Raunikar [20], Seagraves and Bishp [38] and Seaver [39] in particular hypthesized that the amplitudes f the seasnal cmpnents f prices and utput wuld be reduced as a result f vertical integratin. This was sustained by the view that the majr effect f vertical integratin was t make adjustments in prductin and prices smther as a cnsequence f increased ability f grwers t plan the flw f inputs available fr prductin. Rausser and Cargill [33] fund that the seasnal in prices had dampened much faster than the seasnal in utput. This, thse authrs claim, "cnfrms well with the ntin that vertical integratrs, althugh attempting t stabilize bth prices and quantities, actually emphasize the frmer, which results in greater variability f utput relative t prices" ([33], p.120). They als fund little assciatin amng a set f time series after trend remval, except at the seasnal cmpnents. Hence, they cncluded that during the fifties and sixties, "there is n evidence f a meaningful lead-lag pattern except at the seasnal cmpnent" ([33], p. 120). The existence f fixed time differences amng the series wuld be significant fr designing stabilizatin plicies in the industry. Hypthesis (3) maintains that the stabilizing effects f vertical integratin were reversed since the early seventies. Several events ccurring utside f the industry in that decade, such as wrld feed shrtages, changes in the exchange rate regime and il crisis, affected the cst structure f the industry, frced prducers t adjust their energy use patterns [35] and made them mre aware f agricultural exprt demand cnditins [13], [9], [30], [29]. The industry became, again, mre vulnerable t external markets cnditins and instability. The large increase in the variability f briler prices riginating during the seventies is assciated with that increasing dependence n the instability f internatinal markets. It was then believed that this wuld lead t anther restructuring f the briler industry t accmmdate t the new situatin [35] The changes ccurring in the industry after the energy crisis, can prvide evidence n the new managerial plicies f briler firms, and can suggest what their bjectives are, as vertical integratin reaches maturity. The three hyptheses described abve are analyzed in this paper using methds f spectrum analysis new in ecnmetrics, and new data. These allw the updating and reevaluatin f results btained by ther authrs. Using several methds t analyze the data is recmmended by Parzen [31] and Brckwell and Davis [6]. The data supprt the cnclusin that briler integratrs are sale maximizers. Fllwing the advice in Engle [11], I use the spectral methds t aid in the specificatin f time dmain mdels, and then use standard time dmain methds t estimate, and frecast with, them. The bjective is t determine whether univariate time series mdels, based n the spectral analysis, imprve the frecasting perfrmance f the distributed-lag

5 Applied Statistics in Agriculture 33 mdels usually used t frecast in the briler industry. 2 The Data T make research with new data and methds cmparable t lder research, it is imprtant t use the same variables ther authrs have used. Fr this reasn, the fur time series chsen in this paper fr the study f supply in the briler industry are the mst widely used in published research that has addressed the same hyptheses. They allw studying the change in structure f the industry, the change in the relatin between the mst imprtant variables used in the frecasting mdels and the 30 mnth cycle. As seen in the intrductin, the tw utput series represent key steps f the prductin prcess. The price and return series are cvariates that are usually included as explanatry variables in structural mdels. The time series are: (I) Pullet chicks placed in briler hatchery supply flcks, January 1960 t December 1986, thusands. Surce: [41] (II) Whlesale briler prices, January 1964 t December Mnthly 12-city cmpsite, cents per pund, Ready t Ck (RTC). Surce: [42]. (III) Chicks hatched: Briler type in U.S. cmmercial hatcheries, January 1960 t December 1986, thusands. Surce: [41]. (IV) Yung Chicken: Net returns, January 1967 t December 1986, cents per pund, RTC. Surce: [10]. These data are dmestic United States, mnthly and nt seasnally adjusted. Price and returns, as well as the utput series, are shwn in Figure 1. Series (I) has 324 bservatins. Just by lking at the data, it can be discerned that there is a trend in mean, a change in the variability f the cmmdity's seasnal amplitude and a lng wave. The perid 1960 t 1968 is the mst variable. Whlesale briler prices, series II, were fluctuating mildly until After this year, hwever, nt nly did amplitudes f fluctuatins increase cnsiderably, but als the trend in mean tk a sudden jump and increased at a higher rate than previusly. The number f bservatins is 276. Series III shws that chicks hatched, in cntrast t the ther series, des nt shw any marked change in variability at first glance. The number f bservatins in this series is 324. Finally, net returns, series IV, displays a large variability since the seventies, similar t that f whlesale prices. 3 Is there a Thirty Mnths Cycle in the Briler Industry? One f the hyptheses that cncern me in this paper is the existence f a cycle f apprximately 30 mnths length in the briler industry, a questin investigated by Rausser and Cargill using the same time series fr up t the early 1960s. This questin, is there evidence fr cycles?, is best answered by univariate sample spectral methds.

6 34 The predminant apprach t spectrum estimatin in Ecnmetrics is the Blackman Tuckey methd f spectrum analysis [14],[12],[16], [26], [15], [11], [33]. This methd cnsists f smthed peridgrams which are asympttically cnsistent but lack reslutin in the detectin f frequencies [24], [23]. Rausser and Cargill ([33]) used the smth peridgram, after differencing and lg regressin, t detrend their chick placements and whlesale price series, and fund n significant evidence fr a cycle in placements, but they fund a significant 3D-mnth cycle in prices. My data cvers a perid different frm that analyzed by Rausser and Cargill [33], and the methds used are different. The three methds used here are: peridgram (withut smthing), autregressive and Bayesian spectrum analysis [36]. The peridgram withut smthing can be defined as C(w) (1) where C(w) is the Furier Transfrm f the data, X(t), r the inverse Furier transfrm f the autcrrelatin functin f the data, R. An alternative apprach t spectrum estimatin is the Autregressive spectrum estimatr [21]. Assume that the time series we are interested in, X (t), is an autregressive prcess f rder p p X(t) = L a(k)x(t - k) + u(t) (2) k=l where {Ut} is a white nise prcess f zer mean and variance (72, and a(k) are the autregressive parameters. Then, the pwer spectrum when T , takes the specific frm [17], [24] : (J'2 C(W)AR = 11 + l:=1 a(k) exp( -iwk )1 2 ' Substituting in equatin (3) sample estimates f (J'2 and a( k), and finding p, the rder f the mdel, by sme criterin, the autregressive estimatr CAR(W) can be fund ([24], [23]). I use the Burg algrithm t estimate a(k) and (72 ([23], [24]). The rder f the prcess is chsen using the Criterin Autregressive Transfer Functin (CAT). A third methd used t determine the existence f the cycle is the Bayesian frequency parameter estimatin methd [5]. T apply this methd, I assume a plynmial trend plus harmnic mdel fr the data X (t). X(t) = T(t) + Asinwt + B cswt + et (4) (3)

7 Applied Statistics in Agriculture 35 where r T(t) = 'Lf3iti (5) i=l is a plynmial in time, r is the degree f the plynmial and et is an errr term nrmally distributed with mean J1 and variance (J2. The results f a Bayesian analysis depend n the mdel and the prir infrmatin assumed Bretthrst [5] uses nninfrmative prir distributins. Given these and the likelihd functin implied by the mdel given abve, applying Bayes therem, and integrating ut the trend parameters and the amplitudes, we btain the marginal psterir prbability f the frequency parameter wand the variance (J2. Because nninfrmative prirs are used, the result is an induced marginalized likelihd f the frequencies and the variance f the nise ([5], [43]). The degrees (r) f the plynmial trend integrated ut frm each series are: Series I II III IV Degree f the Plynmial T apply the three methds t the time series, I first subtracted frm the data the plynmial trend suggested by the Bayesian methd. The seasnal and its harmnics plus a mass f pwer cncentrated arund the 30-mnth cycle are the mst imprtant cmpnents f the series, accrding t the peridgram f the detrended data and the autregressive spectrum. Mst f the varianc, hwever, is carried by the seasnal cmpnent. The 30-mnth cycle is nly significant fr the price time series. Figure 2 shws the Bayesian lg10 f the marginal psterir prbability f a harmnic frequency f the time series after integrating ut the trend parameters. The mst imprtant peaks bserved crrespnd t the seasnal cmpnent (perid=12) and its first harmnic (perid=6). There are als ther-relatively much smaller-peaks which crrespnd t the ther three harmnics f the seasnal cmpnent, namely 4, 3 and 2.4 mnths. The cyclical cmpnent at mnths, is favred by Bayesian mdel selectin [43] nly in the return series. In rder t see if the imprtance f the cyclical and the seasnal cmpnent change ver time, I als divided the time series int several time intervals. As was predicted, given the rather nnstatinary nature f the series, there are sme perids in which the 30-mnth cycle is significant and ther perids in which it isn't. The results in the fllwing sectin prvide mre infrmatin abut the structural change that this implies.

8 36 4 Have Cmpnents f the Industry and the Relatins Amng them Changed? Hypthesis 2 stated that vertical integratin in the briler industry led t a decrease in the amplitudes f the cyclical and seasnal cmpnents f the industry. Hypthesis 3 stated that this effect had been cunteracted by the events taking place in the early seventies. These tw hyptheses can be studied simultaneusly using the methds f this sectin. The first thing t d is t detect the change in the variability f the detrended time series, in particular whether the series variability decreased during the sixties (hypthesis 2) and then it increased during the seventies (hypthesis 3). We can d this using cmplex demdulatin. Thus, fllwing ([3], [15]) I demdulate-remdulate series I, II, III and IV at the seasnal frequency and three harmnics. The results, as illustrated in Figure 3, reveal that the amplitudes f the fluctuatins f the seasnal cmpnent f each series has nt been cnstant ver time. This is a sign f nnstatinarity. The graphs in Figure 3 measure the amplitudes f the time series in base pints. The degree f nnstatinarity varies fr each series. Thus, the remdulated chick placements reveals that the amplitudes f the seasnal have decreased ver time. The amplitude f the seasnal cmpnent f chicks hatched des nt vary as much as the amplitude f the ther three series. It has been mre stable during the sixties than during the seventies and eighties, but nt drastically. Price and returns suffered by far the largest increase in variability during the seventies, cmpared t the utput series. Overall, the evidence btained frm the cmplex demdulatin f the series reveals that the seventies altered the stabilizing effects f vertical integratin n prices and returns achieved in the sixties (hypthesis 3), as shwn by the decrease in variability in the latter perid and the increased in variability in the frmer. Seeing hw each individual series f the briler industry has changed gives sme evidence n the hyptheses stated earlier. Hwever, mre relevant fr mdeling purpses is t knw whether the lead-lag structure in the relatin between series has been altered. T study this, I apply peridgram and autregressive crss-spectral analysis t the tw time intervals: and The crss-spectral results reveal that the cherence, r degree f assciatin between the series, is lwer in the interval than earlier, particularly at the seasnal perids (12 mnths and lwer). This is mre nticeable in the relatin between prices and utput than in the relatin between utputs. The crss-peridgrams fr the frmer relatins can be fund in Table 1 and in Table 2. Ntice that in thse tables, if the cherence is less than 0.5 it is nt reprted, a standard practice. The phase r lead-lag pattern als changes. Leads and lags becme smaller in the interval, fr all the nnseasnal frequencies, and all series pairs. At the seasnal frequencies, it becmes larger fr price-utput relatins (althugh it is still very small) in the seventies, but it is nt significant. Chicks hatched and chicken placements, hwever, had n lag in either time interval, althugh they are very highly assciated in bth time intervals. These results, cmbined with thse f the cmplex demdulatin, are preliminary

9 Applied Statistics in Agriculture 37 evidence n the sales maximizing behavir f briler suppliers. Lwer relatin between price and utput and lnger lags, plus higher variability in prices in the seventies, tgether with a relative maintenance f the stability f utput, all reveal that the respnse f suppliers t the crisis in the seventies was t stabilize utput and nt let supply respnd t prices. This implies that they pursued sales maximizatin instead f prfit maximizatin as an bjective. This attitude cntrasts with that fund by Rausser and Cargill in the sixties, namely that vertical integratin had stabilized price mre than utput. If the evidence fund here was further cnfirmed, then it wuld imply that there has been a change f managerial gals in the industry as a result f the crisis in the eighties. 5 Frecasting Mdels Mdeling f supply in the briler industry is usually dne by means f distributed-lag adjustment mdels (see Judge et al. [22], p. 350 fr characterizatin f these mdels). The ecnmic theretical cunterpart f thse mdels in agricultural sectr mdeling is the Nerlvian dynamic supply framewrk, which cnsists f an adaptive expectatins equatin fr price, an adjustment equatin fr utput and a supply functin that depends n price and sme exgenus variables ( [27], [28]). Althugh this ecnmic-theretical apprach has been questined n several grunds (Nerlve [25], Askari et al [1] and Heady et al [18] ), it is still the standard justificatin fr empirical briler supply mdeling ([7], [19]). A standard ecnmetric mdel fr briler supply is, fr example, that f Chavas and Jhnsn [7]. These authrs, using quarterly bservatins frm 1965 t 1975, btain by least squares the fllwing equatin ([7], p. 560): Bl P BL2-5.83FC L BIL DV DV3-28.5DV4-65.6TT where Bl = Chick Placements. P B L2 = Whlesale Briler Prices lagged tw quarters. FCL2 = Feed Cst lagged tw quarters. BIL4 = Chick placements lagged 4 quarters. DVI = Seasnal Dummies. TT = Linear trend. Accrding t [7] the estimated elasticities are significant and have the expected sign and the R2 is.87, tw criteria that lead the authrs t cnsider the regressin equatin apprpriate. The lags fr feed cst (FC) and whlesale price (PB) were chsen by preliminary testing. The cefficient in BIL4 indicates that 73 percent f the adjustment in placements ccurs frm ne year t the next. Mdels similar t (6) can be fund in [19]. The bjective f the wrk presented in this sectin is t see whether univariate time series mdels btained frm the preliminary data analysis described abve frecast chick (6)

10 38 placements better than an updated distributed-lag adjustment mdel. Because structural change seems t have ccurred in a nticeable way since 1973, the frecasting mdels have as estimatin perid December 1973 t December After cnducting the analysis described earlier, fcusing nly n this time interval, I translate the results (trend, cycles, autregressive rder f the series) int tw types f time-dmain mdels (harmnic and autregressive) with tw different assumptins abut the type f cefficients f the autregressive mdel. Under the first assumptin, the mdels and frecasts have a single unbserved cefficient vectr f3 but it is assumed that mre infrmatin allws the btentin f a better estimate f the parameters, and better frecasts. Under the secnd, mdels and frecasts allw the cefficient vectr t change ver time. All the mdels incrprate the trend. 1st Assumptin: a single vectr updated Under this assumptin, the types f mdels fitted and used fr predictin are: a) a harmnic mdel fr chick placements; b) an autregressive mdel fr chick placements. The ttal number f bservatins fr the' estimatin perid are 133. That is, t = in the estimated equatins. Of curse, in rder t allw fr lags in the autregressive mdels, the actual estimatin uses as current data the data frm t = P + 1 t 133, where p is the autregressive rder. Using these equatins, I frecast the next 24 mnths, i.e., frm January 1985 t December 1986, as fllws: First, using the equatins mentined abve, and taking the data frm the data series (bth the estimatin and the predictin interval data, depending n whether I frecast with the autregressive r the harmnic mdel) I cmpute ne mnth ahead frecasts. This is called "static ut-fsample" frecasting. As I btain additinal bservatins, the cefficient estimates are reestimated and the value f the dependent variable fr the next mnth is frecasted. Ding this is equivalent t assuming that the cefficient vectrs are cnstant thrugh time but that adding new infrmatin helps t btain better estimates f them. The recmputatin f the regressins after a new bservatin is added is dne very rapidly since I use the Kalman filter. Hw the Kalman filter updates the estimates at each mnth frm their value at time t = December 1984 t t + 24 is described in ([32], p ). The cefficient estimates btained with the Kalman Filter in this situatin, hwever, are identical t thse that I btain if I cmpute each f the regressins by rdinary least squares. 2nd Assumptin: Time-Varying Cefficients I assume nw that the cefficient vectr in the autregressive equatins fllws the prcess f3t = f3t-l + Vt, where var Vt = Mt and Vt is independent f et, the latter being the errr term in the regressins f chick placements. Using the Kalman filter in this situatin, as described in ([32], p. 19-3), I first btain an estimate f f3 using bservatins fr the time interval March 1975-December These time intervals are chsen as base perids t start the cefficient update with the Kalman filter, hence it makes sense t use them as surces f the a priri infrmatin used t apply the filter. Having btained

11 Applied Statistics in Agriculture 39 the prir cvariance matrices frm the regressin fr thse time intervals, the Kalman filter updates the cefficient vectr f3 as additinal mnths are added t the estimatin perid. Using these mdels I frecast the next 24 mnths (January 1985 t December 1986) fllwing the same prcess explained abve with ne exceptin: the mdel cefficients are updated as I add new bservatins in the same manner that they were updated during the estimatin perid. That is, in cntrast with the prcedure fllwed abve under the assumptin that there is nly a vectr f cefficients, the assumptin behind the frecasts with the time varying mdels is that the cefficients change nt nly because new infrmatin is btained but because they fllw the randm walk behavir described abve. The frecast perid starts in January 1985 and ends in December Distributed-lag adjustment structural mdel It is interesting t see whether the frecasts btained with the mdels mentined abve are better r wrse than thse that wuld be btained with a standard chicken briler supply mdel like (6) presented abve. This wuld establish the usefulness f studies like the ne dne in this paper fr bth understanding and frecasting in the industry. T find ut, I translate the quarterly lag structure f (6) int a mnthly lag structure and btain the fllwing mdel: B1standard t TT1 + O.396B1L FCL PBL DV DV DV DV DV DV DV7-3.68DV8-8.55DV DV DVll (7) Summary f Frecast Results With the 24 values f the ne-step-ahead percentage frecast errrs and the predicted and actual values f the series, I cmpute the "Mean Abslute Percentage Errr" (MAPE) statistic fr the frecasts f the 7 mdels f placements. The MAPE is defined (in percentage) as MAPE =.!. t I frecastt - actualt I k t=l actualt (8) where k is the number f frecasts and t is the frecast mnth ( I assume that t = 1 fr the first mnth f the frecasting perid.) The summary f the results can be fund in Table 3. The summary statistics in Table 3 shw the MAPE f the ne-step-ahead frescast (MAPE(l)) and the MAPE fr ther

12 40 lags. MAPE(6), MAPE(12) and MAPE(24) are cnsiderably smaller fr the distributedlag mdel than fr any f the ther mdels assumed t frecast chick placements. Thus, the univariate time series mdels frecast wrse than a standard supply mdel when the frecast is 6, 12 r 24 mnths ahead. They frecast better, hwever, fr less than 6 mnths ahead. 6 Summary and Cnclusins Cnference n Applied Statistics in Agriculture The first hypthesis, the existence f a 30 mnths cycle in the series wuld reflect that the cycle f prductin takes apprximately that much time. It was investigated using peridgram, autregressive and Bayesian spectrum analysis. The thirty mnths cycle is significant in returns, with a Bayesian and frequentist apprach and in price with a frequentist apprach. The cycle is nt significant in the utput series fr the whle length f the series analyzed, althugh it is significan during sme intervals. The existence f the thirty mnths cycle in the price cnfirms Rausser and Cargill's result [33]. They fund a 30 mnth cycle in prices using data fr the fifties and the sixties. Its appearance in returns just reflects that it is there in prices. Hwever, because the cycle in utput series is nt a cnstant feature f the data, it is nt recmmended t base plicy n its existence althugh nt ignring its existence in utput series at times, and in prices, accunting fr its nnstatinarity, can help imprve the frecasting perfrmance f mdels. A clser analysis f ther cmpnents f the time series and their evlutin after the energy crisis supprts these recmmendatins. Cncerning hypthesis 2, the stabilizing effect n seasnal amplitudes f vertical integratin is very nticeable in the placement series, nt s nticeable in the hatched series, during the sixties. Seasnal amplitudes ald decreased in the price and return series. Suggestins by a number f researchers as t the effects f vertical integratin n seasnality are supprted by these results. The energy crisis in the seventies, hwever, altered this statibilizatin. While the cst crisis in the seventies increased cnsiderably the amplitude f the seasnal cmpnents f price and returns, such crisis had n effect n the amplitudes f the seasnals in utput. This reflects that vertical integratrs, althuth attempting t stabilize bth prices and utput, were mst successful at stabilizing utput during the whle perid studied. Changes in feed and il csts and increases in demand were reflected in the industry by the alteratins in prices and returns but nt in utput. This may imply that briler prducers maximize sales and transfer changes in cst and demand nly t prices. This cntradicts the cnclusins reached by Rausser and Cargill. Their evidence led them t believe that briler suppliers emphasize price stabilizatin, instead f utput stabilizatin. But it appears that this is nt the case. The evidence n the changes in the series in the eighties fund in this paper des nt supprt it. The cst shcks f the early seventies drastically altered the stabilizatin f prices and returns that the industry experienced in the sixties. Once thse shcks disappeared, hwever, the industry did nt return t the levels f stabilizatin in the seasnal f prices

13 Applied Statistics in Agriculture 41 that it had in the sixties. The financial and internatinal changes f the eighties have als altered the stabilizatin f the sixties; hwever, because interest csts is nt ne f the majr cst items in the industry, the changes in the eighties did nt affect pultry supply as much as they altered the stabilizatin f prices and returns. Thus variability in csts were als translated int variability in prices, which supprts further the cnclusin that briler suppliers are sales maximizers. The analysis f the relatins between variables (i.e., the degree t which they mve tgether) indicates that such assciatin decreases cnsiderably at the seasnal cmpnents. The price-utput pairs and the utput-utput pairs are less related in the interval than earlier. The fact that the decrease in the relatin price-utput is much mre nticeable, indicates als sales maximizatin behavir when added t the univariate evidence that price amplitudes stabilized less than utput in This cnclusin is further supprted by the insignificant lead-lag pattern in this time interval. The change in the relatin at the cyclical cmpnents and the change in the lead-lag pattern at thse frequencies is less cnclusive. There is sme slight evidence that this relatin remained strng fr the price-utput pairs, and that the lead-lag pattern was significant. This phenmenn helps explain the better frecasting perfrmance f the structural mdel relative t the univariate time series mdels in the larger than 6 mnths ahead frecasts. The superir frecasting perfrmance f the distributed-lags mdel fr lnger stepahead frecasts, with lag structure reflecting the cyclical lead-lag patterns fr which there is slight evidence, suggests that there is still sme relatin between price and quantity that culd perhaps be explited by stabilizatin plicy cnducted in the industry. The variability f this relatin and the nnstatibnarity f the cyclical cmpnent, suggest nevertheless that we can nt rely n a fixed estimated mdel, but rather that these mdels need t be cntinuusly reestimated. The analysis dne in this paper is useful t design univariate time series mdels fr shrt-term frecasts. Acknwledgments The cmments f the annymus reviewer and thse f sme participants at the 1994 Cnference are immensely appreciated. References Cnference n Applied Statistics in Agriculture [1] H. Askari and J.T. Cummings. Agricultural Supply Respnse: A Survey f the Ecnmetric Evidence, Praeger Publ., N.Y., [2] V.W. Bensn, "The Chicken Briler Industry: Structure, Practices and Csts," USDA, Ecnmic Research Service, Agricultural Ecnmic Reprt n. 381, 1976.

14 42 [3] P. Blmfield. Furier Analysis f Time Series: An Intrductin, Wiley and Sns, N.Y., [4] H. Bluestne. "The Cycles in Brilers," Pultry and Egg Situatin, USDA ERS PES-226, July 1963, [5] G.L. Bretthrst Bayesian Spectrum Analysis and Parameter Estimatin, Lecture Ntes in Statistics, Vl. 48, Springer Verlag, [6] P.J. Brckwell and R. A. Davis. Time Series: Thery and Methds, Springer Verlag, [7] J.P. Chavas and S.R. Jhnsn. "Supply Dynamics: The Case f U.S. Brilers and Turkeys," American Jurnal f Agricultural Ecnmics, 64, 3-5, [8] L.A. Christensen et al.. The U.S. Briler Industry, United States Department f Agriculture, Ecnmics Research Service, Agricultural Ecnmic Reprt n. 591, [9] A. de Janvry. "Internatinal Ecnmic Develpment and U.S. Agriculture," Department f Agricultural Ecnmics, University f Wiscnsin, Madisn, [10] E.H. Easterling and F.A. Lasley. Estimating Csts and Returns fr Pultry and Eggs, United States Department f Agriculture, Ecnmic Research Service, Staff Reprt n. AGES850703, [11] R.F. Engle "Interpreting Spectral Analysis in Terms f Time-Dmain Mdels," Annals f Ecnmic and Scial Measurement, 5/1, , [12] G.S. Fishman. Spectral Methds in Ecnmetrics, Harvard University Press, [13] B. Gardner. "Internatinal Cmpetitin in Agriculture and U.S. Farm Plicy," in The United States in the Wrld Ecnmy, M. Feldstein, ed. University f Chicag Press, [14] C.W.J. Granger and R. Engle. "Applicatins f Spectral Analysis in Ecnmetrics," in Handbk f Statistics, Vl. 3, D.R. Brilllinger and P.R. Krishnaiah, eds. Elsevier Science Publishers B.V., N.Y., [15] C.W.J. Granger and M. Hatanaka. Spectral Analysis f Ecnmic Time Series, Princetn University Press, [16] C.W.J. Granger and P. Newbld. Frecasting Ecnmic Time Series, 2nd editin, Academic Press, [17] A.C. Harvey. Time Series Mdels, Phillip Allan Pub., Oxfrd, Cnference n Applied Statistics in Agriculture

15 Applied Statistics in Agriculture 43 [18] E.O. Headyet al.(eds). Agricultural Supply Functins. Estimating Techniques and Interpretatins, Iwa State University Press, [19] D. Heien. "An Ecnmic Analysis fthe U.S. Pultry Sectr," American Jurnal f Agricultural Ecnmics, 58, , [20] W.R. Henry and R. Raunikar. "Integratin in Practice- The Briler Case," Jurnal f Farm Ecnmics 42, , [21] C. Hillinger and M. Sebld. "Identifying Discrete Business Cycles Frequencies," t appear in Prceedings f the 8th Internatinal MAXENT Wrkshp, J. Skilling, (ed.), Kluwer Academic Publishers, Drdrecht-Hlland, [22] G.G. Judge et al.. The Thery and Practice f Ecnmetrics, 2nd editin, Jhn Wiley and Sns, [23] S.M. Kay. Mdern Spectral Estimatin, Prentice-Hall, [24] S.L. Marple Jr. Digital Spectral Analysis with Applicatins, Prentice Hall, Inc., [25] M. Nerlve. "The Dynamics f Supply: Retrspect and Prspects," American Jurnal f Agricultural Ecnmics, 61, , [26] M. Nerlve. "Spectral Analysis f Seasnal Adjustment Prcedures," Ecnmetrica vl 32, n. 3, , [27] M. Nerlve. "Adaptive Expectatins and Cbweb Phenmena," Quarterly Jurnal f Ecnmics, , [28] M. Nerlve. The Dynamics f Supply: Estimatin f Farmer's Respnse t Price, Baltimre: Jhn Hpkins University Press, [29] D. Orden. "Mney and Agriculture: The Dynamics f Mney- Financial Market Agricultural Trade Linkages," Agricultural Ecnmic Research, vl. 38, n.3, 14-27, [30] P.L. Paalberg and A.J. I bb. "Public Plicy and the Reemergence f Internatinal Ecnmic Influences n U.S. Agriculture," Agricultural Ecnmics Research, 38, n. 1, 45-56, [31] E. Parzen. "An Apprach t Empirical Time Series Analysis," in Time Series Analysis Papers, Hlden-Day, [32] T.A. Dan and R.B. Litterman. RATS Manual, Versin [33] G.C. Rausser and T.F. Cargill. "The Existence f Briler Cycles: An Applicatin f Spectral Analysis," American Jurnal f Agricultural Ecnmics, 52, 1970.

16 44 [34] G.B. Rgers. "Pultry and Eggs," in Anther Revlutin in U.S. Farming'?, L.P. Schertz et. al eds. USDA, EcnQmics and Statistics Service, Agricultural Ecnmic Reprt n. 441, [35] G.B. Rgers, V.W. Bensn, D.L. Van Dyne. " Energy Use and Cnservatin in the Pultry and Egg Industry," USDA, Ecnmic Research Service, Agricultural Ecnmic Reprt, n.354, [36] J. Sanchez. "Applicatin f Classical, Bayesian and Maximum Entrpy Spectrum Analysis t Nnstatinary Time Series Data," in Maximum Entrpy and Bayesian Methds, Kluwer Academic Publishers, 1989, p [37] Sanchez, J. "Bayesian, Autregressive and Peridgram Spectrum Analysis," Unpublished dissertatin, (1989). [38] J.A. Seagraves, C.E. Bishp "Impacts f Vertical Integratin n Output and Industry.Structure," Jurnal f Farm Ecnmics 40, , [39] S.K. Seaver. "An appraisal f Vertical Integratin in the Briler Industry," Jurnal f Farm Ecnmics, 39, , [40] B.F. Tbin and H.B. Arthur. Dynamics f Adjustment in the Briler Industry, Bstn, Harvard University Graduate'Schls f Business Administratin, [41] United States Department f Agriculture. Eggs) Chickens and Turkeys, Natinal Agricultural Statistics Service. [42] United States Department f Agriculture. U.S. Briler Industry, Ecnmic Research Service, Electrnic Data Prduct n [43] A. Zellner. An Intrductin t Bayesian Inference in Ecnmetrics, Jhn Wiley and Sns, 1971.

17 Applied Statistics in Agriculture 45 Figure 1.- The Data Placements Price LO C") <0 LO LO N C") Jan 60 Jan 75 Time in mnths Jan 65 Jan 75 Time in mnths Jan 85 Chicks Hatched Returns C") LO... I Jan 60 Jan 75 Time in mnths Jan 70 Jan 80 Time in mnths

18 46 Figure 2.- Lg_10 f the psterir prbability f ne frequency accunting fr trend: (A) Net Returns; (8) Placement; (C) Price; (0) Chicks hatched. =- 0- :::; <C <'Q... <=> p; a;.... b.,f <::;; <> (A) S'.,,$ S ",0 fb'b'!. '-= 0(;;' (8) ",0 fb'b' S S 2... =- - c;;; (C) = <> p; -CD <..:0 <> (5 0) 22B S 2 PERlO» (KOKTHS) S S 2 PERIOD (XORTIS)

19 Applied Statistics in Agriculture 47 Figure 3.- Demdulated-remdulated data at the seasnal frequency (12 mnths perid) and its harmnics Cnference n Applied Statistics in Agriculture chicks placed pnce r LO.. I..q- I Jan 70 Jan 80 Jan 70 Jan 80 Time in mnths Time in mnths chicks hatched returns N N N I N I '<t I Jan 65 Jan 75 Jan 70 Jan 80 Time in mnths Time in mnths

20 48 Table 1.- Crss-peridgram f Chick Placement and Briler Price Cnference n Applied Statistics in Agriculture PERIOD COHERENCE PHASE PERIOD COHERENCE PHASE Table 2.- Crss-peridgram f Chicks hatched and Briler Price PERIOD COHERENCE PHASE PERIOD COHERENCE PHASE Table 3.- Summary f the Frecast Statistic fr all mdels at 1, 6, 12 and 24 Step Ahead Frecasts. Type f Mdel, Assumptin abut parameters and Dependent Variable MAPE(l) MAPE(6) MAPE(12) MAPE(24) Harmnic, Fixed parameter, Chicks Autregressive, Fixed par., Chicks Autregressive, Variable par, Chicks Structural traditinal, Chicks