Poultry supply functions (The relation of technical change to output of eggs, broilers and turkeys)

Transcription

1 Vlume 34 Number 505 Pultry supply functins (The relatin f technical change t utput f eggs, brilers and turkeys) Article 1 May 1962 Pultry supply functins (The relatin f technical change t utput f eggs, brilers and turkeys) Earl O. Heady Iwa State University f Science & Technlgy Yujir Hayami Iwa State University f Science & Technlgy Fllw this and additinal wrks at: Part f the Agricultural Ecnmics Cmmns Recmmended Citatin Heady, Earl O. and Hayami, Yujir (1962) "Pultry supply functins (The relatin f technical change t utput f eggs, brilers and turkeys)," Research Bulletin (Iwa Agriculture and Hme Ecnmics Experiment Statin): Vl. 34 : N. 505, Article 1. Available at: This Article is brught t yu fr free and pen access by the Iwa Agricultural and Hme Ecnmics Experiment Statin Publicatins at Iwa State University Digital Repsitry. It has been accepted fr inclusin in Research Bulletin (Iwa Agriculture and Hme Ecnmics Experiment Statin) by an authrized editr f Iwa State University Digital Repsitry. Fr mre infrmatin, please cntact digirep@iastate.edu.

2 Pultry Supply Functins (The Relatin f Technical Change T Output f Eggs, Brilers and Turkeys) by Earl O. Heady and Yujir Hayami Department f Agricultural Ecnmics Center fr Agricultural and Ecnmic Adjustment cperating AGRICULTURAL AND HOME ECONOMICS EXPERIMENT STATION IOWA STATE UNIVERSITY f Science and Technlgy RESEARCH BULLETIN 505 MAY 1962 AMES, IOWA

3 CONTENTS Summary Intrductin The pultry industry Objectives and empirical apprach Surce f data. Technlgy index Indicatrs f technlgy Chice f technlgy indicatrs in pultry prductin Cnstructin f technlgical variable Supply mdels. Factrs affecting supply. Structural changes in pultry supply relatins Frms f equatins and variables Methds f estimatin Distributed lags and lng-run elasticity Empirical analysis: eggs and farm chickens Cmpsitin f the enterprise. Sme relatins in the multistep mdel Mdel fr single-step analysis. Empirical estimatin and mdificatin f mdels Single-step analysis f egg supply Evaluatin f structural change in single-step mdel Multistep analysis f egg supply Empirical analysis: brilers Mdel fr annual data Mdel fr mnthly data Least-squares estimates fr annual data. Simultaneus-equatin estimates fr annual data Evaluatin f structural change with annual data Least-squares analysis f mnthly data fr brilers. Empirical analysis: turkeys. Results f estimatin Appendix Evaluatin f structural change fr turkeys ,

4 SUMMARY Supply relatins underlie the surplus, price and incme prblems f American agriculture. Yet specific knwledge f supply relatins is stilt small. This study is part f a larger investigatin directed tward increased knwledge f utput respnse r supply in agriculture. It is cncerned with a particular categry f farm cmmdities; namely, pultry prducts. The bjective f the study is t quantitatively identify variables which have been imprtant in the respnse f pultry utput ver time. But methdlgical purpses als are imprtant fr the study, and cn... siderable emphasis is placed n cmparisn f: alternative mdels applicable t egg, briler and turkey supply relatins. Technlgical change has been large in pultry prductin and evidently has had great effect n utput. Hence, the first step in this study is that f quantifying technical change, as a substitute fr time in the regressin equatins estimated. The number f eggs per layer, the briler-feed cnversin rate and the turkey-feed cnversin rate are selected as the utput-input ratis which best indicate the levels f technlgy fr the three pultry prducts. In extracting the net change in technlgy, by eliminating the effects f certain market cnditins, a lgistic functin is fitted t data fr each type f pultry. The values btained frm the estimated lgistic functins are called the technlgy index f egg prductin, briler prductin and turkey prductin. Pultry supply mdels are cnstructed with these technlgy indexes incrprated as variables. An egg supply mdel was estimated fr The results prvide statistical evidence that the egg price f the hatching seasn is an imprtant determinant fr the number f pullets raised, and, hence affects the ttal utput f eggs in the fllwing year. This effect f the egg price n pullet-raising als is cnfirmed by the results f an equatin estimated t shw the effect f the egg-feed price rati n farmers' demand fr pullets. The egg supply functin clearly indicates that technlgical prgress has shifted egg supply t the right. The effects f cmpetitive pultry enterprises n egg utput culd nt be established at the natinal level f aggregatin. The technlgy index prved superir t a time trend in the egg supply functin. The cefficient f determinatin was reduced frm t by substituting time fr the technlgy index in the egg supply functin. Mrever, the influence f the egg price during hatching seasn is bscured by using time in the estimate f egg supply. T see whether any change has ccurred in supply elasticities, the egg supply mdel was estimated fr tw subperids and , and als fr the smaller segments f perids , , and The results f estimatin fr these subperids suggest that the price elasticity f egg supply has been reduced amng these perids. T test the hypthesis that the recent specializatin tendency in egg prductin resulting frm technlgical prgress has caused the reductin, the elasticity f egg supply with respect t the egg-feed price rati was frmulated as a linear functin f the technlgy index fr statistical estimatin. The results shw that the elasticity is reduced by fr a unit increase in the technlgy index. This value is statistically significant at the 5-percent level. The hypthesis is further cnfirmed by the result f estimatin f farmers' demand fr pullets. The demand elasticity fr pullets with respect t the egg-feed price rati is estimated als t decrease by fr a unit increase in the technlgy index. A briler supply mdel was estimated first by least-squares methds fr the perid Briler prices are shwn t have a significant effect n the farmers' demand fr briler chicks in the analysis f mnthly data. A mdel based n simultaneus equatins fr demand and supply f brilers als was estimated fr annual data in the perid. N imprvement ver the single-equatin, least-squares estimate resulted frm this mdel. The technlgy index als prved t be superir ver a time trend variable in the analysis f briler supply. By using time instead f the technlgy index with regressin equatin, the sign f the cefficient fr the brilerfeed price rati became negative. T determine whether a change has ccurred in price elasticity fr brilers, a mdel was estimated fr the tw separate perids, and The supply elasticity with respect t the brilerfeed price rati als was frmulated in a mdel with the technlgy index expressed as a linear functin. The estimates shw that utput elasticity with respect t price has been reduced by fr a unit increase in the technlgy index. The turkey supply mdel was estimated first fr the perid It shwed that the turkeyfeed price rati f the previus fall significantly influences turkey utput in the fllwing year. The effects f cmpetitive pultry enterprises n turkey utput, at the natinal level f aggregatin, culd nt be clearly established. The technlgy index again prved t be superir t a time variable. By substituting time fr the technlgy index, the cefficient f determinatin was reduced by 10 percent, and the effect f the turkey price n the ttal utput was bscured. Separate supply functins were then estimated fr the perids and The results indicate that the elasticity f utput with respect t the turkey-feed price rati has increased appreciably ver time. T test the hypthesis that this increase in elasticity f turkey supply, with respect t the turkey-feed price rati, has been caused by technical change, a linear functin f the technlgy index was used. It indicated that the elasticity has increased by fr a unit increase f the technlgy index. 471

5 The Kyck-Nerlve mdel f distributed lags prvided a reasnable estimate f lng-run supply elasticities fr eggs and turkeys. But the results fr a similar mdel applied t brilers prvided nnsensical results. Evidently, a Kyck-Nerlve mdel cannt be used successfully with data where the dependent variable has a trend f cnsistent increase" r decrease. 472

6 Pultry Supply Functins (The Relatin f Technical Change t Output f Eggs, Brilers and Turkeys) 1 BY EARL O. HEADY AND YUJIRO HAYAMI This study includes a quantitative analysis f supply relatins fr pultry prducts in the United States. There are several stages in the supply f a farm cmmdity - the supply at prducers' level, at the whlesale level and the retail level. This analysis is restricted t the supply f pultry prducts at the farm level. It is an attempt t predict the quantity f pultry prducts which farmers prduce in respnse t the prices f thesa. cmmdities, the prices f majr cst items r inputs, and selected ther variables. The study is made as part f a larger analysis dealing with demand fr r use f resurces in agriculture and the supply f prducts. The surplus and incme prblems f agriculture revlve arund prblems f the magnitudes f inputs and utputs in the farming industry. Even nw, little is knwn abut the rate at which farmers' prductin respnds t changes in price and ther relevant phenmena. Accrdingly, majr debate still prevails ver farm plicy and the extent t which surplus prblems might be slved under varying levels and plicies f price. The prblems f supply are f particular imprtance in the feed grain-livestck sectr f the agricultural ecnmy. Greater knwledge is needed f the nature f supply respnse and the magnitude f utputs and prices which might exist under different degrees f cntrls ver, r freedm in, the market mechanism. Accrdingly, research has been initiated t estimate supply functins r respnse fr majr sectrs f livestck and pultry and demand functins fr feed grains. This study represents ne phase f the ver-all study and cncentrates n supply functins fr pultry prducts. Emphasis is placed n btaining quantitative knwledge f the basic relatins in pultry supply. Necessarily, then, the investigatin invlves methdlgy and the cmparisn f statistics and predictins btained frm alternative supply mdels. THE POULTRY INDUSTRY Pultry prductin prvides abut 20 percent f the cmbined livestck and pultry prductin 1 Prject Iwa Agricultural and Hme Ecnmics Experiment Statin. Center fr Agricultural and Ecnmic Adjustment cperating. 'Of the United States. The industry includes three,majr enterprises which are mre r less distinct peratins: (1) eggs with chicken meat as a by-prduct, (2) brilers and (3) turkeys. Egg prductin primarily has been an enterprise f the family farm, thugh there is a tendency tward specializatin in sme sectins f the natin. A distinct seasnality in egg prductin exists where farmers cause egg prductin t cnfrm with peratin f ther enterprises. Briler prductin is the mst specialized branch f the pultry industry. Gegraphically, briler grwers have becme clustered in the Suth Atlantic regin where prductin is highly cmmercialized and is cntinuus thrughut the year. Turkey prductin, riginally a sideline in farm peratins, is nw highly specialized. Turkey prductin als is highly seasnal because f the seasnality f demand and egg prductin. Because f differences in final prducts and prductin patterns, each f the three majr enterprises is treated separately in the fllwing analysis, except that the empirical mdels emplyed invlve certain interrelatinships amng enterprises. Other pultry enterprises include ducks, geese, guineas, pigens, quails and pheasants. These minr enterprises are negligible, hwever, in terms f their physical and value cntributin t ttal pultry prductin. Therefre, analysis f them is nt included in this study f pultry prductin. Pultry prductin increased by 107 percent between the perids and In the same time span, ttal agricultural prductin increased by nly 52 percent, and ttal livestck prductin, including pultry, increased by nly 59 percent. The rapid grwth f pultry prductin, relative t ther meat prducts and aggregate farm utput, is illustrated in fig. 1. The rates f grwth in utput differ cnsiderably amng pultry enterprises (fig. 2). Egg prductin, the mst imprtant cmpnent f pultry prductin, increased at abut the same rate as ttal pultry prductin. The briler enterprise has grwn mst rapidly. Starting at a negligible level f the mid- 30's, the ttal utput rse t mre than 5 billin punds f liveweight brilers in The increase in ttal utput has been cntinuus, except 473

7 X ljj Z 100 Fig. 1. Index numbers f livestck utput - pultry, meat animal and dairy ( = 100). -- POULTRY --- MEAT ANIMAL x-lc-xdairy I I I I I 1940 I I I YEAR IY= <It: 1&1 :::E 50 Fig 2. Ttal pultry prduc. tln, by prducts. " (1) 3Oe z :> IL z J...J :e x- x -x EGG \ z 2..J..J iii FARM CHICKEN 1000 BROILER ~ TURKEY YEAR 1950 in 1944 and 1946 when small decreases ccurred. Ttal briler utput dubled in each f the perids , , , and The upward trend in turkey prductin generally has been steady, thugh accmpanied by minr fluctuatins. Output in the perid was mre than fur times that f Amng the majr pultry prducts, nly the utput f farm chickens has shwn a decline. The utput f farm chickens was fairly stable befre Wrld War II, increased rapidly during the war and has been decreasing steadily since then. The questin arises: What caused these rapid develpments in the pultry industry? The increase in utput must have been caused by either 474 a rise in the relative price f pultry prducts r a reductin in prductin cst. Price mvements f majr pultry prducts are shwn in fig. 3. The general price level f pultry prducts has nt risen, except during the intrawar perid. Pultry prduct prices have declined appreciably since 1948 and, ver the past 15 years, have nt been high relative t ther types f livestck and relative t feed prices. It is reasnable t assume frm these price mvements that the supply functin fr pultry prducts has shifted t the right mre rapidly than has the demand functin. The cst f prductin, ne basis f the supply functin, is determined by the prices f inputs and the technlgy f

8 Fig 3. Prices f pultry prducts, deflated by cnsumers' price Index (cents per dzen eggs r pund f meat). ~ 25 z w EGG BROILER FARM CHICKEN TURKEY O~~lJ-L~~-LlJ-LJ-~-L~~~~-L~~-L~~~~~~~~ YEAR 4 II) cr «.J.J Fig. 4. Pultry ratin cst, deflated by cnsumers' price Index (dllars per 100 punds f pultry feed). prductin. It is likely, then, that the rapid rightward shift f the supply functin must result frm either a decline f input price r technlgical change which lwers the amunt f inputs ~equired per!1nit. f utput.. Hwever, the.dechne f input price IS nt the likely cause. FIgure 4 shws that, thugh there have been cnsiderable fluctuatins, the price f pultry feed, the mst imprtant cst item, has been at abut the same level in the recent decade as in earlier decades. The technlgy f prductin apparently is the majr factr which has caused the pultry supply functin t change. 2 2 The relative prfitability f cmpeting enterprises Is anther imprtant factr affecting pultry prducti~ and supply. Hwever, analysis suggests that, ver much f the perl~ analyzed, the abs?lute level f returns fr ther livestck enterprises had. nt ~echned. Technlgical change evidently has caused pultry prductin t mcrease in relative prfitability, hwever. OBJECTIVES AND EMPIRICAL APPROACH The bjective f this study is t estimate and interpret empirical supply functins fr eggs, brilers and turkeys fr the United States. In meeting these bjectives, alternative regressin techniques and mdels are applied t time series data. Mst f the analysis is based n singleequatin, least-squares methds. Hwever, applicability f simultaneus mdels als is examined. The basic apprach used in this study is the statistical estimatin f supply equatins frm natinally aggregated time-series data. This is the apprach traditinally used in the analysis f demand and supply. The estimated parameters f the supply equatins are meaningful if (1) the 475

9 data- are accurate, (2) the mdel used is a gd apprximatin' f "real wrld" cnditins, (3) the behaviral pattern f prducers is stable and (4) statistical estimatin prcedures are apprpriate. Here the wrd meaningful is equivalent t useful fr predictins. Whether r nt the cnditins are sufficiently met shuld be judged in terms f the purpse f the analysis. SOURCE OF DATA Basic data used fr estimatin in this study are taken frm the statistics f the Agricultural Marketing Service. 3 In the fllwing text, data cited are frm these surces unless specially nted therwise. TECHNOLOGY INDEX The mst imprtant variables in supply functins nrmally are prices fr inputs and utputs. Hwever, since technlgical change appears t have been extremely imprtant in causing change in pultry supply functins, it is useful and necessary t cnstruct an index r measurement f this phenmenn. The current sectin deals with cnstructin f a technlgy index t serve with ther variables in the supply mdels explained later.. Indicatrs f Technlgy A direct way t apprach the prblem f changing,technlgy :wuld be estimatin f pultry prductinfuiictins fr each year separately frm farm-survey data. The,differences between these estimated functins culd then be measured. This prcedure, hwever, is nt practically feasible because data are nt available. Since direct measurement f change in the prductin functin ver time is nt feasible, we are frced t use sme magnitudes in time-series data which indirectly reflect the change in the prductin functin. The change in a prductin functin is reflected in the ratis between input and utput which have been realized ver time. An utput-input rati in time-series data shws, at each pint in time and fr a given market situatin, an average prductivity fr a certain input level. Nt nly the magnitudes f the prductin functin but als the prices f utput and input can affect,the utput-input rati used by farmers. It is difficult t determine, frm time series data, the extent t which a change in the utput-input rati is caused by a change in the prductin functin r a change in the market situatin. Obviusly, hwever, frm the data presented earlier, the supply functin has changed 3 U. S. Department f Agriculture. 'Egg 'and pultry.tatistics thrugh U. S. Dept. Agr. Stat. Bul ; U. S. Department f Agri" culture. The pultry and, egg situatin. PES 198-PES ; U. S. Department f Agriculture., Agricultural Marketing Service. Agricultural prices. (Mime.) ;' and' U: S. Department r Agriculture. Chickens and eggs - farm prductin, dispsitin, cash receipts and grss incme. U, S. Dept. Agr., Agr. Marketing, Serv POU 2-3 (59) greatly even fr perids when the price f pultry prducts has nt been mre favrable relative t input prices. Frm cmmn knwledge, change in the prductin functin, causing the input-utput rati als t change, has been the imprtant phenmena causing the pultry supply functin t shift t the right. T use the utput-input rati as the indicatr f changes in the prductin functin, the fllwing cnditins shuld be satisfied: (1) the effect f market situatin n the utput-input rati is small enugh t be neglected, relative t the effect f technlgical change; (2) the effect f market change generally fllws a similar pattern ver the cmplete range f time, s that it can be eliminated by a certain scheme; (3) there is a definite trend in change f the prductin functin, such that we can apprximate the net effect f the, change by fitting a certain type f functin. If at least ne f these cnditins is met, we can evaluate the change in prductin functin in terms f the change in the utputinput rati. Therefre, whether we can use the utput-input ratis as the indicatrs f the technlgy f pultry prductin depends n whether these utput-input ratis satisfy either ne f these cnditins. Chice f Technlgy Indicatrs in Pultry Prductin We nw examine the utput-input ratis used t measure the technlgical changes in pultry prductin. We must determine whether any f these utput-input ratis satisfy ne r mre f the necessary cnditins fr extracting the net effect f technlgical change. Theretically, an utput-input rati which indicates the level f the prductin functin is the rati between the utput and the aggregate f all cnventinal inputs fr prductin. Fr pultry prductin, these cnventinal inputs are variable inputs like feed, semivariable inputs like flcks and fixed inputs like huses and equipment. It is difficult t aggregate the inputs fr pultry prductin t a reasnably accurate degree. In early ears, the majr prtin f pultry prductin was cnducted as a sideline f the ttal farm peratin. This situatin still hlds true fr egg prductin. It is difficult t separate the labr devt~d t pultry prductin frm that used in ther farm peratins. Natinal aggregative data are nt available fr the fixed capital f pultry. Under these limitatins, the aggregatin f all inputs wuld result in meaningless figures. ' A mre practical methd is t chse a factr which has made the greatest cntributin in the develpment f the industry. In pultry prductin, develpments in breeding, nutritin, disease cntrl and envirnmental cntrl represent imprtant bilgical innvatins. New devices in ventilatin, feeding and water systems, etc., represent imprtant mechanical innvatins. Mechanical innvatins are reflected mainly in the average prductivity f labr r the utput-labr rati.

10 120 Fig. 5. Index numbers f livestck prductin per man-hur - pultry, meat animal and dairy ( =100). POULTRY DAIRY MEAT ANIMAL YEAR 1950 As is seen in fig. 5, pultry utput per man-hur f labr has increased faster than ther livestck prducts and was 76.3 percent larger in the perid than in the perid Between these tw perids, utput per man-hur increased by 21.6 percent fr meat animals and 65.8 percent fr dairying. It is dubtful, hwever, that the increase in labr prductivity has been the majr factr in the develpment f the pultry industry. First, labr cst is nt a large prprtin f all csts. The recrds f pultry flilrms in Iwa 4 shw that labr cst, thugh it varies widely frm farm t farm, has rarely been abve 30 percent f ttal cst thrughut these 3 decades. Labr represents an even smaller prprtin f ttal csts n large, highly specialized farms. Pultry prductin traditinally was a sideline enterprise, and labr used had an pprtunity cst appraching zer. While n lnger true fr brilers and turkeys, farm flcks fr egg prductin utilize mainly the labr f husewives. Hence, develpment f the pultry industry up t the middle 1930's must be explained mainly by innvatins ther than labr-saving devices. This summary des nt mean that mechanical innvatins have been unimprtant in the develpment f the pultry industry, but nly that bilgical innvatins have dminated. Labr increasingly is becming an explicit cst fr pultry farmers as specializatin prceeds. Still, the main innvatins which have encuraged develpment f the pultry industry in the past 3 decades are prbably f a bilgical, rather than a mechanical, nature. Bilgical innvatins have been represented by imprvements in (1) nutritin, (2) breeding, (3) disease preventin and (4) envirnmental cntrl. Thse innvatins alne have caused an enrmus increase in pultry utput per unit f feed input. USDA figures 5 shw that in 4 Iwa State University f Science and Technlgy, Cperative Extensin Service. Annual reprts f Iwa pultry demnstratin flcks. (Mime.) " Jennings, R. D. Cnsumptin f feed by livestck, U. S. Dept. Altr. Prd. Rpt , 100 punds f feed prduced 18.9 punds f briler and 13.8 punds f turkey. -By 1957, 100 punds f feed prduced 33.9 punds f briler r 17.1 punds f turkey. In the same perid f time, egg prductin per layer increased similarly frm 122 eggs t 198 eggs per year. Feed is the largest single cst item in pultry prductin and currently cmprises mre than 50 percent f the ttal cst f prductin. (In the early days, feed was almst the sle item fr cash expenditure in pultry prductin.) We assume that bilgical innvatins, which are expressed in the change in the utput-feed rati, have had majr imprtance in the develpment f the pultry industry during this century. Hence, we chse the utput-feed ratis (feed-cnversin rates) as the technlgy indicatrs in pultry prductin. Briler-feed cnversin rates and turkey-feed cnversin rates are used in cnstructing the technlgy indexes f brilers and turkeys, respectively. Fr the egg functins, hwever, the number f eggs per layer is used fr this purpse. Trends in the number f eggs per layer, the briler-feed cnversin rate and the turkeyfeed cnversin rate are shwn, in cmparisn t the ttal utputs, in fig. 6. The trends f these technlgy indicatrs are very similar t the trends in the ttal utputs. Cnstructin f Technlgical Variable The number f eggs per layer, the briler-feed cnversin rate and the turkey-feed cnversin rate, by themselves, d nt measure the net effects f technlgical change. Hwever, they prbably serve effectively enugh t be used in cnstructing the technlgical variable t be used later. A lgistic functin is used in cnstructing the technlgical index. There are several methds f estimating the parameters f the lgistic functin. A prblem arises, hwever, in btaining reasnable estimates f upper asympttes, frm the data n hand, by 477

11 '" EGGS PER LAYER!;: TOTAL PRODUCTION II: ~ II: z c iii II: '" > z !;: II: z 0 iii II:... > 8 z 150 iii II: '" > ~ 100 u :< I,,, I I, I,!, '!! I,! I! ' 1!! I I,,!!,, year - CONVERSION RATE 30 TOTAL PRODUCTION _ CO VERSION RATE TOTAL PRODUCTION YEAR,,,,, /' /... _, YEAR 1950,.,.,-' z 40 0 ~ 30 :Ii 5000 UI I c / z,i 4000~ 3000~ :g z ~ 0 Il. Z J..J :E Fig. 6. (a) Number f eggs per layer and ttal utput f eggs. (b) Briler-feed cnversin rate and ttal utput f brilers, live weight. (c) Turkey-feed cnversin rate and ttal utput f turkeys, live weight. any standard methd. The briler-feed cnversin rate is still grwing at an increasing rate. Thugh there is sme sign f slwing dwn in the increase in number f eggs per layer, the deceleratin tendency is nt yet appreciable. The turkeyfeed cnversin rate has declined since But the efficiency f turkey prductin is still rising in an expnential fashin. Frm current timeseries data, the estimates f upper asympttes wuld be subject t great errr. Therefre, the apprpriate asymptte values must be established frm a priri knwledge. The physical limit wuld be 365 eggs per layer and 1 pund f briler r turkey meat per pund f feed. But it is generally believed that the natinal average figures will level ff befre reaching the physical limits. Fr egg prductin, it is reprted ll that the average prductin f hens in the Cnnecticut egg-laying cntests appears t have leveled ff at abut 240 eggs per year. Recrds in ther egglaying cntests indicate that egg prductin per year has attained a 250 level. Hence, 250 eggs is used fr the upper asymptte value in natinal averages. Fr the upper asymptte f the briler-feed cnversin rate, 67 punds f liveweight briler per 6 Bird. H. R. Fifty years f scrambling fr mre efficient egg prductin. Feedstuff. 31, N.8 : punds f feed is adpted. This rati is based n infrmatin given by Cmbs. 7 Fr the 'upper asymptte f the turkey-feed cnversin rate, 33 punds f liveweight turkey per 100 punds f feed is used. This figure is based n the estimate f the pultry scientists at Iwa State University and cnfrms t the figure predicted by Sctt. 8 The estimates f lwer asympttes were btained by extending the trend curves t The estimated values fr lwer asympttes are 100 eggs per layer, 18 punds f liveweight briler per 100 punds f feed, and 12 punds f liveweight turkey per 100 punds f feed. These values cnfrm mre r less t the knwledge expressed by pultry scientists at Iwa State University. The lgistic functins have been estimated frm time-series data, after transfrming the yearly bservatins int linear lgarithmic frm. The estimated functins are as fllws: Eggs per layer, Re 250 (1) Re = t e Briler-feed cnversin rate, Rb 67 (2) Rh = e t Turkey-feed cnversin rate, R'l' 33 (3) R'r = ,,--;:=""'"" e t The riginal bservatins and the estimated values f the number f eggs per layer, the brilerfeed cnversin rate and the turkey-feed cnversin rate are shwn in table 1. Figure 7 indicates the cnfrmance f the lgistic functin t the actual bservatins. The cefficients f crrelatin between the riginal bservatins and the estimated values are fr eggs, fr brilers and fr turkeys. Apparently, this functin fits the data mre effectively than ther types f functins used. 9 7 Cmbs, G. F., University f Maryland. Dept. f Pultry Husbandry, Cllege Park, Maryland. Infrmatin n the upper asymptte fr the briler-feed cnversin rate. (Private cmmunicatin.) (Nte: Dr. Cmbs used the wrds reed cm'ersin as briler utput divided by feed input, which is the reverse f the feed cnversin rate used In this study.) 8 Sctt, M. L. Fifty years In turkey nutritin. Feedstuffs 81, N. S : Fr example, these are the results C the expnential functin fitted t the same data : Eggs per layer (a) Re = 105.2e t Briler-feed cnversin rate (b) Rb = 17.8e t Turkey-feed cnversin rate (c) RT = 12.4e t The crrelatin cefficients between the riginal bservatins and the expnential estimates are Cr eggs fr brilers and fr turkeys.

12 Table 1. Technlgy indicatrs f pultry prductin: values f actual bservatins and estimated values frm lgistic functin. Number f eggs Briler feed Turkey-feed Year per layer cnversin rate cnversin rate Actual Estimated Actual Estimated Actual Estimated iii:ii " S , Surce: Jennings, R. D. Cnsumptin f feed by livestck, U. S. Dept. Agr. Prd. Rpt The number f eggs per layer, the briler-feed cnversin rate and the turkey-feed cnversin rate estimated by the lgistic functin, as explained abve, can be regarded as a measure f the "net effect" f technlgical prgress in pultry prductin. These estimates will be termed the technlgy index f egg prductin, f briler pr~ ductin and f turkey prductin. These indexes are used as the variables f technlgy in the fllwing supply analysis f pultry prducts. In ther wrds, the estimated quantities indicated in table 1 are used as the quantities representing the level f technlgy in each year fr which bservatins are used in estimating regressin equatins. Hence, the bservatins fr estimating Re(t) in equatin 32 are the technlgy index quantities indicated fr eggs in table 1. SUPPLY MODELS A linear equatin r a system f linear equatins is generally used in mdels fr estimating ecnmic relatins frm time-series data_ By a linear equatin, we refer t an equatin f linear cefficients, but nt necessarily f linear variables. Whatever transfrmatins f riginal bservatins (e.g., lgarithmic, quadratic! etc.) are used, the cefficients remain cnstant ver the range f variables. A linear equatin is used as a first apprxima~ tin f a real ecnmic relatinship s that the relatins can be estimated statistically. Nn- iii:ii Ill: 200 Ul li..j Ill: Ul Q. 100 :::<:!,,,! I, I, I! I,,, I '! I,,,,, I,,,!!,!,:t( YEAR Ul <l Ill: z 0 iii Ill:... > 25 8 z ~, "" I Ul 20 ~ II: ~ 15 iii Ill: Ul > z --- ESTIMATED ;~~~!~!~!~!~!~IJ~30~!~'~'~'~'~'~!~!~\9~14~h~!~!~!~!-!~!~!~!19~IOO~'~!~!~!~!~!!!~\:60 _ ESTIMATED!,!!! 1!!,! I,,,!!., YEAR YEAR Fig. 7. (a) Number f eggs per layer, values f actual bservatins and estimated values frm lgistic functin. (b) Brilerfeed cnversin rate, values f actual bservatins and estimated values frm lgistic functin. (c) Turkey-feed cnversin rate, values f actual bservatins and estimated values frm lgistic functin. linear mdels are difficult t estimate, the diffi~ culty multiplying as the number f variables increases. A linear mdel is a necessary device fr cmplex ecnmic prblems, but it has several limitatins. Fr example, suppse a supply relatin frmulated in the general frm (4) F (Xl> X2, X3,, Xm at, a!h., am, e) =0, where Xl is cmmdity price, X 2 is quantity supplied, X3... Xu are variables which affect supply, a's are the parameters, and e is a stchastical residual. The linear apprximate f equatin 4 is written as (5) {3 + {3IX1 + {32X {3nX Il + "I = 0, where the {3's are the parameters and." is a residual. The questin arises: Is it valid t use equatin 5 in analyzing the relatin frmulated in equatin 4? Sme deviatins frm equatin 4 are inevitable in estimating equatin 5. The prblem is nt whether there is deviatin f equatin 5 frm the true relatin, but hw well it apprximates equatin 4. The factrs which affect supply can'be classified int tw categries: (1) market cnditins and (2) structural cnditins. The first categry in- 479

13 cludes the prices f inputs fr prductin and f inputs and utputs in cmpeting enterprises. The secnd categry includes the decisin-making envirnment faced by farmers. The decisinmaking envirnment refers t such things as the prductin functins faced by farmers and the institutinal setting under which farmers make decisins. Tw categries f these influential factrs are different in the way they affect supply relatins. The structural cnditins specify the psitin f the supply functin, as is indicated in the relatin between the prductin functin and the supply functin. The supply curve shifts in a gemetrical fashin as the prices f inputs change. Changes in the prductin functin, n the ther hand, wuld generally cause the supply functin t change its shape and psitin, likely mving t the right with a change in slpe. Changes in the input and utput prices f cmpeting enterprises, and the prductin functins f the latter, wuld alter the pprtunity cst f inputs. These changes have the same effect as a change in the price f input used directly fr the particular cmmdity. The institutinal setting within which farmers wrk g-reatly influences the farmers' respnses t mice changes. If uncertainty is reduced because f institutinal chang-e, it is expected that farmers will respnd mre t price chang-es, and vice versa fr an increase in uncertainty. In general, we expect that changes in market cnditins cause the supply curve t shift, while the changes in structural cnditins alter the shape. as well as the psitin, f the supply curve. A linear equatin is a reasnable mdel fr apprximating the effects f market cnditins n supply. The effects f market cnditins n a linear supply functin are readily adiusted by adding the variables f market cnditins. On the ther hand, a linear equatin des nt seem entirely adequate fr expre,ssing- the effects f structural changes because the structural chang-es nt nly shift the supply functin, but als affect the cefficient r elasticity f supply in the sense f changing the slpe f the curve. Hweve,r, any judgment as t whether r nt these effects can be apprximated by a lineal' equatin must be relative and nt abslute. Even the market cnditins are nt necessarily linear in their effects n supply. Factrs AHectlng Supply The next step in the supply analysis f pultry prducts is the determinatin f the specific variables t be included in the mdel. Selectin, while based n thery and lgic, is necessarily restrained by data available in time-series frms. Variables fr the market cnditins are readily available in fficial statistics. We use the price f pultry feed t represent the price f this main input in pultry prductin. Feed cmprises the majr prtin f variable cst, and farmers are likely t respnd imprtantly t the change in its cst. Hgs and brilers are selected as enterprises 480 which cmpete with egg prductin. Eggs are selected a priri as a main enterprise cmpeting with briler prductin. Eggs and brilers are selected as the main enterprises cmpeting with turkey prductin. These enterprises are the nes which are mst likely t affect the relative prfitability f the pultry industry, in a natinally appreciable magnitude. Hgs are the mst imprtant enterprise which may cmpete against eggs fr nnspecialized family farms. Brilers and eggs are cmpetitive amng specialized briler grwers. Eggs and turkeys r brilers and turkeys are in a cmpetitive relatin. Turkey prductin, hwever, is a relatively minr enterprise in the pultry industry. Turkeys d nt have a natinally imprtant effect n brilers and eggs, althugh turkeys may be affected by eggs r brilers. Pssibly, ther enterprises such as milk cws and cattle feeding may cmpete directly against pultry. Hwever, because f the small degree f cmpetitin and because f prblems f multicllinearity in number f variables pssible, variables fr the latter enterprises are nt included in the supply mdels. The cmpetitive relatins utlined abve are selected a priri as hyptheses t be tested. These tests are accmplished in regressin mdels presented in later sectins f the study. We wish t determine whether these hyptheses are accepted r rejected n the basis f the aggregate time-series data available. Data fr variables fr the structural cnditins are generally difficult t btain. Hwever, we use the technlgy indexes mentined earlier fr this purpse. It shuld be remembered that the technlgy indexes are cnstructed frm the data f the number f eggs per layer, the briler-feed cnversin rate and the turkey-feed cnversin rate. Increases in these ratis are fairly unifrm ver a wide range in size f enterprise. Structural Changes in Pultry Supply Relatins The dminant effects f technlgical prgress in pultry prductin prbably are thse which cause the supply functin t shift. Hwever, we cannt neglect its effect n the cefficients r elasticities f supply. Other structural cnditins, such as the institutinal setting, als affect the supply cefficients. The technlgical indexes may partly reflect change in the institutinal settings, since technlgical prgress has been a primary factr in changing the institutinal envirnment. The tendency tward specializatin, increased flck size and cncentratin in the pultry in",: dustry has been brught abut by technlgical prgress. As the number f pultry farms decreases, and as their size increases, remaining farmers are thse better able t btain infrmatin and t imprve their bargaining pwer. Changes such as these reduce market uncertainty and alter the respnse f prductin t price. Technlgical prgress thus may affect supply cefficients r elasticities (a) directly by changing the prductin functins and (b) indirectly

14 thrugh altering the institutinal and decisinmaking setting. Hence, it is necessary t incrprate the technlgy indexes' int the supply mdels in such a way that they allw reflectin f change in bth supply cefficients and structure. Frms f Equatins and Variables The main variables affecting pultry supply have already been specified. It is theretically pssible t include all these factrs (prices 'f inputs and utputs, technlgy indexes, prices' f inputs and utputs in cmpeting enterprises) as independent terms in the regressin equatins. Since the number f bservatins is limited fr time-series data (and prblems f multicllinearity arise), it is necessary t use a limited number f variables. Because. f these cnsideratins, feed price is intrduced in the mdel thrugh a rati f utput price divided by input price, instead f including feed price as an independent term. The effects f a cmpeting enterprise are synthesized int ne variable called a prfitability index. The prfitability index is the utput-input price rati (multiplied by the technlgy index in the case f pultry). By the deflatin and the synthesis f variables, the infrmatin which therwise might be btained by using each variable as an independent term in an equatin is lst. But these transfrmatins are justified in terms f the empirical difficulties mentined previusly. The riginal bservatins fr all variables are transfrmed int lgarithmic frms. The lgarithmic transfrmatin is used because f lgical bases and because the cefficients f a lgarithmic functin are directly the cefficients f elasticity. One f the limitatins f a lgarithmic functin, hwever, is its cnstant elasticity ver the entire range f estimates. Other algebraic functins prvide mathematical restraints which may be equally realistic r unrealistic. Methds f Estimatin The questin arises as t whether a single equatin r simultaneus equatins shuld be used fr estimating the supply relatins f pultry prducts. Market price and quantity f a prduct are simultaneusly determined at an equilibrium f demand and supply. The simultaneus-equatin methd might seem apprpriate fr estimating supply relatins. It has been shwn, hwever, that the single-equatin least-squares methd is generally apprpriate fr the analysis f supply fr agricultural prducts. 1 A seasnality in prductin and a time lag betweeri a prductin plan and its utcme are characteristic f agricultural prductin. As a result f seasnality and time lag, prices by which farmers determine their ut- 10 Fr example see: Fx, K. A. The analysis f demand fr fann prducts. U. S. Dept. Agr. Tech. Bu! : and Earl O. Heady. Ecnmics f agricultural prductin and resuree use. Prentice-Hall, New Yrk Ch n expectatins and decisins. puts are generally the prices f the previus perid, r expectatins linked t their experience in the previus perids. In this sense, prices f the previus perid serve as predetermined variables fr the utput in the present perid. Sme degree f simultaneity may exist in the adjustments which can be made during a prductin perid. But usually the amunt f adjustment pssible is relatively small and shuld nt prduce appreciable bias in the least-squares estimates. Pssible simultaneity in demand and supply f the pultry prducts is cnsidered in the empirical analysis which fllws. Hwever, we find distinct seasnalities in all pultry prductin except brilers. The seasnal nature f prductin and the time lag between farmers' plans and their utcmes make the traditinal single-equatin least-squares methd appear 'apprpriate in analysis f eggs and turkeys. The simultaneusequatin methd is restricted t the analysis f briler supply, where the simultaneity in the prductin is expected t be s great that the singleequatin estimatin culd prvide meaningless results..' '. J' Distributed Lags and Lng-Run Elasticity In the time-series analysis f supply relatins, time must be cnsidered as a crucial element. Farmers make their prductin decisins, nt instantaneusly, but ver a perid f time. Supply elasticities can be classified n.the basis f length f time needed fr adjusting inputs. A supply elasticity ver a perid lng enugh fr farmers t adjust all inputs is called a lng-run elasticity. If the length f time is such that sme f the inputs are regarded as fixed, the elasticity is shrt run. The elasticity is zer Jr a time perid s shrt that n inputs can be altered. Elasticities may range frm zer t a much larger lng-run ~agnitude: dependi~g n ~h~.j~\h:nber and kind f InPuts WhICh are fixed. '.:.", The supply elasticities estimated frm the timeseries data in this study are'f a shrt-run nature. Lng-run elasticities cannt be measured directly frm time-series data, but can be estimated indirectly by use f distributed lag mdels, which assume a particular path in farmers' adjustment f nrductin. Kyck ll suggests a mdel f distributed lags fr statistical estimatin f ecnmic time series adjustment. His methd is as fllws: Suppse a general mdel f supply as. (6) Qt = a + bpt + blpt -1 + b~pt.:l b"pt." where Qt and Pt are utput and price at a perid t. If the variables in equatin 6 are lgarithmic, the lng-run price elasticity f supply is 00 (7) El = S b t-..; ~ I.- i= 11 Kyck, L. M. Distributed lags and investment analysis. Nrth Hlland Publishing Cmpany, Amsterdam, Netherlands '.-." ' 481

15 The effect f price cnverges, gemetrically as time passes, s that (8) bt = abt-i 0":::: a < 1. It fllws frm equatins 6 and 8 that (9) Qt = a + bpt + b a P t-i + ba 2 Pt_ b a npt_n' If we lag equatin 9 by ne perid, and multiply it by a, we get (10) aqt-1 = aa + bapt-1 + ba 2 Pt_ By subtracting equatin 10 frm equatin 9 we btain (11) Qt = a (1 - a) + bpt + aqt-i' Equatin 11 is readily estimated statistically, and the lng-run price elasticity f supply is given by!xi b (12) EI =::s alb i= 1-a Kyck derives the mdel fr estimating distributed lags and lng-run elasticities frm a general frm f distributed lags. Nerlve l2 arrives at the same basis frm a dynamic mdel f prducers' behavir (r cnsumers' behavir in case f demand), assuming a static expectatin. N erlve's dynamic mdel is frmulated as (13) Qt - Qt-I = "I (Qt* - Qt-I)' where Qt and Qt * are an actual utput and a lng-run equilibrium utput at perid t andy is the cefficient f adjustment. Equatin 13 suppses that, in each perid, prducers adjust utput in prprtin t the difference between the actual utput and the lng-run equilibrium utput. Assuming static expectatins f prducers, a lng-run supply functin is written as (14) Qt* = a + bpt where b is the lng-run elasticity f supply. By substituting equatin 14 int 13, we btain (15) Qt = ay + bypt + (1- "I) Qt-l' Equatin 15 has exactly the same frm as equatin 11, if we replace (1- a) withy and b with by. If the variables are in lgarithmic frm, the lngrun elasticity f supply is given by by (16) El = ----= b. 1-(1-"1) The Kyck-Nerlve methd f estimating the lng-run elasticity is based n the assumptin f a static expectatin. The lng-run elasticities fr pultry prducts are estimated in this study, assuming static expectatins by farmers. EMPIRICAL ANALYSIS: EGGS AND FARM CHICKENS The mdel used fr the empirical analysis f eggs and farm chickens can be deduced frm the 12 Nerlve. M_ Statistical estimatin f lng-run elb8ticities f supply and demand. Jur. Farm Ben. 40 : relatins shwn in fig. 8. The figure includes the relatins which are crucial in understanding the supply f eggs and farm chickens at the farm level. These graphic relatins are presented in a fashin such that the diagrammatical presentatin can be cnverted directly t mathematical mdels fr estimatin. Tw mdels fr the different empirical appraches are cnstructed frm the relatins presented in fig. 8, a mdel fr a single-step analysis f egg supply and ne fr a multistep analysis. Several relatins are invlved in the ttal prductin prcess fr the multistep mdel, as suggested in fig. 8. Where the relatins, indicated by small Arabic letters, are nt self-evident fr the multistep mdel, they will be explained fllwing the designatin f variables. The tw mdels are as fllws: ' I. Mdel fr single-step analysis f egg supply II. Mdel fr multistep analysis f egg and farm chicken supply (a) Pullet-raising (18) X, = { [~:l ',E.. E" n.] (b) Cckerel-raising (19) X k = yxp (c) Hen-culling (20) X -ffrp"l rpcl h'c- _lptj' LPtJ,X h (d) Pullet-culling (21) X,. ={ ~], ~;],x,j (e) Cunting f yung farm chickens prduced (22) Xyc = X k + Xn - Xd + Xp.c (f) Output f farm chickens (23) Qc = W~ Xll c + Wy Xy.c (g) Cunting f average number f layers n farm (24) Xl = XII + Xl' - X II.C - X 1 C - Xl'

16 Fig. 8. RelatIns In egg supply I IDemnd fr Eggs I -[ r IBriler SUPPlY: i ~:DemCind ]-[- fr Frm Chickens l,, :- I J Frm Price ) I Frm Pr.ice l I M arket1 ng I :Marketi-;g I I Prcess I \ f Eg~s f Chickens I Prcess I : JI' t jeq<l-fe.d Price Rati J I{;hlcken-Ieed Price Rati 'J I in Cu IlfnO Time in Cu liin g Time Farm Chicken Egg ~rductln]\ ~ /' Egs Per Layer I ~ Hens Culled ~ i"... + I Average Number f Layers n Farm Prduct in v/ t f Average Average Weight f WeIght Ma1ure f Yung Birds Birds Y Pullets Culte d I ~ Yung Chickens Prduced.. Hens and Pu Ilet s Cckerels n t n Farm, Jan. I Farm. Jan. I I Lss I (Eg-feed Price Rati ') in Hatching Seasn, Pullets Raised: -\ Cckerels Raised I r ( Cmpeting Enter pri ses ) % f Pulle ts in Ttal Chickens Raised Technlgy f Egg Prduc t 10 n1 Percentage f Chic ks Sexed in Ttal Chicks Hatched Prices are enclsed Inside t semicircular rectangles and quantities are enclsed Inside f squares. Arrws shw directin t Inti uence. Demand and marketlnq,elat1ns are enclsed inside f dashed squares. 483

17 (h) Output f eggs (25) Qe = R XI The fllwing variables, cmputed frm data f the surces mentined previusly, are: l~;j : Egg-feed price rati, year average fr calendar year f predictins, t express adjustment within year. Egg-feed price rati, weighted average frm Nvember f previus year t May f current year. Weights are: fr Nvember-1, December-2, January-3, February-4, March-5, April-3, May- 1. Chicken-feed price rati, year average fr year f predictins. E h : Hg prfitability index, average f hg-crn price rati fr Octber, Nvember and December in the previus year. Eb: Briler prfitability index, Nvember-May weighted average f briler-feed price rati multiplied by briler technlgy index. Weights are the same as egg-feed price rati. Qe: Number f eggs prduced in calendar year f predictins (billin). Q.: Quantity f farm chickens prduced in calendar year f predictins, liveweight (millin punds). Re: Technlgy index f egg prductin fr calendar year f predictins. R : Average number f eggs per layer fr calendar year f predictins. 'I : Cckerel-pullet rati, number f cckerels raised in prprtin t the number f pullets raised fr calendar year f predictins. X k : Number f cckerels raised (millin) in calendar year f predictins.. Xp: Number f pullets raised (millin) in calendar year f predictins. X h : Number f hens and pullets n farm, Jan. 1 f calendar year f predictins (millin). XII: Number f cckerels n farm, Jan. 1 f calendar year f predictins (millin). X h : Number f hens culled (millin) in calendar year f predictins. Xpc: Number f pullets culled (millin) in calendar year f predictins. Xd: Number f cckerels lst (millin) in_ calendar year f predictins. XI : Average number f layers n farm (millin) in calendar year f predictins. Xr: Residual in cunting the number f layers (millin). Wm: Average weight f mature chickens, liveweight (punds) in calendar year f predictins. W y : 484 Average weight f yung chickens, liveweight (punds) in calendar year f predictins. Cmpsitin f the Enterprise This sectin utlines the lgic emplyed in cnstructing the mdels: We suppse fr the singlestep mdel that farm chickens, but nt brilers r fryers prduced independently by specialized farmers r in specialized enterprises, are a byprduct f eggs. This assumptin implies that farmers determine the utput f eggs, and thus the utput f farm chickens in respnse t the price f eggs - but nt the price f farm chickens in respnse t ther prices. We d, hwever, later test mdels which suppse chicken, and hence egg, utput is affected by chicken prices. We d nt, hwever, emply mdels f simultaneus relatinships in egg and chicken price respnse. Characteristically, eggs and farm chickens are prduced as jint prducts. Cash receipts frm marketing farm chickens have rarely exceeded ne-furth f the ttal cash incme generated frm eggs and farm chickens. And the relative imprtance f farm chickens t eggs has been decreasing. The ttal value prduct f farm chickens nw is arund 10 percent f the ttal value prduct f eggs alne. The decline in the relative imprtance f farm chickens t eggs stems frm changes in pultry tecnnlgy, especially the practice f chicken-sexing. Until sexing was intrduced, the number f cckerels raised was abut 50 percent f the ttal number f chickens raised. It is nw arund 20 percent. Pullet chicks sexed as a percentage f ttal chicks purchased by farmers are pltted ver time in fig. 9. Available data series are nt lng enugh t shw a lgistic trend. But it seems reasnable t apprximate this trend by the lgistic functin. Sexing practice was intrduced at the beginning f the 1930's, has been accepted at an increasing rate, and it is likely that the rate f acceptance will slw dwn as the percentage f chicks sexed appraches 100. The lgistic functin is fitted t the data with zer as a lwer asymptte and 100 as an upper asymptte. The resulting estimatin is (26) S = 10_ t e where S is the percentage f pullet chicks sexed and t is time with t = 0 at The trend estimated by the lgistic functin is pltted in fig. 9. Estimatin f the chicks sexed by the lgistic functin is imprtant fr the purpse f predictin. It is als necessary fr estimating, frm the reprted data f ttal chickens raised, the number f cckerels and the number f pullets raised in the past years. The prcedures and the results f estimating the number f pullets and cckerels raised are summarized in table 2. Sme Relatins in the Multistep Mdel We nw detail sme f the relatins indicated under the multistep mdel.

18 Fig. 9. Sexed pullets as percentage f farmers' chicks purchased, values f actual bservatins and estimated values frm lgistic functin.... Z 1&1 U 50 II: 1&1 II. --ACTUAL "" -"" - - -ESTIMATED rable 2. Numbers f pullets and cckerels raised: estimatin prcedures frm reprted data n farm chickens raised, Year Number f chicken. raised (millin) (1) Sexed pullets 8s a per.. centage f chicks purchased (2)a Sexed cckerels as a percentage f chicks purchased (3)b Straightrun chicks as a per.. centage f cblcks raised (4)c Sexed pullets (millin) (6)d Estimated Estimated Straight- number f number f run pullets cckerels pullets raised raised (millin) (millin) (millin) (6)e (7)f (S)g S f ' S S S , i Ii.O i S.1 a Data available fr , and estimated fr by lgistic trend. b Data available fr , and estimated fr by multiplying clumn (2) by ne-firth. ratis f sexed cckerel. t sexed pullets a. percentage f ttal chicks purchased by farmer c Clumn (4) = clumn (2) - clumn (3). d Clumn (6) = [clumn (1) X clumn (2) e Clumn (6) =!.> clumn (1) X clumn (4) f Clumn (7) = clumn (5) + clumn (6). I\" Clumn (8) = clumn (1) - clumn (7). One-fifth is the 5-year average fr f 485

19 Relatins f Raising Pullets and Cckerels Pullet-raising is the mst imprtant relatin in determining the utput f eggs and the utput f farm chickens. Assuming farm chickens as a by-prduct, the number f pullets raised shuld be determined by the prices f inputs and utputs in egg prductin, the technlgy f egg prductin and the prfitabilities f cmpeting enterprises. The egg-feed price rati, the technlgy index f egg prductin and the prfitability indexes f hgs and brilers are chsen, respectively, fr the three crrespnding variables in the empirical mdel discussed in this sectin. One prblem in measurement is that f the perid chsen fr the bservatin f these variables. The, majrity f chicks are hatched during the spring mnths, especially March, April and May. Befre 1940, abut 80 percent f the chicks were hatched during these 3 mnths, and mre than 90 percent during the first half f the year. Thugh this seasnality has been gradually leveling ff because f the recent tendency tward specializatin, 70 t 80 percent f the chicks are still being hatched during the first 6 mnths f the year. Cnsidering the seasnality in hatching and the time lag between farm planning and its utcme, the egg-feed price ratis f 7 mnths - Nvember f the previus year thrugh May f the present year - are averaged with the weights explained later. The same perid is chsen fr the briler prfitability index. But befre 1953, when mnthly briler data were nt available, the average f the present year's price and the previus year's price is used as a substitute fr the 7-mnth weighted average. Octber, Nvember and December are chsen fr the perid f bservatin fr the hg prfitability index. These 3 mnths cnstitute the perid in which the winter farrwing f sws largely is determined. The seasnality in pullet-raising and egg prductin and the resulting specificatin f the bservatin perids have very imprtant implicatins fr the estimatin methd. The majrity f pullets hatched during the spring mnths start laying eggs in the fall. Pullets hatched in early spring lay sme eggs befre summer. But the rate f lay is lw fr the first 2 r 3 mnths, and the quantity f eggs prduced by the springhatched pullets is small in magnitude. The eggfeed price rati and the prfitabilities f the cmpeting enterprises in the hatching seasn affect the utput f eggs in the fall, but d nt affect, r have nly a weak effect n, the utput in the hatching seasn itself. The relatin between the number f pullets,raised and the prices in spring thus is generally unilateral rather than simultaneus. Fr this reasn, the single-equatin leastsquares methd is deemed sufficient fr estimating the pullet-raising relatin. The number f cckerels raised is determined directly frm the number f pullets raised, assuming farm chickens as the by-prduct f eggs. Mathematically, this relatinship is frmulated in 486 equatin 19. The cckerel-pullet rati, y, in equa. tin 19 was used frm the prcedures in estimat. ing the number f pullets and cckerels frm the data in table 2. The number f cckerels, Xk, is, by definitin, btained by subtracting the number f pullets, Xp, frm the ttal number f chickens raised, Xc' (27) Xk = Xc - Xl> 'l'he number f pullets raised is determined by adding the number f sexed pullets and half f the number f straight-run chicks. This is given by 1-s-k (28) Xp = s' Xc + 2 Xc where s is the rati f the number f pullets sexed t the number f chickens raised and k is the rati f the number f sexed cckerels t the number f chickens raised. The magnitude f s is btained frm the lgistic functin estimated in equatin 26. Sexed cckerels have cmpsed a small fractin f the ttal chicks purchased by farmers. These sexed cckerels are mainly fr hme cnsumptin and will be reduced t a negligible amunt as the cmmercializatin f the enterprise prceeds. Fr a predictive purpse, the average f the number f sexed cckerels in prprtin t the number f sexed pullets in the preceding 5 years can be extraplated as a rugh apprximatin. Equatin 28 can be transfrmed int (29) Xp=1+~-kXc Slving equatin 29 fr Xc, 2 (30) Xc = 1 + s _ k Xp and by substituting equatin 30 int equatin 27, we btain r 2 (31) XI, = l1 + s _ k The cckerel-pullet,rati is thus derived frm the percentage f chicks sexed. Relatins f Culling Hens and Pullets The culling f hens is an imprtant determinant in the utput f eggs and the utput f farm chickens. Pullets start laying eggs within abut 4 mnths after being hatched, and the rate f lay increases until it reaches a peak at abut 12 mnths. The rate f lay then declines gradually. Whether t cntinue keeping hens r t cull them becmes a prblem fr farmers generally after hens are kept fr ne year r lnger. The number f hens culled in a year is restrained by the number f hens and pullets n the farm at the beginning f the year. The data are reprted fr the number f hens and pullets n the

20 farm, Jan. 1. Other variables which may affect the number f hens culled are the: prices f eggs, farm chickens and pultry feed. If the market is favrable fr eggs, farmers will keep hens lnger, reducing the number f hens culled. On the ther hand, if the market is favrable fr farm chickens, farmers will tend t cull mre hens. The annual averages f egg-feed price rati and chicken-feed price rati are included in the equatin f hen-culling. Amng these three variables in the equatin which affect hen-culling, the number f hens and pullets n farms Jan. 1, is predetermined, but the tw ther variables are nt exactly predetermined. The annual averages f bth the egg-feed price rati and the chicken-feed price rati affect the number f hens culled, and cnsequently the utput f eggs and f farm chickens. These utputs, in turn, affect the prices f eggs and farm chickens. Here is a simultaneus determinatin f prices and utputs. This simultaneity, hwever, is nt expected t be strng. Mst hens are culled because they are ld and have a lw rate f lay. A market situatin is a relatively minr cnsideratin in farmers' decisin-making relative t culling hens. Mrever, the effect f culling n the utput f eggs shuld be discunted because the hens culled are low-laying. Baker13 reprts that the utput f eggs in a crp year can be accurately predicted n the basis f the number f ptential layers n a farm and the number f eggs per layer at the beginning f the crp year. These tw factrs explain 98.7 percent f the variance in the ttal utput f eggs fr the years thrugh Baker's study shws that the adjustment f egg prductin is very small within a crp year. If s, factrs which determine the utput f eggs can he regarded as predetermined. Thugh the seasnality f egg prductin has been leveling ff since 1948, the prductin adjustment within a crp year shuld be much smaller than the adjustment made prir t the decisin year. Hence, even if prices within the year affect the hen-culling, it is dubtful that the effect f culling n the utput can be s large as t cause an appreciable bias n the least-squares estimates. The least-squares methd als seems sufficient fr analyzing the hen-culling relatin. Culling becmes a prblem usually after hens are kept fr 1 year r lnger. Every year, hwever, a small fractin f pullets raised is culled fr hme cnsumptin, r. because f sickness, physical defrmity, etc. The number f pullets culled is largely determined by the number f pullets raised. There is sme pssibility that pullets are culled mre heavily when the market situatin is unfavrable fr eggs r favrable fr chickens. T test whether market situatins affect pullet-culling; an equatin is estimated which 13 Baker. R. L. Sme factrs affecting the quantity and quality f eggs marketed by certain prducers. Unpublished Ph.D. thesi.. Iwa State University Library. Ames. Iwa includes the annual averages f the egg-feed price rati and the chicken-feed price rati. The discussin abut simultaneity in the hen-culling applies equally t the pullet-culling relatin. Cunting Relatin. The utput f eggs and the utput f farm chickens are primarily determined by the relatins f raising and culling chickens. T cnnect the utputs t the number f chickens raised and culled, we frmulate the cunting equatins. These cunting equatins are frmulated ih the prcess f estimating the numbers f hens and pullets raised. The data f hens and pullets culled can be estimated frm the data f chickens sld and cnsumed n the farm where prduced. Data are reprted fr the number f yung birds and the number f mature birds sld frm farms. We assume that, fr chickens sld frm farms, mature birds are hens culled and yung birds are cckerels raised and pullets culled. The number f yung birds and the number f mature birds cnsumed n the farm where prduced are estimated by multiplying the reprted ttal number f chickens cnsumed n the farm where prduced by the percentage f yung birds and mature birds in the ttal number sld. This estimatin prcedure is based n the assumptin that the cmpsitin f chickens cnsumed n the farm where prduced is the same as that f the chickens sld.. Mature chickens sld and cnsumed n the farm where prduced add up t the number f mature birds prduced, r the number f hens culled. Yung chickens sld and cnsumed n the farm where prduced add up t the number f yung chickens prduced fr sale. Quantities arising frm these estimatins are summarized in table 3. The number f pullets culled can be estimated as a residual in cunting the ttal number f yunll chickens prduced. Yung chickens are cmpsed f cckerels raised, cckerels n the farm at the beginning f a year and pullets culled. The number f yung chickens prduced, estimated in table 3, shuld equal the sum f the numbers f cckerels raised. cckerels n the farm n Jan. 1 and pullets culled minus the number f cckerels lst by death. Cckerels lst during the year are estimated in table 4. The data frm prcedures fr estimating the number f pullets culled are shwn in table 5. In the prcess f estimating the number f hens culled and f pullets culled, the number f yung chickens prduced and f mature chickens prduced are btained. The utput f farm chickens is given by summing (a) the number f yung chickens prduced multiplied by the average weight f yung chickens and (b) the number f mature chickens prduced multiplied by the average weight f mature chickens. The utput f eggs is als cunted frm varius surces. The utput f eggs is, by definitin, the average number f layers n the farm multiplied by the average number f eggs per layer. The 487

21 Table 3. Numbers f yung and mature chickens prduced: estimatin prcedures frm reprted data n chickens laid and cnsumed n farms where prduced, Year Number chickens sld Yung Mature (1) (2) Percent chickens sld Yung Mature (3)0. (4)b Ttal (5) Chickens cnsumed n farm where prduced Yung (6)c Mature (7)d Estimated number f chickens prduced Mature Y (hens ung culled) (8)e (9)f (millin) (millin) (millin) (millin) (millin) (millin) , ' Clumn (1) c Clumn (6) :::: [Clumn (3) X Clumn (6)] a Clumn (3)..,C,...0 lu-m-n...;;,('='1)f'i+~c"'0'f-iu-m-n---;(""2):- X 100. d Clumn (7) :::: [Clumn (4) X Clumn (5)] b Clumn (4) :::: Clumn (2) e Clumn (8) :::: Clumn (1) + Clumn (6). X 100. Clumn (1) + Clumn (2) f Clumn (9) :::: Clumn (2) + Clumn (7). Table 4. Number f cckerels lst during a year: estimatin prcedures frm reprted data f ttal chickens raised and lst during a year fr Year Chickens raised (1) _ Chickens lst (2) clumn (2) a Clumn (8) :::: clumn (1) X 100. b Estimated in table 2. Rate f lss (~a Cckerels raised (4)b (millin) Cckerels Estimated n farm lss f Jan. 1 cckerel. (6) c Clumn (6) :::: [clumn (3) X [clumn (4) + clumn (5)J Table 5. Number. f pullets culled: estimated as residuals In cunting yung chickens prduced, Year Yung chickens prduced (l)a Cckerels raised (2)b Cckerels n farm Jan. 1 (3) (mliiln) S 18.4 Estimated number Lss f f pullets culled cckerels as residual (4)c (5)d S S a '.3 a Estimated in table 3. b Estimated in table 2. c Estimated in table 4. d Clumn (5) = clumn (1) - [clumn (2) + clumn (3) - clumn (4»).

22 average number f eggs per layer is reprted, and its trend is estimated in cnstructing the technlgy index f egg prductin. The average number f layers n the farm is determined by (1) hens and pullets n the farm, Jan. 1, (2) pullets raised and (3) hens and pullets culled. The values f these items are already given. Residual in cunting the average number f layers cnsists f sucn items as the lss by death, the pullets which d nt reach the age f laying and the errrs in estimatin. Figures resulting frm the layercunting relatin are shwn in table 6. Mdel fr Single-Step Analysis The preceding discussin explains the lgic in cnstructing the mdel fr the multistep analysis. The mdel fr the single-step analysis f egg supply is cnstructed by cmbining the intermediate relatins int ne equatin. The mst imprtant factr which affects the utput f eggs in a year is the number f pullets raised in the previus year. The lagged values f the independent variables in the equatin f pullet-raising are included in the equatin fr the single-step analysis. These lagged values are the variables which determine the number f pullets raised in the previus year. The secnd factr which affects the utput f eggs is the number f pullets raised in the year. The Nvember-May weighted average f the egg-feed price rati is selected as a variable which determines the number f pullets raised in the present year. The ther Table 6. Cunting f average number f layers n farms during a year, Year Layers n farm during a year (1) Hens and pullets n farm Jan. 1 (2) Pullets raised during a year (3)a Hens culled (4)b (millin) S Pullets culled Residual (5). (6)d S a Estimated in table 2. b Estimated in table 3. c Esumated in table 5. d Clumn (6) [clumn (2) + clumn (3) - clumn (4) - clumn (5)l-clumn (1). variables which affect the number f pullets raised in the present year are excluded frm the equatin t avid multicllinearity with the lagged values. The third factr which affects the utput f eggs is the relatin f culling hens and pullets. Fr the variables which may affect culling, the annual averages f egg-feed price rati and f chicken-feed price rati are included in the equatin. Single-step analysis is cnducted nly fr the supply f eggs. In the supply f farm chickens, the change ver time in the intermediate relatins due t sexing practice has been great. Hence, it is quite meaningless t attempt a simple assciatin between the utput f farm chickens and the price f eggs, r even f farm chickens and chicken price. Empirical Estimatin and Mdificatin f Mdels Mdels have been presented s far in terms f a priri knwledge and lgic. In actual empirical estimatin f these mdels, sme variables may be fund t be insignificant, r t have large multicllinearity with ther variables. The results f estimatin may suggest that sme additinal variables are needed. The mdels are first estimated within the framewrk utlined abve, then are mdified n the basis f the results f estimatin. We present the mdels as utlined abve, then mdify them n the basis f initial empirical results. The single-step supply functin will be presented first. Single-Step Analysis f Egg Supply The result f estimatin f equatin 17, the single-step equatin fr egg supply fr , is: fp p l' (32) lg Qe = lg lpj' (0.0718) f lg flppejl' lg rl~e 1 (0.0712) f t 1 (0.1232) f J lg lr~e 1 J lg E htt. O (0.0726) f (0.0348) lg Ebtt.tl lg Re(tl (0.0620) (0.0970) R" = In this regressin equatin, the cefficients f lg (P~/Pt)' and lg (P~/Pf)'t.1 are significant at the 1-percent level. The values f these cefficients shw the psitive effects f the egg-feed price ratis in the hatching seasn f the previus year, and f the present year n the utput f eggs. The cefficient f the lagged value f (Pe/P f ), which expresses the rati in the previus year and therefre the premium n adding pullets t the flck, is estimated t be larger than that f the present value f the same variable, the latter indicating whether existing hens shuld be culled r' retained. 489

23 The cefficient f lg (Pe/P f ) is cnsiderably smaller than f lg (Pe/Pr)'t-1 and is significant at a prbability level f 30 percent. This suggests that the effect f relative egg price n egg supply is much smaller thrugh hen-culling than thrugh pullet-raising. The cefficient f lg Re is large in value and als highly significant, indicating that farmers have respnded strngly t technlgical prgress in eggs in expanding their prductin. The psitive sign fr the cefficient f lg (Pc/P f ) seems t reject the hypthesis that farmers cull mre hens when the chicken price is favrable. (Egg utput wuld be smaller under this cnditin.) Hwever, the psitive magnitude may be partly caused by the psitive crrelatin between the utput f eggs and the price f farm chickens ver business cycles in the natinal ecnmy. Bth the hg prfitability index and the briler prfitability index have psitive cefficients. At the natinal level f supply, it wuld appear that hgs and brilers are nt the main prducts cmpeting with eggs. Again, these psitive cefficients may als be explained by psitive crrelatin between their assciated variables and the utput f eggs ver the business cycle and between ther time trends at the natinal level. The upward trend ver time in bth the briler prfitability index and the utput f errgs evidently causes a high crrelatin between them, resulting in the psitive cefficient. T determine whether the effects f cmpeting enterprises might be reflected by remving pssible multicllinearity. the mdel is estimated after (Pp/P f ) and (Pc/Pf ) are drpped. The resulting equatin is: (33) lg Q" = lg (lpe lj ' (0.1109) P f lg (P e 1 ' (0.1187) lpfji-' lg Eh lg Eh lg Re (0.0584) (0.1001) (0.1110) R2 = The cefficients f lg Ell and lg Eb remain psitive in equatin 33. Judging frm the resulting statistics, the cmpetitive relatin between eggs and brilers is nt strng at the natinal level f aggregatin, at least nt strng enugh t vercme the psitive crrelatin resulting frm business cycle r trend. Baker indicated that a cmpetitive relatin between eggs and hgs cannt be fund statistically in Iwa. The cmpetitive relatin between these tw enterprises wuld be expected t be prminent in Iwa. If a cmpetitive statistical relatin cannt be fund in Iwa, it is unlikely that it can be established in an aggregative egg supply functin fr the United States. A cmpetitive relatin between eggs and brilers is becming imprtant as the briler industry develps and as briler grwers cnsider egg-laying hens as a substitute fr 490 brilers. Hwever, this relatin between eggs and brilers is f recent develpment. Therefre, it is reasnable that the cmpetitive relatin cannt be fund statistically in natinally aggregated time-series data fr the perid It is expected a priri that the effect n the utput f eggs resulting frm culling hens is much smaller than that resulting frm raising pullets. T test whether the culling f hens has affected the ttal utput f eggs in an appreciable magnitude, the mdel is estimated after the variables f cmpeting enterprises are drpped. The fllwing equatin results: (34) lg Qc = lg r p ej ' (0.0779) l P f lg [~ej' lg [~e] (0.0793) r t-l (0.1273) f R2 = lg [PcJ' lg R. (0.0756) Pt (0.0879) In this estimate, the cefficient f lg (Pe/Pf) is negative, and statistically significant nly at the 50-percent level. The cefficient f lg (Pe/Pf) stili has a significant psitive value. It may be cntended that chickens are nt a by-prduct and the psitive cefficient shws the effect f chicken price n pullet-raising and egg prductin mre than n the culling f hens. It is mre plausible hwever, that the significant psitive value f the cefficient is due t the crrelatin between chicken price and the utput f eggs thrugh the business cycle. Anther pssibility is that simultaneity causes the bias in the least-squares estimates. But it is nt likely that the simultaneity in the relatin f culling can cause such a large bias. Since the effects f cmpeting enterprises and f culling hens and pullets n the utput f eggs are nt fund statistically in a meaningful way, the variables which represent thse effects are drpped frm the mdel. The result f estimatin f the simplified mdel is: (35) lg Qe = lg [ P Pel, (0.1154) t lg r~p], lg Re (0.1175) f t-l (0.0939) R2 = d = 0.76 In this estimate, the cefficients f all three variables are significant at the 1-percent level and have signs which d nt cntradict thery. The value f the Durbin-Watsn d-statistic shws a psitive serial crrelatin f residuals at the 5-percent level. The psitive serial crrelatin is caused by the change in the price elasticity f supply during the war years. As shwn in fig. 10, equatin 35 cnsistently underestimates the utput f eggs fr the years frm 1941 thrugh 1953, and cn-

24 60 Fig. 10. Ttal number f eggs prduced, values f actual bservatins and estimated values frm equatin 35. z J..J iii 40, --ACTUAL ESTIMATED sistently verestimates it fr the years after The cnsistent underestimatin and verestimatin fr particular perids cause the psitive serial crrelatin in the residuals. This underesti-, matin and verestimatin f the utput must be due t the underestimatin f the price elasticity f supply fr and the verestimatin f price elasticity f supply fr During the war, especially in the early years, the farmers' expectatin fr egg price was very ptimistic. And farmers respnded t the price rise in this perid mre than in ther perids, resulting in a dramatic increase in the utput f eggs. During the price decline in the early pstwar years, utput did nt fall at the same rate as it rse during the war. This is cnsistent with the hypthesis f the irreversible supply curve by Cassels.'4 The adptin f technlgy and the investment f fixed capital during, the bm f the war culd nt be reversed quickly when the war was ver. Estimates With TIme and Elasticity Differentials Hence, the price elasticity f egg supply was inflated in the bming perid f the war and early pstwar years and was reduced when the egg price started t fall. Hwever, it is the limitatin f a linear equatin that the cefficients remain cnstant ver the range f bservatins. The elasticity with respect t (P./Pr), in equatin 35 is an average f the elasticities fr different perids. The serial crrelatin f residuals is expected t decrease if we estimate the mdel fr each f the subperids in which the price expectatin f farmers is relatively hmgeneus. Fr the sake f cmparisn and t examine the efficiency f the technlgy variable, a mdel which substitutes time, t, with t = 1 at fr the technlgy index is estimated as fllws: 14 Cassels, J. 1\1. The nature f statistical supply curve. Jur. Farm Ecn. 1Ii : (36) lg Qe = lg [~e J ' (0.2430) t lg rpp~ l' lg t (0.2425) r J t 1 (0.0419) R2 = d = 0.12 The value f R2 is markedly reduced, cmpared with equatin 35, and the cefficients f lg (Pc/Pr)' and lg (P~/Pf)'t-I are nt significant at the 5-percent level. Serial crrelatin is extremely high. On this basis, equatin 36 is inferir t equatin 35. Time is traditinally used as a substitute fr the technlgy variable fr the time-series analysis f supply. The intrinsic weakness f using time t represent technlgical prgress was discussed in a previus sectin. The statistics fund in cmparing equatins 35 and 36 supprt the advantage f using the technlgy index as a variable, rather than time. T btain the lng-run elasticities f egg supply, a Kyck-Nerlve type f mdel was estimated as fllws: (37) lg Q. = lg rp lp" ] ' (0.0635) r lg [~p 1,' lg Re (0.0677) t) t-l (0.0677) R2 = lg Q"lt-t) (0.0849) d = 0.85 In this equatin, the cefficients have signs cnsistent with thery and values significant at the 5-percent level. The lng-run elasticities btained frm equatin 37 are: with respect t (Pc/Pr), and with respect t (Pe/Pf )'(t.1) 491

25 These values are reasnable, cmpared with the shrt-run elasticities estimated in equatin 35: with respect t (Pe/Pc)' and with respect t (P~/Pf)'t-l. The lng-run elasticities are expected t be larger than the shrt-run elasticities. Again, it is indicated that the elasticity is greater with respect t buying chickens and raising pullets than with respect t hen-culling. (The egg-feed price rati f the previus year was selected t reflect effects n flck management thrugh pullet-raising and the egg-feed rati f the current year t affect flck management thrugh culling.) The value f d-statistics, hwever, indicates psitive serial crrelatin in the residuals. The cause f the serial crrelatins in this estimate must be the same as that fr equatin 35. Evaluatin f Structural Change in Single-Step Mdel Previus discussin suggested that technlgical change nt nly.causes a shift in the supply functin, but als generally alters the elasticities f supply. Hence, we nw evaluate the structural change in egg supply as it is caused by technlgical prgress. As a first step, we estimate the supply functins and elasticities fr tw r mre subperids mitting variables representing cmpeting enterprises. The data series frm 1926 t 1958 are divided int tw subperids and with the intra war years excluded. The estimates f the egg supply functin fr these tw perids are: (38) lg Qc = lg [~; J ' (0.1640) lg [~e] lg Rc (0.1675) r (0.3751) R~ = d = (39) lg Qe = lg [~e J ' (0.0617) f lg [~ej ' lg Rc (0.0642) f t-1 (0.0640) R2 = d = 1.37 The elasticities with respect t (Pe/P f )' and (Pel PC)'t-l in these estimates fr the divided perids are much smaller than thse in the estimate fr the whle perid. The reductin f the elasticities in these estimates is caused by excluding the bservatins f the intrawar years frm the analysis. As a result f the exclusin f intrawar years, the ~stimate fr each subperid is exempted frm the mfluence f the unusually high price elasticities during the war, which inflate the elasticities with respect t (Pe/Pr), and (Pe/Pr)'t-l in the estimate fr the whle perid. As was expected, the serial crrelatin f residuals is reduced in the estimate fr The value f the d-statistic f equatin 39 falls in the incnclusive regin. But the serial crrelatin f residuals in the estimate fr seems still t exist, judging frm the value f the d-statistic f equatin 38. As suggested in fig. 11, this serial crrelatin is caused by the verestimatin f the utputs in the years f the great depressin when the farmers' expectatins became unusually pessimistic and utput f eggs was reduced mre than the usual amunt relative t the decline in egg price. This change in the price expectatin causes the verestimatin f the price elasticity and the resulting verestimatin f the utput fr the perid f the depressin. Cmparing the estimates fr and , the marked difference is: The elasticities f supply with respect t (Pe/Pf ), and (Pc/Pf)'t-l fr the frmer perid are twice as large as thse fr the latter perid. Cnsidering the advances f technlgy between these tw perids, the differ- 60 Fig 11. Ttal number f eggs prduced, values f actual bservatins and estimated values frm equatins 38 and 39. Vl Cl Cl ILl z :J..J IX! ACTUAL - - -ESTIMATED 492 YEAR

26 ence in these elasticities wuld suggest that technlgical prgress caused the decrease in the price elasticity f egg supply. Technlgical prgress in egg prductin has been accmpanied by an increase in the amunt f fixed capital used fr prductin. Befre the middle f the 1930's, a relatively small amunt f fixed capital investment was required fr raising farm flcks. Chickens were raised in the yard, range r crner f the barn, salvaging waste grains, weeds and insects. Tday, mst chickens are cnfined in pultry huses with devices f envirnmental cntrl. Investment fr building, ventilatin, feeding equipment and water systems has been increasing. As the prtin f fixed capital increases, it becmes mre difficult fr farmers t adjust the prductin fr price change - at least in the shrt run. Obviusly, technlgical prgress has caused the tendency tward specializatin f egg prductin. As an enterprise is specialized, it becmes mre difficult fr farmers t enter r quit the enterprise n a shrt-term basis. When egg prductin is ne f the branches f a multienterprise farm, the farmer can easily shift the resurces f prductin frm eggs t ther enterprises r frm ther enterprises t eggs. Once the farmer specializes in eggs, he cannt raise anything but chickens, at least in the. shrt run, hwever unfavrable the egg price is relative t the prices f ther cmmdities. Real differences in the magnitude f supply elasticity between equatin 38 and equatin 39 might thus be explained by the technlgical prgress f egg prductin. Again, t cmpare shrt-run and lng-run elasticities, the Kyck-Nerlve mdel is estimated fr each subperid. The equatins fllw: (40) lg Ql' = lg [~. J ' (0.1002) f R2 = lg [~ej ' lg R. (0.1024) f t-l (0.2292) lg Qqt-1) (0.1829) d = 0.98 (41) lg Q = lg [~~J I (0.0672) lg [~ej' lg R,. (0.0687) f t-l (0.1365) lg Q"'t-l) (0.3308) R2 = d = 1.42 The lng-run elasticities btained frm equatins 40 and 41 are: with respect t (Pel Pr)' and with respect t (Pe/Pf)'t-l fr the perid , and with respect t (Pe/Pr), and with respect t (Pe/Pr)'t-l fr the perid f The lng-run elasticities are larger than their crrespnding shrt-run elasticities in bth equatins 40 and 41. The lng-run elasticities fr the perid f seem unreasnably large. This may be due t the underestimatin f the cefficient f adjustment. The cefficient f adjustment is underestimated because the cnsistent increase in the utput f eggs causes the high psitive crrelatin between Qe and Qe(t-l)' The difficulty in applying the Kyck-Nerlve mdel t the case in which the dependent variable has a trend f cnsistent increase r decrease is discussed later in the analysis f briler supply. Thugh the estimates f the lng-run elasticities fr the perid seem t large, it seems reasnable t suppse that the lng-run supply elasticities are at least larger in the prewar years than in the pstwar years. The decline in the lngrun elasticities again might be explained by the difficulty f entry and exit resulting frm specializatin. Frm these statistical estimates, hwever, we cannt say definitely that the elasticity f supply has been reduced because in either estimate, lng-run r shrt-run, the cefficients are nnsignificant at the 5-percent level. Fr further investigatin, regressin equatins are estimated fr the tw perids: and The frmer perid is prir t the rapid prgress in technlgy, while in the latter perid recent technlgy had been initiated and was prceeding rapidly. T examine supply structure fr the war perid, equatins als are estimated fr the perid Since the number f bservatins in each perid is small and because the egg-feed price rati in the hatching seasn f the present year is f relatively minr imprtance in relatin t the utput f eggs in the present year, the term (P.I Pr)' is drpped frm the equatin. Finally, the technlgy index is drpped frm the equatin f , because technical changes were small befre The results fr the fur subperids are summarized in table 7. The elasticity f supply with respect t (Pe/Pf)'t-t is indicated t have decreased except fr the war years. The elasticity estimated fr seems t small, cmpared with the elasticity fr Prbably the elasticity with respect t (P,,/Pr)'t-l is underestimated fr the perid because f the multicllinearity between (p./pr)'t-l and R p The trend in the technlgy index takes ver the upward trend in the egg price during the perid f recvery frm the 1930's depressin. The real respnse f farmers t price and cst wuld have been larger fr the perid than the statistical estimate shws. The elasticity with respect t (P,,/Pr)'t-l is largest fr the perid The causes fr this large price elasticity f supply during the war 493

27 Table 7. Results f estimatin f supply equatin fr fur subperlds. Subperid Degrees f Cnstant Cefficient f Cefficient a f freedm term Jg (P./Pd',-, Jg R. R" (0.0230) (0.0946) (0.2158) (0.0390) (0.1282) (0.8357) (0.6458) (0.0565) (0.0906) Figures in parentheses are the standard errrs f cefficients. years were explained in cnnectin with the serial crrelatin in the residuals fr equatin 35. The results in table 7 supprt the hypthesis that the price elasticity f supply has decreased, except fr the perid Hwever, the statistical evidence is weak, since the estimates f elasticity with respect t (Pp/Prh-1 are significant nly at a lw level f prbability, except fr the perid One hypthesis is that technlgical prgress has been the cause f the decrease in the elasticity with respect t the egg-feed price rati, T test this hypthesis, and t evaluate the effect f technlgical prgress n the elasticity f supply, the nnlinear equatin mdel is estimated. (42) lg Qe = lg (~pj ' (0.3916) r t-l lg Re (0.9064) (0.0026) R2 = d = 0.71 The cefficient f lg (Pc/Pr)'t-1 and the cefficient f lg Re are significant at the I-percent level. The cefficient f the interactin term is significant at the 5-percent level. Equatin 42 can be transfrmed int the fllwing frm with a nnlinear cefficient fr (Pe/Pi ) 't-1: (43) lg Qc = ( [ Pc], R.) lg -P lg R. i t-1 The cefficient f lg (Pc/Pf )'t-1 in equatin 43 wuld indicate that the supply elasticity with respect t (Pe/P,)'t-! decreases by fr a unit increase in the technlgy index f egg prductin. Egg utput estimated frm equatin 42 is pltted in fig. 12, in cmparisn with the actual bservatins. Elasticity with respect t (P"/Pr)'t-! is cmputed fr the average value f the technlgy index in each perid. The results are presented in table 8 in cmparisn with the separate estimates fr the perids. There is a cnsiderable difference between the value cmputed frm equatin 43 and the value estimated separately fr each subperid. This difference might be explained by the change in the expectatin patterns f farmers. Since this change is nt incrprated int the mdel, the value cmputed frm equatin 43 deviates frm the value estimated separately fr each perid. Hence, the nnlinear cefficient in equatin 43 is nt sufficient fr predicting the value f supply elasticity with respect t (Pe/ 60 Fig. 12. Ttal number f eggs prduced, values f actual bservatins and estimated values frm equatin 42. (J) (!) ~ 50 z a..j..j <D 40 --ACTUAL - - -ESTIMATED 494 YEAR

28 rable 8. Supply elasticity f eggs with respect t (P./Pr)' t-. fr subperldl. Subperid Average f the technlgy index fr the peri Cmputed frm equatin 43 Supply elasticity f eggs with re<'!pect t (P./Pr) "-I Estimated separately fr each perid _..._..._ _ _..._ _ ~~~~~ ~ ~~ Prh-l. There is anther weakness f the mdel fr predictive purpses. The nnlinear cefficient is assumed t be a linear functin f the technlgy index. There is a tendency t verestimate the elasticity fr the earlier perids and t underestimate the elasticity fr the later perids. As Re increases, the cefficient will eventually becme negative. Equatin 43 thus cannt be extraplated ver a wide range. The estimate f the nnlinear cefficient f lg (P./Pf )'t-l prvides little infrmatin abut what the elasticity was in a certain perid f the past r what it will be in the future. But it again prvides empirical suggestin that a decline in price elasticity f egg supply ccurs as technlgy advances. IS Multistep Analysis f Egg Supply The preceding empirical analysis has been based n a single equatin, t estimate the egg supply functin in a single-step manner. In this analysis, the varius prcesses, steps r enterprises invlved in raising pullets, culling chickens and related activities were cmbined int a single estimating equatin. We nw turn t the multistep mdel discussed earlier and estimate separate regressin equatins fr separate r distinct peratins in the egg-farming prcess. As explained previusly, the supply f eggs and farm chickens cnsists f fur majr steps in the pultry enterprise: (1) the raising f pullets, (2) the raising f cckerels, (3) the culling f hens and (4) the culling f pullets. Each f these fur relatins is nw analyzed separately. Once the number f pullets raised, the number f cckerels raised, the number f hens culled and the number f pullets culled are estimated, the ttal utput is autmatically given fr eggs thrugh cunting equatins 22 and 23, and fr farm chickens thrugh cunting equatins 24 and 25. Relatin f Raising Pullets The relatin f pullet-raising is frmulated in equatin 18. This equatin als might be termed "the farmer demand functin fr pullets." In the single-step analysis, it was apparent that the effects f cmpeting enterprises n the supply f 15 By the estimate, we can evaluate the effect f technlgical prgress n the ela.ticity with respect t (P./Pt)'t-l. eggs are nt large enugh t be statistically islated in natinally aggregated data. Hence, we start ur analysis in estimating the empirical cunterpart f equatin 18 with Eh and Eh drpped. The resulting equatin is as fllws fr the perid : (44) lg Xp = lg [P e ], (0.1659) P f lg R" (0.1161) R2 = d = 0.42 In this estimate, the cefficient f lg (Pe/P t)' is psitive in sign and significant at the 1-percent level. This indicates a psitive respnse in pulletraising t the egg-feed price rati in the hatching seasn. The cefficient f lg R. has a significant psitive value at the 5-percent level, als shwing a psitive respnse in number f pullets raised as the efficiency f egg prductin has advanced. In ther wrds, the technlgical prgress has shifted the farmers' demand fr pullets upward. The values f estimates fr bth cefficients are statistically significant at the 5-percent level and have signs cnsistent with thery. Hwever, the value f R2 is , indicating a small degree f assciatin between values f bservatins fr the number f pullets raised and the estimated values frm equatin 44. Als, the value f the d-statistic shws that the residuals in the equatin are serially crrelated. We nw examine the causes f this serial crrelatin. Figure 13 indicates that equatin 44 cnsistently underestimates the number f pullets raised fr the perid , and verestimates fr the perid The underestimatin fr the frmer perid again might be explained by the ptimistic price expectatin f farmers during the war years. This ptimistic expectatin increased the elasticity f farmers' demand fr pullets, as well as the elasticity f egg supply with respect t egg price. The verestimatin fr the number f pullets raised in the latter perid results partly thrugh the cmpensatin prcess in the least-squares estimatin - cmpensatin fr the underestimatin f the frmer perid. But the mre imprtant 495

29 \I)!!: td ~ 300 :; -' :! 100 ~ ACTUAL _ ESTIMATED <II II: iii :;:300 -'...J ls ACTUAL... ESTIMATEO YEAR YEAR 1950 Fig. 13. Number f pullets raised fr , values f actual bservatins and estimated values frm equatin 44. factr causing the verestimatin during might be the reductin in the price elasticity resulting frm technlgical prgress. Statistics f the previus sectin indicated that the elasticity f egg supply with respect t (P./Pr), decreased as technlgy advanced. Technlgical prgress wuld similarly affect the demand elasticity fr pullets with respect t the egg price and cst. But the relative reductin in elasticity is larger in the demand fr pullets than in the supply f eggs. Technlgical prgress is reflected in the increase in the number f eggs per layer. As the number f eggs per layer increases, farmers can increase r decrease the utput f eggs with a smaller change in the number f hens. Hence, fr the perid f analysis, the change in the demand elasticity fr pullets with respect t (P./Pr), shuld have been much larger than the change in the supply elasticity f eggs. The small value f R' and the high serial crrelatins fr the pulletraising equatin thus might be explained by a greater change in the demand elasticity fr pullets with respect t (Pe/Pr),. In an attempt t imprve explanatin f variance in pullet-raising and t decrease the serial crrelatin f residuals, it is necessary t allw the change in demand elasticity fr pullets t be reflected. The effect f technlgical prgress n elasticity f prduct supply r n elasticity f factr demand can be incrprated int the mdel frmulated by including an interactin term. Hence, in equatin 45, we have est~ma~ed a regressin equatin where the technlgical mdex serves in this manner with (PeIPr),. (45) lg Xp = lg [~.. J ' (0.4820) r lg Rp (1.1462) R' = d = (0.0031) r"iog [:;] '] This equatin can be transfrmed int a frm with the nnlinear cefficient: 496 Fig. 14. Number f pullets raised fr , values f actual bservatins and estimated values frm equatin 45. (46) lg XII = ( R,.) lg [~: J I lg R,. The nnlinear cefficient f lg (Pe/Pr), indicates that the demand elasticity fr pullets with respect t (P./Pr), decreases by fr a unit change in the technlgy index. This value is significantly larger than the magnitude f the reductin in the supply elasticity f eggs fr a unit increase in the technlgy index, , in equatin 43. The estimates fr the cefficients in equatin 45 are all significant at the 1-percent level. Marked imprvements in the degree f assciatin and in the reductin f the serial crrelatin f residuals are displayed in equatin 45 ver equatin 44. The value f R" increases by 65 percent in equatin 45 as cmpared with equatin 44. Als the value f the d-statistic cmputed fr equatin 45 falls in the indeterminate regin at the 5-percent level. These imprvements in the estimate are suggested in cmparisn f figs. 14 and 13. The change in the d-statistic supprts the hypthesis that the effect f technlgical prgress n the demand elasticity fr pullets is the majr factr in causing the serial crrelatin in the residuals f equatin 44. This change cntrasts t the results fr the egg supply analysis. N appreciable change in the value f the d-statistic was brught abut by adding an interactin term fr price and technlgy in the egg equatin (cmpare equatin 35 with equatin 42). The nature f farmers' expectatin evidently was a majr factr in changing the elasticity fr eggs, and technlgical advance had minr effects. Mdel 45 with the nnlinear cefficient is an imprvement, nt nly fr analysis f respnse elasticity fr pullet-raising, but als fr the purpse f predictin. Relatin f Raising Cckerels Assuming farm chickens t be a by-prduct f eggs, the number f cckerels raised is determined as a fractin f the number f pullets raised. This relatin between the number f pullets raised and the number f cckerels raised is frmulated as

30 Table 9. Number f cckerels raised: estimatin prcedure I frm the number f pullets raised estimated by equatin 45. s k Rati f the Rati f th" X. X. number f number f y Estimated Estimated Year sexed pullets sexed cckerels number f number f t the number t the number Pullet- pullets cckerels f chickens f chickens chicken raised raised raised raised rati (millin) (millin) (1)R (2)" (3)e (4)" (5) _ O.OU (l.00r !l _ O.OOS _ _ _._ _._ _ \\ _ i _... _ _ ll _ Q _ a Clumn (2) f table 2. b Clumn (3) f table y- 1 + s - k d Estimated frm equatin 45. Clumn (5) = clumn (3) X clumn (4). 500 II> ~... -~ iii 300 z..j..j i-actual ESTIMATED 1923 Fig. 15. Number f cckerels raised, values f actual bservalins and values btained thrugh equatin 19 frm numbers f pullets raised estimated by equatin 45. equatin 19. If we estimate the number f pullets raised frm equatin 45, then the estimate f the number f cckerels raised is prvided by multiplying the pullet estimate by the cckerel-pullet rati y btained frm the percentage f pullet chicks sexed. The prcess f estimatin is summarized in table 9, and the estimated values are pltted in fig. 15. Relatin f Culling Hens The effect f prices n egg prductin, thrugh culling hens and pullets, is nt indicated specifically and statistically in the single-step analysis. This is true since, in the mre "grss" prcedure f the single-step analysis, culling relatins are minr in their effects n egg utput relative t the effects f pullet-raising. T test whether the prices f eggs and farm chickens influence the number f hens culled, the hen-culling relatin frmulated in equatin 20 is estimated fr as fllws: (47) [Pe] lg X h c = lg P (0.1119) f lg [:cj lg XII (0.0443) f (0.0811) R~ = d = 1.52 The cefficients f all three independent variables have values significant at the 1-percent level. The d-statistic rejects the hypthesis f the serial crrelatin in the residuals at the 5-percent level. The negative sign in the cefficient f lg (Pc/Pt ) indicates that farmers cntinue keeping hens fr a favrable price rati and cull them fr an unfavrable rati. The psitive sign in the cefficient f lg (Pc/Pr) indicates that farmers cull mre hens when the market situatin is favrable fr chickens and cull fewer when the market situatin is unfavrable. The number f hens culled is largely assciated with the number f hens and pullets n the farm at the beginning f a year. But the results in equatin 47 indicate that farmers als use culling, in respnse t the prices f eggs and farm chickens during a year, t adjust the number f hens. Predicted values fr number f hens culled frm equatin 47 are cmpared with actual bservatins in fig. 16. This feature f estimatin and decisins culd nt be uncvered in the single-step analysis. Relalin f Culling Pullets The next step is t see whether the prices f eggs and farm chickens have any effect n the number f pullets culled. The relatin f pulletraising, as frmulated in equatin 21, is estimated as fllws: (48) lg XJl'r = lg [:e J (1.0617) r R2 = lg [~c J lg XI' (0.3972) f (0.7352) Only the cefficient f lg XII has a value that is statistically significant. Mrever, the signs f cefficients fr lg (Pe/Pr) and lg (P~/Pf) cntradict the hypthesis that farmers cull fewer hens when prices are favrable fr eggs r unfavrable fr chickens. 497

31 (/) ~300 iii illustrated in fig. 18. The fllwing mdel, crrespnding t the relatins in fig. 18 as far as allwed by data, is used: - ACTUAL ESTIMATED YEAR 1950 Fig. 16. Number f hens culled, values f actual bservatins and estimated values frm equatin 47. It may be hypthesized that farmers cull pullets in respnse t favrable egg prices but nt in respnse t favrable chicken prices. Pullets cntinue laying eggs fr lnger perids in the future than d hens. Hence, egg prices must be much mre imprtant than chicken prices in determining prfit frm pullets. T test this hypthesis, the pullet-culling equatin is again estimated with (P elp t) deleted: (49) lg XI"C = lg ~e J W= d = 1.21 (1.1876) f lg Xp (0.8911) The cefficient f lg (Pe/Pf ) nw has a sign cnsistent with the hypthesis, but it is nt statistically significant. It is likely that pullets are culled almst exclusively fr physical causes like sickness and physical defrmity. The estimated values fr the number f pullets culled frm equatin 49 are presented in fig. 17. EMPIRICAL ANALYSIS: BROILERS This sectin deals with farm supply functins fr brilers. The relatins in the briler supply mdel are 150 (/) «100 iii z ::; = ~ 50 - ACTUAL --. ESTIMATED I, I' I', \ I I I," I ~/' I \ I, I YEAR Fig. 17. Number f pullets culled, values f actual bservatins and estimated values frm equatin Mdel Fr Annual Data The supply mdel variables are as fllws and refer t annual data unless therwise specified: (P,,/Pr) : Briler-feed price rati, year average. (Ph/Pf ) t.l: Briler-feed price rati f the previus year, year average. Ee: Egg prfitability index, year average f egg-feed price rati multiplied by the technlgy index f egg prductin. E e (t.l): Egg prfitability index f the previus year. Rb: Technlgy index f briler prductin. Q,,: Quantity f brilers prduced, liveweight (millin punds). In equatin 50, the quantity f brilers prduced is expected t be assciated directly with the factrs which affect the raising f brilers. The intermediate relatins are nt analyzed because f the nature f briler supply and because f data limitatins. The structure f briler supply is much simpler than that f egg supply, because (a) the briler enterprise is a single-prduct enterprise and (b) the perid f briler prductin is relatively shrt. There are tw majr "shrt-run" farmer decisins in egg supply: the number f pullets t raise and the length f time hens shuld be kept. These tw decisins must be made ver a prductin perid lnger than 1 year. With briler supply, there is nly ne majr "shrt-run" decisin; namely, the number f brilers t raise, given the presence f fixed resurces. Once brilers are raised, farmers can d little t adjust utput. Weights can be increased when the market situatin is favrable, r lwered when it is unfavrable. But this adjustment is negligible in effect n the ttal utput, cmpared with adjustment in number f brilers raised. If brilerraising is the majr step in prductin, ttal utput can be predicted largely frm factrs which affect decisins n the number f brilers t be raised. Hence, the single-step analysis appears sufficient in analysis f briler supply. As mentined previusly, lack f data makes it difficult t analyze the intermediate relatins. Data n number f briler chicks purchased are nt reprted befre Amng the factrs affecting briler-raising, the briler-feed price rati, the egg prfitability index and the technlgy index f briler prductin are selected as the imprtant variables fr the mdel. The lagged values f the brilerfeed price rati and f the egg prfitability index are als included in the mdel, because sme time lag is expected in adjusting the relatively fixed facilities f prductin.

32 r , FIg. 18. RelatIns In briler supply. r , ~ ~r ~~ ri ~ ~ _'""'-----tl Far~ _C~:.~k-e-n-s-u-p-P-ly-J L I Marketin Prcels 1 Farm Price f Bri I ers I Briler Prductin \ ~ Brilers Prduced I I Aver~e Weight f Briler \ LOlli, I Brilers Raised : f( Briler -Feed Price Rati Technlgy f Bril e r Prductin Cmpeting Enterpr I ses Prices are enclsed inside f semicircular rectanles and quantities are enclsed instde f squares. Arrws shw directin f influence. Demand and marketing relatins are encl.ed inside f dashed squares. One characteristic feature f briler prductin is its cntinuus nature. Over the past 3 decades, technlgical advance has allwed the prductin perid t be reduced frm abut 100 days t less than 70 days. Briler grwers nw prduce three t six brds per year. The number f brilers can be adjusted t price change even within a year. If the calendar year is used as the prduc~ tin perid, price and utput wuld appear t be simultaneusly determined. Hence, a simultan~ eus~equatin apprach seems apprpriate in esti~ mating briler supply functins frm annual data. (If time~series data were available fr specific intrayear prductin perids, single~equatin, least-squares methds wuld be apprpriate.) T apprpriately express simultaneity, the ver-all mdel necessarily includes a demand equatin. An equatin f cnsumers' demand fr brilers, t be used fr the simultaneus-equatin apprach, is as fllws: 499

33 (51) [~ J = { [':;+ 0.9 ~ ]. ~ F, ] The variables in the mdel are: (Pb/L): Farm price f brilers fr the current year deflated by the cnsumer price index (cents per pund). (Q,,/N): Per-capita utput f brilers in the current year, liveweight (punds). ~ (Q,./N): Per-capita utput f farm chickens in the current year, liveweight (punds). (lin) : Per-capita dispsable incme in the current year deflated by cnsumer price index (dllars). Fe: Percentage f farmers' share in retail price f chickens fr current year. In the demand equatin, per-capita utput f brilers and per-capita prductin f farm chickens are aggregated int a single variable, as indicated in equatin 51, because brilers and farm chickens are a hmgeneus cmmdity fr cnsumers after they are prcessed fr the readyt-ck meat. The farm price f brilers is abut 10 percent higher than the farm price f farm chickens in terms f liveweight. This difference results frm the difference between brilers and farm chickens in dressing efficiency and in the bargaining pwer between the specialized briler grwers and the farmers wh keep small egg flcks. Accrdingly, farm chickens are given a price weight 10 percent less than that f brilers in equatin 51. Per-capita dispsable incme is included in the demand equatin as a standard variable which shifts demand. In representing the effect f the marketing mechanism n the farm price f brilers, the percentage f the farmers' share in retail price is included in the demand equatin. The prductin f brilers is cnnected t cnsumptin thrugh the relatins f marketing. It is pssible t cnstruct a large system f simultaneus equatins, including varius equatins representing marketing relatins. Hwever, it is nt the primary bject f this study t analyze marketing relatins. The frmulatin f a cmplex system f market relatins nt nly increases the cmputatinal burden, but als usually results in estimates cnfunded by multicllinearity. Hence, the relatin f demand and supply fr brilers is frmulated as a simple tw-equatin system represented in equatins 50 and 51. Mdel fr Mnthly Data The mdel just presented is fr analysis f annual data.. The shrt perid f briler prductin, hwever, 'requires analysis f mnthly data. Mnthly data f briler chicks purchased by farmers have been reprted since Abut 3 weeks are required fr chicks t be delivered after a farmer rders them frm hatcheries. Cnsidering this time lag, the briler-feed price rati, the e,gg-feed price rati f the previus 500 mnth and the technlgy index f briler prductin are chsen as the variables affecting briler prductin. The mdel fr the briler supply analysis f mnthly data is: (52) X"lm) = f[ [pp"j ' [pp"j ' Rb(ll1,l f 111 \ f m [ The variables in this mdel are: (PI.!Pf ) Ill \ : Briler-feed price rati f the previus mnth. (P~/Pf)ll1.1! Egg-feed price rati f the previus mnth. Rb(m): Technlgy index f briler prductin f present mnth. Xb(m): Number f briler chicks purchased in the present mnth (thusand). Equatin 52 can be regarded as a mdel f farmers' demand fr briler chicks. The farmers' demand fr briler chicks almst exclusively determines the supply f brilers 2 r 3 mnths later. The single-equatin least-squares methd is sufficient fr estimating equatin 52, because the prices which determine the number f briler chicks t purchase are the prices f the previus mnth. Least-Squares Estimates fr Annual Data Befre prceeding t the simultaneus-equatin apprach, the relatin f briler supply is estimated by the single-equatin, least-squares methd. Fr the least-squares estimate f equatin 50 is as fllws where the perid cnsidered is a year: (53) lg Q" = lg ~"J (0.7932) IF, lg r;hj lg E" (0.8052) IF, t 1 (0.5992) lg E,.(t.J) lg Rh (0.5460) (0.7033) R2 = The cefficients f lg (Ph/Pr) and lg (PI,/PC) t.l have signs cnsistent with thery but are significant nly at lw prbability levels. The cefficient f lg (Pt,/Pr) has a psitive value larger than that f lg (Ph/Pr) t.1. suggesting that farmers adj ust briler prductin mre in respnse t the price f the present year than t the price f the previus year. The statistical evidence is nt strng, hwever, cnsidering the lw value f the regressin cefficients relative t their standard errrs. The cefficients f l.g' E" and lg E.'It-ll have psitive values, cntradicting the hypthesis that the egg enterprise cmpetes strnq"ly with brilers. The psitive sig-ns in these cefficients must be caused by the psitive crrelatin between the utnut f eggs and the egq" prfitability index thrughut the business cycle. The cefficient f

34 lg R.. has a large psitive value which is highly significant. This cnfirms ur a priri knwledge that technlgical prgress is a majr factr cntributing t the miraculus grwth f briler prductin. Since the effect f egg prfitability n briler prductin is nt prved t be statistically meaningful, the mdel is simplified by drpping Ee and Ee(I-11 frm the equatin. The results fr'the simplified mdel are: ' (54) lg Q" = lg [~" J (0.8515) f lg (ppbj (0.8667) f t-l R" = d = lg Rb (0.5516) In this equatin, all cefficients are cnsistent in sign with thery, but the cefficient f lg (Pbl Pf) (t-1) is extremely small relative t its standard errr. The relative prductin csts f brilers have been reduced cnsistently as the technlgy f briler prductin has advanced. The ttal utput f brilers has increased almst cntinuusly since 1934, the increase in the efficiency f prductin evidently ffsetting the effect f price declines in the years f unfavrable markets. Other pssible causes f price cefficients with lw statistical significance are the simultaneus bias in the least-squares estimates and the bias resulting frm the serial crrelatin in the residuals. The pssibility f simultaneus bias is examined later with the simultaneus-equatin mdel. The d statistic indicates that the residuals f equatin 54 are serially crrelated. As we see in fig. 19, equatin 54 cnsistently underestimates the ttal utput fr the perid This underestimatin f the ttal utput again must be caused by the ptimistic price expectatins f farmers during the war years. On the ther hand, the change in the price elasticity f supply resulting frm technlgical prgress might have caused the verestimatin in recent years. The effect f tech- nlgical prgress n the elasticity is examined in the fllwing sectin. Fr the sake f cmparisn, a mdel which substitutes time, t, with t = 1 at 1935, fr the technlgy index f briler prductin is estimated. (55) l~ Qb = lg [~bj, (0.5963) f lg [~bj (0.6579) t 1-1 R2 = d = lg t (0.0679) In cmparing equatins 55 and 54, there is little difference in the values f R2 and the d-statistic. But the cefficients f lg (Ph/Pr) and lg (Pb/P f ) t-1 in equatin 55 are negative in sign and incnsistent with thery. On this basis, the use f the technlgy index appears pr.eferable t the use f the time variable. A mdel with the lagged value f ttal utput included as an additinal variable is estimated t btain the lng-run elasticities: (56) lg Qb = lg [~;1 (0.3521) [ Pb] +(~.~i~~~g Pf t-l R2 = d= lg R" lg Q,,(t-l) (0.6728) (0.0841) The results f estimatin in equatin 56 seem meaningless because the cefficient f lg Rb has a negative value. Technlgical prgress is a basic factr which has caused rapid grwth f briler prductin. A negative cefficient fr lg Rh wuld indicate that ttal utput has decreased as technlgy has advanced. The nnsensical esti Fig. 19. Quantity f brilers prduced (Iiveweight), values f actual bservatins and estimated values frm equatin I/) ~ 4000 ::l Q. z 3000 :l 2000 i -- ACTUAL ESTIMATED _I I I I, I- I, I 1000 O~~-J-i-=-~-=-~-=C-~-~L-:J.II~I-J~!~'~!~I~'~~I~I-LI-L~~~~~ YEAR 501

35 mate fr the technlgy index shws the inapplicability f the Kyck-Nerlve mdel t the case in which a dependent variable is increasing r decreasing cnsistently. In the case f briler supply, the ttal utput has increased cnsistently, except fr minr setbacks in 1944 and The psitive crrelatin between the ttal utput f brilers and its lagged value is s high that the lagged value f the ttal utput takes ver the upward trend in the technlgy index in the statistical estimatin. Simultaneus-Equatin Estimates fr Annual Data Simultaneus-equatin estimatin f briler supply frm annual data is suggested, since the price and utput f brilers can be simultaneusly determined within a year. The mdel t be used is the system f tw equatins: equatin 50 with Ee and Ee(l-l) drpped fr supply and equatin 51 fr demand. The limited-infrmatin, maximum-likelihd methd 16 is used fr estimating these tw equatins. The results f estimatin fr annual data are these: Supply Equatin (57) lg Q" = lg (;,,] (2.9219) t Demand Equatin lg [~bj lg RlJ (2.3939) f t-1 (1.2429) (58) lg [~J = lg [~+ 0.9~J (0.0964) lg [~ J lg Fe (0.4122) (0.1655) In cmparing the results f estimatin in equatin 57 with the results in equatin 54, it is difficult t determine whether the least-squares r the limited-infrmatin, maximum-likelihd methd is. superir fr empirical estimatin f the briler supply mdel specified in equatin 50. In the least-squares estimate, the cefficients f lg (Pb/Pc) and lg (Pb/Pf ) t.l have signs cnsistent with thery, but have values which are significant nly at lw prbability levels. Lg (Pb/P f ) in the limited-infrmatin estimate has a cefficient with a sign cnsistent with thery and with a value which is significant at even the 5-percent level. Hwever, the value f the cefficient seems large, and the cefficient f lg (Ph/Pr) 1-1 has a nega- 16 Fr a discussin f the limited infrmatin. maximum-likelihd methd, see: Chernff, H. and Di"insky. N. The cmputatin f maximum-likelihd estimates f linear structural equatins. In. Hd. W. C. and Kpmans, T. C., eds. Studies in ecnmetric methd. pp Jhn Wiley and Sns, New Yrk, N. Y. 1963; Klein, L. R. A text bk f ecnmetrics. Chap". III and IV. Rw, Petersn and Cmpany, Evanstn, Illinis. 1956; and Kpmans, T. C. and Hd, W. C. 'l'he estimatin f simultaneus linear ecnmic relatinships. In. Hwd. W. C. and Kpmans, T. C.. cds. Studies in ecnmetric methd. PP Jhn Wiley and Sns, New Yrk, N. Y tive sign which cntradicts thery. It is hard t determine why the cefficient f the latter becmes negative in the limited-infrmatin estimate. Multicllinearity between the exgenus variables in the system likely is the cause. Evidently estimatin by the simultaneus-equatin apprach des nt cntribute appreciably t knwledge f briler supply functins. Fr the sake f cmparisn, the least-squares estimate f the demand equatin is shwn in equatin 59. (59) lg [~J = lg (~+ 0.9~J (0.1061) lr [~] lg F,. (0.4432) (0.1414) R2 = In cmparing the empirical estimates in equatin 58 with the results in equatin 59, the limitedinfrmatin methd seems superir fr the analysis f briler demand. In bth equatins, the cefficients f per-capita utput f chickens and f farmers' share f the retail price f farm chickens have signs cnsistent with thery, but the cefficients f per-capita incme have negative signs which cntradict thery. In limited-infrmatin estimatin, hwever, the cefficient fr percapita utput f chickens is statistically significant at the 1-percent level. Evaluatin f Structural Change With Annual Data T evaluate pssible change in briler supply structure, supply analysis is cnducted separately fr tw divided perids: and Cnsidering the shrt series f data, the war years are nt excluded. The least-squares estimates f briler supply functins fr these tw perids are: (60) lg Qh = lg [~bj (1.4519) f lg (~,,] lg Rb (1.4046) f 1-1 (2.3508) R" = d = (61) lg Qh = lg [~;J (0.8251) lg r~"j lg R" (0.3127),f t l (1.9297) R" = d = 0.49 Fr the perid, the cefficients f lg

36 (Ph/P f ) and lg (P,/Pt ) t-l are negative in sign. During this perid, grwth f briler prductin increased rapidly, by 800 percent. The upward trend in the ttal utput resulting frm technlgical imprvement is s great that it dminates the effects f prices. Cnsequently, the regressin f utput n the briler-feed price rati is negative. The same explanatin undubtedly applies fr the negative cefficient f lg (Pb/Pi ) in the estimate. T, multicllinearity between lg (Pb/P!) and lg (P,,/Pt )t-l, brught abut by the dwnward trend in briler price since 1950 while utput has cntinued t increase because f technical imprvement, is anther cause fr the negative sign. Frm the estimates fr and separately, it is difficult t determine whether the supply elasticity because f price had changed; the price. cefficients are meaningless in sign and statistically nnsignificant. T test separately whether technlgical prgress has had imprtant influence n the farmers' respnse t price, a mdel with nnlinear cefficients is estimated fr : (62) lg Qh = lg (~b J (4.0800) f lg R" [Ri lg [~b] l (6.6383) (0.1689) t R2 = d = 0.44 In this estimate, the cefficients are nnsignificant at the 5-percent level except fr the cefficient f lg Rb Judging frm the d-statistic, equatin 62 gives n imprvement in serial crrelatin f residuals ver equatin 54. Technlgical change apparently is nt the majr factr causing the serial crrelatin f residuals in equatin 54. Outputs estimated frm equatin 62 are pltted in fig. 20 fr cmparisn with fig. 19 and equatin 54. We nw transfrm equatin 62 int the frm with a nnlinear cefficient fr lg (Ph/Pf): (63 ) lg Qb = ( R,,) lg [~: J lg R" The nnlinear cefficient in equatin 63 indicates that elasticity f briler utput with respect t (Pb/Pf ) decreased by fr a unit increase in the technlgy index f briler prductin. Hwever, the cefficient fr the interactin term in equatin 62 is nt large relative t the magnitude f its standard errr. Frm the statistical estimates analyzed, we are nly able t say that technlgical prgress has shifted the briler supply functin, upward. Any effect which it has had n the elasticity f supply must be weak. Technlgical prgress might have increased r decreased the price elasticity f briler supply. But the effect f the change n elasticity is relatively small s that it is vershadwed by the shift per se in the supply curve. Least.. Squares Analysis f Mnthly Data fr Brilers We nw turn t estimatin f briler supply frm mnthly data. The mdel f equatin 52 is estimated by least-squares frm the data f 56 mnths frm January 1955, thrugh August 1959: (64) lg Xh(m) = lg [~bj. (0.1412) f m-l lg Rh(DlI (0.0961) t ml (0.3789) g[~eJ R2 = d = ACTUAL Fig. 20. Quantity f brilers prduced (livewelght), values f actuiii bservatins lind estimllted values frm equlltin 62. til 0 z :::l Z 0 ::i J ~ ESTIMATED YEAR 503

37 1'he cefficients f lg (Pb/Pr)m-l and lg Rb(nl) are significant at the I-percent level and have signs cnsistent with thery. The cefficient f lg (pp/pr)m-lt significant at the 30-percenv level f prbability, is negative in Rign, indicat., ing a cmpetitive relatin between eggs and brilers. The value f the d-statistic shw~ the psitive serial crrelatin f residuals~ Equatin 64 tends t underestimate the utput f brilers in the first half f the perid and t ver.. estimate it in the secnd half f the perid. The' price f brilers has been declining quite cn~ sistently since 1955, and the rate f increase iill the utput has slwed dwn but is still psitive. The effect f the briler-feed price rati n ttal,utput is statistically significant in regres.., sin fr mnthly data. (The effect f price n the utput was vershadwed by the upward trend in the ttal utput fr the regressin f annual data.) Equatin 64 indicates that farmers adjust briler utput t price, althugh sme bias in estimates is expected because f serial crrelatin in residuals. T determine any advantage r disadvantage in use f the technlgy index, in the mdel using mnthly data, time designated as m, with m=1 fr January 1955, is substituted fr the technlgy variable in the fllwing regressin equatin: (65) lg XII(III) = lg (~b] (0.1336) r ml lg [; ej lg m (0.1015) f m-l (0.0239) R2 = d = 0.49 The R2 value is lwered slightly by substituting time fr the technlgy index. The cefficient f lg (Ph/Pr)m-l and its t value are reduced. On the ther hand, the cefficient f lg (Pe/Pr)m-l becmes larger and statistically significant. Hwever, it cntradicts a priri knwledge that the egg-feed price rati has greater effect n briler utput than the chicken-feed price rati. Accrdingly, the technlgy index is preferred t the use f time in the briler supply equatin. As a final step in analysis f mnthly data, a Kyck-Nerlve mdel is estimated as fllws: 504 (66) lg XI,(IlI) = lg [~hj (0.1510) f m-l lg [~ej lg RII(m) (0.0931) r m-l (0.4524) lg Qh(m-1l (0.0259) R2 = d = 0.67 The lng-run elasticities cmputed frm equatin 66 are: with respect t (Ph/Pr) m-1 and with respect t (P,,/Pr)m-l' There is very little difference between the values f the shrtrun elasticities in equatin 64 and the values f the lng-run elasticities cmputed frm equatin 66. rhe values btained frm 66 prbably underestimate the lng-run elasticities. The cefficient fr ~g QII(m-l) is extremely small fr time series f the nature analyzed. This is the reversal f the utcme in estimatin f the lng-run elasticities btained frm the annual data. The cntinuus upward trend in the technlgy index again dminates the effects f the lagged utput variable. With the cefficient f adjustment being verestimated, the lng-run elasticities are prbably t small, and the mdel has little efficacy in briler supply analysis. EMPIRICAL ANALYSIS: TURKEYS This sectin includes empirical analysis f turkey supply functins. The relatinships in turkey supply are indicated by blck diagram in fig. 21. A mdel smewhat paralleling fig. 21 is presented as equatin 67 and later is used in quantitative estimatin f the turkey supply functin. The variables in the mdel are: [PTJ ' Pr t-l [~:J [1J ' : Turkey-feed price rati, average fr Octber-December f the previus year. : Turkey-fe.ed price rati, year average fr the current year. : Pultry ratin cst per 100 punds, average fr January-June f the current year, deflated by agricultural price index (dllars). E. : Egg prfitability index, Nvember-May weighted average f egg-feed price rati f the current year multiplied by the technlgy index f turkey prductin. E.. : Briler prfitability index, Nvember-May weighted average f briler-feed price rati f the current year multiplied by the technlgy index f briler prductin. Q'r: Quantity f turkeys prduced in the current year, liveweight (millin punds). R,l' : Technlgy index f turkey prductin. The quantity f turkeys prduced is directly assciated with the factrs which are deemed imprtant in affecting the raising f turkey pults. The intermediate relatins f fig. 21 are nt analyzed, partly because f the nature f turkey prductin and partly because f the data limitatins. The turkey enterprise is a single-prduct enter-

38 FIg. 21. Relatins In turkey supply. r , I Marketing Prcess I --.r j Frm Price f Turkeys I Turkey Prductin I Turkeys Prduced I I Average Weight f Turkeys f Lss I Turkey-feed Pr ice Rati During a Year -" I~I I- '..J.- " Turkeys Raised il l Feed Pri ce in Hatching seasn) Turkey Breeder Hens n Farm, Jan. I TechnleJY f Turkey Prduct in Tur key -fee d Price Ra1i f Previus... Fil ') Cmpeting Enterp rises Prices are enclsed inside 0' semicircular rectanqles and quanfities are enclsed inside f squares. Arrws shw directin f Influence. Demand and marketing relatins re enclsed Inside f dashed squares. prise like brilers. Once farmers purchase a certain number f pults, they can d little t adjust utput, except thrugh marketing weight. Adjustment f utput thrugh feeding and ther care is mre difficult in turkey prductin than in briler prductin and, when cmpared with the adjustments made thrugh the number f pults purchased, can be cnsidered t be negligible. In cntrast t brilers, turkey prductin is seasnal because f the seasnal pattern f demand fr turkeys and f egg-laying. Turkeys are cnsumed mainly during the hliday seasn - Thanksgiving thrugh Christmas. Farmers '.start 505

39 raismg pults during the spring mnths, when pults becme available frm current-year egg prductin and in rder t have them available fr the hliday seasn. This seasnality in prductin f turkeys is clearly shwn in fig. 22. Amng the variables which determine the number f pults raised, the turkey-feed price rati in the previus fall, the feed price in the hatching seasn, the technlgy index, the egg prfitability index and the briler prfitability index are selected, amng thse fr which data are available, as thse f mst imprtance. Octber, Nvember and December f the previus year are chsen fr the perid f bservatin fr the turkey-feed price rati, because the prices in these mnths are crucial in determining the prfit which farmers can get frm turkeys and necessarily affect the intentin f farmers t raise turkeys in the succeeding year. Als, the prices in these 3 mnths affect the decisins f hatcheries t keep breeder hens and, hence, affect the prices f pults in the fllwing spring. The average f feed prices frm January thrugh June f the current year is included in the mdel as a variable in prductin cst imprtant t farmers' decisins n the number f turkey pults t purchase. The Nvember-May (N vember f the previus year t May f the current year) weight~ ed averages f the egg prfitability index and the 400 LLI a: LLI I J: <.li ~300...J UI UI )- LLI!II: a: ::J l- ll CIJ Z ::J Il. Z ::::i :! ::I; 100 I /1" I \ / I, \ I I I \ I \ I \ I " \\, I I \ I I : \ I \ I \ I \ I I I I I \ I ",\ I I ' I II \ --TURKEYS SLAUGHTERED - - -POUl TS HATCHED \ \"...,," " "---,,,' 0'~.6L7.~~~~~~~~~~~~~~ Jan. Feb. Mar. Apr. May June July AUQ. Sept. Oct. Nv. Dec. MONTH 15 0 LLI J: l e[ J: CIJ ~ ::J loll. Z...J...J i Fig. 22. Seasnal mvements In pultry hatching and turkey slaughter, average briler prfitability index are used as the variables f enterprises cmpeting with turkeys. In thse 7 mnths, farmers largely determine the number f chickens t raise. Besides thse variables which determine the number f turkey pults raised, the current-year average f the turkey-feed price rati is included in the mdel. This is t test whether there is any appreciable adjustment in the ttal utput in respnse t price after the pults are purchased. A multistep analysis wuld be desirable fr analyzing the adjustment within a prductin perid, but is nt cnducted because f the data limitatin. If the prices within a prductin perid materially affected utput, the simultaneusequatin methd wuld be mst apprpriate. Hwever, prductin adjustment afte.r the pults are raised is hardly large enugh t cause appreciable bias in the least-squares estimates. Single-equatin, least-squares methds are used exclusively fr estimating turkey supply functins. Results f Estimatin The quantitative estimate f equatin 67 fr is that shwn in equatin 68: (68) lg Q'r = lg [;T], (0.1783) f t t lg [;T] lg rrtl' (0.1780) t (0.2981) lg E lg Eh lg R'r (0.2375) (0.2078) (0.3450) R2 = The cefficient f lg (PT/P r)' t.t is significant at the 5-percent level, indicating the psitive effect f the turkey price f the previus fall n the utput. Lg (PT/Pr) has a negative cefficient which cntradicts the hypthesis that farmers adjust the turkey prductin within a crp perid in respnse t price. The negative cefficient may be due t "sampling variatin," but mre likely indicates that the effect f price is minr after pults are raised. The negative sign in the cefficient f lg (Pr/ A)' is cnsistent with the hypthesis that farmers reduce the number f turkeys when the feed price is high and increase it when the feed price is lw. The negative cefficients f lg Ee and lg Eb wuld indicate that, as prfitability f the cmpetitive enterprises increases, turkey prductin decreases. Hwever, the standard errr fr the cefficient f lg Eb is large relative t the magnitude f the cefficient itself. The cefficient f lg RT is highly significant, again indicating the psitive effect f technlgical prgress n turkey prductin. T evaluate the effects f the cmpetitive enterprises mre clearly by remving pssible multi-

40 cliinearity, the turkey supply functin is estimated after (PT/Pt ) and (Pf/A), are drpped: (69) lg QT = lg r~tl ' (0.1481) l t t-l g'Ee lg Eb lg RT (0.2310) (0.1880) (0.3174) R2 = In this estimate, the cefficient f lg Ell is increased relative t the magnitude f its standard errr. The sign f the cefficient f lg Ee, hwever, is nw negative. In general terms, the statistics fail t quantify, with definiteness at the natinal level, the cmpetitive effect between the egg and briler enterprises and the turkey enterprise. The mdel is recmputed after Ee and Eb are drpped t examine the effects f (PT/Pf ) and (P t / A)/: (70) lg QT= lg [~T 1), (0.1502) f t,l R2 = lg [~l'l lg [rr 1 I (0.1572) t (0.2818) lg RT (0.2420) N imprvement in this estimate is created in the cefficients f lg (PT/Pf ) and lg (Pf/ A)', relative t their standard errrs, cmpared with the estimate f equatin 68. Finally, the mdel is estimated with nly the tw variables: (71) lg QT = lg [~T], (0.1106) f lg RT (0.1557) R2 = d = 0.72 In this estimate, the cefficients f bth independent variables have values significant at the 5-percent level and have signs cnsistent with thery. The d-statistic, hwever, indicates serial crrelatin in the residuals. Figure 23 shws that equatin 71 underestimates the utput f turkeys fr and verestimates it fr In the years frm the great depressin thrugh the start f Wrld War II, the level f turkey price was generally lw, but the technlgy f turkey prductin advanced rapidly during this perid. The unusually large elasticity f turkey supply with respect t RT in this perid causes the cnsistent underestimatin f utput fr Since 1954, the turkey price has been declining cnsistently. This declining price must have made the farmers' price expectatin pessimistic and resulted in the reductin in the price elasticity f turkey supply. This is likely the cause f verestimatin fr Thus, the serial crrelatin - f residuals in equatin 71 can be explained by the changes in the elasticities f supply. Fr the sake f cmparisn, the variable time, t, is substituted fr the technlgy index in equatin 72. fpt], (72) lg QT = lg Lpf t-l (0.1923) lg t (0.0537) R2 = d = 0.45 The value f R2 declines by abut 10 percent as the time variable in equatin 72 is substituted fr the technlgy variable in equatin 71. Als, the value f the cefficient fr lg (PT/Pt )'t-l becmes statistically nnsignificant in equatin 72. The d-statistic indicates that serial crrelatin is high in equatin 72. Equatin 71 appears superir t equatin 72 in estimating the turkey supply functin. As fr eggs and brilers, the technlgy index evidently has an advantage ver the time variable. The Kyck-N erlve mdel is used t allw estimatin f lng-run supply elasticities fr turkeys: (73) lg QT= lg [~TJ ' (0.0908) f t-l R2 = d = M lg RT lg Q]'{t-I) (0.5360) (0.1456) The lng-run elasticity btained by equatin 73 is with respect t (PT/Pt )'t-l' This value is abut duble that f the shrt-run elasticity estimated in equatin 71. This difference between lng-run elasticity and shrt-run elasticity appears realistic. The value f the lng-run elasticity is als fairly reliable because the cefficients in equatin 73 are all significant at the I-percent level, thugh the d-statistic falls in the indeterminate regin. Evaluatin f Structural Change fr Turkeys T determine whether change has ccurred in the supply elasticity, the turkey supply mdel is estimated fr tw separate perids: and The results f estimatin are: (74) lg QI': = lg l~tl ' (0.0871) f I-I R2 = d = lg RT (0.4377) 507

41 ACTUAL Fig. 23. Quantity f turkeys prduced (liveweight), values f actual bservatins and estimated values frm equatin 71. I/) ~ 1000 ::J G Z...J...J ~ -- -ESTIMATED YEAR (75) lg QE = lg [PT), (0.1742) P f t-l lg RT (0.3252) R2 = d = 1.29 The cefficient f lg (PT/Pf)'t-l is significant at the 5-percent level in the estimate fr In the estimate fr , it is significant at the I-percent level. In bth estimates, the cefficients f lg RT are significant at the I-percent level: The d-s~atistic fr ~ rejects the hypthesis f serial crrelation f residuals at the 5-percent level, and the value fr falls in the indeterminate range. By cmparing these tw estimates, the supply elasticity with respect t (PT/Pt)'t-l fr is appreciably smaller than fr This chan?,~ is in cntrast t t~at fr the egg ~upply elasbcity. Fr eggs, the price elasticity was larger in t~e prewar years than in the pstwar years. A pssible explanatin fr the grwth in price elasticity fr turkey supply is: Turkey grwers tend t be mre price-cnscius and adjust utput mre between years,!n respnse t price change, as the turkey enterprise becmes mre specialized a!ld cmmercialized. But why has this specializabn tendency nt affected the elasticity f egg supply in the same directin? An answer t this questin might be as fllws: Tw frces in specializatin f an enterprise influence the price elasticity f supply in ppsite directins. Specializatin with greater fixed investment makes it mre difficult fr farmers t enter int r drp frm prductin as prices vary b.etween years. O~ the ther hand, as the perabn f an enterprise becmes larger in scale and mre cmmercialized, farmers becme mre price cnscius. Small prducers with less flexible supplementary enterprises represent a smaller prt!n f th~ i~du~try aggregate. In turkey prducbn, spe.ciahzation started earlier than fr egg prductin. Turkeys were raised almst exclusively by specialized turkey grwers as early as Even tday, hwever, the majr prtin f United States egg prductin cmes frm nnspecialized farms where ther enterprises dminate laying flcks in ttal returns. In cntrast t the change in the elasticity with respect ~ (PT/Pf ) 'tt the ela;sticity f turkey supply WIth respect t RT declmed in the secnd perid. Evidently farmers respnded t technlgical prgress at a faster rate in the perid than in the perid The reductin in the serial crrelatin f residuals in the estimates fr the divided perids, crrespnding t the difference in the elasticity with respect t RT between the tw perids, supprts the previus argument; namely, that the majr cause fr the serial crrelatin in the residuals f equatin 71 is the ~hange in the elasticity with respect t RT CnSIstent verestimatin r underestimatin is nt indicated in fig. 24. Fr the tw subperids abve, the intrawar years are included in the last perid under the assumptin that the war did nt greatly disturb the nrmal turkey supply relatins. It might be suspected, hwever, that the war years inflate t~e price elastic!ty f turkey supply fr the enbre pend. T test this hypthesis, the supply mdel f turkeys is estimated fr excluding the war years: ' (76) lg QT = lg [PpTJ ' (0.1604) t t-t lg R'r (0.3692) R2 = d= 0.74

42 1500 ACTUAL Fig. 24. Quantity f turkeys prduced (livewelght), values f actual bservatins and estimated values frm equatins 74 and 75. VI ~IOOO ::J 0. 2 ::;...J :IE 500 ESTIMATED YEAR N appreciable difference exists between the elasticity estimate fr this perid and the estimate fr the entire perid. The hypthe,sis that the nrmal relatin f turkey supply was nt much disturbed by war influences appears acceptable, and these years are included in further analysis. T btain the lng-run elasticities fr the divided perids, the Kyck-Nerlve mdel is estimated: (77) lg QT = lg (PpTJ ' (0.1020) f I-I lg RT lg QTlt-11 (1.6311) (0.2813) R2 = d = 1.52 (78) lg QT = lg (PpTJ ' (0.1644) f t-l lg RT lg QT(t-l) (0.6959) (0.2145) R2 = d = 1.85 The results fr these equatins are quite psitive. Regressin cefficients fr price and technlgy indexes are significant at levels f prbability acceptable fr time-series data. Signs f cefficients are lgically cnsistent, and ver 95 percent f the variance in pultry prductin is explained by each equatin. But again, as in the previus applicatins f the lng-run mdel, the cefficients fr lagged utput, QT(t-lh are nt significant. The lng-run elasticities with respects t (PT/ P r )"-1 btained frm these estimates are: fr and fr The lng-run elasticity seems decisively larger in the perid than in the perid Hwever, since the cefficients f lg QT(t-l) are extremely small relative t their standard errrs in the estimates fr bth perids, the values f the lng-run elasticities are nt highly reliable. Finally, t test whether technlgical prgress per se has had an effect n the price elasticity f turkey supply, the mdel with a nnlinear price cefficient is estimated fr : (79) lg QT = lg (PpTJ ' (1.0386) t I-I lg RT ~T lg [PT] :J (2.4387) L P f 1-1 R2 = d = 0.76 Equatin 79 is nw transfrmed int the frm f a nnlinear price cefficient: (80) lg QT = ( RT ) lg [PpTJ I lg R" t t-l The nnlinear cefficient shws that the elasticity with respect t (PT/Pt)'t-l increases by fr a unit increase f RT the variable f technlgical prgress. The psitive assciatin between the price elasticity and technlgical change cnfrms t the separate estimates fr the divided perids. Since the cefficient f the interactin term is nt significant in equatin 79, the statistical evidence frm equatin 80 wuld appear w.eak. In table 10 the values btained frm the separate perids are cmpared with thse fr 509

43 1500 ~ 1000 z ::J n. z :I :i 500 _ ACTUAL ESTIMATED Fig. 25. Quantity f turkeys prduced (liveweight), values f actual bservatins and estimated values frm equatin 79.,~-_= YEAR 1950 equatin 80. The average elasticities cmputed frm equatin 80 are very clse t the values estimated separately fr the subperid and fr the ttal perid But fr the subperid , the value cmputed frm equatin 80 is appreciably smaller than the separately estimated value. Als, by cmparing fig. 25 with fig. 24, it is seen that the mdel f nnlinear cefficient des nt imprve predictins f turkey utput. Table 10. Supply elasticity f turkeys with respect t (PT/P,)'.-. fr subperlds. ====~ ============~~~~~~====== Subperid Average f the technlgy Index fr the perid Frm equatins 77 and 7R Supply elasticity f turkeys with respect t (PT/P,) '-1 Cmputed frm Estimated equatin 80 separately fr each perid' ,n ' 510

44 APPENDIX The pssible simultaneus determinatin f prices and quantities in the culling relatins f hens and pullets was discussed in the text. It was suggested that simultaneity was prbably nt great enugh t cause appreciable bias in leastsquares estimates f culling relatins. Nevertheless, since the pssibility f simultaneity exists, regressin equatins als were generated by simultaneus-equatins methds, t serve as a basis f cmparisn with least-squares estimates. The system f simultaneus equatins prjected fr this analysis was as fllws: (1) Layers (mature birds) sld and cnsumed n farms Xm = f [~:, ~;, Xh J (2) Pullets sld and cnsumed n farms Xr = f [~;. ~;. Xv] (3) Cunting relatin f yung farm chickens prduced Xy= Xk + Xnh - Xd + X. (4) Ttal utput f farm chickens q~ = XyWy + XmWm (5) Cunting relatin f average number f hens n farms XI. = Xh + Xp - Xm + XR (6) Ttal egg utput qe = XLRe (7) Demand fr eggs Pe f [qe IF] L= N' N' e (8) Demand fr farm chickens p. f [qc qe IF) L= N' N' N' The variables indicated in these equatins are as fllws where all quantities refer t the same year; namely, the current year in which egg utput is measured: Endgenus Variables farm price f eggs farm price f chickens quantity f eggs prduced quantity f chickens prduced mature birds (layers) culled pullets culled yung chickens sld and cnsumed n farms average number f layers n farms price f pultry feed Predetermined Variables X h hens and pullets n farms, Jan. 1 Xv : pullets raised Xnh : cckerels n farms, Jan. 1 Xk : cckerels raised Xd : death lss, yung chickens XR : residual, average number f layers W y : average liveweight, yung birds W Dl average liveweight, mature birds Re : eggs per layer N : ppulatin L : cnsumer price index Fe : farm share f egg retail price Fe : farm share f chicken retail price The lgic f the equatins was explained in the text. In principle, the frm f the demand equatin parallels that fr brilers. The farmers' share f egg and chicken retail price is included t reflect market mechanisms. Amng eight equatins in the system, equatins 1, 2, 7 and 8 are equatins t be estimated (i.e., are nt equatins f identity). All equatins are linear in riginal bservatins, fr cnsistency with the identity equatins. The limited-infrmatin methd has been used in estimatin, because all equatins are veridentified. Equatins estimated by least-squares and presented in the text are thse with bservatins cnverted t lgarithms. T prvide parallel bservatins with the limited-infrmatin estimates, equatins 1, 2, 7 and 8 have been estimated by least-squares methds with linear equatins fr riginal bservatins. The least-squares estimates fr hen-culling prvide cefficients which have signs cnsistent with thery and which are highly significant. In cmparisn, the cefficients fr the limited-infrmatin equatin are smaller, and the standard errrs are relatively larger, with nne f the price cefficients being significant. Bth methds f estimatin indicate that the variable fr hens n farms n Jan. 1 strngly dminates predictins f mature birds culled. In the pullet-culling relatins estimated by limited-infrmatin methds, the sign fr the cefficient f Pe/Pt is negative and indicates that a higher price fr eggs causes mre pullets t be retained n farms. Hwever, the sign fr Pe/P! in bth the least-squares and limited-infrmatin equatins estimates is incnsistent with thery. Since it is negative, it suggests that mre chickens are~ held Oli farms as their price increases relative t feed price. When Pe/Pr is deleted in the limited-infrmatin estimate, the cefficient f Pe/Pf is increased in level f significance (as was true fr the same step in the least-squares estimate where the sign als turned cnsistent with thery). Bth least-squares and limited-infrmatin methds suggest that physical r health cn- 511