Demand for U.S. Lamb and Mutton by Country of Orgn: A Two-Stage Dfferental Approach Kethly G. Jones*, Wllam F. Hahn* and Chrstopher G. Davs* The authors are economsts wth the Anmal Products Branch, Markets and Trade Economcs Dvson, Economc Research Servce, USDA. Contact authors at 1800 M Street NW, Washngton DC. Phone 202-694-5172 (KJ), 202-694-5157 (WH), 202-694-5167 (CD). Emal: kones@ers.usda.gov, whahn@ers.usda.gov, and Chrsdavs@ers.usda.gov Paper prepared for presentaton at the Amercan Agrcultural Economcs Assocaton Annual Meetng, Montreal, Canada, July 27-30, 2003
Demand for U.S. Lamb and Mutton by Country of Orgn: A Two-Stage Dfferental Approach Abstract Estmates of prce and scale demand elastctes for lamb and mutton consumed n the Unted States are derved. The U.S. lamb and mutton consumpton comprses prmarly of domestc producton, and mports from two countres Australa and New Zealand. The Netherlands Central Bureau of Statstcs (CBS) demand system derved by Keller and Van Drel (1985) s employed. The CBS model s preferred as t combnes non-lnear Engel curves wth the smplcty of the Slutsky matrx and allows for the ease of mplementng concavty and other restrctons. The Hausman specfcaton test reveals that both prces and quanttes are endogenous n lamb mport demand. Emprcal results for own-prce elastctes of demand ndcate nelastc demand for all three countres wth New Zealand beng hghly nelastc. The scale elastcty results ndcate that f the U.S. ncreases total demand for lamb, Australa and New Zealand s share of total demand wll more than proportonately ncrease whle the U.S. share of total demand wll less than proportonately ncrease. Key words: CBS, mports, lamb and mutton, condtonal demand, scale elastcty. 2
Demand for U.S. Lamb and Mutton by Country of Orgn: A Two-Stage Dfferental Approach Introducton Lamb consumpton s an area of concern for U.S. producers. Whle consumers n countres such as New Zealand and Australa tradtonally eat lamb and mutton and have consstently consumed above 12 pounds per capta per annum, the U.S. per capta lamb and mutton consumpton has been farly stable at ust about 1 pound per annum. Consumpton s confned to ethnc nches and small segments of consumers who reman focused on purchasng hgh-valued products and demandng hgher-qualty, hgher-prced prme cuts. Snce 1975, total use of lamb and mutton consumpton has ncreased only enough to keep pace wth populaton ncreases and enable per capta consumpton to reman farly stable. Commercal producton of lamb and mutton has mrrored the long-term declne n the U.S. sheep nventory. Hstorcally, the lamb and mutton ndustry was developed as a by-product of the wool ndustry. Over tme, the depressed wool ndustry has heavly nfluenced the drecton of the U.S. sheep ndustry. The result s a declnng nventory and a declnng number of anmals avalable for market each year. Although productvty gans (output per anmal) have been regstered t has been far outweghed by declnng nventores. As a result, mports have grown to offset the domestc producton declnes and to mantan stable per-capta consumpton. Lamb and mutton mports have surged snce the md-1980 s, wth very sharp ncreases snce 1994. In 2001, lamb and mutton mports were 12.3 percent hgher than n 2000 and 440 percent hgher than n 1975. Imports, whch currently account for more than one-thrd of U.S. lamb and mutton consumpton, are nearly all from Australa (61 percent) and New Zealand (37 percent). Lamb mports from both countres have ncreased dramatcally, wth Australa showng a much faster rate of mport growth snce 1995. In July 1999, followng the rapd rse n lamb mports n the md-1990 s, (fgure 1) the U.S. establshed a 3-year tarff-rate quota (TRQ). The TRQ essentally ratons the avalable supples among wllng domestc consumers by adustng the prce upward by the value of the ad valorem dutes leved on lamb. 3
The ad valorem duty s commonly stated as a percentage of a readly observed nternatonal prce and s desgned to ncrease the prce to domestc consumers and thereby reduce the supply of mported lamb. Ad valorem dutes were leved for both n-quota and over-quota amounts of mported lamb. Removal of the TRQ, as requred by a World Trade Organzaton (WTO) rulng, could lower domestc prces, and thereby ncrease domestc consumpton of mported lamb. Ths wll lkely result n a further ncrease n mports from strong U.S. compettors such as Australa and New Zealand. Fgure 1. U.S. Lamb and Mutton Producton, and Imports as a percent of Total U.S. Lamb Dsappearance 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 1990 1995 2000 2002 New Zealand Australa Unted States However, estmaton of the U.S. demand for lamb and mutton based on the source country of producton has not been explored. Ths study attempts to examne the U.S. total lamb and mutton demand and U.S. elastctes for demand for lamb dfferentated by source country of producton. Specfcally, the paper ams to: (1) emprcally estmate the total demand for lamb by the U.S. and the condtonal mport demand for lamb consumed n the U.S. wth an econometrc model; (2) to calculate short-run and longrun elastctes of total demand and condtonal mport demand from estmated demand parameters; (3) determne the mpact of seasonalty on U.S. lamb consumpton; (4) and determne the mpact of the 29- month TRQ on U.S. mport demand. 4
Past Studes Past research on U.S. lamb demand has been lmted. Purcell (1989) estmated quarterly lamb demand over the 1978-1988 perod and found that lamb prce was only margnally sgnfcant n determnng demand and that other economc ndcators normally relevant n determnng demand were not mportant. He estmated the short-run elastcty to be 0.51 but found no substtuton effect and found that lamb consumpton declned as consumer ncome ncreased. Byrne, et al. (1993) also estmated a quarterly lamb model over about the same tme perod, 1978-1990, but, unlke Purcell, found that per capta lamb consumpton was sgnfcantly related to lamb prce wth a short-run elastcty of 0.63 and a long-run elastcty of 0.79. Agan, contrary to Purcell, Byrne et al observed weak substtuton effect between lamb and pork. Schroeder, et al. (2001) estmated a quantty-dependent lamb demand model usng quarterly data from 1978 to 1999. Due to the unavalablty of a consstent lamb retal prce seres durng the study perod, a derved lamb retal prce ndex from a Bureau of Labor Statstc (BLS) U.S. cty retal lamb average prce between 1991 and 1993 was constructed. Smlar to Byrne, et al. (1993) they found that lamb prce was a sgnfcant determnant of lamb demand, but, contrary to the prevous studes they observed a more senstve consumer prce response. They estmated an own-prce elastcty for lamb of -1.09. Schroeder, et al. attrbuted the elastc lamb demand to the changng behavor of lamb consumers. Agan, contrary to Purcell (1989), who found no substtutablty between lamb and other meats, Byrne et al. (1993) found substtuton between lamb and pork, and Schroeder et al. (2001) found substtuton between only lamb and beef. Whle the cted prevous studes of lamb demand offer many nsghts, there are obvous data lmtatons observed n all of them. In all cases, the analysts attempted to estmate retal lamb demand but, due to the unavalablty of a consstent retal prce seres, had to use proxy varables to represent retal lamb prce. 5
Also, none of the prevous studes looked at lamb as a product dfferentated by source country. Ths study extends prevous analyses by estmatng an aggregate U.S. demand for lamb and mutton and also U.S. demand by source country of orgn. The advantage of estmatng country of orgn elastctes s that the mpact of country specfc producton shocks or polcy changes can be evaluated through ts mpacts on demand. Model Specfcaton In ths paper, the Netherlands Central Bureau of Statstcs (CBS) demand system derved by Keller and Van Drel (1985) s used to estmate demand parameters. The CBS model combnes the non-lnear expendture effects of the Almost Ideal Demand System (AIDS) (Deaton and Muellbauer, 1980b)) and the prce effect of the Rotterdam model (Thel, (1966) and Barton, (1969)). The Rotterdam model meets the negatvty condton on the Slutsky matrx requred for a downward slopng demand curve f ts prce coeffcents are negatve, sem-defnte. It s a set of partal dfferental equatons. Dfferental demand systems are estmated based on the assumpton that the dfferental systems are well approxmated by dfference systems. Usually, these models are specfed usng frst dfferences. Consder the general CBS model: (You could say, The general CBS model has the followng followng form:) (1) w Lnq w Lnq = a + c Lnp + b Lnx w Lnp where: (2) w = p q x In (1) and (2) above, q s the quantty of good, p s the prce of good, and x the total expendture on all goods. The terms ln q,. ln p, and ln x are the partal dervatves of the logarthms of the quantty, prce, and expendtures, and the c and b are coeffcents. The budget share for the th good. w s the 6
In order to be consstent wth utlty maxmzaton, the coeffcents have to meet the followng restrctons: (3) c = c = b = a = 0, mplyng homogenety of degree zero and the addng-up condton holds for the budget constrant. (4) c = c,, mplyng symmetry Further, the matrx formed by the c has to be negatve, sem-defnte, a restrcton that mples, among other thngs, that the compensated demand slopes downward. It s not usually mposed when estmatng the CBS or related demand systems models. The U.S. lamb demand model s bult on the assumpton of a two-stage budgetng process, where n the frst stage the quantty of lamb and mutton consumed by the U.S. s expressed as a functon of a mxed weghted lamb prce, the prce ndex for all meats, prces of substtutes and expendtures. The two-stage budgetng approach mples a relatonshp between the frst stage (aggregate demand), and the second stage, (source country of orgn demand) accordng to Kesavan, et al., (1993). Based on the methodology of Pollak and Wales (1969), we assume that an ndvdual consumer s preferences are represented by a well-behaved utlty functon, U ( x,..., xn ) where x sgnfes the rate of consumpton of the th good, say lamb and mutton, and hs or her utlty s maxmzed subect to a budget constrant. If we further assume a theoretcally plausble complete system of market demand functons, we can derve the aggregate utlty functon and the correspondng aggregate demand functon (mxed quantty dvsa ndex). As such, n the frst stage the aggregate demand for U.S. lamb s expressed as a functon of a mxed weghted lamb prce based on all the source countres, the prce ndex for all meats, prces of substtutes, and expendture on all food. Ths procedure yelds a dfferental total U.S. demand for lamb represented by the mxed quantty dvsa ndex. 7
In the second stage, the demand for lamb and mutton, both domestc and mported s specfed as a functon of prces and the mxed quantty dvsa ndex from the frst stage. Separablty s assumed n the demand for lamb from other products,.e. beef, pork, etc. for each country. See Deaton and Muellbauer (1980b) and Moschn et al. for a good exposton of the valdty of the separablty assumpton n demand systems. Unlke, Kesavan, et al., (1993) who assumed a theoretcal relatonshp between stage I and stage II, but derved both processes under statc condtons, here the mxed quantty ndex whch was endogenous n the frst stage s exogenous n the second stage, thus capturng the expendture effects wth regards to the country mport demands. Consumers are unlkely to adust to equlbrum n every tme perod (Anderson and Blundell (1983) and Kesvan et al (1993)). Habt persstence, adustment costs, ncorrect expectatons and msnterpreted real prce changes have been cted as possble reasons for ths short-run dsequlbrum. Ths s consstent wth the fndngs of Kesvan et al., (1993), who observed a reecton of these restrctons n the short-run and nstead had to assume that the restrctons were met. A dynamc approach s appled to the general CBS model to capture both the short-run and long-run relatons n the two stages of lamb and mutton demand. In the frst stage a dfferental total demand equaton s specfed: (5) dbq + β dex 7 t = α + β dbq t 1 1 + δ t 1 + β dbp + β dbp dsp t 2 + γ t m m 3 dsp t 1 mt 1 + β dcpi 4 + 3 k k t + β dcpi k 5 t 1 [ τ D ] + λ T + ν 1 + β dex t 6 t where dbq = the mxed quantty dvsa ndex (lamb and mutton consumpton) dbp = the mxed prce dvsa ndex (lamb and mutton prce) dcpi = the consumer prce ndex for all meats 8
dex = consumpton expendture dsp = the prce of substtutes (beef and pork) D = represent a vector of seasonal dummes for the k th quarter T = dummy for the perod of the TRQ mposton α 1, β ( = 1,...,7), δ, γ m, τ k and λ 1 are parameters to be estmated and ν t s the dsturbance term. Subscrpts =1 and 2 for beef and pork prces; subscrpt m=1 and 2 for lagged beef and pork prces; and subscrpt k=1, 2, 3 for frst, second and thrd quarters. The CBS model used n the second stage allows for the estmaton of source country lamb and mutton demand wthout mposng restrctve a pror assumptons wth regard to expendture effects (Deaton and Muellbauer 1980a). (6) w + t Lnq 3 k [ g k D k w Lnq = a ] + f T + e t + c Lnp t + d Lnp t 1 + b 1 dbq t + b l 2 dbq t 1 where w s the expendture share of lamb consumed from the t th source country, p s the dfferental prce based on the unt value of mports and the domestc wholesale prce, and a, c d, b 1, b 2, g k, and f are parameters to be estmated and e s the dsturbance term. The source countres ncluded n the model are Australa, New Zealand and the Unted States. The Unted States was omtted to avod sngularty n estmaton of the emprcal model. Own-prce, cross-prce, and expendture elastctes, η are calculated for mport from each country. ( c d + w w ) η = Own-prce and cross-prce elastctes w (7) (8) β η + y = 1 Expendture elastcty w 9
Data The data are monthly mport quanttes and expendtures for lamb and lamb cuts obtaned from the U.S. Department of Commerce, U.S. Census Bureau; Foregn Trade Statstcs. Import prces are based on unt values of total mports, whch are assumed to be the wholesale values. U.S. wholesale lamb prces and domestc sheep and lamb producton are obtaned from the USDA, Natonal Agrcultural Statstcs Servce. Snce U.S. lamb exports are neglgble, domestc producton was assumed to be all consumed domestcally. Imports from countres other than New Zealand and Australa are also neglgble. Thus, U.S. producton along wth mports from Australan and New Zealand provdes a farly accurate account of U.S total lamb and mutton consumpton. Import data are converted to carcass weght equvalent to correspond wth U.S. producton data. The demand analyss s done at the wholesale level. A summary of the descrptve statstcs s presented n table 1. Emprcal Results and Dscusson A separate system of demands s estmated for total lamb and mutton consumed and lamb and mutton dentfed country of orgn. A set of hypotheses s tested to examne the seasonal effects on lamb and mutton mport demand and also to look at the effect of the tarff rate quota mposed on lamb mported from Australa and New Zealand between July of 1999 and November of 2001. The 3sls procedure n SAS was used to estmate both the frst stage and the second stage equatons as a system. The U.S. equaton was deleted n the second stage due to addng up restrctons. Symmetry and homogenety restrctons were mposed on the lagged varables, followng Anderson and Blundell (1983) and Kesvan et al., (1993). The CBS model used here assumes endogenous quanttes and predetermned prces. The Hausman statctc was used to test weather all prces can be taken as predetermned. Reectng the CBS model suggests that prces and quanttes are endogenous and shows that employng a 3sls s an approprate method of estmaton. Table 2 shows the test of predetermnedness of prces as a group and one at a tme. 10
Specfcaton test results suggests that both prces and quanttes are endogenous n the lamb demand system usng monthly data ndcatng that monthly prces and quanttes from U.S. and mportng countres adust to changng factors wthn the entre lamb demand system. Table 3 shows the parameter estmates for the frst stage total lamb and mutton demand and Table 4 shows the parameter estmates for second stage lamb and mutton demand by country of orgn. The mxed quantty ndex that was endogenous n the frst stage became exogenous n the second stage, thus capturng the expendture effects wth respect to the country mport demands. Homogenety and symmetry were reected n the long-run. The U.S. share equaton was calculated based on the addng-up restrctons. In terms of seasonalty, a sgnfcant dfference s seen n the 2 nd and 3 rd quarters total demand, though there were no quarterly dfferences n mport demand from ether Australa or New Zealand. Ths s expected snce U.S. lamb demand s hghest durng the relgous holdays, Easter and Passover, whch often occur n the early Aprl. The TRQ had no statstcal sgnfcance on ether total lamb demand or ndvdual country mport demand. Ths was probably due to the fact the despte mplementaton of the TRQ, mports from Australa and New Zealand dd not slow as effects of the TRQ were largely offset by the strong U.S. dollar and unusually weak Australan and New Zealand currences. However, the fact that the TRQ dummy s not sgnfcant lends valdty to the demand system. If our demand system s vald, t has all the explanatory varables n t that t needs to explan lamb demand. The TRQ rases mported lamb prces, and that should be ts only effect on demand. Estmated condtonal prce and share demand elastctes (the share demand elastcty could be referred to as a scale elastcty) are reported n table 5. The condtonal own-prce elastctes represent both the substtuton and the ncome effect of prce changes. The condtonal elastctes are averaged over the values for the years 1989 to 2002, the entre sample perod. The own-prce elastctes for both the short- 11
run and the long-run were negatve. Own-prce elastctes were less than one for all three countres mplyng that t s possble for them to ncrease revenue by ncreasng prce. New Zealand was hghly nelastc, suggestng that they stand to gan most from ncreases n prces. The results suggest sgnfcantly dfferent effects from prce changes on U.S. lamb and mutton demand. If the prce of U.S. and Australa lamb and mutton ncreases by 1-percent, the quantty demanded for lamb and mutton from these countres wll decrease by 0.88 percent and 0.82 percent, respectvely, n the short-run, and 0.88 percent and 1.93 percent n the dynamc long-run framework. Own-prce changes have a greater effect on New Zealand lamb and mutton mport demand. A 1-percent ncrease n New Zealand lamb prce would decrease the mport quantty demanded by the U.S. by about 0.29 percent n the short-run and 0.35 percent n the dynamc long-run framework. The condtonal scale elastcty measures the degree by whch the U.S. country of orgn demand changes when U.S. total lamb and mutton demand changes. Emboded n the scale elastcty s the expendture effect, whch captures the amount by whch the lamb quanttes demanded change when U.S. lamb expendture changes. The condtonal scale elastctes n table 5 are calculated based on the average total demand share for lamb from 1989 to June, 2002. In both the short-run and the dynamc long-run modelng frameworks, scale elastctes for all three countres were postve and greater than one but the U.S. scale elastctes, whle postve was less than 1. These results ndcate that, n the short-run, f the U.S. demand for lamb ncreases by 1 percent the quantty demanded of lamb and mutton from Australa and New Zealand ncreases by 1.12 percent and 1.15 percent, respectvely, whle the quantty demanded of U.S. lamb ncrease by 0.96 percent. A smlar pattern was seen n the long-run and dynamc frameworks where Australa and New Zealand have postve scale elastctes of 1.23 percent and 1.63 percent, respectvely, and the U.S. have a postve scale elastcty of 0.89 percent. Snce the scale elastctes capture the ncome effect, t s expected that ncreases n ncome would cause lamb consumers 12
to consume more of the hgh-valued products, suppled by Australa and New Zealand, whch may explan sze of the scale elastctes of these two countres. Table 6 presents the estmated condtonal prce and scale demand elastctes for the CBS model based on the average shares between 1989-1995 and table 7 presents smlar condtonal prce and scale demand elastctes based on average shares between 1996 and June, 2002. The two tme-perods were evaluated n order to look at elastcty changes especally snce 1995 when ncreases n lamb mports to the U.S. were most dramatc. The results show a smlar pattern to those reported n table 5 wth average shares for the 1989-2002 perod. However, relatve own prce elastctes for Australa and the Unted States was less between 1996 and 2002 than the perod pror to 1996. Ths suggests that the U.S. dependence on lamb mports snce 1995 has caused t to be less prce responsve. For Australa, the short-run own prce elastcty of mport demand through 1995 was elastc at -1.29, whle snce 1995, t became nelastc at - -0.69. For the U.S. the condtonal short-run own-prce elastctes became even more nelastc over tme, changng from -0.96 pror to 1996 to -0.73 snce 1995. The condtonal own-prce elastcty for New Zealand also showed a relatve ncrease snce 1995, ncreasng from -0.44 to -0.27. Based on the condtonal scale demand elastcty estmates presented n tables 6 and 7 the relatve scale elastctes for all three countres also declned. Between 1989 and 1995, mport demand responses for Australa and New Zealand were large n the short-run, 1.26 percent and 1.30 percent, respectvely, whle the U.S. showed a scale elastcty of -0.97 percent. Snce 1995, the share mport demand responses from Australa and New Zealand have decreased though they reman greater than 1. Snce 1995, the U.S. scale elastcty of total demand decreased even further. A 1-percent ncrease n U.S. total lamb demand wll result n 0.88 percent ncrease n U.S. share of total lamb demanded. 13
Conclusons Prevous studes, have attempted to examne lamb demand n the U.S., but have had a narrow focus, usng sngle-equaton, quantty-dependent models as the analytcal tool to estmate lamb demand. Ths study estmates U.S. demand for lamb and mutton by lookng at source country of orgn. The model assumes a two-stage budgetng process, where n the frst stage the aggregate U.S. demand of lamb s estmated and n the seconds stage the aggregate demand ndex whch was endogenous to the frst stage becomes exogenous to the second stage thus capturng the expendture effects wth regards to the country mport demands. Ths allows us to better evaluate the potental mpacts that producton and polcy shocks that come from source country of orgn wll have on the U.S. demand for lamb, through ther effects on prce. For ths purpose, a CBS verson of the almost deal demand system was employed. The CBS model combnes Engel condtonng wth the smplcty of the Slutsky matrx to allow for mplementng concavty and other restrctons wth relatve ease. The resultng model allows for both short-run and long-run specfcatons n a two-stage framework, whle explorng effects of seasonalty and the mpact of a TRQ establshed for a 29-month perod between July 1999 and November 2001. The emprcal results ndcate a sgnfcant dfference n the second quarter total demand for lamb but no dfference n quarterly mport demand from ether Australa or New Zealand. The TRQ, however, had no mpact on ether total lamb demand or ndvdual country mport demand. The condtonal own-prce elastctes for both the short-run and the long-run were negatve. No sgnfcant dfferences were observed n elastctes n the short-run and long-run due to the slow rate of adustment n consumer demand behavor to prce changes. There s evdence that, over tme, condtonal own-prce elastctes of demand for New Zealand and Australa have shown relatve decreases whle the condtonal own-prce elastcty for the Unted States has shown relatve ncreases. 14
A postve but less than proportonate scale elastcty was observed for the Unted States whle postve, and more than proportonate scale elastctes were observed for Australa and New Zealand lamb, suggestng greater preference for lamb from other countres. Over tme, however, scale elastctes for Australa and New Zealand have shown relatve decreases, though stll postve and greater than 1, whle the Unted States scale elastcty has moved even closer to unty. The study results reported here suggest that Australa s able to ncrease ts revenue whle decreasng prce due to ts elastc own-prce elastcty of mport demand whle the U.S. and New Zealand sheep producers could ncrease ther total revenue by ncreasng prces because of the nelastc nature of ther share demands. Also, the negatve scale elastcty of total demand for the U.S. suggests a lack of preference for domestc lamb by U.S. consumers. Lmtatons of the Study In the absence of retal prces and quanttes, wholesale level data was used for the analyss. Ideally, retal level prces and quanttes would be more approprate to gauge consumer response. However, retal level tme seres data s unavalable for lamb and mutton. Also, t s hghly lkely that the results of the study were nfluenced by the fact that dfferent countres supply dfferent mxes of lamb and mutton cuts. An nterestng feature would be to evaluate the source country demand for lamb and mutton based on types of cuts. However, although mported quanttes and unt values can be obtaned for some cuts, though lmted, the U.S. supply s not dfferentated by cuts. 15
Table 1. Descrptve Statstcs on U.S. Consumpton of Lamb and Mutton by Source Country, January 1989 to 2002. Australa New Zealand U.S. Value (000 USD) Mean $5,513.53 $4,159.96 $35,297.70 Medan 4,396.84 3,457.13 35,488.75 Mnmum 1,082.60 869.27 20,763.20 Maxmum 21,247.48 10,995.32 53,840.00 Coeffcent of Varaton 70.83 67.68 15.41 Quantty (000 pounds) Mean 4,715.00 2,146.85 23,800.60 Medan 3,766.70 1,867.42 23,000.00 Mnmum 1,329.49 652.93 15,100.00 Maxmum 16,689.51 5,298.45 36,000.00 Coeffcent of Varaton 56.55 52.75 20.43 Unt Value ($ per hundred Pound) Mean 109.10 178.95 151.49 Medan 112.05 172.33 152.74 Mnmum 54.53 98.26 106.50 Maxmum 161.50 301.48 216.75 Coeffcent of Varaton 26.27 25.48 15.70 Expendture Shares Mean 0.12 0.09 0.79 Medan 0.10 0.08 0.83 Mnmum 0.03 0.02 0.49 Maxmum 0.33 0.22 0.94 Coeffcent of Varaton 64.03 60.58 15.70 16
Table 2. Hausman Test Results of Predetermnedness of Prces, Grouped and One by One Varables Grouped Australa New Zealand Unted States Prce 172.9* 90.3* 124.5* 108.9* Statstcs are Ch-square at 91 and 59 degrees of freedom, respectvely. Cut-off for 0.01 at df=>50 s 29.06 17
Table 3. Estmated parameters for the total lamb and mutton demand model Parameters Coeffcent Standard error t rato α 1 0.293 0.055 5.31 β 1-1.262 0.101-12.54 β 2-0.009 0.241-0.04 β 3 0.906 0.392 2.31 β 4-3.398 2.589-1.31 β 5-1.322 0.384-3.45 β 6 1.162 0.356 3.26 β 7-0.122 0.368-0.33 δ 1 2.944 3.242 0.91 δ 2-1.416 0.612-2.31 γ 1 2.630 0.546 4.81 γ 2-0.543 0.637-0.85 τ -0.153 0.090-1.7 1 τ -0.685 0.088-7.78 2 τ -0.300 0.090-3.34 3 λ -0.067 0.118-0.57 1 18
Table 4. Three Stage Least Squares parameters of the dynamc CBS of U.S. lamb and mutton demand Parameters Coeffcent Standard error t rato α 11 0.013 0.006 2.05 β 1-1.443 0.056-25.64 C 11-0.088 0.012-7.61 C 12-0.012 0.011-1.10 C 13-0.013 0.033-0.39 D 11-0.121 0.022-5.64 D 12-0.024 0.020-1.23 D 13 0.071 0.052 1.36 B 11 0.015 0.023 0.64 B 12 0.013 0.035 0.37 τ 11-0.011 0.012-0.94 τ 12-0.004 0.012-0.36 τ 13-0.030 0.011-2.67 λ 11 0.001 0.013 0.10 α 21-0.010 0.007-1.32 C 21 0.006 0.014 0.44 C 22-0.017 0.013-1.26 C 23 0.060 0.040 1.50 D 21 0.033 0.024 1.35 D 22-0.002 0.023-0.07 D 23 0.016 0.063 0.26 B 21 0.013 0.028 0.48 B 22 0.043 0.043 1.00 τ 21 0.029 0.014 2.06 τ 22 0.008 0.014 0.60 τ 23 0.019 0.013 1.44 λ 21-0.018 0.016-1.12 19
Table 5. Estmated condtonal prce and share demand elastctes for the CBS model, 1989-2002. Australa New Zealand Unted States Share of total Demand Short-run Australa -0.882-0.206-1.000 1.124 New Zealand -0.067-0.293-0.239 1.150 Unted States -0.010-0.048-0.825 0.965 Dynamc long-run Australa -1.927-0.419-0.484 1.234 New Zealand 0.246-0.354-0.443 1.635 Unted States 0.110-0.010-0.879 0.894 Table 6 Estmated condtonal prce and share demand elastctes for the CBS model, 1989-1995 Australa New Zealand Unted States Share of total Demand Short-run Australa -1.629-0.275-1.354 1.258 New Zealand 0.064-0.443 0.189 1.303 Unted States 0.036-0.010-0.924 0.969 Dynamc long-run Australa -3.785-0.708-0.307 1.487 New Zealand 0.755-0.522-0.327 2.284 Unted States 0.139 0.021-0.965 0.907 Table 7. Estmated condtonal prce and share demand elastctes for the CBS model, 1996-2002 Australa New Zealand Unted States Share of total Demand Short-run Australa -0.687-0.214-0.815 1.082 New Zealand -0.151-0.273-0.309 1.100 Unted States -0.052-0.085-0.729 0.959 Dynamc long-run Australa -1.379-0.358-0.468 1.154 New Zealand 0.037-0.328-0.411 1.422 Unted States 0.091-0.037-0.799 0.878 20
References Alston, J., C. Carter, R. Green and D. Pck. 1990. Whther Armngton Trade Models? Amercan Journal of Agrcultural Economcs. 72: 455-467. Anderson, G. J. and R. W. Blundell. 1983. Testng Restrctons n a Flexble Dynamc Demand System: An Applcaton to Consumers Expendture n Canada. Revew of Economc Studes 50:397-410. Barten, A.P., 1969. Maxmum Lkelhood Estmaton of a Complete Demand System of Equatons. European Economc Revew. 1, 7-73. Byrne, P.J., O. Capps, Jr. and G.W. Wllams. 1993. U.S. Demand for Lamb, The Other Red Meat. Journal of Food Dstrbuton Research. 24. February: 158-166. Chen, P.Y. and M.M. Veeman. 1991. An Almost Ideal Demand System Analyss of Meats wth Habt Formaton and Structural Change Canadan Journal of Agrcultural Economcs. 39:223-235. Davs, G. C. and K. L. Jensen. 1992. Two-Stage Utlty Maxmzaton and Import Demand Systems Revsted: Lmtatons and an Alternatve. Journal of Agrcultural and Resource Economcs 19: 409-424 Deaton, A. S. and J. Muellbauer. 1980a. An Almost Ideal Demand System. Amercan Economc Revew 70:312-326. Deaton, A. S. and J. Muellbauer. 1980b. Economcs and Consumer Behavor. New York: Cambrdge Unversty Press. Eales, J.S. and L. J. Unnevehr. 1993. Smultanety and Structural Change n U.S. Meat Demand. Amercan Journal of Agrcultural Economcs.75: 259-268. Kesvan, T., Z. A. Hassan, H. H. Jensen and S. R. Johnson. 1993. Dynamcs and Long-run Structure n U.S. Meat Demand. Canadan Journal of Agrcultural Economcs 41: 139-153. Keller, W. J. and J. Van Drel. 1985. Dfferental Consumer Demand Systems. European Economc Revew 27: 375-390. Moschn, G. and K. D. Melke. 1989. Modelng the Pattern of Structural Change n U.S. Meat Demand. Amercan Journal of Agrcultural Economcs 71:253-261. Moschn, G. and D. Mora and R.D. Green. 1999. Mantanng and Testng Separablty n Demand Systems. Amercan Journal of Agrcultural Economcs 76:1:61-73. Pollak, R. 1970. Habt Formaton and Dynamc Demand Systems The Journal of the Poltcal Economy. 78:ssue 4 part 1: 745-763. Pollak, R. A. and T. J. Wales. 1969. Estmaton of the Lnear Expendture System. Econometrca 37:611-628. 21
Purcell, W.D. 1989 Analyss of Demand for Beef, Pork, Lamb and Brolers: Implcatons for the Future. Research Insttute of Lvestock Prcng, Vrgna Tech: Blacksburg, VA Research Bulletn, 1-89, July. Schroeder, T.C., R. J. Jerrck, R. Jones and C. Spaeth. 2001 U.S. Lamb Demand. Sheep and Goat Research Journal. Vol 17, Number1 Thel, H., 1975. Theory and Measurement of Consumer Demand. North Holland Amsterdam. 22