A Demand System for Major Dairy Products in Ontario

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2 A Demand System for Maor Dary Products n Ontaro Dr. Rakhal Sarker Assocate Professor Department of Food, Agrcultural and Resource Economcs Unversty of Guelph Guelph, Ontaro E-mal: rsarker@uoguelph.ca Prosper Koto Department of Economcs Unversty of Mantoba Wnnpeg, Mantoba Emal: Prosper.koto@umantoba.ca and, Heather Cassdy Food Safety Polcy Coordnator Mnstry of Agrculture, Food and Rural Affars 1 Stone Road West, 2 nd Floor Guelph, ON. N1G 4Y2 E-mal: heather.cassdy@ontaro.ca June 11, 2015 A paper prepared for presentaton at the 29 th Trennal Internatonal Conference of Agrcultural Economsts n Mlan, Italy, August 9-14, An earler verson of ths paper was presented at the Consumer and Market Demand Research Network s Annual Meetng at the Delta Hotel n Guelph, Ontaro, August 15-16, The fnancal supports from the Dary Farmers of Ontaro and from the Ontaro Mnstry of Agrculture, Food and Rural Affars are gratefully acknowledged. The usual dsclamer apples. 0

3 A Demand System for Maor Dary Products n Ontaro Abstract Despte sgnfcant meda and research nterests drawn nto the Canadan dary sector n recent years, no study has estmated prce and ncome elastctes of demand for maor dary products at the provncal level usng longtudnal data. Ths artcle attempts to brdge ths gap by estmatng a demand system for seven maor dary products n Ontaro. Employng Barten s General Model, four alternatve demand systems were nested and the NBR demand system was found to be the most approprate for the data set n Ontaro on both theoretcal and emprcal grounds. The symmetry, homogenety and concavty condtons are all supported by the data. Emprcally, all own-prce elastctes are negatve and statstcally sgnfcant. The expendture elastctes of all dary products are postve, less than unty and statstcally sgnfcant. Fnally, most dary products are net substtutes n consumpton. Keywords: Demand Systems; Barten s General Model; Prce and ncome elastctes; Dary Products; Ontaro. 1

4 A Demand System for Maor Dary Products n Ontaro Introducton: The dary sector n Canada s governed by supply management. Under ths polcy, prces receved by dary producers are determned based on a cost-of-producton formula and for a gven level of demand for mlk, supply s restrcted through bndng producton quotas at the farm level to acheve ths prce. To sustan ths prce, trade n dary products s also regulated through tarff-rate-quotas. The over-quota tarffs for all dary products are set at such hgh levels that t s mpossble for anybody to make a proft by mportng any dary product nto Canada beyond the mnmum access quanttes. The prces consumers pay, however, vary across locatons and over tme. Supply management n the dary sector nvted controversy rght from ts ncepton n the 1960s (Barchello, 1981; Forbes et al., 1982). After almost half-a-century of ts exstence, supply management n dary contnues to receve sgnfcant attentons from the meda, polcy makers, trade negotators and the academcs (Clemens and Crowley, 2012; Gfford, 2005; Conference Board of Canada, 2009; Ivson, 2012; Wallece, 2011). Whle the ssues entertaned n many of these peces are relevant for the dary sector n Ontaro and n Canada, the dscussons often revolve around personal opnons. The own-prce elastcty and ncome elastcty of demand for dfferent dary products are used for a wde varety of polcy analyss, dscussons, dalogues and polcy choces. For example, f one wshes to assess the effects of changes n domestc quota regulatons, polcy related to health and nutrton, trade lberalzaton under the WTO or Trans-Pacfc Partnershp (TPP) or trade dsputes on the dary sector, he/she would requre relable estmates of prce and ncome elastctes of demand and the supply elastctes. To the best of our knowledge, no study has estmated a set of demand elastctes for maor dary products consumed n Ontaro or n any other provnce n Canada. Most emprcal studes rely on such parameters from prevous studes and n many nstances those from other countres (see Veeman, 1982; van Kooten, 1990; Melke et al., 1998; Conference Board of Canada, 2009; Rude and An, 2013). As a consequence, the results from prevous studes whle nformatve may not be useful for meanngful polcy dalogues and for long-term polcy choces n supply managed sectors n Canada. Despte sgnfcant attenton drawn nto the dary sector n recent years, lttle effort s nvested to estmate 2

5 these elastctes usng longtudnal data. Ths artcle makes an attempt to brdge ths gap by estmatng a demand system for seven maor dary products n Ontaro. Ontaro has the largest consumer base for varous dary products and enoys the second hghest share of natonal producton, popularly known as the Market Sharng Quota (MSQ) n Canada. Although the market for manufactured dary products such as butter, cheese, yogurt and ce cream account for about 66 percent of all dary products consumed n Ontaro, few studes attempted to estmate the prce and ncome elastctes of demand for manufactured dary products. Goddard and Telu (1988) employed quarterly data from 1971 to 1984 and estmated the own-prce elastcty of demand for flud mlk to be Smlarly, employng data from 1973 to 1984, Venkateswaran and Knnucan (1990) estmated the prce elastcty of demand for flud mlk to be Fnally, Goddard and McCutcheon (1993) employed data from and estmated the prce elastcty of demand for flud mlk to be Whle these results suggest that the prce elastcty of demand for flud mlk s low hoverng around and stable n Ontaro, the estmated prce elastctes are dated. In addton, none of these studes estmated the prce elastctes of demand for other dary products even though they account for over 60% of all dary products consumed n Ontaro. In lght of these nadequaces, we selected seven maor dary products n ths study: flud mlk, butter, cheese, yogurt, ce cream, cream and skm mlk powder whch accounted for about 98% of total dary products consumed n recent years. Substantal progress has been made n consumer demand analyss snce the 1970s. An mportant segment of ths progress focuses on the development of alternatve specfcatons of demand systems whch are theoretcally consstent, amenable to econometrc estmaton and yeld polcy relevant prce and ncome elastctes (Okarent and Alston 2011). The qualty of the estmated elastctes from a demand system vary consderably dependng on the choce of the functonal form, the type of data used, assumed separablty structure and the econometrc technque used n estmaton. The Almost Ideal Demand System (AIDS) (Deaton and Muellbauer 1980) and the Rotterdam Model (RM) (Thel 1975a, b; Barten 1968, 1977) have been the two most popular demand systems used n agrcultural economcs. The popularty of these two demand systems s drven by the fact that both share desrable propertes not possessed by other locally flexble functonal forms such as the Translog (Chrstensen et al., 1975) and the Generalzed Leontef (Dewert, 1971). They are also consstent wth demand theory, lnear and have dentcal data 3

6 requrements. However, the two demand systems generated so dfferent results n some applcatons that the approprateness of ether specfcaton for a partcular dataset has been questoned (Alston and Chalfant, 1993). Snce economc theory provdes lttle bass for ex ante dscrmnaton between these two functonal forms, the choce of an approprate functonal form for a partcular demand system n agrcultural economcs has been adhoc, often motvated by the personal famlarty of the researcher (Alston and Chalfant 1991a, 1991b; Lee et al., 1994). Snce these demand systems are not nested wth each other, some analysts employed varous non-nested tests for choosng between these two systems. The results of ths exercse n many nstances have been dsappontng because the results of the non-nested tests were nconclusve (Okarent and Alston 2011). In ths context, Barten s (1993) approach provdes an emprcally attractve alternatve. Ths approach s based on a general model whch not only nests the two most popular demand systems, the Rotterdam and the dfferental lnear AIDS, but also two mxed demand systems, the Central Bureau of Statstcs (CBS) demand system (Keller and Van Drel 1985) and the Natonal Bureau of research (NBR) demand system (Neves 1987). Thus, t s useful for determnng the most approprate demand system for a gven data set from ths set of four alternatve functonal forms. The data drven nestng procedure ntroduced by Barten (1993) s employed n ths study to determne the approprate functonal form for studyng the demand for selected dary products n Ontaro. Secton two provdes a bref exposton of Barten s general model and the nestng procedure. Secton three focuses on data descrpton, econometrc ssues and the estmaton strategy. Estmaton results are dscussed n secton four. The fnal secton provdes a summary of the man fndngs, hghlghts ther polcy mplcatons and concludes the paper. Barten's General Model: A Bref Exposton To provde a bref exposton of the BGM, one can convenently starts wth the Rotterdam model whch s specfed as: w d ln q b d ln Q c d ln p Where w s the budget share of the th commodty, p and q are the prce and quantty of the th commodty respectvely. The Dvsa volume ndex for the change n real ncome s d ln Q whch (1) 4

7 can be wrtten as: d lnq w d ln q. Thus, n the Roterdam model, b s represent margnal budget shares, and c s are the compensated prce effects. Both ncome and prce effects are assumed to be constant n the RM. However, there s no a pror reason that prce and ncome effects both should be held constant. The AIDS can also be expressed n dfferental form (Deaton and Muellbauer, 1980; Barten, 1993). For smplcty, f we replace b and c n the Rotterdam model (eq.1) wth and w w w respectvely, we obtan a dfferental verson of the AIDS model as, w d lnq w w d ln p w d ln q. (2) Unlke those n the Rotterdam model, the margnal budget shares are, compensated prce effects are, w w w, and the for the AIDS model. It s clear that both prce and ncome effects n the AIDS model vary over tme. Snce the dependent varables n equatons (1) and (2) are the same, wth approprate redefnton of the unknown parameters one can specfy a model whch nests both the Rotterdam and dfferental AIDS models. Ths s the dea behnd Barten's General Model whch can be specfed as: w d d w d ln Q e w w d ln p ln q 2 Where, d, 1, e and 2 1 of the Rotterdam and dfferental AIDS parameters, e s defned e 2 c are the unknown parameters of BGM and can be estmated. In terms d s defned as, d 1 1 1b 2 1. The parameters 1 and 2 are called the nestng (3), whle parameters. The values of these parameters determne whether one has the Rotterdam model or the dfferental AIDS model. If we set, 0 n eq. (3), the BGM becomes the Rotterdam 1 1 model. Smlarly, f we set 1 then the BGM becomes the dfferental AIDS model as n 1 1 equaton (2). However, f we set 1 0 and, 1 2, then the BGM becomes: w d ln q d ln Q ( e w ( w )) d ln p (4) 5

8 Ths s a mxed demand system whch contans the Rotterdam ncome effects and the AIDS prce effects. It s known as the Natonal Bureau of Research (NBR) model and was developed n the md-1980s (Neves, 1987). Fnally, f we set 1 1 and, 0 2, then the BGM reduces to: w d ln q ( d w ) d ln Q e d ln p (5) Ths model contans the AIDS ncome effects and Rotterdam prce effects and s known as the Central Bureau of Statstcs (CBS) model (Keller and van Drel, 1985). It was also developed n the md-1980s. Thus, by mposng smple restrctons on two nestng parameters of the BGM, 1 and 2 we can select one of the four alternatve demand systems from the BGM by applyng the lkelhood rato test (LRT). The lkelhood rato tests can also be used to test for homogenety, symmetry and structural changes (Amemya, 1985). BGM Propertes & Elastctes The addng-up, homogenety and symmetry propertes can all be mposed usng restrctons on the parameters of the BGM. In partcular, testng for symmetry requres that e e. Snce the BGM already has real ncome effects, only the prce related parameters are nvolved n testng the homogenety property (e 0 ). However, testng for addng-up s not as straghtforward. If we add up the equatons n BGM, we obtan: whch can be smplfed as, d 1w d ln Q e w w d ln p, wd ln q 2 wd ln q d ln Q d d ln p 2 e w w 1 Therefore, the addng-up condton requres that d 1 1 and, e 0. Income elastctes for the BGM are expressed as: d w 1, w d ln p. 6

9 and, the compensated prce elastctes are expressed as: e 2w w w. Uncompensated prce elastctes can then be recovered usng Slutsky's equaton. Fnally, dependng upon the values of the nestng parameters, 1 and 2 the elastcty formulae wll be dfferent as they wll pertan to ether the Rotterdam model or the LA/AIDS model or the CBS or the NBR models. Data Descrpton The data set used n ths study conssts of quarterly observatons of consumer demand and correspondng prces of seven maor groups of dary products ncludng flud mlk, cream, yogurt, ce cream, butter, cheese, and skmmed mlk powder n Ontaro from 1986:1 to 2010:4. The per capta dsappearance of each of the selected dary product s used as a proxy for ts demand and s measured as a sum of ntal stock, domestc producton and mports, less exports and stocks at the end of the perod. Whle t does not account for spolage or other wastage of the product n queston, t does ncorporate away-from-home consumpton and ts use n processed foods. Quanttes of cream, skmmed mlk power, cheese, butter, and yogurt consumed were converted (from ether ltres or klograms of product) nto equvalent ltres of flud mlk usng converson factors suppled by the Dary Farmers of Ontaro (DFO) 1. Statstcs Canada does not report nomnal prces of the selected dary products consumed n Ontaro. Instead, monthly, quarterly and yearly prce ndces for dfferent dary products are reported. We obtaned quarterly prce ndces for the selected dary products and converted them nto nomnal prces followng the procedure used by Moschn and Vssa (1993). 2 Summary statstcs of the data used to estmate the demand system are reported n Table 1. Flud mlk has the largest budget share followed by cream, cheese and yogurt n Ontaro. Except for cheese, the real prces of dary products are farly stable. However, they are 1 We wsh to thank Phl Carns and Krstn Benke of the Dary Farmers of Ontaro for several helpful dscussons and for provdng us the revsed converson factors for Ontaro. 2 Data from the Famly Food Expendture Surveys as reported by Statstcs Canada were obtaned for the years 1986, 1990, 1992, 1996, 2001 and From weekly famly expendtures and quanttes consumed, prces of the commodtes were calculated by dvdng expendtures by quanttes. The prces were then regressed on the respectve annual consumer prce ndces for Ontaro. The estmated coeffcents were then used to generate nomnal prces for the entre perod. 7

10 more varable than the correspondng budget shares whch s ndcatve of adustments n volumes consumed over tme. Fgure 1 shows changes n per capta consumpton of selected dary products n Ontaro. Whle the consumpton of flud mlk, butter and skm mlk powder declned over tme, the consumpton of cheese, cream, ce cream and yogurt all have ncreased. Ths s reflected n the evoluton of budget shares for these dary products whch s presented n Fgure 2. Despte a declnng trend, flud mlk stll has the largest budget shares among dary products, followed by cream, cheese, ce cream and yogurt. The budget shares for butter and SMP slowly declned and remaned very low n Ontaro (Table 1 and Fgure 2). Ths study assumes a two-step budgetng procedure n total expendture allocatons by the consumers. In ths framework, total expendture s allocated to broad group of commodtes n the frst stage and then the expendtures allocated to broad groups are allocated to ndvdual commodtes wthn each group. Therefore, t s assumed that dary products as a group s weakly separable from other commodtes consumed n Ontaro. Thus, the dary demand system we estmate s a condtonal demand system and the elastctes are condtonal on the expendture allocated to the dary products as a group. Econometrc Estmaton and Emprcal Results: Barten s General Model and four alternatve specfcatons of a demand system such as the Rotterdam, AIDS, CBS and NBR were estmated employng quarterly data from 1986:1 to 2010:4. Snce we used quarterly data, log dfferences are computed between the same quarters n consecutve years nstead of log dfferences between two contguous quarters n the same year. Also the shares used to multply each of the equatons were averages for the same quarters. All fve systems were estmated wth homogenety and symmetry condtons mposed on them for the ease of comparson. We also tested for structural stablty of the estmated model by splttng the data set nto two sub-perods and usng the lkelhood rato test for all fve demand systems. To avod sngularty of the estmated varance-covarance matrx, t was necessary to drop one of the demand equatons from the system and estmate n-1 system of equatons. As t does not matter to the estmated parameters whch equaton s deleted (Barten, 1969), we dropped the demand equaton for butter from each of the system before estmaton. The parameters of all fve demand systems are computed usng the terated seemngly unrelated regresson procedure of 8

11 SHAZAM 11. Iteraton ensures that the estmated parameters asymptotcally approach ther maxmum lkelhood values (Judge et al., 1980). The hypotheses of homogenety, symmetry and both homogenety and symmetry are tested usng the Wald test. To mplement these tests, each demand system was estmated wthout mposng symmetry and homogenety condtons. Then, we mposed these condtons separately and ontly on each of the fve demand systems. Based on the Wald test, the mantenance of homogenety and symmetry condtons ether separately or ontly could not be reected at 5 percent level of sgnfcance only for the NBR demand system (Table 2). These fndngs suggest that only the results from ths functonal specfcaton are theoretcally consstent wth homogenety and symmetry condtons. The acceptance of the homogenety condton can be nterpreted as an acceptance of the exogenety of changes n ncome (Attfeld, 1985). Based on a number of dscussons wth DFO personnel, we explored the structural stablty ssues n the demand for maor dary products n Ontaro by estmatng the models wth the full sample and wth 1986:1-1996:4 and 1997:1-2010:4 sub-samples. Then, we examned f the estmated parameters from the sub-samples were sgnfcantly dfferent from those of the full sample. The results of the lkelhood rato tests are presented n Table 3a and 3b. The results demonstrate that the estmated parameters from all fve models are structurally stable over the study perod. The results of the model selecton test presented n Table 4 ndcate that all but the NBR model are reected at 5 percent level of sgnfcance. Thus, the NBR model can best explan the demand for maor dary products n Ontaro. Accordngly, the NBR model s estmated wth both homogenety and symmetry condtons mposed on t pror to estmaton. The estmated parameters of the NBR model also satsfy monotoncty and concavty condtons of the underlyng cost functon. Monotoncty s satsfed at each data pont snce all budget shares n ths model are strctly postve. The estmated parameters of the NBR model are presented n Table 5. The explanatory power of the model s satsfactory as ndcated by the system s R 2 of All estmated parameters are ontly sgnfcant as ndcated by the test of overall sgnfcance whch reects the null hypothess that the slope coeffcents are ontly zero. The lkelhood rato statstcs of the dagonal covarance matrx reveals that the model does not suffer from heteroskedastcty. Over 83% of the coeffcents are statstcally sgnfcant at 5% level of error probablty. All 9

12 expendture coeffcents are postve and statstcally sgnfcant ndcatng that the budget shares for all dary products would ncrease f total expendture s ncreased. Table 6 presents the estmated Marshallan elastctes of demand for seven maor dary products n Ontaro. All but one of the estmated prce elastctes and all expendture elastctes appear to be nelastc. All own-prce elastctes are negatve and except that for the skm mlk powder, all are statstcally sgnfcant at the 5 percent level of error probablty. The Marshallan own-prce elastcty of demand for flud mlk, butter, cheese, yogurt, ce cream, cream and skm mlk powder respectvely are -0.71, -0.41, -0.73, -0.87, -1.15, and The negatve and statstcally sgnfcant own-prce elastcty of demand for all dary products suggest that the correspondng demand curves are downward slopng and hence, satsfy the law of demand. All expendture elastctes are postve and statstcally sgnfcant at the 5 percent level. Snce the expendture elastctes of all dary products consdered n ths study are less than unty, they can be consdered as necessary goods n Ontaro. Snce the Hcksan elastctes of demand can capture only the substtuton effect and leave out the ncome effect, they can be used to shed lghts on the substtutablty of maor dary products n consumpton. The Hcksan elastctes of demand are negatve but smaller than ther Marshallan counterparts (Table 7). In partcular, the Hcksan own-prce elastcty of demand for flud mlk, butter, cheese, yogurt, ce cream, cream and skm mlk powder are -0.57, -0.41, -0.72, -0.84, -1.08, and respectvely. The concavty of the cost functon at the sample mean s ensured snce all own-prce Hcksan elastctes are negatve. Snce all own-prce Hcksan elastctes are statstcally sgnfcant at 5% level, the underlyng Slutsky matrx s negatve sem-defnte. The cross-prce Hcksan elastctes suggest that over 76% are net substtutes n consumpton n Ontaro (Table 7). How consstent are the estmated elastctes of demand for dary products n Ontaro wth other studes? The estmated elastcty of demand for flud mlk n Ontaro presented n ths artcle s much hgher than those reported n prevous studes (Table 8). These dfferences can be attrbuted to dfferences n purposes, data, perods covered and methods employed. Whle Goddard and Telu (1988) used the Lnear Expendture System to measure elastcty of demand for flud mlk, both Venkateswaran and Knnucan (1990) and Goddard and McCutcheon (1993) used sngle equaton demand functons to estmate the prce elastcty of demand for flud mlk n Ontaro. None of these studes ether estmated the Hcksan demand for flud mlk or estmated 10

13 demand for butter, cheese, yogurt, ce cream, cream and skm mlk powder consumed n Ontaro. Therefore, ths artcle makes an mportant emprcal contrbuton by beng the frst study to estmate and report the elastcty of demand for seven maor dary products n Ontaro employng a theoretcally consstent demand system. Whle the use of tme seres econometrcs may generate a dfferent set of estmated prce and ncome elastctes, they are less lkely to be very dfferent from the results presented n ths paper because we estmated a dfferental demand system. Canada s a vast country wth sgnfcant regonal dfferences n sol and clmatc condtons, resource endowments and consumpton behavours. These dfferences are lkely to nfluence the nature of dary consumpton across provnces n Canada. The dfferences n the allocatons of dary producton enttlements across provnces under the Supply Management system and the dscovery of dfferences n dary consumpton patterns across provnces can have sgnfcant polcy mplcatons. It s lkely that the ncorporaton of provnce-specfc prce and ncome elastctes of demand for maor dary products n economc analyss wll generate dfferent set of welfare consequences for Canada as a whole and for dfferent provnces. The provnce-specfc estmates can also be used to generate the mpacts of future trade agreements and how those mpacts would be dstrbuted across provnces. It s hoped that the new results wll better nform long-term polcy choces n Canadan agrculture. Concludng Remarks: Supply management as a polcy tool n the dary sector n Canada has been controversal snce ts ntroducton n the md 1960s. A number of factors churned up the controverses n recent years. Whle there are strong proponents and opponents of supply management n the dary sector, the arguments are often flled wth guesstmates because no one has estmated a set of relable prce and ncome elastctes of demand for maor dary products consumed n Ontaro or n any other provnces n Canada. An attempt s made n ths artcle to brdge ths gap by estmatng a demand system for seven maor dary products n Ontaro employng quarterly data from 1986:1 to 2010:4. Barten s (1993) General model and the data drven approach has been used to determne the most approprate functonal specfcaton of the demand system, gven the data set for seven maor dary products n Ontaro. 11

14 The estmated model (the NBR demand system) fts the data well. In addtonal, standard statstcal tests of model adequacy were satsfactory. In partcular, the NBR model supported the theoretcal propertes of homogenety and symmetry. It also satsfes the montoncty and concavty condtons. Thus, the estmated prce and ncome elastctes of demand for dary products n Ontaro reported n ths artcle are theoretcally consstent, relable and vald for polcy analyss. All own-prce elastctes have the expected negatve sgn and all are statstcally sgnfcant at the 5% level. All Hcksan elastctes are smaller than ther Marshallan counterparts as expected. All expendture elastctes are postve and sgnfcant at the 5% level ndcatng that all dary products are consdered necessary goods n Ontaro. All but two estmated own-prce elastctes are less than unty. Whle cross-prce elastctes of demand for dary products vary across commodtes, more than three-quarter of those are postve. Prevous elastcty estmate of demand for flud mlk n Ontaro are much lower than those reported n ths artcle. It s hoped that the prce and ncome elastctes of demand reported n ths artcle wll lead to nterestng polcy analyss and contrbute to more nformed polcy choces n the long-run n Canadan agrculture. 12

15 References Alston, J. and J. Chalfant. 1991a. Can We Take the Con Out of the Meat Demand Studes? Western Journal of Agrcultural Economcs, 16(1): Alston, J. and J. Chalfant. 1991b. Unstable Models from Incorrect Forms. Amercan Journal of Agrcultural Economcs, 73(4): Alston, J. and J. Chalfant The Slence of the Lambdas: A Test of the Almost Ideal and Rotterdam Models. Amercan Journal of Agrcultural Economcs, 75(2): Amemya, T Advanced Econometrcs. Cambrdge: Harvard Unversty Press. Attfeld, C Homogenety and Endogenety n Systems of Demand Equatons. Journal of Economcs, 27(2): Barchello, R The Economcs of Canadan Dary Regulaton. Techncal Report No. E/12. Ottawa: Economc Councl of Canada. Barten, A. P Estmatng Demand Systems. Econometrca, 36(2): Barten, A. P Maxmum Lkelhood Estmaton of a Complete System of Demand Equatons. European Economc Revew, 1(1): Barten, A. P The System of Consumer Demand Approach: A Revew. Econometrca, 45(1): Barten, A. P Consumer Allocaton Models: Choce of Functonal Form. Emprcal Economcs, 18(1): Chrstensen, R., D. Jorgenson, and L. Lau Transcendental Logarthmc Utlty Functons. Amercan Economc Revew, 65(3): Clemens, J. and B. Crowley Mlkng the System: How Agrcultural Supply Management Impedes Trade Opportuntes and Egregously Transfers Income. Hungry for Change Seres. Ottawa: McDonald-Laurer Insttute. Conference Board of Canada. (2009). Makng Mlk: The Practce, Players, and Pressures Behnd Dary Supply Management. Report, November, Deaton, A. and J. Muellbauer An Almost Ideal Demand System. Amercan Economc Revew, 70(3):

16 Dewert, W An Applcaton of the Shephard Dualty Theorem: A Generalzed Leontef Producton Functon. Journal of Poltcal Economy, 79(3): Forbes, J., R. Hughes, and T. Warley Economc Interventon and Regulaton n Canadan Agrculture. Economc Councl of Canada and the Insttute for Research on Publc Polcy. Ottawa: Supply and Servces Canada. Gfford, M Canada s Dary Industry: Can Supply Management Survve n a More Open Internatonal Trade Envronment? Polcy Optons (November): Goddard, E. and M. McCutcheon Optmal Producer Investment n Generc Advertsng: The Case of Flud Mlk n Ontaro and Quebec. Canadan Journal of Agrcultural Economcs, 41(3): Goddard, E. and A. Telu Assessng the Importance of Flud Mlk Advertsng n Ontaro. Canadan Journal of Agrcultural Economcs, 36(2): Ivson, J Kss Goodbye to Supply Management. Natonal Post, June 21. Accessed May 15, Judge, G., W. Grffths, R. Hll, H. Lutkepohl and T. Lee The Theory and Practce of Econometrcs. New York: Wley. Keller, W. and J. van Drel Dfferental Consumer Demand Systems. European Economc Revew, 27(3): Lee, J., M. Brown, and J. Seale Jr Model Choce n Consumer Analyss: Tawan, Amercan Journal of Agrcultural Economcs 76(3): Melke, K., R. Sarker, and D. LeRoy. (1998). The Potental for Increased Trade n Mlk and Dary Products between Canada and the Unted States under Trade Lberalzaton. Canadan Journal of Agrcultural Economcs, 46(2): Moschn, G. and A. Vssa Flexble Specfcaton of Mxed Demand Systems. Amercan Journal of Agrcultural Economcs, 75(1): 1-9. Neves, P Analyss of Consumer Demand n Portugal, Memore de Matrse en Scences Economques. Unversty Catholqque de Louvran, Louvan-la-Neuve, France. Okrent, A. and J. Alston Demand for Food n the Unted States: A Revew of Lterature, Evaluaton of Prevous Estmates, and Presentaton of New Estmates of Demand. Gannn Foundaton Monograph #48, Unversty of Calforna, Aprl. 14

17 Rude, J. and H. An Trans-Pacfc Partnershp: Implcatons for the Canadan Industral Dary sector. Canadan Publc Polcy, 39(3): Thel, H. 1975a. Theory and Measurement of Consumer Demand, Vol. 1, Amsterdam: North- Holland. Thel, H. 1975b. Theory and Measurement of Consumer Demand, Vol. 2, Amsterdam: North- Holland. Van Kooten, G.C. (1990). Measurng the Welfare Costa of Supply Management: The Role of Indrect Benefts n Program Evaluaton. Canadan Journal of Economcs, 17(1): Veeman, M. M. (1982). Socal Costs of Supply Restrctng Marketng Boards. Canadan Journal of Agrcultural Economcs, 30(1): Venkateswaran, M. and H. Knnucan Evaluatng Flud Mlk Advertsng n Ontaro: The Importance of Functonal Form. Canadan Journal of Agrcultural Economcs, 38(3): Wallace, K Is the Prce of Mlk too Hgh? Toronto Star, November 20, Accessed May 15,

18 35.00 Cheese Per Capta Consumpton of Dary Productons per Quarter SMP Flud Mlk Butter Cream 5.00 Ice Cream 0.00 Yoghurt Fgure 1. Changes n the Consumpton of Seven Dary Products n Ontaro 16

19 Budget Share n % 0.30 Flud Mlk Cream Ice Cream 0.20 Cheese 0.10 Yoghurt 0.00 Butter SMP Fgure 2. Evoluton of Budget/Expendture Shares of Maor Dary Products n Ontaro 17

20 Table 1. Summary Statstcs of Prces and Budget Shares of Maor Dary Products n Ontaro Varable Mean Standard Dev. Mn Max Real Prces Cream Yogurt Butter Cheese SMP Ice Cream Flud Mlk Budget Shares Cream Yogurt Butter Cheese SMP Ice Cream Flud Mlk

21 Table 2. Statstcal Test for Homogenety and Symmetry Condtons Models LLV U LLV H LRT H LLV S LRT S LLV S$H LRT S$H Barten s AIDS Rotterdam CBS NBR Degrees of Freedom Crtcal value 1 ( At the 5% level of sgnfcance Notes: LLV U : Unrestrcted; LLV H : Homogenety; LLV S : Symmetry 19

22 Table 3a. Statstcal Test for Structural Stablty Sub-Perod Models Unrestrcted Lkelhood Rato Test Homogenety Lkelhood Rato Test Symmetry Lkelhood Rato Test Symmetry and Homogenety Lkelhood Rato Test Barten s (Unrestrcted) AIDS Rotterdam CBS NBR Crtcal value ( At the 5% level of sgnfcance wth 35 degrees of freedom Table 3b. Statstcal Test for Structural Stablty Sub-Perod Models Unrestrcted Lkelhood Rato Test Homogenety Lkelhood Rato Test Symmetry Lkelhood Rato Test Symmetry and Homogenety Lkelhood Rato Test Barten s (Unrestrcted) AIDS Rotterdam CBS NBR Crtcal value At the 5% level of sgnfcance wth 15 degrees of freedom 20

23 Table 4. Statstcal Test for Model Selecton Models Log of Lkelhood Values Lkelhood Rato Test Barten s (Unrestrcted) AIDS Rotterdam CBS NBR Crtcal Value 1 ( ) 1 Because the functonal form restrctons are based on two parameters n the general model, the Lkelhood Rato Test s dstrbuted as wth two degrees of freedom. The crtcal value s 5.99 at the 5% level of sgnfcance

24 Table 5 Parameter Estmates of the NBR Model for Seven Dary Products n Ontaro (0.0073) (0.0109) (0.0035) (0.0080) (0.0085) (0.0027) System (0.0125) (0.0109) (0.0006) (0.0104) (0.0205) (0.0102) (0.0044) (0.0109) (0.0191) (0.0007) (0.0127) (0.0043) (0.0051) (0.0060) (0.0007) (0.0112) (0.0075) (0.0097) (0.0005) (0.0104) (0.0127) (0.0075) (0.0171) (0.0014) (0.0053) (0.0122) (0.0014) (0.0097) (0.0103) (0.0240) (0.0068) (0.0044) (0.0051) (0.0005) (0.0053) (0.0068) (0.0045) (0.0009) (0.0124) (0.0053) (0.0103) (0.0110) (0.0038) FM=Flud Mlk, CS=Cheese, YO=Yoghurt, IC=Ice Cream, SMP=Skm Mlk Powder, BU=Butter (0.0114) (0.0143) (0.0093) (0.0139) (0.0178) (0.0058) R 2 22

25 Table 6. Marshallan Elastctes of Demand for Maor Dary Products n Ontaro Flud Mlk Butter Cheese Yoghurt Ice Cream Cream Skm Mlk Powder Expendture Elastcty Flud Mlk (0.1158) (0.0717) (0.1855) (0.1204) (0.1201) (0.1344) (0.2924) (0.0284) Butter (0.1256) (0.0314) (0.0128) (0.2789) (0.1270) (0.0046) (0.0657) (0.0206) Cheese (0.1222) (0.0797) (0.2114) (0.1152) (0.2238) (0.1462) (0.3189) (0.1149) Yoghurt (0.0329) (0.0649) (0.0525) (0.0232) (0.0268) (0.0934) (0.0887) (0.1636) Ice Cream (0.0121) (0.1810) (0.0084) (0.0842) (0.0955) (0.2833) (0.2118) (0.1622) Cream (0.2157) (0.0135) (0.3390) (0.1529) (0.1683) (0.2364) (0.0155) (0.1438) Skm M.P (0.0402) (0.0254) (0.0728) (0.0291) (0.0346) (0.0460) (0.0627) (0.1510) Notes: Standard errors n parenthess

26 Table 7. Hcksan Elastctes of Demand for Maor Dary Products n Ontaro Flud Mlk Butter Cheese Yoghurt Ice Cream Cream Skm Mlk Powder Flud Mlk (0.0201) (0.0485) (0.0236) (0.0194) (0.0103) (0.0283) (0.0469) Butter (0.1200) (0.2653) (0.1273) (0.2092) (0.0054) (0.1462) (0.2057) Cheese (0.1102) (0.2813) (0.0949) (0.0740) (0.0058) (0.0971) (0.1426) Yoghurt (0.0842) (0.0211) (0.0955) (0.1810) (0.2833) (0.1121) (0.0183) Ice Cream (0.0934) (0.3114) (0.0209) (0.0736) (0.1584) (0.0086) (0.1649) Cream (0.0842) (0.2118) (0.0955) (0.1810) (0.2833) (0.1121) (0.1837) Skm Mlk Powder (0.1102) (0.2813) (0.0949) (0.0740) (0.1518) (0.0371) (0.1426) Notes: Standard errors n parenthess. 24

27 Table 8. Comparson of Own-Prce Elastctes of Demand for Maor Dary Products n Ontaro Study Area Perod Marshallan Estmates Hcksan Estmates FM BU CS YO IC CM SMP FM BU CS YO IC CM SMP Goddard and Ontaro Telu 84 Venkateswa Ontaro ran & Knnucan 84 Goddard & Ontaro McCutcheon 89 Ths Study Ontaro FM=Flud Mlk, BU=Butter, CS= Cheese, YO=Yogurt, IC=Ice Cream, CM= Cream and SMP= Skm Mlk Powder 25