Testing for Separability and Structural Change in Urban Chinese Food Demand

Transcription

1 DRAFT No for Caon Tesng for Separably and Srucural Change n Urban Chnese Food Demand Fengxa Dong, Assocae Scens Cener for Agrculural and Rural Developmen Iowa Sae Unversy 571 Heady Hall Ames, Iowa fdong@asae.edu Frank Fuller, Scens Cener for Agrculural and Rural Developmen Iowa Sae Unversy 575 Heady Hall Ames, Iowa ffuller@asae.edu May 17, 2004 Seleced Paper prepared for presenaon a he Amercan Agrculural Economc Assocaon Annual Meeng, Denver, Colorado, Augus 1-4, 2004 Absrac: Ths paper esmaes and ess separable demand specfcaons n food expendures by urban consumers n Chna. Boh paramerc and nonparamerc echnques are employed o oban nformaon abou shfs n consumer preferences and approprae commody groupngs. The resuls have mplcaons for pas and fuure research and polcy analyss. Key Words: Separably, Food Consumpon, Srucural Change, Chna, Nonparamerc Copyrgh 2004 by and Fengxa Dong and Frank Fuller. All rghs reserved. Readers may make verbam copes of hs documen for non-commercal purposes by any means, provded ha hs copyrgh noce appears on all such copes.

2 Tesng for Separably and Srucural Change n Urban Chnese Food Demand Chna s economc reforms, whch began n 1978, resuled n remarkable growh n GDP, averagng 8-9 percen annually n he laer half of he 1990s. Per capa nomnal GDP ncreased from 379 Yuan n 1978 o 8,184 Yuan n Economc prospery and domesc polcy reforms have changed he marke envronmen for consumers n Chna. The removal of raonng, ncreased abundance and varey of foods, and changes n he markeng sysem have lkely conrbued o shfs n consumer preferences. Over he las wo decades, urban Chnese consumers have dramacally ncreased her consumpon of mea, oher lvesock producs and frus and have decreased consumpon of gran-based foods. Chna s per capa gran consumpon declned from kg n 1981 o kg n 2002 n urban areas, whereas he per capa consumpon of meas, eggs, and aquac produc ncreased from 20.52kg, 5.22kg, 7.26kg n 1981 o 32.52kg, 10.56kg, and 13.20kg n 2002, respecvely (Sae sascal bureau of Chna). Gven he sze of Chna s populaon and he poenal mpacs of even mnor changes n consumpon behavor on nernaonal agrculural markes, numerous demand sudes have been conduced o esmae he mpacs of he marke reforms and ncome growh on consumpon paerns. Many of hese sudes have ulzed he dea of separably n her demand specfcaon o lm he scope of her analyss o parcular commodes or food aggregaes. However, few demand sudes ha employ separably assumpons acually es for he valdy of hese assumpons, gven her commody groupngs. Inapproprae aggregaons can lead o fauly demand elascy esmaes ha may provde msleadng resuls from hypohess ess, proecons, and polcy analyss (Moschn e al; Ncol). 1

3 Ths paper conrbues o he growng leraure on Chnese food consumpon n wo respecs. Frs, we ulze he srucure descrbed by Moschn and Melke o esmae and es for shfs n parameer values over me for mporan commody groupngs, such as grans, meas, vegeables, and aquac producs. Knowledge of he naure of parameer shfs n recen years wll ad n proecng and accommodang fuure changes n polcy analyss. Second, we explo he srucural change resuls o es separable demand specfcaons commonly used n he analyss of food expendures by urban consumers n Chna. The organzaon of he paper s as follows. Frs, we descrbe he mehodology for esng srucural change usng boh paramerc and nonparamerc approaches. Then we conduc he emprcal ess of srucural change for Chnese urban food demand. Followng he srucural change ess, we brefly dscuss mehods for emprcally esng weak separably n demand. Based on he fndngs from srucural change ess, we es a number of separable demand srucures for Chnese food consumpon. We conclude wh a bref summary of our fndngs and suggesons for furher research. Mehodology for Tesng Srucural Change Tes for Srucural Change In demand analyss, srucural change s ofen referred o changng ases and preferences (Moschn and Moro). These changes can be refleced by he change n he shape of ndvdual uly funcons. In hs sudy, boh nonparamerc and paramerc mehods are used o nvesgae srucural changes n Chnese urban food demand. Two of he mos popular funconal forms, he lnear verson of he Almos Ideal Demand Sysem (LA/AIDS) and he Roerdam model, are boh esmaed o check he robusness of our resuls. 2

4 The LA/AIDS model developed by Deaon and Muellbauer s exensvely used n demand esmaon because of s conssency wh he axoms of choce, aggregaon properes, and flexbly n approxmang arbrary demand funcons. Sarng from a prce ndependen generalzed logarhmc (PIGLOG) cos funcon, he AIDS demand funcons n budge share form s expressed as w n y = α + γ log( p ) + β log( = 1 P ), where w s he budge share of good ; p s he prce of good ; y s he oal expendure; and P s a he ranslog prce ndex below. log( P) = α 1 n n n 0 + α k log( pk ) + γ k log( pk ) log( p ) k = 1 2 = 1 k= 1 We lnearze he model by replacng he ranslog prce ndex above wh he correced Sone prce ndex, log( P ) s = n = 1 p w log( p ) 0, where p 0 s mean prce (Moschn). Addng up, homogeney, and symmery mply he followng parameer resrcons. n = 1 n n n = 1, β = 0, γ = 0, = 1 = 1 = 1 α γ = 0, and γ = γ. Followng Moschn and Melke, srucural change can be characerzed by allowng he se of parameers of he demand sysem o change over me. Wh a common me pah h, he general lnear AIDS model can be reparameerzed as follows. n y w = α + γ h + ( γ + ah )log( p ) + ( β + bh )log( ) (1) P = 1 s Addonal paramerc resrcons n he srucural change model assocaed wh homogeney, n addng up, and symmery are γ 0, b = 0, and a = 0. To approxmae he acual shape = 1 n = = 1 = 1 n 3

5 of me pah, h s consruced as he pece-wse lnear funcon defned below (Ohan and Kaayama; Moschn and Melke). h h h = 0, = ( τ ) /( τ τ ), = 1, for for for = 1,..., τ ; = τ + 1,..., τ 1; 1 = τ,..., T where 1 s he end pon of he frs regme and 2 s he sarng pon of he second regme ( 1 < 2). The dfference beween 1 and 2 defnes he ranson pah. If 2 = 1 +1, he srucural change s abrup; oherwse, he change s gradual. To capure he dynamc behavor of Chnese food demand, he frs dfference form s used for esmaon; hus, he esmaed model s gven n equaon (2) w n y y = γ h + ( γ log( p ) + a ( h log( p )) + β log( ) + b ( h log( )) (2) P = 1 P A esng he hypohess ha he me pah parameers (, a, and b ) are equal o zero s same as a es of he hypohess of no srucural change. The srucural change verson of he Roerdam model s smlar o he LA/AIDS model. By nroducng a me pah varable, he Roerdam model s re-specfed n equaon (3) n w d log( q ) = ( c + k h ) w d log( q ) + ( c + k h ) d log( p ) (3) = 1 = 1 Homogeney, addng-up, and symmery requre he followng parameer resrcons. c k = 1, = 0, c k = = c k n = 0, c = 0, k Unlke he LA/AIDS model whch approxmaes he demand funcon n he varable space, Roerdam model approxmaes he demand funcon n he parameer space. Alhough canno = c = k,. 4

6 be consdered as an exac represenaon of preferences whou srong condons, he Roerdam model s sll very useful as a flexble funcon form for approxmang a demand sysem. Nonparamerc Tess of Sable Preferences The paramerc approach for esng srucural change n consumer preferences s ulmaely dependan on he funconal form used o perform he analyss. Reecon of he hypohess of sable preferences s condoned on he assumpon ha he es resuls are nsensve o he funconal form chosen (Alson and Chalfan). Repeang he analyss usng a varey of flexble funconal forms s one means of assessng he robusness of evdence of preference shfs n a parcular daa se. However, nonparamerc mehods provde an alernave approach ha does no requre any assumpons regardng funconal forms. The nonparamerc analyss of srucural change s derved from he dea ha a vecor of prces and a correspondng vecor of consumpon bundles generaed by consumers wh sable preferences wll sasfy he necessary and suffcen condons for he daa o be raonalzed by a uly funcon. Buldng on he work of Samuelson, Houhakker, and Afra, Varan (1982) demonsraed ha generalzed axom of revealed preference (GARP) s a suffcen condon for uly maxmzaon. Consequenly, a smple es for sable preferences checks he daa for complance wh GARP. GARP saes ha f a consumpon bundle, x, s revealed preferred o anoher bundle, x, hen x canno be srcly drecly revealed preferred o x. The bundle x s revealed preferred o bundle x (wren {x, x k, x l,,x}. x Rx ) when he relaonshp n equaon 1 holds for he sequence of bundles p x p x, p x p x,..., p x p x (4) k k k k l m m m 5

7 In equaon 4, he bundle x s drecly revealed preferred o x k (wren R x ) because he cos x 0 of purchasng x k a prces p s less han or equal o he cos of purchasng x. In oher words, f a consumer purchases x when x k s affordable, hen he consumer mus prefer x. Revealed preference esablshes a ransve closure for a sequence of bundles ha are conneced hrough he drecly revealed preferred relaonshp. GARP spulaes ha f x Rx, hen x canno cos less han x evaluaed a he prce vecor assocaed wh bundle x; oherwse, he daa s no conssen wh uly-maxmzng behavor (Varan, 1982). Quesons have been rased abou he power of nonparamerc ess, parcularly when he real expendures grow rapdly over me. Income effecs may mask shfs n he underlyng preferences by causng each successve consumpon bundle o le ousde of he consumpons se of he prevous observaon, despe relave prce changes. Real food expendures for urban Chnese consumers ncreased an average of 3.3% annually snce Consequenly, ncome effecs may be a poenal problem n our daa se. Chalfan and Alson suggesed usng pror nformaon abou ncome elasces o adus he expendure daa as a means of removng he effecs of ncome growh from he analyss, allowng he poenal mpacs of srucural change o be observed n he resdual daa. Applyng a smlar concep, Sakong and Hayes argue ha he mpacs of shfs n consumer preferences could be solaed from ncome and prce effecs usng he compensaed demand curve. When all goods n he consumpon se are normal goods and preferences are sable, changes n consumpon from one perod o he nex can be descrbed by movemens along he compensaed demand curve. If an opmal consumpon bundle les off he compensaed demand curve, he dsance from he demand curve o he observed bundle s a measure of ase changes. Sakong and Hayes proposed a lnear programmng sysem ha combnes he consrans mpled by 6

8 revealed preference heory wh a pror nformaon abou ncome elasces o solve for he opmal se of consumpon bundles ha mnmze ase changes, gven observed prces and expendures. Daa Annual daa from for per capa consumpon, expendures, and real prces are obaned from Chnese Urban Household Income and Expendure Survey and Chna Sascal Yearbooks. Ten food commodes (gran, pork, beef/muon, poulry, eggs, fsh, vegeables, fru, mlk, and oher foods) were ncluded n he nonparamerc analyss. Pork s he mos commonly consumed mea produc wh relavely low prce. Beef currenly only represens a small proporon of oal mea producs consumed and per capa beef and especally muon consumpon s much hgher n he wesern pasoral provnces. Beef and muon are always aggregaed no one mea group n Chna s sascal sysem. Expendures on oher foods was calculaed by deducng food expendure on hose nne commody groups from oal food expendure. The consumer prce ndex was used as he prce of oher foods and quany was calculaed from food expendure by dvdng by prce ndex. In he paramerc analyss, he lmed number of observaons and he relavely large number of parameers preven ncluson of all en commodes. Seven food groups (gran, mea, eggs, fsh, vegeables, fru, and ohers) are ncluded n he paramerc analyss. The Tornqvs quany ndex s used for aggregang pork, beef/muon, and poulry no mea. And aggregae mea prce s recovered from mea expendure dvded by mea quany. In addon, n order o compare he groupng effecs on srucural change and separably ess, an alernave groupng s also esed. A fve-commody group, whch ncludes gran, mea and eggs, fsh, vegeables/fru, and oher foods, s used o 7

9 conduc he ess. Tornqvs quany ndces are also used for mea and egg aggregaes, and vegeables and fru aggregaes. All prces and ncome were normalzed by her sample mean. Emprcal Resuls from Srucural Change Tess Paramerc Tess The dynamc lnear AIDS model n (2) and he Roerdam model n (3) were esmaed usng he maxmum lkelhood esmaon procedure n TSP 4.5. Boh wo models have sx equaons wh he equaon for oher foods omed o avod sngulary problem. Homogeney, symmery, and addng-up resrcons were mposed on he model parameers. There are 210 possble combnaons of 1 and 2, and he wo demand sysems were esmaed for each combnaon assumng seven and fve commody groups. Wh he lmaon of degree of freedom, no all ses of combnaons can have esmable parameers of he sysem of equaons. For AIDS model, all he parameers of sysem of equaons are esmable for and ; and for Roerdam, all he parameers are esmable for and The maxmum lkelhood esmaes of he srucural change pons ( 1, 2 ) are shown n Table 1. These resuls ndcae a raher abrup change n he mddle of he observaon perod. Based on log-lkelhood rao ess, he addonal srucural change pons n Table 1 are combnaons of ( 1, 2 ) whch canno be reeced wh fve commody groups n boh AIDS and Roerdam models. Undersandng he denfed possble srucural change pons, requres some knowledge of he urban food raonng polcy n Chna. The Chnese food raonng began n 1953 o guaranee he food secury for urban resdens. Raoned foods were obaned from mandaory sae procuremen of agrculural producs from farmers. The governmen was he sole seller of 8

10 hese raoned foods and urban resdens could only buy he raoned foods wh raonng coupons. From 1978, Chnese cenral governmen sared he economc reforms. Durng he frs phase of reform, , he sae monopoly or prescrbe purchases of agrculural produce decreased dramacally, for example, from 113 knds n 1981 o 60 knds n Then, farmers were allowed o sell her surplus produce n free markes. However, snce here were sll rgd nsuonal consrans on he free markes and he marke prces were much hgher han raonng prces, durng , he raonng sysem sll domnaed free marke n urban food supply. Then n lae 1984, prce conrols for 15 nonsaple foods, ncludng pork, eggs, sugar, and vegeables, were lfed, bu he governmen dsrbuon of hese goods was sll mananed wh raon prces well below free marke prces. I was no unl ha raonng of he 15 nonsaple foods was oally elmnaed. Afer ha, only grans and edble ols were subec o raonng. In he followng years, wh ncreasng urban household ncome and abundan supply of farm produce, he free marke became more and more mporan n he dual marke sysem and fnally led o he abolon of he raonng sysem n 1993 and gran and edble ols became nonbndng. Our emprcal resuls of srucural change ess are very conssen wh hose polcy change pons, alhough dfferen groups capure dfferen change pons. Wh seven commody groups, boh AIDS model and Roerdam capure he pon of elmnaon of gran raonng, whch occurred n Wh fve commody groups, Roerdam model capures boh pons where elmnaons of nonsaple foods and grans raonng occurred. AIDS model wh fve commody groups has more exensve ndcaons. I capures no only he exac polcy change pons bu also he polcy ransformng perods. 9

11 From above resuls, we can see ha polcy change has domnang effecs on Chnese urban food demand shf. In addon, groupng also affecs he ndcaon of srucural change pons by models. In hs sudy, he more dsaggregaed model wh seven food groups s only able o capure he pon of elmnaon of gran raonng; and more aggregaed model capures more polcy change pons. One explanaon for hs resul may be ha dsaggregang he daa dsperses he raonng effecs on food demand across he ndvdual commody groups, and he effecs of he elmnang gran raonng may domnae he effecs of oher, somewha more gradual polcy ransformaons n specfc commodes. On conrary, when commodes experencng smlar marke ransformaon are aggregaed no a sngle group, such as meas and eggs, he effecs of polcy changes n he ndvdual markes renforce one anoher, allowng he model o deec addonal change pons. To nvesgae he sgnfcance of he srucural change, condonal on he opmal combnaon of ( 1, 2 ), we conduced lkelhood rao ess for he hypohess of consancy of he parameer vecor over me,.e. coeffcens for me pah varables equal o zero. The resuls were repored n Table 2 for boh AIDS and Roerdam models wh seven and fve commody groups, respecvely. The hypohess of no srucural change n he full se of parameers s reeced a 0.05 sgnfcance level, suggesng ha a consan se of parameers canno be posulaed o characerze Chnese urban consumer behavor whn he assumed models and ha some srucural change over he perod mus be ncorporaed. Prce, ncome and nercep srucural change parameers are also esed o shed lgh on he naure of he srucural changes. We do no reec he hypohess of no srucural change for prce parameers a 0.05 sgnfcance level n Roerdam model wh fve commody groups; however, nercep and ncome ndcae sgnfcan srucural change. All ess n oher models and under oher aggregaon assumpons 10

12 reeced he hypohess of no srucural change, whch sugges ha hose changes no only resul from prce and expendure change, bu also from nercep change. The average marshallan prce elasces for AIDS model wh seven and fve commody groups before and afer he opmal srucural change pons are repored n Table 3 and Table 4, respecvely. Wh seven commody groups, excep grans, all own prce elasces are negave. The posve own prce elascy for gran manly resuls from he ransformaon of polcy and marke developmen. Wh raonng and meager supply of foods as well as scarce varey of food supply, Chnese urban food demand was skewed n favor of grans. Wh raonng reform and ncreasng food supply and varees, here was an adusmen n urban food demand. Therefore, durng hs perod and hereafer, even hough gran prces wen down, he demand for grans also wen down. Ths could be confrmed by ncome elasces, whch show ha grans change from necesses o nferor goods. Afer he srucural change, excep grans and mea, all oher food demands become more elasc. Moreover, fsh, vegeables, and oher foods change from prce nelasc o prce elasc. Grans change from necesses o nferor goods and vegeables change from nferor o luxury goods. Mea and frus change from necesses o luxures, and opposely, eggs change from luxures o necesses. In boh regmes, mea shows subsuon relaonshp wh boh eggs and vegeables, whle mea shows complemenary relaonshp wh boh grans and fsh. For comparson, he model wh fve commody groups was evaluaed a a smlar srucural change pon. We compued elasces a he (1991, 1993) srucural change pon. The resuls were repored n Table 4. Before srucural change, fsh s own prce elascy has posve sgn, and he same occurs for gran afer he srucural change. Same nerpreaon of he resuls for grans as wh seven commody groups could be appled here. The change n he own- 11

13 prce elascy for fsh may be due o he dversy and qualy varaon of he fsh producs ncluded n he aggregae. Along wh he deepened reform and marke developmen, aquac producs qualy and varey were ncreased grealy. However, he daa canno show qualy change. Alhough prces ncreased wh average qualy of aquaculure producs, demand also ncreased, poenally generang he posve own prce elascy before he srucural change. Excep gran, all oher foods became more prce elasc afer srucural change. Lke he analyss wh seven commody groups, grans changed from necesses o nferor goods, whereas fsh changed from nferor o luxury goods. The aggregae of mea and egg changed from ncome nelasc o ncome elasc. Grans are complemenary o mea/egg, whle mea/egg s subsuon o vegeable/fru n boh regmes. Comparng he elascy esmaes from boh groupng, we can conclude ha dfferen groupng do have some degree of effecs on elascy esmaons. I no only affecs values bu also somemes sgns. To furher analyze exclusve srucural change effecs on quany demand and also groupng effecs, we esmaed he bas of srucural change holdng prces and expendure consan for boh seven and fve commody groups for AIDS model. Le B denoe he change of share before and afer he srucural change, B =w a -w b, where w a s he share afer he srucural change and w b s he same share before he srucural change. If B >0, hen he srucural change favors he h good; and f B <0, hen he srucural change s agans he h good. Evaluang he shares a he sample mean of he exogenous varables, from equaon (1), B could be expressed as B =. The esmaed bas of srucural change and s sandard errors were repored n Table 5. The resuls show ha he srucural change s sgnfcanly based agans gran and n favor of fsh n boh seven and fve groups. In seven groups, he srucural change s neural for mea and fru, and sgnfcanly agans eggs 12

14 and vegeables. In fve groups, he srucural change s neural for boh mea/egg, and vegeable/fru. Compared wh mean shares before srucure change, shows ha here was abou 28% decrease n gran share afer he srucural change for seven and fve commody groups, respecvely, whle here was abou as hgh as 85% ncrease for fsh wh seven commody groups and abou 23% ncrease wh fve commody groups. Nonparamerc Tess of Srucural Change The algorhms suggesed by Varan (1982) for checkng drec revealed preference and ransve closure were appled o he Chnese urban consumpon daa usng hree dfferen aggregaons of he 10 prmary food caegores. GARP was nally esed on all 10 food groups, and no volaons were found. As n he paramerc analyss, beef, pork, and poulry were aggregaed no a mea group usng a Tornqvs quany ndex. Repeang he GARP es on he se of seven commodes revealed a volaon n he relaonshp beween observaons n 1981 and Fnally, eggs were added o he mea group, and frus and vegeables were combned no a sngle aggregae. The resulng 5 food groups were esed for conssency wh GARP and a volaon was denfed n he relaonshp beween he observaons n 1996 and The es resuls may provde some evdence of srucural change n 1985 and n 1997; however, s also possble ha he volaons ndcae a reecon of our separably assumpons raher han preference sably. As Chalfan and Alson noe, s no possble o dsngush wheher aggregaon bas, omed goods, or preference shfs generae volaons of GARP; however, falure o fnd nconssences n he daa sugges ha one s separably assumpons do no creae sgnfcan problems. In he presen analyss, he fac ha he group of 10 commodes dd no volae GARP, whle oher aggregaons of he same daa dd generae volaons, pons 13

15 oward aggregaon bas and no srucural change as he lkely cause. The conssency of he more dsaggregaed daa wh GARP does no rule ou he possbly of srucural change We appled he Sakong and Hayes model o he Chnese urban consumpon daa usng he same hree aggregaon assumpons appled above. Lke Corez and Senauer, we ncorporae he adusmens o he model suggesed by Chalfan and Zhang o avod dependence of he es resuls on scalng and prce deflaor choces. Our expendure elascy assumpons were derved from a bref survey of he leraure on urban food consumpon n Chna. In parcular, he model allows he analys o selec a range over whch he expendure elascy for each may vary. We aemped o selec bounds ha would nclude he maory of he esmaes found n he leraure. Some sensvy analyss was conduced o deermne wheher he broadenng he seleced ranges would sgnfcanly aler he resuls. Whle he magnudes of some ase changes dd vary, parcularly gran, he qualave resul dd no change subsanally. Table 7 dsplays he ranges seleced for hs sudy. Fgures 1-3 dsplay he cumulave ase changes for he hree smulaons. I s neresng o noe ha he cumulave ase changes n all hree aggregaons dsplay a negave shf n gran consumpon around 1985 and a posve shf n demand for frus. Ths me perod roughly corresponds o he perod of marke lberalzaon for vegeables, frus, aquac producs, and lvesock producs. In he md-1980s, he wo-rack prce sysem was nroduced for grans, and procuremen quoas for mos non-gran producs were elmnaed, gvng farmers more flexbly and ncenves o ncrease producon of frus, vegeables, and lvesock producs (Tuan and Ke). Consequenly, avalably of hese producs ncreased n urban areas, perhaps leadng o he shfs on consumpon dsplayed n Fgures

16 Preferences appear o be farly sable from he md 1980s unl he md 1990s, bu mlk, beef, and fsh consumpon all show ncreases n he laer half of he 1990s. Durng he same perod, egg and gran consumpon experence negave changes. Agan, hese shfs concde wh subsanal changes n Chna s food markeng sysem. Urban gran raonng ended n 1993 n mos urban areas, and real food markeng n he larger coasal ces began o rapdly move oward supermarkes as a prmary channel for food delvery n he lae 1990s. Boh changes ncreased he varey of food producs avalable o urban consumers, as well as relave prces. The resuls of hs analyss are conssen wh he observaon ha marke reforms and ncome growh n Chna have promped consumers o move away from saple foods, such as grans and eggs, oward more dverse des ncludng greaer quanes of fru, fsh, and dary producs. Somewha surprsng s he fac ha pork and poulry dd no dsplay any ase change. Prce and ncome effecs appear o be suffcen o explan changes n consumpon of hese wo meas. Tess for Separably Paramerc Tess To lm he scope of analyss o parcular commodes or food aggregaes, or o use aggregae daa when dsaggregaed daa are unavalable or of poor qualy, many sudes have ulzed he dea of separably n demand specfcaon. Wh separably of preferences, he commodes can be paroned no groups so ha choces whn groups can be deermned are only mpaced by oher goods hrough group expendures. Consequenly, he decson behavor can be explaned hrough a much smaller number of varables. Separably opens up he possbly of mul-sage budgeng and decson makng. Gven he convenence of he assumpon of separably, many sudes of Chnese food consumpon use hs dea whou esng s valdy (e.g., Wang e al, Gao, Wales, and Cramer, Wang and Chern, Wu, L, and 15

17 Samuel, Lews and Andrews, and Wu and Wu). To auhors knowledge, only Fan and Chern brefly menon he separably es usng Varan s mehod n her sudy of Chnese urban food consumpon paerns for he perod of Subsequenly, we use ess for weak separably ha are based on a combnaon of resuls from Goldman and Uzawa, and Blackorby, Davdson, and Schworm. For dealed developmens he reader s referred o Moschn, Moro, and Green. Le be Allen-Uzawa elascy of subsuon beween goods and ; and be ncome elasces. For any wo goods (, ) I g (group g) and a good k I s (group s) (g s), he necessary and suffcen condons for goods and weakly separable from k can be expressed n elascy erms as σ k = σ k ε ε The Allen-Uzawa elascy =e /w, where e s he compensaed prce elascy; and s ncome elascy. From AIDS model (2), Marshallan demand elasces ha reflec he effecs of srucural change are e e = ( γ + b h ) / w = ( γ + b h ) / w ( β + b h ) 1 ( β + b h ) w / w And ncome elascy ha reflecs he srucural change s ε ( β + b h ) / w + 1 = From slusky equaon, he Hcksan demand elasces are e e = ( γ = ( γ + b h ) / w + b h ) / w + w + w 1 Followng Moschn, Moro, and Green, he separably resrcons based on nformaon of srucural change for he lnear AIDS model (2) can be expressed as 16

18 γ k γ k + a + a k k h + w wk h + w w k = w w + β + bh + β + b h or γ k ( w + β + b h ) = ( γ ( w + β + b h ) k + a k h + w w ) ( a h k k + w w k ) Due o he characerscs of AIDS model ha s separably-nflexble, s of neres o consder he separably resrcons a he mean pon, whch we chose he mean shares. In addon, we rea parameers a and b, and me pah varable h as known based on he nformaon from srucural change esmaon n order o make he esmaon converge easly. Unlke AIDS model, Roerdam model s separably-flexble for he purpose of modelng weak separably (Moschn, Moro, and Green). Therefore, he separably resrcons wll hold no only locally, bu also globally whou any furher resrcons. The separably resrcons for Roerdam model only depend upon coeffcens and are much smpler han hose for AIDS model. The separably resrcons for Roerdam model (3) are: c c m m + k + k m m h h c = c + + kh k h or c m c + k h = ( c m + k mh ) c + k h k m h Smlarly, me pah varable and s parameers are reaed as known based on he fndngs from srucural change o make he esmaon converge easly. Nonparamerc Tess 17

19 Varan s 1983 arcle developed nonparamerc esng procedures for weak separably. Suppose we assume ha preferences over a se of n goods can be represened by he separable uly funcon n equaon 5. ( x, x,..., 2 x, v( x x )) u,..., 1 k l n (5) Varan showed ha any weakly separable uly funcon can be suppored by he daa f he goods n he separable group sasfy he followng hree condons. 1. Goods x l x n mus sasfy GARP as a group. 2. Prce and quany ndces 1, V ha sasfy he Afra Inequaly µ ( V V + p ( x x ) µ mus exs. 3. The se of goods {x 1,,x k,v } and he correspondng prces {p 1,,p k,1/ } sasfy GARP. The greaes dffculy ha mus be overcome n applyng hs nonparamerc es of weak separably s denfyng approprae prce and quany ndces ha sasfy he Afra nequaly. The mehod proposed by Varan s compuaonally nensve and has had dffcules denfyng separable srucures n mone carlo sudes (Barne and Cho). Flessg and Whney proposed an alernave mehod for compung approprae prce and quany ndces usng a lnear programmng sysem ha mnmzes he errors appled o a superlave ndex subec o he Afra Inequaly. Dewer has shown ha a superlave ndex, such as he chaned Tornqvs ndex, provdes a second-order approxmaon o an unknown aggregaor funcon. Flessg and Whney use he Tornqvs ndex augmened wh posve and negave error erms o consruc prce and quany ndces ha sasfy he Afra Inequaly. The lnear programmng soluon provdes he error-mnmzng ndces, whch are used o es conssency of he assumed separable srucure wh GARP. 18

20 Emprcal Tess of Separably Paramerc Resuls Snce Wald es for separably lacks nvarance when nonlnear resrcons are mposed, he sze-correcng lkelhood rao es was conduced o es separably (Dagenas and Dufour; and Moschn, Moro, and Green). The ess resuls for dfferen ypes of weakly separable srucures wh seven and fve commody groups, condonal on he opmal ( 1, 2 ), were repored n Table 6. Wh seven commody groups, he resuls show ha all of he nne separably srucures are reeced. Wh fve commody groups, condonal on he opmal ( 1, 2), excep he separable model ha fsh s separable from all oher groups canno be reeced a sgnfcance level, all oher separable models are reeced. Nonparamerc Resuls We appled Flessg and Whney s approach o he urban consumpon daa. As n he paramerc ess, we checked for asymmerc separably for each commody. We also esed separably of mea, mea and eggs, frus and vegeables, and mlk and oher foods. The es resuls are dsplayed n Table 8. The es for asymmerc separably of ndvdual commodes s essenally a es of wheher or no he remanng 9 commodes can be consdered a separable group. In mos cases, asymmerc separably was no suppored. However, he ess of fsh and mlk could no reec he null hypohess of asymmerc separably. Eggs and oher foods passed he es of condon 3, bu he remanng 9 food groups volaed condon 1. The separably ess for mea, mea and egg, fru and vegeable, and mlk and oher groups faled n all cases, excep mea and eggs. Frus and vegeables had only one volaon of condon 3, as dd he mea group. Gven he low 19

21 number of volaons for he mea and fru and vegeable groups, separably of hese groups may no be ruled ou. Conclusons Several paramerc and nonparamerc ess were performed on aggregae food consumpon daa for urban Chnese resdens. Alhough he resuls were que mxed, a number of paerns dd emerge from he daa. Frs, boh paramerc and nonparamerc ess revealed evdence of ase changes n he md-1980s and early o md 1990s. Boh me perods concde wh perods of maor change n domesc marke polces. Second, boh paramerc and nonparamerc es ndcae ha ase changes moved agans grans and eggs n favor of fsh and mlk. Resuls for frus and vegeables were mxed, bu boh approaches faled o demonsrae sgnfcan srucural change for meas. Thrd, separably ess were also mxed, wh he paramerc ess reecng asymmerc separably for all commodes excep fsh. The paramerc ess also reeced separably for meas, mea and eggs, and frus and vegeables. The nonparamerc ess also found evdence of asymmerc separably for fsh; however, asymmerc separably for mlk also could no be reeced. Of he four commody groupngs esed wh nonparamerc mehods, only he mea and egg aggregae was suppored by he daa. Much of he recen emprcal work n Chnese food consumpon has employed crossseconal and panel daa because of he rchness of hese daa ses compared o he avalable aggregae me seres daa. Whle hs sudy s one of he frs o emprcally es for evdence of srucural change and separably n Chnese food demand, he relevance of our resuls for he exsng leraure would be enhanced f he ess ulzed n hs paper were appled o survey and panel daa. Moreover, he dverse resuls obaned n hs sudy usng dfferen paramerc specfcaons and aggregaon assumpons ndcae ha researchers n he fuure should seek o 20

22 uncover separable srucures n he daa and employ alernave funconal forms before selng on a fnal emprcal specfcaon. 21

23 References Afra, Sydney N The Consrucon of Uly Funcons from Expendure Daa. Inernaonal Economc Revew, 8(1): Alson, Julan M. and James A. Chalfan Can We Take he Con Ou of Mea Demand Sudes? Wesern Journal of Agrculural Economcs, 16(1): Barne, Wllam. A. and Seungmook. Cho A Mone Carlo Sudy of Tess of Blockwse Weak Separably. Journal of Busness and Economcs Sascs, 7(3): Blackorby, C., R. Davdson, and W. Schworm Implc Separably: Characerzaon and Implcaons for Consumer Demands. Journal of Economc Theory 55(2): Chalfan, James A. and Julan M. Alson Accounng for Tase Changes. Journal of Polcal Economy, 96(2): Chalfan, James A. and Bn Zhang Varaons on Invarance or Some Unpleasan Nonparamerc Arhmec. Amercan Journal of Agrculural Economcs, 79(4): Corez, Rafael and Ben Senauer Tase Changes n he Demand for Food by Demographc Groups n he Uned Saes: A Nonparamerc Emprcal Analyss. Amercan Journal of Agrculural Economcs, 78(2): Dagenas, M., and J. dufour Invarance, Nonlnear Models, and Asympoc Tess. Economerca 59(6): Deaon, A., and J. Muellbauer An Almos Ideal Demand Sysem. Amer. Econ. Rev., 70 (3): Dewer, W. E Superlave Index Numbers and Conssency n Aggregaon. Economerca, 46(4): Fan, J., and W. Chern Analyss of Food Consumpon Paerns n Chna: Nonparamerc and Paramerc Approaches. Journal of Famly and Economc Issues, 18(2): Flessg, Adran R. and Gerald A. Whney A New PC-Based Tes for Varan s Weak Separably Condons. Journal of Busness and Economc Sascs, 21(1): Gao, X., E. Wales, and G. Cramer Paral Raonng and Chnese Urban Household Food Demand Analyss. Journal of Comparave Economcs, 22(1): Goldman, S., and H. Uzawa A Noe on Separably n Demand Analyss. Economerca 32:

24 Houhakker, Hendrk S Revealed Preference and he Uly Funcon. Economca, 17(66): Huang, J., and S. Rozelle Marke Developmen and Food Demand n Rural Chna. Chna Economc Revew, 9(1): Lews, P., and N. Andrews Household Demand n Chna. Appled Economcs, 21(6): Moschn, G Uns of Measuremen and he Sone Index n Demand Sysem Esmaon. Amer. J. Agr. Econ. 77 (1): Moschn, G., and K. Melke Modelng he Paern of Srucural Change n U.S. Mea Demand. Amer. J. Agr. Econ., 71(2): Moschn, G., and D. Moro Srucural Change and Demand Analyss: A Cursory Revew. European Revew of Agrculural Economcs, 23: Moschn, G., D. Moro, and R. Green Mananng and Tesng Separably n Demand Sysems. Amer. J. Agr. Econ., 76(1): Ncol, C The Effec of Expendure Aggregaon on Hypohess Tess n Consumer Demand Sysems. In. Econ. Rev., 32(May): Ohan, K., and S. Kaayama A Gradual Swchng Regresson Model wh Auocorrelaed Errors. Econ. Leers, 21: Sakong, Yong and Dermo J. Hayes Tesng he Sably of Preferences: A Nonparamerc Approach. Amercan Journal of Agrculural Economcs, 75(2): Samuelson,, Paul A Consumpon Theory n Terms of Revealed Preference. Economca, 15(60): Tuan, Francs C. and Bngsheng Ke A Revew of Chna s Agrculural Polcy: Pas and Presen Developmens. In Agrculure n Chna and OECD Counres: Pas Polces and Fuure Challenges. Organzaon for Economc Co operaon and Developmen, Pars, France. Varan, Hal R The Nonparamerc Approach o Demand Analyss. Economerca, 50(4): Non-Paramerc Tess of Consumer Behavour. Revew of Economc Sudes, 50(1):

25 Wang, Q., F. Fuller, D. Hayes, and C. Halbrend. July Chnese Consumer Demand for Anmal Producs and Implcaons for U.S. Pork and Poulry Expors. Journal of Agrculural and Appled Economcs, 30(1): Wang, Z., and W. Chern Effecs of Raonng on he Consumpon Behavor of Chnese Urban Households durng Journal of Comparave Economcs, 16 (1): Wu, Y., E. L, and S. Samuel Food Consumpon n Urban Chna: an Emprcal Analyss. Appled Economcs, 27(6): Wu, Y., and H. Wu Household Gran Consumpon n Chna: Effecs of Income, Prce and Urbanzaon. Asan Economc Journal 11(3):

26 Table 1.Maxmum Lkelhood Srucural Change Pons Dynamc AIDS Model Roerdam Model Seven GroupCommodes (1990, 1993) (1992, 1994) Fve Commody groups (1984, 1987) (1993, 1994) -Addonal Pons [(84, 85, 86), (87, 88,93, 94)]* (1986, 1987) [(82, 83, 88, 91, 92), (93,94)]* *The numbers n he frs parenhess are possble values for 1, and he numbers n he second parenhess are possble values for 2. These combnaons are srucural change pons ha canno be reeced. ndcaes he possble srucural change pons canno be reeced a sgnfcance level. For AIDS model, (88, 94) canno be reeced a level; all oher canno be reeced a 0.05 sgnfcance level. Table 2. Lkelhood Raos for Srucural Change Tess for AIDS and Roerdam Models wh Seven/Fve Commody groups Hypohess Resrcons Lkelhood Rao AIDS Model No Srucural Change n: -all parameers -Seven group Fve group nercep parameers -Seven group Fve group prce parameers -Seven group Fve group expendure parameers -Seven group Fve group Roerdam Model No Srucural Change n: -all parameers -Seven group Fve group prce parameers -Seven group Fve group * expendure parameers -Seven group Fve group * ndcaes canno be reeced a 0.05 sgnfcance level

27 Table 3. Average Marshallan Elasces for AIDS Model wh 7 Commody groups Gran Mea Egg Fsh Vegeable Fru Before Srucural Change Oher Foods Expendure Gran Mea Egg Fsh Vegeable Fru Oher Foods Afer Srucural Change Gran Mea Egg Fsh Vegeable Fru Oher Foods *srucural change pon s (1990, 1993). Table 4. Average Marshallan Elasces for AIDS Model wh 5 Commody groups Gran Mea/Egg Fsh Vegeable/Fru Oher Foods Expendure Before Srucural Change Gran Mea/Egg Fsh Veg/Fru Oher Foods Afer Srucural Change Gran Mea/Egg Fsh Veg/Fru Oher Foods *srucural change pon s (1991,1993). 26

28 Table 5. Bas of Srucural Change from AIDS Model Commody Seven Groups Bas Sandard Error Mean Share Before Srucural Change Gran Mea Egg Fsh Vegeable Fru Oher Foods* Fve Groups Gran Mea/Egg Fsh Veg/Fru Oher Foods *bas of oher foods s recovered from he oher groups and we dd no calculae he sandard errors. For seven groups, he srucural change pon s (1990, 1993); and for fve groups he srucural change pon s (1991,1993). 27

29 Table 6. Sze-Correced Lkelhood Rao Tess of Separably wh Seven and Fve Commody groups Commody separable from ohers Sze-correced LR AIDS model Roerdam model Seven Commody Groups Gran Mea Egg Fsh Vegeables Fru Oher foods Mea/egg Vegeables/fru Number of resrcons Fve Commody Groups Gran Mea Fsh * Vegeables Oher foods Number of resrcons * ndcaes canno be reeced a level. Table 7. Expendure Elascy Bounds by Food Group Food Group Lower Bound Upper Bound Food Group Lower Bound Upper Bound Pork Gran Beef Vegeables Poulry Fru Eggs Mlk Fsh Oher Mea Fru & Veg Mea & Eggs Mlk & Oher

30 KG/Person Gran Pork Beef Poulry Eggs Fsh Vegeables Fru Dary Oher Fgure 1. Urban Consumpon Cumulave Tase Changes: 10 Food Groups KG/Person Gran Eggs Fsh Vegeables Fru Mea Oher Fgure 2. Urban Consumpon Cumulave Tase Changes: 7 Food Groups 29

31 KG/Person Gran Fsh Oher Mea&Egg Veg&Fru Fgure 3. Urban Consumpon Cumulave Tase Changes: 5 Food Groups Table 8. Resuls from Nonparamerc Separably Tess Separable Commody/Group Tes of Condon 1 Tes of Condon 3 Asymmerc Separably Gran Pass Fal (5 volaons) Pork Pass Fal (12 volaons) Beef Pass Fal (1 volaon) Poulry Fal (1 volaon) Fal (1 volaon) Eggs Fal (1 volaon) Pass Fsh Pass Pass Vegeables Pass Fal (4 volaons) Frus Pass Fal (2 volaons) Mlk Pass Pass Oher Foods Fal (1 volaon) Pass Separable Groups Mea Pass Fal (1 volaon) Mea & Eggs Pass Pass Frus & Vegeables Pass Fal (1 volaon) Mlk & Oher Pass Fal (11 volaons) 30