Estimating Food Demand in Rural China. Under the Perspectives of Agricultural Household Models

Transcription

1 Estmatng Food Demand n Rural Chna Under the Persectves of Agrcultural Household Models Wenye Yan and Wen S. Chern Deartment of Agrcultural, Envronmental, Develoment Economcs The Oho State Unversty yan.42@osu.edu, chern.@osu.edu Selected Paer reared for resentaton at the Amercan Agrcultural Economcs Assocaton Annual Meetng, Provdence, Rhode Island, July 24-27, 2005 Coyrght 2005 by Wenye Yan and Wen S. Chern. All rghts reserved. Readers may make verbatm coes of ths document for non-commercal uroses by any means, rovded that ths coyrght notce aears on such coes.

2 Abstract We resent n ths study an agrcultural household model that descrbes the ont roducton-consumton decson makng of Chnese rural households under merfect market. We conclude that the margnal value of a food roduct consumed s the sale rce f there s a net sale for ths food tem; t s the urchase rce f there s a net urchase; and t s the shadow rce f there s no urchase or sale. A relmnary emrcal food estmaton analyss confrms that t rovdes sueror demand estmates to use these effectve rces rather than tradtonally used urchase rces or weghted average of sale and urchase rces n rural food demand analyss n less develoed countres (LDCs).

3 Introducton Ths study amed at ganng a credble knowledge of food consumton behavor n rural Chna, by estmatng a comlete demand system, n a way consstent wth the mcroeconomc behavor of a Chnese agrcultural household not only as a food consumer, but also as a food roducer, under merfect market stuatons. Our study focuses on food roducts snce they have been the center of all economc actvtes n most of the rural Chna. Rural households allocate a large orton of ther resources for food roducton, so as to guarantee ncome sources for consumton, be t on food or on other commodtes and servces. Ths s esecally true for farmers wth lmted off-farm work oortuntes. The rural households n Helongang Provnce, for examle, allocate about 39.0% of ther total cash exendtures n agrcultural roducton uroses and gan about 70.3% of ther cash ncomes from the sales of farm and lvestock roducts n 200. For these farmers, when we deal wth ther ont food consumton-roducton behavor n an agrcultural household model, we cover most of ther economc actvtes. Much more effectve welfare and olcy analyss can result from ths study. In ths study, we model rural food demand under the ersectve of agrcultural household models, n order to take nto account how consumton decson s affected by roducton decson and market stuatons. The nfluence of roducton decson on consumton s catured through the roft effect (Sngh and Strauss 986). As a food roducer, an agrcultural household may suly art of the food consumed from ts own roducton (self-suffcency). When the rce of a food tem ncreases, a rural household 2

4 wll roduce more of the food roduct to obtan more ncome. As far as consumton s concerned, the ncreased rce may ncrease the consumton of the exact same food tem due to ncreased ncome from roft. Thus a ostve own rce resonse of consumton may result, whch should never haen n the tradtonal demand theory. In the emrcal estmaton of demand characterstcs (usually reresented by a set of arameters n a comlete demand system) of rural households, a based and nconsstent estmaton wll result when ths ont roducton-consumton decson s gnored. And the tycal ndcaton of a based estmaton s often reflected n a ostve own rce elastcty (For examle, Halbrendt, Tuan, Gemesaw and Dolketz 994). Market stuatons also affect the consumton decson of an agrcultural household. Hgh transacton costs, due to low nfrastructure and relatvely lttle market develoment n most less-develoed countres (LDCs), usually ncrease the costs of acqurng and sellng food roducts and make self-suffcency of food consumton more attractve. Prevous rural food demand studes n Chna mostly gnored the ont consumton-roducton decson-makng under varous market stuatons and drectly estmated a food demand system (Fan, Wles and Cramer 994, 995; Gao, Wales and Cramer 996; Halbrendt, Tuan, Gemesaw and Dolketz 994; Huang and Davd 993, 998; Lews and Andrews 989; Ton and Wahl 998; Wang, Fuller, Hayes and Halbrendt 998). The legtmacy and accuracy of ths relatvely smle aroach are under queston snce t s based on the mcroeconomc model of utlty maxmzaton gven fxed rces and ncome. Ths assumton s no longer arorate here snce 3

5 ratonal rural households constantly adust ther food roducton and thus ncomes accordng to market rces, and n some occasons, even rces mght not be exogenous. We resent n ths study an agrcultural household model that descrbes the ont roducton-consumton decson makng of Chnese rural households under merfect markets wth transacton costs. We conclude that the margnal value of a food tem consumed s the sale rce f there s a net sale for ths food tem; t s the urchase rce f there s a net urchase; and t s the shadow rce f there s no urchase or sale. A Quadratc Almost Ideal Demand System (QAIDS) s used to comare demand estmatons under tradtonal aroaches and a smlfed aroach derved from the agrcultural household model. The demand estmaton under the ersectve of an agrcultural household model shows sgnfcant mrovement. Future agenda for further mrovement n estmaton s also addressed n ths aer. An Agrcultural Household Model for Chnese Rural Households Agrcultural household models have been used to address a varety of ssues n the LDCs, such as agrcultural rce olcy (Yotooulos and Lau 974), labor suly (Goodwn and Holt 2002), food demand and nutrton (Strauss 984), envronmental ssues (Vandusen 2000), mgraton (debrauw, Taylor and Rozelle 2002) and many more. Also, the alcatons of the agrcultural household models are not restrcted to less develoed countres (LDCs) only. Offutt (2002), Admnstrator of the Economc Research Servce, U.S. Deartment of Agrculture, onts out the mortance of alyng agrcultural household models n the future farm olcy analyss, snce off-farm ncome 4

6 has become a maor source of ncome for farmers n the Unted States and they can no longer be treated only as a roducer. Concetualzaton of Alternatve Scenaros Wthout loss of generalty, we assume that an agrcultural household roduces and consumes two food tems only, gran (good ) and vegetables (good 2), wth gven endowment such as land. The obectve of ths agrcultural household s to maxmze ts utlty. There are three scenaros that can be constructed for ths model. The frst two are adoted from Taylor and Adelman (2003). Scenaro : Mssng market Fgure llustrates the extreme case of no markets for ether gran or vegetables. The household roduces a certan bundle of vegetables and gran. Constrant n the technology s llustrated by the roducton ossblty fronter ( PPF ). Under ths scenaro, the agrcultural household consumes all of ts own-roduced roducts. Thus, ts otmal choce of roducton and consumton should be at the ont E, where the margnal rate of substtuton s equal to the margnal rage of transformaton ( MRS = MRT = ). Although unobservable, the absolute value of the sloe for the / 2 tangent lne s ust the relatve shadow rces for gran and vegetables. Scenaro s of lttle nterest n terms of olcy mlcatons. Snce the markets are mssng, the agrcultural household wll always stck to the autarky and thus few olces can hel mrove ts welfare, excet a drect subsdy of gran or vegetables or constructon of nfrastructures to hel develo markets. 5

7 Vegetables PPF E U / 2 O Fgure : Agrcultural Household Behavor wth Mssng Market Gran Scenaro 2: Perfect Market Suose market exsts for both vegetables and gran and the market s erfect n the sense that there are no transacton costs. Suose the exogenously determned relatve rce for gran and vegetables s / 2. Wth the erfect market, the agrcultural household can make decsons on roducton and consumton searately. It frst maxmzes ts roft (ts only ncome source n ths case). The roft maxmzaton ont s A n Fgure 2, where the margnal rate of transformaton s equal to the relatve rce ( MRT = ). Wth attanable ncome assocated wth maxmzng outut choce of / 2 A, the agrcultural household then trades the roducts to attan a bundle of consumton 6

8 of E, whch yelds maxmum utlty. Comared to the autarky, the exstence of the market benefts the agrcultural household. Vegetables ' / ' 2 / 2 PPF B U U 2 > U 2 A E 2 E O Gran Fgure 2: Imact of an Increase n Vegetable Prce wth a Perfect Market Now we are nterested n what may haen f the relatve rce of vegetables ncreases (.e. / ' < / ). Frst the agrcultural household would change ts ' 2 2 roducton lan to B, roducng more of vegetables snce vegetable rce ncreases. Wth the new budget constrant assocated wth the roft attanable at ont B, the household can trade vegetables for gran to attan the consumton bundle at ont E 2. Notce that at E 2, the consumton of vegetables ncreases from the level at E even though vegetable rce has ncreased. Thus we have a ostve correlaton between rce and consumton for vegetables. Ths wll never haen n the tradtonal demand model, where 7

9 households are treated as consumers only and thus there s always a negatve relatonsh between the consumton of a commodty and ts rce. Emrcally, we can use ths searablty of roducton and consumton decson under erfect markets for the ease of demand. The rocedure s smle. We frst treat the sum of exogenous ncomes and the maxmzed level of roft from food roducton as the fxed ncome, and then use ths ncome and rces of all commodtes consumed to estmate a sngle demand functon or a comlete demand system. After estmaton of the demand, we may be nterested n rce olcy analyss. In ths case we cannot leave the roducton decson out of the cture. Frst we need to redct how roducton lan and rofts may react to rce changes. Then wth the udated changes n roft (and thus those n ncome) and the udated rces, we can then use the estmated demand functon to redct the future food demand under new rces. Predcton of food roduct suly can be conducted by calculatng the dfference between redcted roducton and redcted consumton. Scenaro 3: Imerfect Market wth Transacton Cost Scenaro 3 deals wth an merfect market common n the LDCs, ncludng Chna. One common cause of market merfecton s the exstence of transacton costs. For the same food roduct, a household tycally sells t for a lower rce than the rce at whch he can urchase n the market. Suose the urchase rce for gran s and the sale rce for gran s s < ; suose the urchase rce for vegetables s 2 and the sale rce for vegetables s s 2 < 2. The bundles of gran and vegetables avalable for consumton (after self roducton and trade) are n the curve DBAC as llustrated n Fgure 3. 8

10 Vegetables D s / 2 PPF B A O / s 2 Fgure 3: Budget Constrant n a Market wth Transacton Costs C Gran Let A and B be the tangent onts of two rce lnes on the PPF as shown n Fgure 3. The agrcultural household chooses to roduce at onts A or B or any onts on curve AB along the PPF. When the household roduces at ont A, t can acqure addtonal gran from the market by tradng vegetables for gran (t can acqure more gran from roducton too, but that s more costly snce the shadow rce of roducton wll be no less than the market rce). The effectve urchase rce for gran n relatve term s / s 2. Thus any ont on lne AC s attanable for the agrcultural household. When the agrcultural household roduces at ont B, on the other hand, t can acqure more vegetables from the market by sellng gran. The effectve sale rce for gran n 9

11 relatve term s s / 2. The effectve urchase rce s always hgher than effectve sale rce / s2 > s / 2. When the agrcultural household chooses to roduce at a ont on the curve AB along the PPF, there s no ncentve to trade, snce the shadow rce n relatve term for gran (the absolute value of the sloe for the tangent lne) s between the effectve sale rce and urchase rce. A loss wll always occur wth trade under ths roducton lan. In summary, the curve DBAC reresents the set of best attanable bundle of gran and vegetables under the technology and the market wth transacton cost. Thus, t s the budget constrant for the agrcultural household. Wth ths budget constrant n mnd, we have a clear cture of utlty maxmzaton for the agrculture household (Fgure 4). Vegetables D s / 2 U 3 E 3 PPF B U 2 E 2 A U O / s 2 Gran Fgure 4: Agrcultural Household Behavor n a Market wth Transacton Costs E C 0

12 Deendng on the reference of the agrcultural household, there are three dfferent cases of roducton and consumton ont decson: () Wth utlty secfed asu, the agrcultural household chooses the roducton lan at ont A. It then trades vegetables for gran to attan the utlty maxmzaton bundle of consumton at E. The vegetables consumton s comletely self-suffcent. In ths case, the gran consumton s artally selfsuffcent. The effectve relatve market rce under ths scenaro s / s 2 because there s a net sale of vegetables and a net urchase of gran. In the emrcal demand estmaton, we can use the budget gven as lne AC. Only the sale rce of vegetables and the urchase rce of gran are relevant for demand estmaton. (2) Wth utlty secfed asu 2, the agrcultural household chooses the roducton lan at ont E 2. Ths also haens to be the utlty maxmzaton choce of consumton. There s no ncentve to trade snce the shadow rce s between effectve sale and effectve urchase rce. Both gran and vegetable consumtons are comletely self-suffcent. For the emrcal estmaton of demand, we need to solve for reference characterstcs and roducton characterstcs together under the frameworks of general equlbrum, usng the frst order condton that the negatve of shadow rces (n relatve term) are equal to both MRS and MRT. (3) Wth utlty secfed asu 3, the agrcultural household chooses the roducton lan at ont B. It then trades gran for vegetables to attan the utlty

13 maxmzaton bundle of consumton E 3. The gran consumton s comletely self-suffcent, and the vegetable consumton s artally selfsuffcent. The effectve relatve market rce under ths scenaro s s / 2 because there s a net urchase of vegetables and a net sale of gran. In the emrcal demand estmaton, we can use the budget gven by BD. Only the sale rce of gran and the urchase rce of vegetables are relevant for demand estmaton. Ths model can be easly generalzed to the case of multle food roducts. The bottom lne s: n emrcal estmaton, we should use sale rce for a food roduct wth net sale; we should use urchase rce for a food roduct wth net urchase; and for the food roducts wthout any trade (comletely self-suffcent), we need to estmate ts shadows rce and aly the shadow rce n estmaton. The formal roof wll be rovded n mathematcal model that follows. A Model for Chnese Rural Households Wthout consderng the lesure-labor choce, an agrcultural household model s develoed below to cature the ont roducton-consumton decsons of a Chnese rural household. Ths model s secfed to cature the essental on roductonconsumton decsons for the estmaton of food demand. A general agrcultural household model can be found n Sadoulet and de Janvry (995). Let X ( =,2,, N ) be the th commodty consumed, wth ts corresondent urchase rce. Esecally let X be food roducts when =,2,, F, where F < N. The agrcultural household can choose only food roducts to roduce and sell. And let the sale rce be not larger than the urchase rce ( s ) due to merfect market. For 2

14 convenence, we may wrte the comlete consumton bundle as X. Let G( Q, v, K) = 0 descrbes the roducton technology for the agrcultural household, where Q = Q, Q,, Q ) s a set of oututs of food roducts, v = v, v,, v ) s a set of ( 2 F ( 2 I requred nuts wth q = q, q,, q ) as ts set of market rces, and K reresents land ( 2 I and catal stock. Wth gven exogenous ncome E, utlty functon secfed as U( X, X 2,, X N ), technology secfed as G( Q, v, K) = 0, and the market rces, the agrcultural household chooses a ont roducton-consumton scheme, ncludng the amount of food roducts to sell ( S = S, S,, S ) ) or to urchase ( P = P, P,, P ) ), to maxmze ts utlty: ( 2 F ( 2 F MAX Q, v, S, P, X U( X, X 2,, X N ), () subect to the followng constrants: N F, (2) F N F P + X = ( sk Sk qlvl ) + E (3) = = F + k = l= I X X s > 0 for all =,2,, F, (4) = Q + P S 0 for all =,2,, F, (5) 0 for all = F +, F + 2,, N, (6) P 0, for all =,2,, F, (7) S 0, for all =,2,, F, (8) and G( Q, v, K) = 0, (9) Equaton (2) says that the total number of commodtes (ncludng food roducts) s larger than the total number of food roducts, whch s obvous. 3

15 Equaton (3) s the cash budget constrant. We assume that the agrcultural household roduces food roducts only. The food tems consumed come from ether urchase or self-roducton whle the non-food commodtes consumed come from urchase only. The urchases for all these commodtes are suorted by the cash ncome, the sum of roft from sales of food roducts, ( sk Sk qlvl ), and exogenous ncome F k= l= E, such as roerty ncome or transfer ncome. Equaton (4) says that urchase rce s usually hgher than, f not equal to, the sale rce for the same food roduct, due to transacton costs. The sale rce could not be hgher than the urchase rce for the same food roducts. Otherwse, arbtrage wll occur. Equaton (5) s the balance equaton for the food roducts. The agrcultural household acqures food roducts from roducton Q or urchase P, and t uses them on consumton X or sale S. In the real world, however, rural households n Chna stock food roducts, esecally gran, ether for future consumton, or for seedng for next season. Storage and seedng usage are gnored n our model to avod the need of constructng a comlcated nter-temoral utlty maxmzaton roblem. Also, some food roducts may be acqured n ways other than roducton or urchase; and they may be used for other uroses than sale. For examle, frut s commonly used as a gft n Chna and a art of gran s used as feed. All these are gnored for smlcty. Another set of constrants s non-negatvty for the amounts of commodtes consumed, urchased or sold for any food roduct. Ths s catured n equatons (5), (6), (7), (8). Equaton (9) s the technology constrant for roducton, wth K reresentng land and other catal goods, under the assumton of no labor constrant. I 4

16 The Lagrangean functon for ths otmzaton roblem s as the followng: L = U( X + F =, X 2 γ ( Q,, X ) + µ ( k k k= l= q v + P S X ) + θg( Q, v, K) N F s S I l l + E F P N = = F + X ) (0) Frst, notce that snce > s for all =,2,, F, we wll have ether P = 0 or S = 0 for all =,2, F. Snce urchase rce s greater than sale rce, there s, no reason for urchase and sale of the same tem at the same tme snce ths means a loss of money. In the real world stuaton, however, a rural household may sell and also urchase the same roduct wthn the same erod. For examle, we see many households who sell and also urchase vegetables wthn the same year. One ossble exlanaton s that the vegetables sold and those urchased are not of the same knds. In ths case, there s an ssue of heterogenety n roducts whch s not handled n ths study. Another ossble exlanaton s seasonal consumton smoothng. Durng the roducton seasons, rural households may roduce more vegetables than they can consume and thus would sell the extra. In other seasons durng the same year, they may be short of self-roduced vegetables and need to urchase them for consumton. In our model, we wll gnore all these factors, and concentrate on the net sale amount (or the net urchase amount). where Frst order condtons for utlty maxmzaton yeld: L / X = U / γ = 0 () X µ s f S > 0 and P = 0 wth γ = µ f P > 0 and S = 0, for m =,2,, F (2) * θ G / Q = µ f S = P = 0 * s a convenent notaton for the shadow rce of th food roduct. 5

17 L / X = U / X µ = 0, for all = F +, F + 2, N (3), For non-food commodtes, the frst order condtons are famlar the margnal rate of substtuton (MRS) s equal to the rce rato: U / X U / X k = k for, k { F +, F + 2,, N}, (4) snce U / X = µ, U / X = µ for, { F +, F + 2,, N}. k k For a food roduct {,2,, F}, there are three ossble stuatons: () If there s net sale for ths roduct, U / X = µ s, and thus the MRS s U / X U / X = s for { F +, F + 2,, N}. (5) Let e be the effectve rce for the consumton of food tem. Wth a net e sale for a food roduct, the sale rce serves as the effectve rce ( = s ). From the margnal ont of vew, the agrcultural household chooses ether to sell one extra unt or kee ths extra unt of food roduct for consumton. Therefore the effectve rce for the consumton of ths food tem s the sale rce. (2) If there s net urchase for ths roduct, U / X = µ, and thus the MRS s U / X U / X = for { F +, F + 2,, N}. (6) e In ths case, the urchase rce serves as the effectve rce ( = ). From the margnal ont of vew, the consumton of one extra unt of ths food roduct comes only from urchase. Therefore the effectve rce for the consumton of ths food tem s the urchase rce. 6

18 (3) If there s no trade for ths roduct, U µ * / X =, and thus the MRS s U / X U / X = * for { F +, F + 2,, N}, (7) where * s the shadow rce for ths food roducts whch satsfes / * γ θ G Q * = = = µ µ ( s,, q, K, E) and s < * <. (8) e In ths case the shadow rce serves as the effectve rce ( = * ). Shadow rces can be solved accordng to the set of ont equaton system as (7) and (8). For the non-food commodtes, the effectve rces for ther consumton are ust the urchase rces. For convenence, we can defne the set of effectve rces for e e e e consumton as,,,,,,, ) : = ( 2 F F + F + 2 N where s f S > 0 (for food roduct wth net sale) = f P > 0 (for food roduct wth net Purchase), =,2, F * f S = P = 0 (for food roduct wthout trade) e, (9) Notce that the effectve rce s not exogenous. An agrcultural household chooses an otmzng roducton, sale, urchase and consumton scheme, whch n turn determnes the effectve rce vector. The utlty maxmzng choce of consumton bundle for the utlty maxmzaton roblem descrbed n equatons ()~(9) can be wrtten as: * * X = X (, s, q, K, E). (20) 7

19 It s decded by the agrcultural household s utlty and roducton characterstcs and exogenous factors, ncludng rces, catal stock and exogenous ncome. For convenence, the mled full ncome can be wrtten as: Y * e * = P ' X (, s, q, K, E). (2) Ths s the value of consumton of all the commodtes by the agrcultural household. For emrcal demand estmaton, notce that gven the same utlty functon as U, gven the vector of rces for the commodtes as P e, and gven the full ncome Y * e * = P ' X (, s, q, K, E) as the budget, a consumer (and here we consder hm as a consumer only, not an agrcultural household who needs to deal wth roducton and * * lesure-labor choce) wll choose exactly X = X (, s, q, K, E) as hs utlty maxmzaton choce of consumton bundle snce U X X = X * e = µp. Therefore, when we have data that gve us the consumton bundle choce and effectve rce, we are able to recover the (ndrect) utlty functon. The clam n the scenaro 3 of the grahc resentaton of the agrcultural household model for Chnese rural households (llustrated n fgure 3 and 4) s thus roved to be legtmate. Prelmnary Analyss of Rural Food Demand We conclude n the theoretcal model that t s crucally mortant to fnd the rght rce of consumton n food demand estmaton. Ths aer also resents our relmnary econometrc results for food demand estmaton. Our demand system ncludes eght food grous: () gran, (2) ol, (3) vegetables, (4) ork, (5) oultry, (6) eggs and egg roducts, (7) aquatc roducts, and (8) fruts. Tradtonal aroaches of 8

20 constructng rces and a new aroach, stll smle but more close to the srt of agrcultural household models resented n ths aer, are comared n demand estmaton. Table : Self-suffcency of Maor Food Products (%) Jangsu Helongang Henan Gran Ol Vegetables Bean and Bean Products Pork Poultry Eggs Aquatc Products Frut Source: Rural Household Survey, unublshed data. The data emloyed n ths relmnary analyss s from the rural household survey (RHS) for Henan Provnce n 995, wth a samle of 4200 households. Evdence of ont roducton-consumton decson can be found n the hgh self-suffcency rates for many food tems n three rovnces of Jangsu, Helongang and Henan (Table ). The demand system used n our analyss s the Quadratc Almost Ideal Demand System (QAIDS) ncororatng demograhc varables by lnear translatng. It has the followng functonal form: w = + x λ x α γ log + ( β ) log( ) + ln A( ) B( ) ( ) A, (22) 2 where log A( ) = α0 + α ln γ ln ln. (23) λ B( ) =. (24) 9

21 Wth ths demand system, we ncororate the followng demograhc varables: SIZE : household sze, A GE: number of chldren wth age below n the household, AGE 27 : number of ersons wth age2 ~ 7 n the household, EDUC : number of ersons wth at least hgh school graduaton, FAFH : total exendture on food away from home. Demograhc varables are ncororated by lnear translatng,.e. smly relacngα wth α + αsize + α2 AGE + α3age27 + α4educ + α5fafh n the demand equaton (22). Slutsky symmetry, lnear homogenety and addng-u condton requres: 8 = 8 = 8 = 8 = α =, (25) α = 0, for k =,2,,5 (26) k β = 0 (27) λ = 0 (28) The homogenety condton can be exressed as: 8 = γ = 0, for =,2,,8 (29) The symmetry condton requres: γ = γ, for any, =,2,,8 (30) 20

22 The method of seemngly unrelated regresson (SUR) s used n the estmaton of arameters n the system wth homogenety and symmetrc condtons mosed. The addng-u restrctons are automatcally satsfed n ths system of budget share equatons. Three aroaches of demand estmaton are comared n the analyss. They dffer only n ways of constructng food rces for consumton. The frst aroach uses the urchase rce, derved from the rato of total exendture to the total urchase quantty for a food tem. Examles for ths aroach are the studes by Halbrendt, Tuan, Gemesaw and Dolketz (994), and Tong, Han and Tomas I. Wahl. (998). The second aroach uses the weghted average of urchase rce and sale rce: Sale Prce Self Suffcency Amount + Purchase Prce Amount urchased Total Amount of Consumton (3) It takes nto account that wth self-suffcency, the unt value of food consumed mght not necessarly be the urchase rce, and that the sale rce, as art of the roducton sde nformaton, should be ncororated. An examle for the second aroach s Gao, Wales and Cramer (996). The last aroach s roosed n ths study usng the agrcultural household model wth some modfcaton. For ths relmnary study, we wll not ncororate shadow rces nto estmaton due to the extreme comlcacy n ther comutaton. Rather, we use county level average urchase rces for the food tems wthout trade; we use householdlevel urchase rces for food tems wth net urchase; and we use household-level sale rces for food tems wth net sale. There are outlyng rces from the RHS data. For examle, the sale rces of some foods for some households maybe more than ten tmes that of county average rce. We relace these outlyng rces wth county level averages 2

23 also. The descrtve statstcs of the rces constructed n three dfferent aroaches are resented n Aendx Table A. Table 2 resents estmated exendture and own-rce elastctes from the three aroaches. Let us summarze the results of comarng these three aroaches. We frst note that tradtonal aroaches ( and 2) of rce constructon do not roduce entrely satsfactory own-rce elastctes estmates. We fnd ostve own rce elastcty n the demand for oultry n aroach and ostve own rce elastcty n the demand for vegetables n aroach 2. These are sgns of roducton decson nterferng. The new aroach (aroach 3) of constructng rce results n better and more satsfactory arameter and elastcty estmates. Table 2: Estmated Demand Elastctes Aroach Aroach 2 Aroach 3 Food Item Exendture Elastctes Own-rce Elastctes Exendture Elastctes Own-rce Elastctes Exendture Elastctes Own-rce Elastctes Gran Ol Vegetables Pork Poultry Eggs Aquatc Products Fruts The estmators from the new aroach are much more robust. It s hghly nsenstve to outlyng rces. The estmators from tradtonal aroaches, however, are hghly senstve to outlers. The estmated own-rce elastctes can change by a large magntude. And wth outlers, the roblem of ostve own-rce elastctes s more rofound. 22

24 We note that the relatve magntudes of the estmated exendture elastctes for several food tems are not exected. In artcular, we are troubled by the very hgh exendture elastctes for gran and vegetables, close to unty. Ths could also be an ndcaton that we do not get rd of roducton nteracton comletely, snce ncrease n ncome may nduce rural households to sell less of gran or vegetables for cash. As a second verson, we also ncororate the self-suffcent rates for each food tem consumed nto the model, by means of lnear translatng. Ths s ust to relace 8 α wth α + αsize + α2 AGE + α3age27 + α4educ + α5fafh + k= δ SS k k, where SS s the self-suffcency rate of the th food roducts. The estmated exendture and rce elastctes are resented n Table 3. Interestngly, we do not fnd ostve own-rce elastctes by urchase rce aroach any more, but ths erssts when weghted average rces are used. The results of the aroach 3, verson 2 ncororatng self-suffcency rates are not much dfferent form those of the new aroach wthout ncororatng self-suffcency. Ths s an ndcaton that the new aroach has taken care of much roducton sde nformaton (through sale rces), whle the tradtonal aroaches have not. Table 3: Estmated Demand Elastctes, Verson 2 Aroach Aroach 2 Aroach 3 Food Item Exendture Elastctes Own-rce Elastctes Exendture Elastctes Own-rce Elastctes Exendture Elastctes Own-rce Elastctes Gran Ol Vegetables Pork Poultry Eggs Aquatc Products Fruts

25 Table 4 llustrates how mortant t s to ncororate self-suffcency rates nto the demand system. Regardless of the aroaches, all coeffcents of self-suffcency rate for the own roduct are shown to be sgnfcant. Ths ndcates that ts ncluson surely hels account for some of the roducton sde comlcaton n estmaton from all three aroaches. We fnd all coeffcents for self-suffcency ostve, ndcatng that a hgher self-suffcency of a roduct wll nduce the rural household to consume more of the same roduct. These results are, of course, reasonable. The estmated coeffcents for aroach 3 are also sgnfcant, robably due to the nablty to comute and adot the shadow rces for households wthout trade. However, the estmated elastctes show no much dfference wth or wthout ncororatng selfsuffcency Table 4: Gran Ol Vegetables Pork Poultry Eggs and Egg Products Aquatc Products Frut Estmated Coeffcents for Self-suffcency Rates Aroach Aroach 2 Aroach 3 Coeffcent (t-rato) Coeffcent(t-rato) Coeffcent(t-rato) (22.02) (35.44) (33.90) (20.6) (29.28) (9.62) (2.29) N/A (22.3) (35.53) (32.93) (20.66) (29.64) (9.34) (2.44) N/A (22.4) (35.32) (33.97) 0.72 (20.57) (29.37) (20.9) (.90) N/A Although the urchase rce aroach ncororatng self-suffcency roduces somewhat more satsfactory results, ths estmator s stll very senstve to outlers. Only 24

26 after relacng the outlyng rces wth the county average rces, can the estmator yeld results as good as those obtaned from the new aroach. In summary, the new aroach s shown to be referable to the tradtonal aroaches. It s much more robust and t ncororates roducton sde decson by usng sale rces for roducts wth a net sale. 25

27 Concludng Remarks Both theoretcal analyss and the relmnary emrcal estmaton conclude that the use of effectve rces nstead of tradtonally used urchase rces (or the weghted averages of sale and urchase rces) s most consstent wth the mcroeconomc behavor of Chnese agrcultural households. Secfcally, we should use sale rces when there are net sales and use urchase rces only when there are net urchases. When there s no trade, we should use the shadow rces. In our relmnary emrcal estmaton, we smly use the county-level average of urchase rces as aroxmaton for shadow rces. In the future, we wll further ntroduce roducton nformaton (by secfyng a roft functon or roducton functon) and derve the shadow rces for more consstent food demand estmaton. Another econometrc roblem s to deal wth s the endogenety of the self-suffcency rates used n the estmatons n verson 2. A two-stage estmaton can be used to correct ths roblem. Fnally, the censorsh roblem should be dealt wth for the food roducts wth zero consumton, esecally when some food categores such as beef and fresh mlk are ncororated n the demand system. 26

28 Aendx Table A: Descrtve Statstcs of Prces and Exendture Shares a Varables Aroach Aroach 2 Aroach 3 Mean Mn Max Mean Mn Max Mean Mn Max w w w w w w w w a The eght food grous are: () gran, (2) ol, (3) vegetables, (4) ork, (5) oultry, (6) eggs and egg roducts, (7) aquatc roducts, and (8) frut. For ol, there were no sales. Thus, urchase rces are used for all aroaches. Some households do not trade some food roducts. In ths case the corresondng rces are mssng. Sometmes the rces wll have extreme value. The mssng rces and the uer and lower 5% outlyng rces are relaced by county-level average rces. 27

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