Effects of Model Specification and Demographic Variables on Food. Consumption: Microdata Evidence from Jiangsu, China. The Area of Focus:

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1 Effects of Model Specfcaton and Demographc Varables on Food Consumpton: Mcrodata Evdence from Jangsu, Chna Kang Ernest Lu and Wen S. Chern Department of Agrcultural, Envronmental, and Development Economcs The Oho State Unversty The Area of Focus: Area II Changng Consumer Correspondng Author: Kang Ernest Lu Department of Agrcultural, Envronmental, and Development Economcs The Oho State Unversty 2120 Fyffe Road, Room 227 Columbus, OH E-mal: Telephone: (614) Fax: (614) Paper Presentaton for 11 th Annual World Food and Agrbusness Forum, World Food and Agrbusness Symposum of the Internatonal Food and Agrbusness Management Assocaton to be held n Sydney, Australa, June 27-28, 2001.

2 Effects of Model Specfcaton and Demographc Varables on Food Consumpton: Mcrodata Evdence from Jangsu, Chna Abstract Choosng among functonal forms and specfyng demographc effects are the two major tasks n ths paper. Household data from Jangsu, Chna, s employed by applyng the Workng-Leser form, the LES, QES, and LA/AIDS. Eght demographc varables ndcatng modernzaton, regon, householder, and household composte are ncorporated as well. The results show that the Workng-Leser and LA/AIDS provde smlar results, and the LES and QES are qute the same due to nestng. However, the performance of the LA/AIDS and LES are dfferent. In addton, demographc varables mprove the performance of the selected model. Key words: food consumpton, demographc translatng, Urban Chna, demand analyss 2

3 Effects of Model Specfcaton and Demographc Varables on Food Consumpton: Mcrodata Evdence from Jangsu, Chna 1 I. Introducton Chna s a huge market wth 1.2 bllon people and thus has attracted much attenton n the global economy. Almost every country n the world wants to develop an economc te wth Chna. Chna s market structure has changed dramatcally after ts economc reforms n These socoeconomc changes not only mproved the lvng standards and welfare among the Chnese people but also provded trade opportuntes for other countres. In order to take the best advantage of ths huge market, t s crucal to nvestgate the mportant factors whch affect the consumpton patterns of Chnese nhabtants. Jangsu s not only a good representatve of the Chnese culture but also a good ndcator to foresee the potental consumpton changes n Chna. Geographcally speakng, t s adjacent to Shangha, the most prosperous cty n Chna. In addton, the Yangtze Rver runs through ts southern part, whch provdes many natural resources for Jangsu provnce. Jangsu s n the mddle of Chna and has a hghly vared populaton. Wth these features, t s mportant to take Jangsu as an example to nvestgate food consumpton patterns n Chna. We studed Jangsu to evaluate the effects of model specfcaton and demographc varables on food consumpton n Chna usng two dstnct approaches. Frst, the demand analyss s based on urban household data n Chna after economc reform. Mcrodata conssts of rch demographc detals and varaton n expendture levels and provdes much valuable nformaton other than prces and ncome. Second, the mpact of demographc varables on alternatve functonal forms s compared n order to nvestgate the nfluence of model specfcaton. Chern (1997) revewed and assessed the lterature on the estmated demand n Chna. The methodologes, estmaton results, and assessments of the recent studes of urban household demand for food, such as Lews and Andrews (1989); Wang and Chern (1992); Chern and Wang (1994); Wu, et al. (1995); Sh, et al. (1995); have already been dscussed. Snce food control polcy was stll legtmate durng the sample perods covered by these studes, most of the studes ncludng Chern (1997) dscussed or ncorporated ratonng n ther emprcal analyses. However, there exsted several problems wth respect to data lmtaton and model specfcatons. Frst, all the prevous studes dd not make best use of the demographc varables. Accordng to the consumpton theory, economc factors such as prces and ncome are not the only determnates. Demographc profles play a crtcal role when consumers make decsons. Therefore, how to ncorporate the demographc varables n the analyss s profound. Second, whch model specfcaton s preferable n analyzng Chnese urban food demand s vague. Even though the AIDS 2 and the LES 3 are the most popular specfcatons for analyzng Chnese consumer behavor, the results showed dfferences between the LA/AIDS 4 and the LES (Chern, 1997). Chern and Wang (1994) presented smlar estmated results n both the LES and the QES. 5 None of the studes, to our knowledge, compare the model specfcaton usng cross-sectonal data. Ths wll be nterestng and mportant. The remander of the paper s organzed as follows. In secton II, we show the model specfcatons and dscuss the treatment of demographc varables. In secton III, we descrbe the data and present descrptve statstcs of the varables under consderaton. In secton IV, we present the emprcal results and dscuss the effects concernng the treatment of demographc varables. In secton V, we provde a bref summary and concluson. II. Theoretcal Framework Under the neoclasscal utlty maxmzaton framework, the quantty demanded can be expressed as a functon of prce and ncome wth regularty condtons- addng-up, homogenety, symmetry, and negatvty. Theoretcally, the model selecton s undetermned. Ths allows great freedom to choose or test n emprcal studes. 1 We thank n depth to Ms. Weland and Mr. Dangler for ther constructve suggestons and comments from a semnar at The Oho State Unversty. 2 The AIDS ndcates the Almost Ideal Demand System developed by Deaton and Muellbauer (1980a). 3 The LES means the lnear expendture system. 4 The LA/AIDS s the lnear approxmated AIDS model to elmnate the complexty n computaton. 5 The QES s an abbrevaton of the quadratc expendture system ntroduced by Pollak and Wales (1978). 3

4 There are two sets of functonal forms n demand analyss. One s sngle equaton, and the other s complete demand system (CDS). In the CDS, t can be dvded nto two subgroups. One s the LES and QES, n whch the regularty condtons have already mposed; the other s called flexble functonal forms such as the AIDS, Rotterdam, and Translog, n whch we can mantan or test the theoretcal propertes. We select the AIDS as an example n ths study. (I) Selecton of Functonal Forms A. The Workng-Leser Form (Sngle Equaton) Sngle equaton s easy to estmate and has less computatonal work than the CDS. However, t s sometmes hard to satsfy the propertes. The Workng (1943)- Leser (1963) form s selected as an example due to ts satsfacton of the addng-up property compared wth the other sngle equatons. The Workng-Leser n share form s expressed as: n = 0 k k L, k = 1 (1) w α + α ln p + β ln X = 1, n, where w means budget share of commodty, p k s the prce of commodty k, and X ndcates the correspondng expendture. Subscrpts of and k ndcate commodtes. a 0,a, and b are the parameters to be estmated. B. The LES and QES Stone (1954) developed the LES and Pollak and Wales (1978) ntroduced the QES. Snce the LES s nested wthn the QES, the LES can be derved from the QES. The QES n budget share form can be expressed as: (2) w = ph µ (, Ρ) c k 2 µ pb pk bk pkbk = µ + a 1 µ + p µ k ( c a ) λ 1 wth a c = 1, where w ndcates the budget share of food, whch s between 0 and 1, p s the prce of = food, h (µ, Ρ) s the Marshallan quantty demand functon for food, and µ s the total expendture. Parameters to be estmated n the QES are a s, b s, c s, and λ. If λ=0 or a = c for all, then the QES s reduced to the LES. C. The AIDS and LA/AIDS Deaton and Muellbauer (1980b) developed a flexble demand system and named the Almost Ideal Demand System (AIDS). Ths demand system has several characterstcs. The AIDS demand functons n budget share form can be expressed as: (3) wth = 1 ( µ, Ρ) ph µ w = = α + γk log pk + β log µ k Ρ α, = γj = γj = 0 ndex (P*) n the orgnal AIDS s gven by β, and j γ j j (4) log Ρ = α 0 + αk log pk + γj log p log p j. If ths prce ndex s replaced by Stone s ndex, log 1 2 Ρ = γ = to satsfy the regularty condtons. The prce w log p k k µ, the AIDS becomes the LA/AIDS, whch reduces the AIDS to a lnear model. The parameters to be estmated n the AIDS are a s, b s, and g s. (II) Incorporaton of Demographc Varables Pollak and Wales (1980, 1981) descrbed four general procedures to ncorporate demographc varables nto demand systems. For demonstraton, ths study employs lnear demographc translatng as an example. Hence, the treatments of demographc effects n these three cases are expressed n (5)-(7), respectvely. 4

5 m 0 = 0 δj j=1 * (5) The Workng-Leser form: α α + d, m = j=1 * (6) The LES and QES: b b + δ d, * (7) The AIDS and LA/AIDS: α α + δ d, j m = j=1 j where d j s are demographc varables and d j s are parameters ntroduced to estmate. To compare the mpact of the demographc translatng to elastctes, for the LES and QES, demographc translatng wll not affect the ncome elastctes, but nfluence prce elastctes. It s nterestng to nvestgate the dfferent consumpton behavor caused by demographc varables. On the other hand, for the AIDS and LA/AIDS, snce demographc varables are not drectly shown n the elastctes, t s dffcult to reflect the demographc effects. (III) Margnal Budget Share (MBS) and Elastctes Margnal budget share ndcates the margnal atttude of the householder to dstrbute hs/her addtonal one-dollar of budget. That shows the relatve mportance of the consumpton tems to the household. The hgher the MBS, the more utlty ganed from that addton amount of food tem. On the other hand, elastctes are another measurement. Once we estmate the parameters, we can compare the MBS as well as prce and expendture elastctes. III. j Data and Descrptve Analyss Urban household data of Jangsu, Chna, collected and released by the Natonal Bureau of Statstcs (NBS) n 1994, s utlzed n ths study. The database conssts of 800 household data and provdes detaled food consumpton and demographc varables. Besdes the quanttes and expendtures, we selected eght mportant demographc varables n our analyss. The varables used n the analyss are lsted n Table 1 wth ther descrptve statstcs. As can be seen, there are sx food tems under consderaton: rce (16), flour (257), pork (3), mlk (271), fresh vegetables (1), and fresh fruts (0). The fgures n parentheses are the number of zero value. For example, flour and mlk have almost 40 per cent of zero consumpton. The demographc varables used n ths paper are expressed as follows: 1. Frdge: Modernzaton ndex: dummy varable of havng refrgerators=1 yes (603 6 ) and =0 no (197); 2. Sze: Household sze (HS) =1-7; 3. Kd: Chldren under age 17 (NOCUA17) =0 (292), =1 (482), and =2 (26); 4. Gender: =1 male (590) and =0 female (210); 5. Age: =0 (378) year-old, =1 (257) year-old, and =2 (165) above 60 year-old; 6. Edu: =0 mddle school or lower (369), =1 hgh school (279), and =2 college and above (152); 7. Regon: =0 north (200) and =1 south (600); and 8. Urban: Urbanzaton: =1 cty (600) and =0 county (200). As mentoned before, the demographc varables may be the crtcal factors to nfluence the consumpton pattern. For example, wll household sze a major factor to nfluence household consumpton n Jangsu? Besdes, calcum ntake s the most serous problem to Chnese nhabtants, would refrgerator be the key pont, or the consumer habt? We would answer these questons later n the emprcal analyss. IV. Emprcal Results and Comparson To estmate the unknown parameters of the selected models, ths study employs the Ordnary Least Square (OLS) and Iteratve Seemngly Unrelated Regresson (ITSUR) procedure for sngle equaton and CDS, respectvely. The 6 Number of observatons of each category s n parentheses. j j 5

6 estmates, both wth and wthout demographc varables, of the Workng-Leser, LA/AIDS, LES, and QES are presented n Tables 2-6, respectvely. Tables 2 and 3 show the parameter estmates of the Workng-Leser form (sngle equaton) wth and wthout demographc effects. As can be seen, most of the parameters are statstcally sgnfcant. However, t s surprsng that the prces of rce and pork are not sgnfcant n the correspondng equatons. In addton, ncome s not sgnfcant factor to rce equaton wthout demographc varables. We mght guess that the ratonng stll nfluenced the consumpton behavor n rce. For flour, the ncome s not sgnfcant, ether. As to the demographc varables, refrgerator and regon have sgnfcant mpact on the performance of the model. For mlk, we can tell that educaton s another mportant factor except refrgerator and regon. The number of chldren under age 17 s nfluental to budget share of pork and fresh vegetables. Surprsngly, household sze has no effect at all. The reason mght due to the multcollnearty to the number of chldren. In our analyss, we suppose that the food consumpton patterns of Jangsu urban household satsfes utlty maxmzaton. Therefore, the addng-up, homogenety, and symmetry propertes are mantaned n the model. Tables 4 and 5 represent the parameter estmates of the LA/AIDS model both wth and wthout demographc varables. As can be seen, more than halves of the parameters are sgnfcant n both cases. Not surprsngly, the parameters of γ 11 (rce) and γ 33 (pork) are nsgnfcant. However, all the betas are sgnfcant from zero. That ndcates the ncome effects are statstcally sgnfcant n the LA/AIDS. Includng the demographc varables, the nfluence of refrgerator s stll obvous except pork. Educaton of householder s another mportant factor to consumpton except rce. Regon dfference of rce and flour s stll sgnfcant. As to mlk consumpton, only refrgerator and educaton varables are sgnfcant. However, household sze s stll not mportant except to pork consumpton n the LA/AIDS. Comparng the LA/AIDS wth the Workng-Leser functonal forms, t s obvous that they are very smlar. For example, the sgns of the rce, flour, and mlk n the Workng-Leser and the LA/AIDS are the same wth lttle dfference n magntude. The functons of pork and fresh vegetables n both models have a few opposte sgns only. The results of the LES and the QES both wth and wthout demographc effects are presented n Table 6. As can be seen, most of the estmates are statstcally sgnfcant. The overall performances are good to the LES and QES. All the sgnfcant parameters a s ndcates that ncome effects are sgnfcant. It s smlar to the LA/AIDS model. It s not clear to tell the prce effect wth the result of parameter estmates. However, λ n the QES wth demographc varables s not sgnfcant ndcates that t s possble to reduce the QES to the LES. The demographc effects n the LES and QES are qute smlar due to nestng. There are several nterestng evdences between the LES and QES wth demographc varables. Frst, all the varables (8 demographc varables tmes 6 commodtes) are ncluded n each functon to be estmated. It s hard to tell the nfluence of the demographc varables on the commodtes. Second, gender of householder s not sgnfcant n all the estmates. It can be due to the property of the LES and QES. Thrd, unlke the LA/AIDS, demographc varables for mlk equaton are all nsgnfcant. On the other hand, all the demographc varables excludng gender are sgnfcant n both the LES and QES. Forth, the educaton, regon, and urban varables performed dfferent n the LES and QES. Most of the regon varables are sgnfcant n the QES, but nsgnfcant n the LES, whereas urban varable s sgnfcant n the LES, but not sgnfcant n the QES except mlk. Table 7 represents the Root MSE and adjusted R 2 n the selected models. The Root MSE and R 2 ndcate the same crtera but n the opposte drecton to the performance of the model. Namely, the larger the R 2, the less the Root MSE, the better the performance. As can be seen, the performance wth ncorporatng demographc varables s much better especally n flour equaton of complete demand systems. For example, n the LA/AIDS model, the R 2 s mproved from 20% to 45%. However, there s one excepton that the fresh vegetables n the QES have lower R 2 wth demographc varables (droppng from 72% down to 66%). Generally speakng, the R 2 of the LES and QES for rce, pork, and fresh vegetables (the three major food tems n Chnese food consumpton) are outstandng. However, the sngle equaton model for flour and mlk both wth and wthout consderng the demographc effects s superor to the complete demand systems. Therefore, the selecton of models s an mportant work. Table 8 shows the comparson of margnal budget share of the selected models. It s hardly to see the comparson of budget share n the lterature especally for the AIDS model. The MBS of the Workng-Leser and LA/AIDS have the same formula, that s the sum of budget share and parameter estmate beta. The MBS of the LES s constant (a ) but has a complcated form for the QES. As can be seen, t s obvous that people n urban Jangsu wll spend addtonal budget on pork, rce, and fresh vegetables more than the other food tems. Moreover, the MBS s dfferent for flour, pork, and mlk, but qute smlar for rce, fresh vegetables, and fresh fruts. For example, the 6

7 MBS for pork n the LA/AIDS s lower than the others. However, the MBS of mlk n the LES and QES s hgher than that n the LA/AIDS and Workng-Leser; whereas the MBS for flour between these two groups s reversed. Expendture and prce elastctes are the major ndcators n demand analyss. Tables 9 and 10 show the expendture and own-prce elastctes among the selected models n Jangsu, In Table 9, the expendture elastctes perform the smlar trend lke MBS due to the usage of the same parameter estmates. The demographc effects on expendture elastctes are ambguous except fresh fruts. The elastctes go up n the selected models. Expendture elastcty for flour n the LA/AIDS s close to 1.5 and that of mlk n the LES s more than 1.6, both wthout demographc effects. That means as ncome ncreases, people would lke to spend more to eat flour and mlk to ncrease ther utlty. In Table 10, snce the demographc varables affect the prce elastctes n the LES and QES drectly, we have to specfy the demographc varables n order to demonstrate the prce elastcty for classfcaton. In the case of no effects from demographc varables, the results have the smlar trend except rce and flour n the LES, whch are below unty. It s obvous that the own-prce elastctes of flour n the LES and QES are qute dfferent wth and wthout demographc effects. It s very hard to explan n the QES due to ts complexty. However, n the LES, the reason of postve own-prce elastcty s not only due to the sgnfcant estmate of b 2 and has a large value (58.96, n table 6) but also due to the decomposton of b n equaton (6). For example, we can specfy the prce elastctes for dfferent demographc group of people n the LES and QES, whereas we only general elastctes for the LA/AIDS and Workng-Leser. V. Concluson In our study, we frst summarze three commonly used demand models ncludng sngle equaton and complete demand systems such as the LES, QES and LA/AIDS. Snce the cross-sectonal data are utlzed n analyzng the consumpton behavor n Jangsu, 1994, the effects of demographc varables on food consumpton are nvestgated. Most of the parameter estmates are statstcally sgnfcant and sutable to analyze the margnal budget share and elastctes. The comparsons of the selected models, both wth and wthout ncorporaton of the demographc varables ndcate that the choces of functonal forms and treatment of translatng demographc effects are mportant n the emprcal studes. As to the model specfcaton, the performance of the Workng-Leser s smlar to that of the LA/AIDS. However, sngle equaton functonal form s easy to execute computaton work but dffcult to mpose or test the regularty condtons. On the other hand, the LES s nested n the QES. Hence, the results of the LES and QES are not extremely dfferent. Snce the demand propertes have already been mposed n the model, we can hardly test whether or not the regularty condtons are satsfed usng the urban household data. Therefore, before usng the LES and QES, we should guarantee that the observatons satsfed the assumpton of utlty maxmzaton. The eght plausble demographc varables are selected n the study. The effects of each demographc varable are dfferent n the selected models. Generally speakng, the modernzaton ndcator, the dummy varable of refrgerator, s sgnfcant, whereas the dummy varable of gender of householder s not. As mentoned before, the effects of demographc varables n the LES and QES are ambguous. We stll can conclude that, for rce and flour, the dummy varables for regon and urbanzaton are sgnfcant. For mlk, educaton level s sgnfcant n the Workng-Leser and LA/AIDS. Household sze and the number of chldren under age 17 are sgnfcant n the LES and QES, whereas t s not qute obvous n the Workng-Leser and LA/AIDS. The statstcal crtera also ndcate that ncorporaton of the demographc effects s valuable. As for flour and mlk, even though there exsts serous problem of zero consumpton n the database, the performance of flour and mlk are acceptable based on the Root MSE or adjusted R 2 crtera. The censored regresson and prce endogenous approaches are not appled n ths study. It should be very nterestng to compare the results usng the dfferent approaches to solve the problem. 7

8 References 1. Chern, W. S. and G. Wang, The Engel functon and Complete Food Demand system for Chnese Urban Households. Chna Economc Revew, 4: Chern, W. S., Estmated Elastctes of Chnese Gran Demand: Revew, Assessment and New Evdence. a Report to the World Bank. 3. Deaton, A. and J. Muellbauer, 1980a. Economcs and Consumer Behavor. Cambrdge: Cambrdge Unversty Press. 4. Deaton, A. and J. Muellbauer, 1980b. An Almost Ideal Demand System. Amercan Economc Revew, 70: Gao, X. M., E. J. Wales, and G. L. Cramer, Partal Ratonng and Chnese Urban Households Food Demand analyss. Journal of Comparatve Economcs, 22: Leser, C. E., Forms of Engel Functon. Econometrca, 31: Lews, P. and N Andrews, Household Demand n Chna. Appled Economcs, 21: Moschn, G Unts of Measurement and the Stone Index n Demand System Estmaton, Amercan Journal of Agrcultural Economcs, 77: Pollak, R. A. and T. J. Wales, Estmaton of Complete Demand Systems from Household Budget Data: The Lnear and Quadratc Expendture Systems. Amercan Economc Revew, 68: Pollak, R. A. and T. J. Wales, Comparson of the Quadratc Expendture System and Translog Demand Systems wth Alternatve Specfcatons of Demographc Effects. Econometrca, 48: Pollak, R. A. and T. J. Wales, Demographc Varables n Demand Analyss. Econometrca, 49: Sh, H, R. Mttelhammer, and T. I. Wahl, Aggregate Food Demand Analyss for a Transtonal Economy: An Applcaton to Chnese Household Expendture Data. Journal of Food Dstrbuton Research, 26: Stone, J. R. N., Lnear Expendture Systems and Demand Analyss: An Applcaton to the Pattern of Brtsh Demand. Economc Journal, 64: Wang, Z. and W. S. Chern, Effects of Ratonng on the Consumpton Behavor of Chnese Urban Households durng Journal of Comparatve Economcs, 16:

9 15. Wu, Y., E. L, and S. N. Samuel, Food Consumpton n Urban Chna: An Emprcal Analyss, Appled Economcs, 27: Workng, H., Statstcal Laws of Famly Expendture. Journal of the Amercan Statstcal Assocaton, 38:

10 Table 1 Defntons and descrptve statstcs of varables used n the selected models* Group Varable** Sample Mean Standard Devaton Mnmum Value Maxmum Value # of Zero Value Budget W Share W W W W W Prce P P P P P P Expendture X X X X X X X*** Log(Prce) LOGP LOGP LOGP LOGP LOGP LOGP Demographc FRIDGE Varables SIZE Or KID Dummy GENDER Varables AGE EDU REGION URBAN * Total observatons are 800. ** Subscrpt ndcates the food tems analyzed n the models: 1=rce, 2=flour, 3=pork, 4=mlk and ts products, 5= fresh vegetables, and 6= fresh fruts. *** Total expendtures of the food tems ncluded n the model. 10

11 Table 2 The parameter estmates of the Workng-Leser form wthout demographc effects, Jangsu, Items Rce Flour Pork Mlk and ts Intercept * * * * (0.0936) (0.0484) (0.1002) (0.0500) (0.0692) LOGP * * (0.0310) (0.0160) (0.0332) (0.0166) (0.0229) LOGP * * * * (0.0256) (0.0132) (0.0274) (0.0137) (0.0189) LOGP * * * (0.0371) (0.0192) (0.0397) (0.0198) (0.0274) LOGP * * * * (0.0047) (0.0024) (0.0050) (0.0025) (0.0035) LOGP * * * (0.0169) (0.0087) (0.0181) (0.0090) (0.0125) LOGP * * * * * (0.0112) (0.0058) (0.0120) (0.0060) (0.0083) LOGX * * * (0.0088) (0.0045) (0.0094) (0.0047) (0.0065) Note: * the astersk ndcates that the estmated coeffcent s statstcally sgnfcant at 5% or better. Fruts * (0.0877) * (0.0291) (0.0240) (0.0347) * (0.0044) (0.0158) * (0.0105) * (0.0082) Table 3 The parameter estmates of the Workng-Leser form wth demographc varables, Jangsu Items Rce Flour Pork Mlk and ts Intercept * * * * (0.1042) (0.0482) (0.1076) (0.0553) (0.0759) LOGP * * (0.0312) (0.0144) (0.0322) (0.0166) (0.0227) LOGP * * * * (0.0258) (0.0119) (0.0266) (0.0137) (0.0188) LOGP * (0.0392) (0.0181) (0.0405) (0.0208) (0.0286) LOGP * * * * (0.0048) (0.0022) (0.0050) (0.0026) (0.0035) LOGP * * * (0.0177) (0.0082) (0.0183) (0.0094) (0.0129) LOGP * * * * * (0.0113) (0.0052) (0.0117) (0.0060) (0.0082) LOGX * * * (0.0101) (0.0047) (0.0104) (0.0053) (0.0073) δ 1 (FRIDGE) * * * * (0.0085) (0.0039) (0.0088) (0.0045) (0.0062) δ 2 (SIZE) (0.0044) (0.0021) (0.0046) (0.0024) (0.0032) δ 3 (KID) * * (0.0082) (0.0038) (0.0084) (0.0043) (0.0059) δ 4 (GENDER) * (0.0075) (0.0035) (0.0077) (0.0040) (0.0054) δ 5 (AGE) * (0.0054) (0.0025) (0.0056) (0.0029) (0.0039) δ 6 (EDU) * * (0.0045) (0.0021) (0.0046) (0.0024) (0.0033) δ 7 (REGION) * * * * * (0.0110) (0.0051) (0.0114) (0.0058) (0.0080) δ 8 (URBAN) * * * (0.0086) (0.0040) (0.0089) (0.0046) (0.0063) Note: * the astersk ndcates that the estmated coeffcent s statstcally sgnfcant at 5% or better. Fruts * (0.0939) (0.0281) (0.0232) (0.0353) (0.0043) (0.0160) * (0.0102) * (0.0091) * (0.0077) (0.0040) (0.0074) * (0.0067) * (0.0049) * (0.0040) * (0.0099) * (0.0078) 11

12 Table 4 The estmated parameters of the LA/AIDS wthout demographc effects, Jangsu, Parameter Rce Flour Pork Mlk and ts α I * * * * (0.0605) β I * (0.0082) γ (0.0228) γ * (0.0123) (0.0371) * (0.0046) (0.0716) * (0.0090) (0.0293) * (0.0045) (0.0429) * (0.0060) (0.0132) γ (0.0211) (0.0146) (0.0300) γ * * (0.0041) (0.0025) (0.0045) (0.0024) γ * (0.0114) * (0.0078) (0.0132) * (0.0030) * (0.0110) Note: * the astersk ndcates that the estmated coeffcent s statstcally sgnfcant at 5% or better. Table 5 The estmated parameters of the LA/AIDS model wth demographc varables, Jangsu, Parameter Rce Flour Pork Mlk and ts α I * (0.0635) (0.0333) * (0.0713) * (0.0310) (0.0460) β I * (0.0091) * (0.0044) * (0.0096) * (0.0050) * (0.0067) γ (0.0249) γ * (0.0113) * (0.0109) γ (0.0215) * (0.0126) (0.0281) γ * (0.0043) * (0.0022) (0.0045) * (0.0025) γ * * * (0.0126) (0.0073) (0.0136) (0.0032) (0.0122) δ 1 (FRIDGE) * (0.0081) * (0.0039) (0.0084) * (0.0044) * (0.0060) δ 2 (SIZE) (0.0043) (0.0021) * (0.0045) (0.0024) (0.0032) δ 3 (KID) (0.0080) (0.0038) (0.0083) (0.0044) * (0.0059) δ 4 (GENDER) (0.0073) (0.0035) (0.0076) (0.0040) * (0.0054) δ 5 (AGE) (0.0052) * (0.0025) * (0.0054) (0.0029) (0.0038) δ 6 (EDU) (0.0044) * (0.0021) * (0.0045) * (0.0024) * (0.0032) δ 7 (REGION) * (0.0091) * (0.0043) * (0.0090) (0.0045) (0.0065) δ 8 (URBAN) (0.0082) * (0.0039) * (0.0085) (0.0045) (0.0061) Note: * the astersk ndcates that the estmated coeffcent s statstcally sgnfcant at 5% or better. 12

13 Table 6 The parameter estmates of the LES and QES, Jangsu, Wthout demographc varables Wth demographc varables Parameter LES QES LES QES A * (0.0086) * (0.0095) * (0.0103) * (0.0180) A * (0.0047) * (0.0057) * (0.0045) * (0.0077) A * (0.0102) * (0.0154) * (0.0118) * (0.0180) A * (0.0039) * (0.0035) * (0.0042) * (0.0103) A * (0.0071) * (0.0101) * (0.0081) * (0.0123) B * (14.158) * (21.378) (53.927) (39.586) B (4.5761) (6.9746) * (9.4155) * (9.0829) B * (3.9081) * (7.6165) * (15.067) (11.040) B * (0.5741) * (0.5847) (2.7075) * (1.9531) B * (16.918) (21.993) * (69.154) (52.375) B * (6.7649) * (7.8259) * (30.845) * (24.589) C (0.1508) * (0.1795) C * (0.1178) * (0.0715) C * (0.2439) * (0.1478) C (0.0516) * (0.1632) C * (0.2507) * (0.1054) λ * (0.0006) (0.0000) Note: the astersk ndcates that the estmated coeffcent s statstcally sgnfcant at 5% or better. Wth demographc varables Wth demographc varables Parameter LES QES Parameter LES QES δ * * δ * * ( ) ( ) (5.0611) (4.7882) δ * * δ * * ( ) (9.6845) (2.2580) (2.1435) δ * * δ * * ( ) ( ) (4.6553) (4.3284) δ δ ( ) ( ) (3.9897) (3.8774) δ δ * * ( ) ( ) (2.9512) (2.7849) δ δ * * ( ) ( ) (2.3498) (2.2693) δ * δ * * ( ) ( ) (4.8005) (4.6599) δ * δ * * ( ) ( ) (4.7054) (4.4648) δ * * δ (7.2756) (5.7141) (1.3106) (1.0487) δ * * δ (3.4915) (2.6261) (0.6592) (0.4662) δ * * δ (7.0855) (5.6671) (1.2598) (0.9395) δ δ (6.0068) (4.7985) (1.1357) (0.8381) δ δ (4.3973) (3.4250) (0.8204) (0.6021) δ δ (3.5569) (2.8231) (0.6909) (0.5013) δ * * δ (7.9074) (5.8679) (1.5264) (1.1119) δ * * δ (7.1272) (5.3845) (1.3168) (0.9745) δ * * δ ( ) ( ) ( ) ( ) δ * * δ * * ( ) ( ) (7.0385) (5.7459) δ * * δ * * ( ) ( ) ( ) ( ) δ δ ( ) ( ) ( ) (9.7462) δ δ * * ( ) ( ) (8.7562) (7.2413) δ * δ ( ) ( ) (6.8379) (5.7594) δ * δ * ( ) ( ) ( ) ( ) δ * δ ( ) ( ) ( ) ( ) Note: the astersk ndcates that the estmated coeffcent s statstcally sgnfcant at 5% or better. 13

14 Table 7 Comparson of Root MSE and Adjusted R 2 n the selected models, Jangsu, Group Items Rce Flour Pork Mlk and ts Fruts No DemographcVarables Workng-Leser Root MSE Adj. R LA/AIDS Root MSE Adj. R LES Root MSE Adj. R QES Root MSE Adj. R Wth DemographcVarables Workng-Leser Root MSE Adj. R LA/AIDS Root MSE Adj. R LES Root MSE Adj. R QES Root MSE Adj. R Table 8 Comparson of MBS n the selected models, Jangsu, Group Rce Flour Pork Mlk and ts Fruts No DemographcVarables Workng-Leser LA/AIDS LES QES Wth DemographcVarables Workng-Leser LA/AIDS LES QES

15 Table 9 Comparson of Expendture elastctes n the selected models, Jangsu, Group Rce Flour Pork Mlk and ts Fruts No DemographcVarables Workng-Leser LA/AIDS LES QES Wth DemographcVarables Workng-Leser LA/AIDS LES QES Table 10 Comparson of own-prce elastctes n the selected models, Jangsu, Group Rce Flour Pork Mlk and ts Fruts No DemographcVarables Workng-Leser LA/AIDS LES QES Wth DemographcVarables Workng-Leser LA/AIDS LES QES