Key Words: AIDS model, Cross-section, Income Elasticity, Japan, Rice Consumption.

Transcription

1 Income Elastcty of Rce Demand n Japan and Its Implcatons: Cross-Sectonal Data Analyss Kyosh Tanguch and Wen S. Chern ** Paper prepared for 2000 AAEA meetng. Abstract Researchers beleve that rce n developed countres such as Japan became an nferor good a few decades ago. Ths study employs the flexble complete demand system for the recent cross-sectonal data n Japan. Our results clearly show that rce n Japan s a normal good contrary to the precedng studes. The objectve of ths research s to analyze the food consumpton patterns and to conduct econometrc analyss of food demand structure. We use the monthly bass cross-sectonal household data, Annual Report on the Famly Income and Expendture Survey (FIES) n Food tems are non-glutnous rce, bread, noodle, fresh fsh, and shellfsh, fresh meat, mlk, eggs, fresh vegetables, fresh fruts, fats and ol, and food away from home. We apply varous sngle equaton models: Workng-Leser model s estmated by OLS, Heckman s two-step estmator, and Tobt estmator. All coeffcents have correct sgns and are statstcally sgnfcant. For the complete demand system analyss, we apply the almost deal demand (AIDS) system. To correct a censored dependent varable problem, we addtonally utlze a censored regresson approach. Results from AIDS models show that the expendture elastcty of rce s postve and close to one. Marshallan and Hcksan ownprce elastctes for rce are hghly elastc for all models. Fresh meats and rce are mld complements n all models; however, fresh fsh and rce show the mxed results. Key Words: AIDS model, Cross-secton, Income Elastcty, Japan, Rce Consumpton. Ph.D. student, Department of Economcs, The Oho State Unversty, and Development Economst, Food and Agrculture Organzaton of the Unted Natons ** Professor, Department of Agrcultural, Envronment, and Development Economcs, The Oho State Unversty Correspondng Address: Kyosh Tanguch Address: Room C311, Food and Agrculture Organzatons of the Unted Natons Vale delle Terme d Caracalla Rome, Italy E-mal: Kyosh.Tanguch@fao.org Telephone: Copyrght 2000 by Kyosh Tanguch and Wen S. Chern. All rghts reserved.

2 I. Introducton The 1994 Marrakech agreements of the General Agreement on Tarff and Trade (GATT) Uruguay Round have started a process of agrcultural market lberalzaton. The new round of World Trade Organzaton (WTO) negotatons to be launched the year 2000 are expected to brng ths process further. The world rce market s a thn market. Nnety percent of producton and consumpton occurs n Asa. The GATT/WTO decsons wll desgn a new pcture of the world agrcultural markets, and t s mportant to understand how ths wll nfluence the rce market n the near future. Japan reached hgh economc growth earler than other Asan natons. Recently, the Newly Industralzed Economes (NIEs) have been rapdly catchng up and attanng hgher per capta ncome. Many Asan natons may eventually reach the economc standards of Japan, Europe, and the U.S.. Japanese consumpton behavor s a key ndcator to forecast the future consumpton patterns of Asan natons. For example, Korea accepted the same mnmum access mport requrements n the GATT negotatons, and Tawan has a very smlar agrcultural socety to Japan. By nvestgatng Japanese consumpton behavor as beng representatve of hgh-ncome consumers, ths study wll shed some lght on the future drecton of Asan and world rce demand. In addton to a general concern about Japanese consumpton behavor, t s of great nterest to ascertan whether rce s a normal or nferor good,.e. as the ncome ncreases, whether rce consumpton goes up or down. Snce rce s a very mportant food staple n Asan countres, many domestc agrcultural as well as nternatonal trade The authors apprecate recevng valuable comments from an anonymous referee. The vews presented n ths study do not necessarly represent those of Food and Agrculture Organzaton of the Unted Natons. 2

3 polces are centered on rce. Such mportant agrcultural polces would be msdrected f they were based on the belef that rce s an nferor good, wthout a rgorous and robust estmaton of that characterstc. When assessng food balances, the lterature on the rce market s manly concerned wth supply sde factors. (See Onk (1996) and Fujk (1993, 1998, 1999).) Consderng the uncertan envronment of the rce market n the future, one cannot neglect demand sde study. In order to obtan an accurate forecast of Japanese rce market lberalzaton, precsely estmated elastctes are necessary. The man objectve of ths research s to analyze food consumpton patterns and to conduct econometrc analyss of food demand structure n Japan. We use the crosssectonal household data from the Annual Report on the Famly Income and Expendture Survey 1997 (FIES) compled by the Statstcs Bureau, Management and Coordnaton Agency n Japan. FIES s monthly bass and cross-sectonal. The total number of observatons used for estmaton s 95,223. Food tems are non-glutnous rce, bread, noodle, fresh fsh, and shellfsh, fresh meat, mlk, eggs, fresh vegetables, fresh fruts, fats and ol and food away from home. Ths research s unque n the sense that ncome elastctes of rce and other related foods are estmated wth a large degree of freedom. Ths knd of cross-sectonal survey study s vrtually non-exstent n regard to Japanese consumpton patterns. To our knowledge, these survey data have never been used for estmatng a food demand system. Therefore, the results produced n ths paper are potentally ntrgung to demand analysts and polcy makers. In order to ncorporate household-level mcrodata, we apply varous sngle equaton models: Workng-Leser model estmated by OLS, Heckman s sample selecton 3

4 model, and Tobt model. All coeffcents have correct sgns and are statstcally sgnfcant. For complete demand system analyss, we apply the lnearly approxmated almost deal demand system (LA/AIDS). The concept of a flexble complete demand system yelds consumpton behavor estmates wth many desrable propertes: the addng-up, homogenety, and symmetry condtons can be tested, whch precedng demand studes on ths topc had rarely mposed. The LA/AIDS poses the unt of measurement problem. In order to obtan more accurate estmaton, the LA/AIDS model wth two prce ndexes s compared: the Stone prce ndex and the Laspeyres prce ndex. In order to correct a censored dependent varable problem, we also utlze a censored regresson approach. In secton II of the paper, we dscuss the background of Japanese consumpton behavor. We show the hstorcal path that has led to the recent consumpton patterns. In secton III, we present the data used for ths research. In secton IV, the sngle equaton model and complete demand system used n ths study are descrbed. In secton V, we make estmates wth the model usng cross-sectonal data from secton III. Secton VI s the summary and concluson. II. Background Japan reached hgh per capta ncome much earler than other Asan natons. As per capta ncome grew, the consumpton pattern changed. Many studes have reported that the Japanese det has become more westernzed; calore ntake s less from rce and more from anmal meat, and the fat content of food has ncreased. Because of 4

5 Table 1: Industry Output (1995 Input-Output Data) Unt: Mllon Yen Purchased Sector Output of Rough Rce Purchased Sector Output of Mlled Rce Mllng 3,232, % Household Consumpton 2,604, % Rce Wne 195, % Restaurants and Hotels 553, % Rough Rce 28, % School and Hosptal Lunch 118, % Agrcultural Servces 6, % Rce Powder and Snacks 94, % Lve Stock 3, % Alcohol Beverages 67, % Other Food Stuff % Prepared Instant Food 63, % Other (non-food use) % Total 3,467,610 Total 3,502,485 Data Source: 1995 Input-Output Tables Management and Coordnaton Agency, Government of Japan geographcal reasons and preferences, calore ntake from fsh has a larger share than from meat. In ths study, we estmate the ncome elastcty from cross-sectonal survey data to shed some lght on some mportant questons. 1) Is Japanese rce an nferor good? Rce s a staple food n Japan, and ts great mportance n the Japanese det s well known. In ,748,000 metrc tons of rce were produced domestcally, and 10,485,000 metrc tons were consumed. Rce s used by a varety of sectors, but mostly by the household. Accordng to the 1995 nput-output table (Government of Japan, 1999), 93.21% of rough rce s purchased by the mllng sector, and 74.38% of mlled rce s consumed by the households. (See Table 1.) It s mportant to understand whether rce s a normal or nferor good. Japan has one of the hghest per capta GDP n the world. By defnton, rce consumpton would keep fallng wth per capta GDP growth, f rce were an nferor good. If that s the case, and f Japan could be consdered as the leadng case for other Asan countres, we could project lower world rce demand n the future as Asan natons ncome ncreases. 5

6 It has been consdered as the stylzed fact among researchers that ncome elastctes for rce and other food staples declne as per capta ncome ncreases. Researchers beleve that rce n developed countres such as Japan became an nferor good a few decades ago. There s conflctng evdence on whether rce s an nferor good. Emprcal studes are conducted by Ito el. al. (1989). Ito and colleagues conclude that rce s an nferor good n hgh-ncome Asan countres. Kako (1997) projected Japanese rce demand applyng log lnear functon, and estmated t by OLS. They fnd evdence that rce s an nferor good and meat products are substtutes for rce. Bous (1991) objects to Ito et al. s study; the author clams that tme-seres estmates of gran consumpton have a downward bas due to the urban-rural mgraton pattern and decreasng mportance of rce producton. From the estmaton of calore-ncome elastctes, Bous and Haddad (1992) and Bous (1994) clam that cross-sectonal data estmates of ncome elastcty are upwardly based due to leakage from actual consumpton, such as meals for guests and anmal feedng n developng countres. As Chern (1998) and Huang and Bous (1986) pont out, plottng aggregate consumpton aganst per capta ncome smply shows the correlaton between two varables. It does not necessarly reveal the true consumpton behavor. Accurate ncome elastcty can be obtaned from cross-sectonal data, and we wll estmate ncome elastcty among varous ncome classes. 2) Is rce a substtute or complement for meat and/or fsh? Many tme-seres studes show that people consume more meat and poultry as per capta ncome ncreases. Japan s not an excepton: the consumpton of meats and poultry has been ncreasng, whle the consumpton of rce has been decreasng snce the 1960s. 6

7 Fgure 1 Annual Per Capta Rce Consumpton kg Rce Data Source: Food Balance Sheet (1997) Year Fgure 2 Annual Per Capta M eat, Poultry and Fsh Consum pton kg M eats and poultry Fsh Data Source: Food Balance Sheet (1997) Y ear Fgure 3 Per Capta Per Day Average of C alore Intake kcal M eats and Poultry Fsh Y ear Data Source: Food Balance Sheet (1997) 7

8 We estmate demand relatonshps among rce, meats, poultry, fsh, and other products, and results are shown n secton V. Fgures 1 to 3 show descrptve consumpton patterns n Japan. All data are taken from the Food Balance Sheet by Japan Mnstry of Agrculture, Forestry, and Fsheres (1997). Fgure 1 plots the annual per capta rce consumpton n Japan. It s a wellknown fact that aggregate rce consumpton n Japan has been declnng over the years, whch s common amongst hgh-ncome countres. The peak of the per capta consumpton of rce s n It s almost halved by the end of the 1990s. Fgure 2 shows annual per capta meat (beef and pork), poultry, and fsh consumpton. In klogram terms, Japanese consume more fsh than meat and poultry. Ths s one of unque features of the Japanese consumpton pattern. Fgure 3 plots the average per capta daly calore ntake from meat, poultry, and fsh. Snce 1980, meat and poultry have become a larger source of calores compared to fsh. In sum, n klogram terms, Japanese consume more fsh; whle n nutrton terms, Japanese ntake more calores from meat and poultry. Two consderatons should be noted for these fgures. Frst, they provde lttle nformaton about prce and ncome elastctes of each commodty. Calore ntake s purely a behavoral varable, and t does not reveal any clear prce nformaton. Second, the food balance sheet provdes macro data; t may not accurately capture ndvdual household consumpton patterns. That s, there may be an aggregaton problem. For estmatng ncome elastctes, household survey data probably provdes a better pcture of ndvdual household consumpton patterns. 8

9 Table 2: Classfcaton of household by ncome level Household Class Annual Income Level Income Class 1 less than 4,020,000 Income Class 2 between 4,020,000 and 5,680,000 Income Class 3 between 5,680,000 and 7,450,000 Income Class 4 between 7,450,000 and 9,900,000 Income Class 5 between 9,900,000 and hgher III. Data To analyze food consumpton patterns and to conduct econometrc analyss of food demand structure n Japan, we use the cross-sectonal household data, Annual Report on the Famly Income and Expendture Survey 1997 (FIES) compled by the Statstcs Bureau of the Management and Coordnaton Agency n Japan. These are monthly and cross-sectonal survey data. Amongst all households n Japan, farm, one-person, and non-ctzen households are excluded. Partcpants are asked to keep a Household Schedule, Famly Account Book, and a Yearly Income Schedule. The total number of observatons n ths survey data s 95,225. Food tems estmated for ths study are non-glutnous rce, bread, noodle, fresh fsh and shellfsh, fresh meat, mlk, eggs, fresh vegetables, fresh fruts, fats and ol, and food away from home. In order to nvestgate the dfferences n demand structure amongst ncome groups, we dvded the sample accordng to ther household head annual ncome level. (See Table 2.) Table 3 shows the dstrbuton of sample by ncome and age. Age refers to the household head s age. Table 4 shows the average household sze by ncome group. In FIES, one-person households are not ncluded. Hence, the mnmum number n a household s two people. In addton, f a household has more than eght members, then 9

10 Some Selected Sample Descrptve Statstcs Table 3 Dstrbuton of Sample by Income and Age Income Level ( ten thousand yen) Income 1 Income 2 Income 3 Income 4 Income 5 Age < < < 35 2,864 4,257 2,745 1, ,341 4,125 5,638 4,664 2, ,460 2,797 4,260 6,500 7, ,158 3,686 3,694 3,944 5, < 8,488 4,684 2,408 1,627 1,922 Total 20,311 19,549 18,745 18,155 18,465 Table 4 Household Sze by Income and Age Income Level ( ten thousand yen) Income 1 Income 2 Income 3 Income 4 Income 5 Age < < < < Table 5 Daly Consumpton of Non-glutnous Rce ( g ) per Household by Age and Income Income Level ( ten thousand yen) Income 1 Income 2 Income 3 Income 4 Income 5 Age < < < < All Ages Table 6 Prce of Non-glutnous Rce (Yen/100g) by Income and Age Income Level ( ten thousand yen) Income 1 Income 2 Income 3 Income 4 Income 5 Age < < < < Table 7 Average Retal Prce of Non-glutnous Rce (Yen/100g) Voluntary Rce 10 Government Rce Year Superor Good Normal Standard N/A Data Source: Rce Wheat Data Book 1998

11 the demographc varables of nnth or more famly members of the young are omtted from the sample. As a result, the maxmum household sze s eght. It s nterestng to see that the hgher ncome households tend to have a larger number of household members. The FIES contans demographc varables and monthly data on expendture and the quantty of food tems consumed. The monthly data are converted to a daly bass for the estmaton n order to correct for dfferent numbers of days n months. Table 5 shows the daly consumpton of non-glutnous rce. There s a tendency for hgher-ncome and more elderly household to consume more rce. Table 6 shows non-glutnous rce prce dependng on the age and the ncome. It ndcates that the hgher the ncome s, the more expensve rce the household consumes. The prce used for estmaton s obtaned by dvdng expendture by the quantty purchased. The zero consumpton problem poses a serous estmaton flaw; there s no prce data for zero consumpton household. In order to obtan prce data for households wth zero consumpton, we make the assumpton that each household s facng the mean prce of each commodty dependng on regon, month and ncome class. In FIES, there are ten regons: Hokkado, Tohoku, Kanto, Hokurku, Touka, Knk, Tyugoku, Shkoku, Kyushu, and Oknawa. There are twelve months n a year, and fve ncome classes defned above. Therefore, there are sx hundred prce varatons accordng to locaton, tme, and ncome group for zero consumpton samples. Amongst eleven food tems, food away from home does not have a quantty unt. We use the Consumer Prce Index (CPI) from Annual Report on the Consumer Prce Index, by Statstcs Bureau, Management and Coordnaton Agency, for food away from home. 11

12 Table 7 shows the annual average retal prce of non-glutnous rce for dfferent classfcatons. Data are taken from Rce Wheat Data Book Rce can be categorzed by two types accordng to ts dstrbuton system: voluntary rce and government rce. Begnnng n 1969, the Japanese government ntroduced the system of quas-ratoned rce. Japanese rce s categorzed as government rce and voluntary rce. At the producton level, the agrcultural cooperatves collect government rce. The agrcultural cooperatves sell ether to the Japan Food Agency (JFA) under the Japan Mnstry of Agrculture, Forestry, and Fsheres (MAFF) or to lcensed wholesalers. Government rce s manly transferred to storage for food securty purposes and for foregn ad. Voluntary rce has more varetes of prce and qualty as mentoned above. The prce of voluntary rce s determned by aucton, whle the government sets the prce for government rce as a prce support. Tables 6 and 7 show that the unt prces from FIES data le between good and normal crtera. IV Model The applcaton of the theory of the household requres a specfc model. In general, econometrc studes on demand nclude both sngle equatons and systems of demand equatons. The demand functons can be generalzed for a consumer or a household buyng n goods as: x = x (p 1, p 2, p j, p n, I), = 1, 2,, n. (1) where x s quantty demanded, p s the prce, the subscrpt denotes the commodtes, and I s ncome. These n equatons can be estmated by sngle equatons or by systems of equatons. In ths study, equaton (1) s estmated n a budget share form. 12

13 IV-1: Sngle Equaton Model The frst emprcal model appled n ths study s the Workng-Leser model 1. In the Workng-Leser model, each share of the food tem s smply a lnear functon of the log of prces and of the total expendture on all food tems n queston. The Workng- Leser food demand functon can be expressed as: (2) w = α0+ α logx+ β log p + γ H + ε j j k k j k where (, j) Œ eleven food tems, w = expendture share of food among eleven food tems, p j = prce of food j, and x = total expendture of all food tems ncluded n the model. H k ncludes dummy varables where k Œ 25: AGE = log age of household head, SIZE = log of household sze, WE = number of wage earners, BABY = number of chldren aged 5 or under, PRIM = number of chldren aged between 6 and 12, HIGH = number of chldren aged between 13 and 18, M = dummy varables for month (M 1,, M 10 ) 2, and REG = dummy varables for regon (REG 1,, REG 9 ). 1 Orgnal form of Workng-Leser was dscussed by Workng (1943) and Leser (1963). See Intrlgator et. al. (1996) and Deaton and Muellbauer (1980b) for a more detaled dscusson of ths functonal form. 2 Only ten monthly dummes are ncluded n the model, because CPI for food away from home s monthly bass. 13

14 ε s are random dsturbances assumed wth zero mean. Each food tem s estmated by OLS. Expendture and uncompensated own-prce elastctes are estmated at ther sample mean. IV-2: Elastcty Estmates n Workng-Leser model It s easy to show the elastcty estmates of Workng-Leser models. The expendture elastcty of Workng-Leser model e as: e 1 w = 1+ w ln( x). (3) Takng dervatve wth respect to ln(p j ) yelds uncompensated own (j=) and cross (j ) prce elastctes, e j, are as follows: e j 1 w = 1+ w pj (4) In ths study, expendture, own-prce, and cross-prce elastctes are evaluated at ther sample mean. IV-3: Income Elastcty n Workng-Leser model Snce the Workng-Leser model uses total expendtures for the group of food tems ncluded n the model, t does not provde a drect estmate of ncome elastcty. In order to estmate ncome elastcty, we estmate the followng Engel functon: = α + α + β + γ + ε (5) logx 0 1logX logp khk k where x = Total expendtures of the food ncluded n the model, X = Total expendtures of food and non-food consumer goods and servces, 14

15 P = Laspeyres prce ndex, and other demographc and dummy varables are the same as prevously defned. Remanng varables are the same as equaton (2). From equaton (2) and equaton (5), ncome elastcty can be estmated. From equaton (2), we can estmate expendture elastcty, e q x xq =. From equaton (5), we can derve the responsveness of expendture on food tems by ncome change, x X s =. Hence, ncome elastcty s X x estmated as follows: e ncome ( ) q x x X q X xq X x Xq = es = =. (6) Table 8 Percentage of Households wth Zero Consumpton Major 11 commodtes Food Varables % Non-glutnous Rce 43.75% Bread 4.15% Noodle 6.14% Fresh Fsh and Shell Fsh 2.45% Fresh Meat 1.92% Mlk 8.36% Eggs 5.51% Fresh Vegetables 0.24% Fresh Fruts 5.50% Fats and Ol 42.12% Food Away From Home 12.65% 15

16 IV-4: Tobt Model In order to estmate ncome elastctes, household-level mcro data are preferable, snce one can avod the aggregaton problem by usng them. Wth the use of household mcro data for detaled commodtes; however, we encounter an econometrc problem wth some households havng zero consumpton, as stated before. Ths problem stems from the fact that some households do not consume some of the tems consdered. Ths zero consumpton problem s partcularly severe for the case of rce, ol and fats, and food away from home n FIES. (See Table 8.) It s known that usng only observed postve purchase data to estmate consumpton behavor by OLS regresson produces nconsstent estmates of coeffcents. The dependent varables, whch are the budget shares for the eleven food tems specfed, are zero f a household does not purchase a food tem and postve f one does purchase the food tem. Zero shares are censored by an unobservable latent varable. Ths zero consumpton stems from the decson not to purchase the partcular tem n the monthlong survey perod. Because rce s a staple food, t s unlkely that people consume t nfrequently n Japan. However, some people mght not purchase t as frequently as they consume t. In order to correct the sample bas problem on rce consumpton, we appled Heckman s two-step estmaton (Heckt) procedure suggested by Heckman (1978). In the frst stage, a probt regresson s computed n order to estmate the probablty that a gven household consumes the food tem n queston. Ths regresson s used to estmate the nverse Mlls rato (l) for each household, whch s used as an nstrument n the second 16

17 regresson. In the second stage, the ntal Workng-Leser model (equaton (2)) and the nverse Mlls rato are estmated. In the frst stage, the decson for the household s modeled as a dchotomous choce problem; (7) Y = α0 + α logx+ β log p + γ H + ε j j k k j k where Y s one f a household consumes th food tem (.e., w > 0 ), and zero otherwse. Other varables were defned prevously. From equaton (7), the nverse Mlls rato (l) for every household can be computed as: φ( P) λ = Φ ( P) (8) where P s a vector of prces for the household. f s the densty probablty functon, and F s the cumulatve probablty functon. In the second step, the followng Workng-Leser demand functon, n addton to the computed nverse Mlls rato as an nstrument varable s estmated: (9) w = α0+ α logx+ β log p + γ H + λ + ε j j k k j k Censored and uncensored models are estmated for the whole sample. For comparson, the uncensored models are also estmated usng every household wth non-zero consumpton. IV-5: Elastcty Estmates of Tobt Model Ths secton descrbes the elastcty calculaton of Tobt estmator. There are 17

18 many studes cted on ths topc. Notaton manly follows Amemya (1985) and Maddala (1983). The Tobt model s defned as follows; * * * 2 y = y = xβ + u f y > 0 y N( µσ, ) y = 0 otherwse (10) β s a k 1 vector of unknown parameters; x s a k 1 vector of known constants; u are resduals that are ndependently and normally dstrbuted, wth mean zero and a common varance σ 2. In our study, Workng-Leser Model s denoted as follows: 1,, * = α0+ αlog + βjlog + γ k k + ε j k w x p H n (11) * w = w f w > 0 w = 0 f w 0 and ε 2 N(0, σ ) where subscrpt denotes a good n queston. x denotes total expendture on eleven commodtes. p and q denote prce and quantty for th commodty, respectvely. w pq denotes budget share of th good, w =. x McDonald (1980) descrbes that total change n y can be dsaggregated nto two parts: the change n y above the threshold, weghted by the probablty of beng above the threshold; and the change n the probablty of beng above the threshold, weghted by the expected vale of y. Uncondtonal elastcty descrbes the elastcty of y from the mean of all observed y s. Condtonal elastcty s the elastcty measure condtonal on the consumer s choce of non-zero quantty purchase of the good. 18

19 Consderng the model gven above, and the non-zero observatons y we get φ E( y y > 0) = xβ + Eu ( u > xβ) = xβ + σ (12) Φ where φ and Φ are the densty functon and dstrbuton functon of the standard normal xβ evaluated at σ. Defne z as xβ z for notatonal convenence. σ In order to obtan predcton values usng all the observatons, we have: E( y ) = Py ( > 0) E( y y > 0) + Py ( = 0) E( y y = 0) φ =Φ ( xβ + σ ) + (1 Φ)0 Φ =Φ xβ + σφ (13) Uncondtonal and condtonal elastcty can be obtaned as follows: Uncondtonal elastcty e, uncondtonal Ey [ ] x = (14) x Ey [ ] Condtonal elastcty e, condtonal Ey [ y > 0] x = x Ey [ y > 0] (15) In ths study, we apply two dfferent models to obtan Tobt estmator: Heckman s two-step model and standard Tobt estmator. Ths s the dervaton of elastcty measure for each model. The predcton of y, gven x, can be obtaned from the dfferent expectatons functons: uncondtonal and condtonal expectatons. We follow Maddala (1983) and McDonald (1980). In order to obtan uncondtonal expectaton, we take dervatve of the second equaton (Equaton (12) wth ˆÖand ˆ φ ). We drop subscrpt, whch denotes observaton. 19

20 E( y) β xβ = φ( zx ) β +Φ( z) σ φ( z) x σ σ = βφ ( ( z) +Φ( z) φ( z)) = βφ( z) (16) From equaton (12), partal dervatve calculates: * 2 E ( y y > 0) φ( ) ( ) 1 z φ β z z = x Φ( z) Φ( z) (17) See McDonald (1980) for the detaled dervaton. From these general formulas for elastcty estmaton, we can derve the estmaton measures for Leser-Workng model. 1) Estmaton on expendture elastcty peq ( ) Ew ( ) = x Ew ( ) x Eq ( ) = p Ew ( ) x Eq ( ) x Ew ( ) x x = + x x Eq ( ) p Eq ( ) p Eq ( ) Ew ( ) logx = 1+ Ew ( ) (18) We can apply ths formula for equaton (14) evaluated at the sample mean. Hence, uncondtonal expendture elastcty s: Eq [ ] ( ˆ ) ˆ x Φ z α eˆuncondtonal, = = 1+ x Eq [ ] Φ ( zˆ ) xβˆ + σφ ˆ ( zˆ ) (19) where upper bar denotes sample mean. Condtonal expendture elastcty s 20

21 * Eq [ 0] ( ˆ) ( ˆ) q > x Φ z Φ z * x Eq [ 0] ˆ ( zˆ) q > φ xβ + σˆ Φ( zˆ) eˆ = = 1+ αˆ 2 φ( zˆ ) φ( zˆ ) 1 zˆ (20) where φ and Φ are the densty functon and cumulatve densty functon of the standard normal evaluated at z, respectvely. 2) Own-prce elastcty Eq ( ) = p Ew ( ) x Ew ( ) x p p 2 Ew ( ) Ew ( ) x Ew ( ) x Eq ( ) p p p log p p q q Ew = = 1+ 2 p ( ) (21) Uncondtonal own-prce elastcty s Φ( zˆ ) ˆ β eˆ, uncondtonal = 1+ (22) Φ ( zˆ ) xβˆ + σφ ˆ ( zˆ ) Condtonal own-prce elastcty s eˆ = 1+, condtonal βˆ 2 φ( zˆ ) φ( zˆ ) 1 zˆ ( ˆ ) ( ˆ Φ z Φ z) ˆ φ( zˆ) xβ ˆ + σ Φ( zˆ ) (23) 3) Cross-prce elastcty Eq ( ) = p j Ew ( ) x p p j j 21

22 Ew ( ) x Ew ( ) Eq ( ) pj pj pj log p = = p q q p Ew ( ) j j (24) Uncondtonal cross-prce elastcty s eˆ j, uncondtonal Φ( zˆ ) ˆ βj = (25) Φ ( zˆ ) xβˆ + σφ ˆ ( zˆ ) Condtonal own-prce elastcty s eˆ j, condtonal = βˆ j 2 φ( zˆ ) φ( zˆ ) 1 zˆ ( ˆ ) ( ˆ Φ z Φ z) ˆ φ( zˆ) xβ + σˆ Φ( zˆ ) (26) IV-6: Heckman s Two-stage (Sample Selecton) model In order to correct the sample bas problem, we appled Heckman s two-step estmaton procedure (Heckman, 1978). Ths procedure nvolves two steps. In the frst stage, the decson for the household s modeled as a dchotomous choce problem, whch s estmated as a probt model. In order to obtan consstent estmate, we set dummy varable for equaton (11): I= 1 f y > 0 I= 0 otherwse (27) Replacng dependent varables of equaton (11) by (27), we get estmates of β σ. Usng these values, we get estmates values of φ ( z ) and Φ ( z ) for each observaton. At the second stage, we estmate equaton (11) by OLS usng ˆÖand ˆ φ n place of wth Öand φ. 22

23 IV-7: Standard (Type 1) Tobt Model We estmate the equaton (11) as a censored normal regresson model. We apply the same elastcty formulas for both Heckman s Two-step and standard Tobt model. IV-8: Complete Demand System Deaton and Muellbauer (1980a, 1980b) developed a flexble demand system called the almost deal demand system (AIDS). The concept of a flexble demand system s extremely useful for estmatng a demand system wth many desrable propertes. As Moschn (1998) ponted out, the AIDS model automatcally satsfes the addng-up restrcton, and wth smple parametrc restrctons, homogenety and symmetry are handled. In addton, the non-lnear Engel curves of the AIDS model mply that an ncrease n ncome wll decrease the share of ncome allocated on the partcular commodty as well as the ncome elastcty of that good f the ncome elastcty of the good s less than one. However, the AIDS model may be dffcult to estmate because the prce ndex s not lnear n parameters estmated. Due to the smplcty, the lnear approxmated almost deal demand system (LA/AIDS) s popular amongst emprcal studes. Therefore, both LA/AIDS and AIDS models are appled n ths study. The AIDS model can be estmated as follows: w = α + γ jln( pj) + β ln( x/ P) + µ = 1,, 11 (28) j 23

24 where w s the budget share of good, p j s the prce of good j, x s the total expendture of the goods n queston, µ s are random dsturbances assumed wth zero mean, and P s a translog prce ndex defned by: 1 logp= α0+ αk log pk + γ * kl log pk log pl 2 (29) k k l and the parameters γ are defned as follows: k = 1,, 11 l = 1,, 11 1 γ j = ( γ * j + γ * j ) = γ j j = 1,, 11 (30) 2 The model defned by the equatons (28) to (30) s called the AIDS model. It s easy to check that the addng-up restrcton s satsfed wth gven w = 1 for all j; α = 1, β = 0, and γ kj = 0 (31) k The homogenety restrcton s satsfed for the AIDS model f and only f, for all j; γ jk = 0 k (32) The symmetry s satsfed by: γ j = γ j (33) Usng the prce ndex n equaton (29) rases the estmaton dffcultes due to non-lnearty n parameters. In addton, the theory of the household does not provde any emprcally plausble value for α The mnmum expendture on the commodty s wdely used for the value of α 0 n order to overcome emprcal dffcultes. The nterpretaton and ratonal s that α 0 represents a subsstence good. 24

25 For the emprcal tractablty, approxmaton of prce ndex s appled. In ths study, we apply two dfferent types of prce ndex approxmatons. Frst, the Stone prce ndex P* s used, and then the log-lnear analogue of the Laspeyres prce ndex s used. As Asche (1997) ponted out, the Stone ndex s wdely used for LA/AIDS estmaton. ln( P*) = w ln( p ) = 1,, 11 (34) where w s budget share among eleven commodtes. The Stone ndex s an approxmaton proportonal to the translog. P = ϕ P* where E(ln(ϕ)) = α 0. The LA/AIDS model wth the Stone ndex can be seen as follows: w = α* + γ ln( p ) + β ln( x/ P*) + µ * j j j (35) where α = α βα and * µ = µ β (ln( ϕ) (ln( ϕ))). * E Snce prces wll never be perfectly collnear, t s wdely cted that applyng the Stone ndex wll ntroduce the unts of measurement error. (See Alston (1994), Asche (1997), and Moschn (1995).) The Stone ndex does not satsfy the fundamental property of ndex numbers, because the Stone ndex s varant to changes n the unts of measurement of prces. One of the solutons to correct the unts of measurement error s that prces are scaled by ther sample mean. Followng Moschn s suggeston (1995) we created the Laspeyres prce ndex n order to overcome ths measurement error. The loglnear analogue of the Laspeyres prce ndex s obtaned by replacng wth w n equaton (34) 0 w, whch s a mean budget share. Hence, the Laspeyres prce ndex becomes a geometrcally weghted average of prces: 25

26 = L 0 ln( P ) w ln( P) (36) Substtuton of (36) nto (35) wll yeld a LA/AIDS model wth the Laspeyres prce ndex as follows: (37) w = α + γ ln( p ) + β (ln( x) w ln( p )) + µ ** 0 ** j j j j j j where α = α β ( α w ln( p )). ** j j j Followng Pollak and Wales (1981, 1978), we appled lnear demographc translatng, N D ( η) = δη, where δ s and η s are assocated parameters and the r= 1 r r demographc varables, respectvely. In ths study, the lnear demographc translatng replaces equaton (28) as follows: (38) w = α + δη + γ ln( p ) + β (ln( x) w ln( p )) + µ *** 0 *** k k j j j j k j j where α = α δη. Demographc and dummy varables used n the complete *** ** k k k demand system are the same as the ones used n sngle equaton models. The addng-up restrcton requres *** α = 1, and δk = 0, k = 1,, m (39) where m s the number of demographc and other dummy varables. In order to correct the zero consumpton problem, we appled the generalzed Amemya s two-stage estmators to a smultaneous-equaton model. (See Amemya (1974), Lee and Ptt (1986), and Henen and Wessels (1990).) In the frst stage, the probt model of the dchotomous choce model s estmated. From the regresson results, we derve the nverse Mlls rato. For the LA/AIDS model, we only use the nverse Mlls 26

27 rato of rce, fats and ol, and food away from home. These three nverse Mlls ratos are used as an nstruments n the second stage. Smlar arguments are appled from the Heckman s two-step estmator secton. IV-9: Elastcty Estmates n the AIDS model The elastcty measures of the AIDS and the LA/AIDS model are wdely nvestgated and well documented. Followng Bues (1994) and Green and Alston (1990), takng the dervatve of equaton (35) wth respect to ln(x), we can obtan the expendture elastcty e as follows: e 1 w = 1+ w ln( x) β = 1+. (40) w Takng the dervatve wth respect to ln(p j ), uncompensated own (j=) and cross (j ) prce elastctes, e j, become as follows: e j 1 w = δj + w ln( pj) γ j β 0 = δj + wj, j = 1,, n, w w (41) where δ j s the Kronecker delta that s unty f = j and zero otherwse. We can derve the Hcksan compensated prce elastctes for the AIDS and the LA/AIDS model. The compensated prce elastctes becomes as follows: * s j at the pont of normalzaton s = e + ew * j j j γ = δj + + = w j 0 0 wj, j 1,, n. (42) 27

28 V Emprcal Results The orgnal data consst of 95,225 observatons. When only non-zero consumpton data are utlzed, the number of observatons drops to 21,496 n the whole sample case, 3173 n ncome class 1, 4007 n ncome class 2, 4436 n ncome class 3, 4875 n ncome class 4, and 5005 n ncome class 5. When the Workng-Leser model s estmated wth the prce data constructed above, zero consumpton households wth a zero budget share are assumed to be facng the mean prce for the partcular geographc locaton, month, and ncome level. In the censored regresson, data are corrected by Heckman s two-step procedure. The estmates of expendture and ncome elastctes from whole-sample workng- Leser model are shown n Table 9. Frst of all, the results ndcate that rce s not an nferor good from ths estmaton. Expendture elastcty exceeds one. Other commodtes are relatvely expendture elastc. Only rce and food away from home exceeds the expendture elastcty of one. It s noteworthy that own-prce elastcty for rce s very elastc. Ths ndcates that Japanese consumers are senstve for the prce change. If ths estmate represents consumers behavor correctly, then rce mports, whch lead to the reducton of prce, mght beneft not only consumers but also rce farmers. The same estmaton has dvded nto ncome levels n the Tables 10 and 11. Table 10 shows the expendture elastctes by ncome bracket. All estmates are nvarant wth ncome level. Fresh fsh and meat show that lower ncome consumers demands tend to be expendture elastc, whle hgher ncome consumers are nelastc. Table 11 shows the own-prce elastctes by ncome bracket. There are no sgnfcant varatons of elastcty estmates by ncome level. 28

29 The parameters of the LA/AIDS and AIDS model wth demographc and seasonal dummy varables are estmated by droppng one equaton, whch s food away from home. We apply for the teratve seemngly unrelated regresson procedure (ITSUR) n Table 9: Whole Sample Elastcty Estmates for Major 11 Products (OLS) Mean Own Prce Expendture Budget Food Items Share Elastcty Elastcty Non-glutnous Rce 8.05% (0.029) (0.009) Bread 5.56% (0.003) (0.005) Noodle 3.83% (0.008) (0.007) Fresh Fsh 13.14% (0.005) (0.005) Fresh Meat 12.43% (0.006) (0.004) Mlk 4.71% (0.012) (0.007) Eggs 1.89% (0.006) (0.005) Fresh Vegetables 14.30% (0.005) (0.003) Fresh Fruts 7.94% (0.006) (0.006) Fats and Ol 0.86% (0.014) (0.016) Food Away from Home 27.29% (0.171) (0.005) Notes: The numbers n parentheses below the elastcty estmaton are standard error. All estmates are statstcally sgnfcant at 5% level. 29

30 Table 10: Expendture Elastcty for Major 11 Income Level (thousand yen) Income 1 Income 2 Income 3 Income 4 Income 5 < < Food Items Mean Mean Mean Mean Mean Budget Elastcty Budget Elastcty Budget Elastcty Budget Elastcty Budget Elastcty Share Estmate Share Estmate Share Estmate Share Estmate Share Estmate Non-glutnous Rce 10.21% % % % % (0.017) (0.020) (0.021) (0.022) (0.021) Bread 5.66% % % % % (0.012) (0.013) (0.012) (0.013) (0.012) Noodle 4.16% % % % % (0.015) (0.015) (0.016) (0.016) (0.017) Fresh Fsh 14.33% % % % % (0.010) (0.011) (0.012) (0.012) (0.011) Fresh Meat 11.88% % % % % (0.010) (0.009) (0.010) (0.010) (0.009) Mlk 5.00% % % % % (0.015) (0.015) (0.016) (0.016) (0.015) Eggs 2.05% % % % % (0.012) (0.012) (0.013) (0.012) (0.013) Fresh Vegetables 15.92% % % % % (0.007) (0.008) (0.008) (0.008) (0.008) Fresh Fruts 9.08% % % % % (0.013) (0.015) (0.016) (0.016) (0.016) Fats and Ol 0.99% % % % % (0.035) (0.037) (0.036) (0.039) (0.040) Food Away 20.73% % % % % from Home (0.013) (0.011) (0.011) (0.011) (0.010) Notes: The numbers n parentheses below the elastcty estmaton are standard error. All estmates are statstcally sgnfcant at 5% level. Table 11: Own Prce Elastcty for Major 11 Income Level (thousand yen) Income 1 Income 2 Income 3 Income 4 Income 5 < < Food Items Mean Mean Mean Mean Mean Budget Elastcty Budget Elastcty Budget Elastcty Budget Elastcty Budget Elastcty Share Estmate Share Estmate Share Estmate Share Estmate Share Estmate Non-glutnous Rce 10.21% % % % % (0.058) (0.067) (0.069) (0.066) (0.065) Bread 5.66% % % % % (0.008) (0.007) (0.007) (0.007) (0.007) Noodle 4.16% % % % % (0.017) (0.016) (0.017) (0.017) (0.018) Fresh Fsh 14.33% % % % % (0.010) (0.011) (0.011) (0.011) (0.011) Fresh Meat 11.88% % % % % (0.013) (0.012) (0.013) (0.012) (0.012) Mlk 5.00% % % % % (0.027) (0.026) (0.027) (0.026) (0.025) Eggs 2.05% % % % % (0.013) (0.012) (0.012) (0.012) (0.013) Fresh Vegetables 15.92% % % % % (0.010) (0.011) (0.012) (0.012) (0.012) Fresh Fruts 9.08% % % % % (0.013) (0.014) (0.014) (0.014) (0.015) Fats and Ol 0.99% % % % % (0.031) (0.030) (0.028) (0.030) (0.032) Food Away 20.73% % % % % from Home (0.486) (0.393) (0.360) (0.354) (0.344) Note: The numbers n parentheses below the elastcty estmaton are standard error. All estmates but the lowest ncome class mlk are statstcally sgnfcant at 5% level. 30

31 SAS. ITSUR runs less than 15 teratons to meet the convergence crtera of 1e-4 for all models. The regresson results summarzed n appendx show the values of the estmated coeffcents and ther absolute t-values except demographc and seasonal dummy varables. The last column n appendx represents the parameters of food away from home s obtaned by usng addng-up condton n equaton (31). The row of γ 11 can be generated by the homogenety restrcton n equaton (32), and the blank cells can be recovered by usng symmetry condton n equaton (33). Heckman s two-step, Tobt estmator, and nverse Mlls rato are estmated by LIMDEP verson 7.0. Tables 12 and 13 show the elastcty estmates from AIDS model wth nverse Mlls rato of rce, fats and ol, and food away from home. Table 12 shows the results of uncompensated prce elastcty and expendture elastcty. Expendture elastcty of rce ndcates that rce s normal good, and t exceeds one. Rce s mld complement wth all commodtes but food away from home. Partcularly, the estmated cross prce elastctes between rce and both fsh and meat carry negatve sgns. Thus, we may conclude that fsh and meat are complements to rce. In Table 13, compensated prce elastcty shows the mxed results. Rce s substtutes wth fresh fsh, whle t s complements wth fresh meat. Table 14 compares the own-prce elastcty estmates from all models. It s surprsng that uncompensated own-prce elastcty for rce exceeds 1.7 n absolute term. Hgh own prce elastcty of rce s robust across models. The lowest estmate of ownprce elastcty for rce s 1.2 n condtonal estmates of Heckman s two-step and Tobt estmators. 31

32 Table 15 s the comparson table of expendture elastcty estmates. All expendture elastcty estmates are transferred to the ncome elastcty usng the formula n equaton (6) 4. Table 16 shows the ncome elastcty from all models. In all estmaton, t turns out that Japanese rce s normal good. Ths result s robust across models. VI. Concluson In the consumpton lterature, grans n developed countres are consdered as an nferor good. Based on that, t would be natural to assume that rapd economc growth of Asan countres should result n lower rce demand. Ths bref survey strongly contradcts these assumptons for rce n Japan. Rce consumed n Japan s a normal good, although the ncome elastcty does not exceed unty. Marshallan and Hcksan own-prce elastctes for rce are hghly elastc for all models; on the other hand, the own prce elastcty for meat s relatvely prce nelastc. From the results of the AIDS model, we show that rce n Japan s a mld complement wth fresh meat and fsh. 4 Engel functon s estmated; however, the estmaton results are not shown n ths study. Results are provded by the author upon request. All coeffcents are statstcally sgnfcant and correct sgns. 32

33 Table 12: Elastcty for Major 11 Products: AIDS model wth Inverse Mlls Rato Mean Uncompensated Prce Elastcty Expendture Budget Elastcty Food Items Share Rce Bread Noodle Fsh Meat Mlk Eggs Vegt. Fruts Ol FAFH Non-glutnous Rce 8.05% Bread 5.56% Noodle 3.83% Fresh Fsh 13.14% Fresh Meat 12.43% Mlk 4.71% Eggs 1.89% Fresh Vegetables 14.30% Fresh Fruts 7.94% Fats and Ol 0.86% Food Away from Home 27.29% Table 13: Elastcty for Major 11 Products: AIDS model wth Inverse Mlls Rato Mean Hcksan Compensated Prce Elastcty Budget Food Items Share Rce Bread Noodle Fsh Meat Mlk Eggs Vegt. Fruts Ol FAFH Non-glutnous Rce 8.05% Bread 5.56% Noodle 3.83% Fresh Fsh 13.14% Fresh Meat 12.43% Mlk 4.71% Eggs 1.89% Fresh Vegetables 14.30% Fresh Fruts 7.94% Fats and Ol 0.86% Food Away from Home 27.29%

34 Table 14: Elastcty Comparson: Own-Prce Elastcty Food Items Mean % of Workng Heckt Tobt Budget zero Leser Un- Condtonal Un- Condtonal Share Cons (OLS) condtonal condtonal Non-glutnous Rce 8.05% 43.75% (0.029) Bread 5.56% 4.15% (0.003) Noodle 3.83% 6.14% (0.008) Fresh Fsh 13.14% 2.45% (0.005) Fresh Meat 12.43% 1.92% (0.006) Mlk 4.71% 8.36% (0.012) Eggs 1.89% 5.51% (0.006) Fresh Vegetables 14.30% 0.24% (0.005) Fresh Fruts 7.94% 5.50% (0.006) Fats and Ol 0.86% 42.12% (0.014) Food Away from Home 27.29% 12.65% (0.171) Notes: The numbers n parentheses below the elastcty estmaton are standard error. All estmates are statstcally sgnfcant at 5% level. 34

35 Table 14 (contd.) Elastcty Comparson: Own-Prce Elastcty Mean % of LA/AIDS AIDS Budget zero Stone Prce Index Laspeyres Prce Index Share Cons wthout wth wthout wth wthout wth IMRs IMRs IMRs IMRs IMRs IMRs Uncom- Com- Uncom- Com- Uncom- Com- Uncom- Com- Uncom- Com- Uncom- Com- Food Items pensated pensated pensated pensated pensated pensated pensated pensated pensated pensated pensated pensated Non-glutnous Rce 8.05% 43.75% (0.028) (0.028) (0.020) (0.020) (0.028) (0.028) (0.020) (0.020) Bread 5.56% 4.15% (0.003) (0.003) (0.003) (0.003) (0.003) (0.003) (0.003) (0.003) Noodle 3.83% 6.14% (0.008) (0.008) (0.008) (0.008) (0.008) (0.008) (0.008) (0.008) Fresh Fsh 13.14% 2.45% (0.005) (0.005) (0.005) (0.005) (0.005) (0.005) (0.005) (0.005) Fresh Meat 12.43% 1.92% (0.005) (0.005) (0.005) (0.005) (0.005) (0.005) (0.005) (0.005) Mlk 4.71% 8.36% (0.012) (0.012) (0.012) (0.012) (0.012) (0.012) (0.012) (0.012) Eggs 1.89% 5.51% (0.005) (0.005) (0.005) (0.005) (0.005) (0.005) (0.005) (0.005) Fresh Vegetables 14.30% 0.24% (0.005) (0.005) (0.005) (0.005) (0.005) (0.005) (0.005) (0.005) Fresh Fruts 7.94% 5.50% (0.006) (0.006) (0.006) (0.006) (0.006) (0.006) (0.006) (0.006) Fats and Ol 0.86% 42.12% (0.013) (0.013) (0.012) (0.012) (0.013) (0.013) (0.012) (0.012) Food Away from Home 27.29% 12.65% Note: The numbers n parentheses below the elastcty estmaton are standard error. All estmates are statstcally sgnfcant at 5% level. 35