Demand for food in Ondo state, Nigeria: Using quadratic almost ideal demand system

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1 E3 Journal of Busness Management and Economcs Vol. 4(1). pp , January, 2013 Avalable onlne ISSN E3 Journals 2013 Full length research paper Demand for food n Ondo state, Ngera: Usng quadratc almost deal demand system Olorunfem Sola Department of Economcs, Adeunle Aasn Unversty, Aungba-Aoo, Ondo State, Ngera , E-mal: olorunfem@adeunleaasnunversty.edu.ng Accepted 18 December, 2012 There has been great emphass, on how to reduce the consequences of food nsecurty on the people of Ondo State, Ngera, as a result of whch there s a lot of research nto demand for food. Estmaton of demand for food has gnored requred connecton between theory and emprcal analyss and concentrated on the estmaton of sngle lnear demand equaton. Even where non lnear models such as Almost Ideal Demand System (AIDS) models were used; there was no allowance for a non-monotonc relatonshp between the margnal budget share and total expendture. Thus, ths study examned demand for food n Ondo State usng standard Quadratc Almost Ideal Demand System (QUAIDS) and the specfc obectves are: () to examne the expendture pattern, () to determne how household demography affects household expendture for food, and () to analyse the dfference n expendture purchase among the households n the three senatoral dstrcts of the State. Data collected from 1,200 heads of households, through multstage samplng methods were analyzed. Result shows that the QUAIDS test s more relable, as the Wald test{ch2(9)=340.71; Prob Ch2=0.0000} ndcates that lambda coeffcents are ontly sgnfcantly dfferent from zero and that the quadratc ncome terms are mportant, showng the superorty of QUAIDS model over the AIDS model. The estmated expendture elastctes for all Ondo State are all postve and statstcally sgnfcant at the 5%, ndcatng that all the food tems are normal goods and that rce, beans, yam-flour, meat and vegetable and fruts are luxury goods snce the coeffcents are 1.419, 1.017, 1.385, and respectvely whch are greater than 1. However, garr, yam, bread and plantan are all necessty goods. The study conclude that polcy-maers should consder consumer behavor at dfferent ncome and prce levels, as ths wll affect the rate at whch people have access to food. Key words: AIDS, QUAIDS, Elastcty, Expendture, Food Demand and Household. INTRODUCTION The poverty stuaton n Ngera s qute dsturbng. Most quanttatve measurements attest to the growng ncdence and depth of poverty n the country (Ounmadewa, 1996). Ths stuaton however, presents a paradox consderng the vast human and physcal resources that the country s endowed wth. It s even more dsturbng that despte the huge human and materal resources that have been devoted to poverty reducton by successve governments, no sgnfcant success has been acheved. Although, predcted poverty reducton scenaros vary greatly dependng upon the rate and nature of poverty related polces, actual evdence suggests that the depth and severty of poverty s stll at ts worst n Ngera, Sub-Saharan Afrca and South Asa (Hanmer and Nasehold, 2000; Barber, 2000; Ounmadewa, 1996). Accordng to Yem (2012), mllon Ngerans lve n relatve poverty condtons, whch represents 69% of the country s total populaton.

2 002 E3 J. Bus. Manage. Econ. Ths s staggerng when compared wth the country s estmated 163 mllon populaton. Yem (2012) estmates that ths trend may ncrease further nto the future f the potental mpacts of several ant-poverty programmes, such as food securty nterventon programme, are not taen nto account. Food s a basc necessty of lfe. Its mportance, at the household level, s obvous snce t s a basc means of sustenance. In vew of the mportance of food n man s lfe, food s rated as the most basc of all human needs. Man needs food for lfe s sustenance, preventon of scness and n provdng energy for the normal psychologcal actvtes of the body ncludng the normal state of mnd. Hence, the need for food securty becomes pertnent as t eventually affects a naton s productvty and growth. Food securty exsts when all people at all tmes have access to safe nutrtous food to mantan a healthy and actve lfe (FAO, 2002 ). The man goal of food securty s for ndvduals to be able to obtan adequate food needed at all tmes, and to be able to utlze the food to meet the body s needs. Food securty requres access to food both n terms of avalablty whch s descrbed as the ablty of people to access food of adequate nutrtonal qualty and quantty and be able to afford t. There s adequate access when there s adequate food avalablty to the household and, at the same tme, the household has adequate capacty for effectve demand for avalable food. In the recent years, attenton has been focused on the means to elmnate food nsecurty and hunger worldwde. The Internatonal Conference on Nutrton, 1992 and the World Food Summt 1996, both emphaszed the crtcal need to decrease food nsecurty and hunger globally. Accordng to Sen (1981), Maxwell and Franenberge r (1992), Bentley and Pelto (1991) and USAID (1999), food securty ncludes the related concepts of physcal access to food, economc access to food and food utlzaton. Accordng to USAID (1999), food access, otherwse referred to as food demand or economc access to food s ensured when households and ndvduals wthn them have adequate resources to obtan approprate foods for a nutrtous det. Access depends on ncome avalable to the household, the dstrbuton of ncome wthn the household, and the prce of food. In Ngera, food prces contnue to soar up day by day, and, ultmately gong out of the reach of the common man whle household ncomes n the country are sgnfcantly debased by the staggerng nflaton rate. The retal prce ndex for food n 1970, was 12.5% but ths has rsen outrageously to 548.2% n Ths underscores the fact that households ncome can hardly cope wth soarng food prces, whch has compelled ncreased food spendng out of households ncome of between 60 percent and 80 percent coupled wth poor ncome per capta, n Ngera. Wth ncreased emphass on how to acheve food access so as to reduce consequences of food nsecurty on the people n Ngera, there s the urgent need to carry out more research on food demand. The compellng reason beng that the country s populaton has grown to 167mllon wth the growth rate of 3.75 per cent per annum (James, 2011) whch causes a heavy pressure on demand for food. More research evdence on food demand s necessary, partcularly at the State level, as natonal surveys may not be approprate for proddng possble solutons. Ondo State s one of the States wth a growng populaton rate and ths should mae the government and the polcy maers to be nterested n food access (demand) by the people. The obectves of the study therefore, are as follows: ) to examne the expendture pattern for food n Ondo State. ) to determne how household s demography affect household s expendture for food. ) to analyse the dfferences n expendture purchases among the households n the three senatoral dstrcts of the State. The sequence of the study s clear. The lterature revew s dscussed n Secton 2 whle Secton 3 deals wth the methodology. Secton 4 presents and dscusses the emprcal results and Secton 5 deals wth the study s concluson. Lterature Revew Estmaton of demand functons consstent wth economc theory has been hghly researched n the last four decades. Estmaton of demand for goods and servces has also attracted the attenton of both theoretcans and emprcsts, and a very dense lterature s now avalable. Some of these studes such as Blundell (1998) have gnored requred connectons between theory and emprcal analyss, whle concentratng on the estmaton of sngle lnear demand equatons. Gven the doubts about the results of such an approach, emprcal wor such as Po (2002) and Po (forthcomng) has been drected towards the estmaton of complete demand systems. Estmaton of demand functons s very useful as t provdes nformaton on ncome and prce elastctes. The measurement of ncome and prce elastctes s requred for the desgn of many dfferent polces. For example, ntellgent polcy desgns for ndrect taxaton and subsdes that requre nowledge of these elastctes for taxable commodtes and servces. The goal of demand analyss s to model households expendture patterns on a group of related tems n order to obtan estmates of prce and ncome elastctes and to estmate consumer welfare. As emphaszed by Blundell (1988), there are few aspects of poltcal economy that do not requre some nowledge about consumers household behavor. Emprcal evdence on consumer s behavor s ncreasngly mportant n the formulaton and

3 Olorunfem. 003 analyss of economc polces. Consumpton affects economc actvty n several dmensons. For nstance, one of the most often used practces to measure the effect of prce changes on consumpton s to estmate demand functons. The analyss of consumer behavor s ndspensable snce there are few aspects of economc polcy that do not requre some nowledge of household behavor. To be able to estmate demand functon, many functonal forms are avalable, economc theory does not answer the queston of whch specfcaton s the best to choose n estmatng t. Dfferent approaches for comparson have been proposed n the lterature. An elementary approach conssts of estmatng dfferent specfcatons of demand functons wth a gven data set and selectng the one that has the best goodness of ft statstcs (Berndt et al., 1977; Fsher et al, 2001). A second approach uses the fact that the propertes of demand functons, derved from neoclasscal preferences are nown only n the regon wthn whch the functons satsfy theoretcal regularty condtons. Knowng the locaton and sze of the regular regon can help support the choce of one functonal form over another (Caves and Chrstensen, 1980; Barnett and Lee, 1985). A thrd approach uses a Monte Carlo study to explore accuracy of the demand model, when the true elastctes of substtutons are nown (Barnett and Cho, 1989). There has been wdespread nterest n choosng an estmate system of equaton to represent household demand for varous goods. These nclude the Lnear Expendture System (LES) of Stone (1954) whch has been the poneer n ths area. However, LES has some lmtatons such as proportonal ncome and prce elastctes, and the rulng out of complementary relatonshps among goods. These lmtaton opened doors to the development of other models. Rotterdam model (Thel, 1965) and Translog model (Chrstensen, et al. 1975) can be lsted among these more flexble models. However, Deaton and Muellbauer ( 1980) proposed an alternatve modellng whch they called Almost Ideal Demand System (AIDS). AIDS gves an arbtrary frst-order approxmaton to any demand system; t satsfes exactly the axoms of choce; t perfectly over aggregates consumers choces wthout nvong parallel lnear Engel curves; t has a functonal form whch s consstent wth nown household-budget data; t s smple to estmate, largely avodng the need for non-lnear estmaton; and, t can be used to test the restrctons of homogenety and symmetry through lnear restrctons on fxed parameters. Although many of these desrable propertes are possessed by one or the other of the Rotterdam or translog models, nether possesses all of them smultaneously. Thus AIDS modellng has attracted a great deal of attenton; and, t has been used extensvely n emprcal studes. Though AIDS has been wdely used n analyzng consumpton n developng countres, there s now evdence to suggest that the lnearty of budget shares n the logarthm of household expendture maes t a very restrctve model (Meenash and Ray, 1999). The AIDS model s locally flexble, n the sense that t does not put a pror restrctons on the possble elastctes at any one pont. The model thus possesses enough parameters to approxmate any elastctes at a gven pont. But, ts locally flexble functonal form often exhbts small regular regon consstent wth mcroeconomc theory. As a result, a number of alternatve flexble functonal forms wth larger regular regons have been developed. Examples nclude the Quadratc AIDS model (QUAIDS) (Bans et al, 1997). Ths extenson of AIDS s developed to mae the model as rch as possble. Studes across the world have emerged that confrm the approprateness of QUAIDS n modellng preferences. Examples usng developed countres data, nclude Abdula (2002) who apples QUAIDS to the food expendture data from Swtzerland, Moro and Scoa (2000) who use Italan food expendture data; Gould and Vllarreal (2006) usng food expendture data from urban Chna. Bans et al. (1977) and Blundell and Robn (1999) who both use expendture data on broad consumpton goods from the U.K., and Fsher et al. (2001) who apply QUAIDS to the U.S. aggregate consumpton data. A number of studes n developng countres are also emergng that support QUAIDS. However, these studes are fewer compared to those from developed countres. Examples nclude Abdula and Aubert (2004) usng Tanzanan food expendture data, Meenash and Ray (1999) usng Indan food expendture data, and Molna and Gl (2005) usng aggregate consumpton data from Peru. Most of these studes, however, dd not tae nto consderaton demographc varables. In Afrca, studes had also been carred out on food demand analyss usng AIDS and a few studes usng QUAIDS. These nclude Talaard et al (2004), Ahmad et al (1993), and Robert (2009). Some of the studes, n South Afrca, have typcally been based on hghly aggregate data and have ether been lmted to examnng only one commodty (e.g. Talaard, 2003; Neuwoudt, 1998) or gnored any mpact of demographc factors on food demand (Bowmaer and Neuwoudt, 1990). The excepton s the study by Agboola (2003) whch s based on mcro data and ncorporates household demographcs. However, he used cross sectonal data collected n 1993, one year pror to the maor reforms ntroduced by the democratc government. Furthermore,Agboola s study s based on a

4 004 E3 J. Bus. Manage. Econ. Fgure 1: Map of the Study Area (nset: Ngera showng Ondo) Source: Ondo State Mnstry of Lands and Housng, Aure restrctve lnearzed Almost Ideal Demand System (LA/AIDS) model, whch does not allow for adequate curvature n the Engel curves. In a related study, usng the KIDS data-set, Bopape and Myers (2000 ) explctly tested for whether the demand model should be specfed wth a quadratc (QUAIDS) or a lne ar AIDS expendture term and found evdence aganst AIDS. Ths study also tests for expendture endogenety and control for t where necessary. In Ngera, there are few lteratures on food demand, maorty of whch centered on the demand for ndvdual food tems. Such studes nclude the study on the demand for rce by Odusna (2008) usng AIDS model. In addton, scanty emprcal studes have looed closely at the demand for food usng QUAIDS model n Ngera. For example, Abodun et al (2009) looed at the mpact of soco-economc varables on households food demand. Ths dd not consder the demographc factors. Also, t was a research consdered for the North Central Ngera. Ths present study devated from the prevous study as t looed at the pattern of food demand n Ondo State usng QUAIDS model. The effect of the demographcal factors was also taen nto consderaton. METHODOLOGY Study Area Ondo state covers a land area of 14,793 square lometres wth ts admnstratve captal at Aure. The populaton of the State n the 1991 Census, was 2,249,548 whle the 2006 census put the populaton at 3,441,024. The State s made up of 18 Local Government Areas (LGAs); and, t s bounded n the North by Et and Kog States and n the South by the Atlantc Ocean. Ondo State s located entrely wthn the Tropcs (see Fgure 1). The tropcal clmate of the State s broadly of two seasons: rany season (Aprl -October) and dry season (November March). The temperature throughout the year ranges between 21 oc to 29 oc and humdty s relatvely hgh. The annual ranfall vares from 2,000mm n the Southern areas to 1,150mm n the northern areas. The State enoys luxurant vegetaton wth hgh forest zone (ran forest) n the south and sub-savannah forest n the northern frnge. There s a maze of numerous rvers, crees and laes n and around Ondo State wth very promnent rvers le

5 Olorunfem. 005 Owena, Ala, Oluwa, On, Awara, Ogbese and Ose. Generally, the land rses from the coastal part of Ilae, Ese-Odo and Otpupa areas to hghlands and nselbergs to the northern parts of the state. The State s economy s bascally agraran wth large scale producton of cocoa, palm produce, tmber and rubber. Other crops le maze, yam and cassava are produced n large quanttes for both consumpton and commerce. Nature and Sources of Data Both prmary and secondary data were used for ths study. The Questonnare schedule was admnstered to generate necessary (prmary) nformaton. Data collected from 1,200 heads of households, through a multstage samplng method were analyzed. The eghteen LGAs n the state were the frst stage samplng unts. From these, sx LGAs were selected, to reflect dfferences along senatoral dstrcts. The selected LGAs are Aoo North East, Aure South, Ese Odo, Owo, Otpupa and Ondo East (see Fgure 1). Data were collected on some household characterstcs such as ncome, expendture, quanttes of food commodtes consumed etc. Data on mportant demographc varables were also collected, such as age and household szes. The secondary data such as populaton growth and prce ndex etc were obtaned from varous ssues of the Central Ban of Ngera (CBN) publcatons. Data Descrpton Data used were from a collecton of households budgets whch have been opportunely organzed n a data-set n order to gve them a common structure and mae room for comparson. By household budgets, data were collected on one or more famles n relaton to the followng: I. ts demographc structure; II. ts expendtures on food tems; and III. ts ncome. Model Specfcaton Consderaton was gven for a consumer s demand for a set of goods, for whch the consumer has budgeted y sums of currency. For example, the goods could represent dfferent categores of food and the amount to be spent on food y, was chosen based on a two-stage budgetng process. Alternatvely, the goods could represent broad categores le rce, beans, garr, yam and yam flour and m s household ncome. Demand systems are typcally specfed wth expendture shares as the dependent varables. Accordng to Po (2002), the household s expendture share for good s defned as w pq y where p s the prce pad for good, q s the quantty of good purchased or consumed, and y s the total expendture on all goods n the demand system. Wth ths defnton of y, 1 w 1 where K s the total number of goods n the system. The QUAIDS model assumes that household preferences belong to the followng quadratc logarthmc famly of expendture functons: ub() p In( u,)() p Ina p 1()() p b p u Where u s utlty, p s a vector of prces, a(p) s a functon that s homogeneous of degree one n prces, b(p) and (p) are functons that are homogeneous of degree zero n prces. The quadratc AIDS model of Bans, Blundell, and Lewbel (1997) s based on the ndrect utlty functon. ln( V,)() p y ln y ln() a p b() p 1 where y s total expendture. The specfc functonal form s () p InP 1, where 1 0 and where = 1,, denote the number of goods enterng the demand model. And where In a(p) s the transcendental logarthm functon 1 ln() a p 0 ln p ln lnp p P s the prce of good for = l., b(p) s the Cobb- Douglas prce aggregator b() p and 1 1 p () p ln p The fact that w 1 s often called the addng-up condton and ths condton s satsfed f the followng p 1

6 006 E3 J. Bus. Manage. Econ. hold, that s f: and 1 0 The addng-up restrctons are not testable, and are mposed by droppng one of the share equatons and estmatng the remanng equatons. Moreover, snce demand functons are homogeneous of degree zero n (p,y), 1 0 Slutsy symmetry mples that Usually, 0 s dffcult to estmate drectly and so s set equal to the mnmum level of expendture that would be needed for subsstence f all prces were equal to one. To be able to specfy the expendture model f q denote the quantty of good consumed by a household, and p q defne the expendture share for good I as w. y Applyng Roy s Identty as used n Po (2012 ) to equaton (1), 2 y y w ln p ln ln, a()()() p b p a p y y w ln p xln ln 1 yxa p bpc p, x y0 xap When for all I, the quadratc term n each expendture share equaton drops out, and we are left wth Deaton and Muellbauer s (1980a) orgnal AIDS model. Consder the orgnal AIDS model wthout the quadratc term: y w ln p ln, a() p Ths set of expendture share equatons requres nonlnear estmaton technques because of the prce ndex ln()a p. Deaton and Muellbauer (1980) suggests replacng that prce ndex wth the approxmaton ln() a p ln w p, resultng n a set of equatons that can be ft by lnear estmaton technques. If a demographc varable s ntroduced, usng the scalng technque by Po (2012) and extended to the quadratc AIDS model. We use x to represent a vector of s characterstcs. In the smplest case, x could be a scalar representng the number of people n a household. Let R e ( p,) u denote the expendture functon of a reference household, where a reference household mght be one that contans ust a sngle adult. Ray s method uses for each household an expendture functon of the form R e p, x, u y p, x, u. e p, u 0 The functon y0 p, x, u scales the expendture functon to account for the household characterstcs. Ray further decomposes the scalng functon as m p, x, u y z. p, x, u 0 0 The frst term measures the ncrease n a household s expendtures as a functon of z, not controllng for any changes n consumpton patterns. Followng Po (2012) QUAIDS parameterzes y x px 0 1 y0 x as Where p s a vector of parameters to be estmated. As n Po (2002) QUAIDS parameterzes p, x, u ln p, x, u 1 u x n p p 1 1 ln p 1 The expendture share equatons tae the form represents the th column of s x parameter. Where c p, x 1 x n p The addng-up condton requres that r=1.s, f we set 1 as r 0 for for all, we are left wth the AIDS model wth demographcs used by Po (2012). Accordng to Po, the formulas for elastctes for the standard AIDS model and models wthout demographcs are nested wthn the more general varants and that the uncompensated prce elastcty of good wth respect to changes n the prce of good s 1 2 y x ln w bpc p, x y0 xa p x 2

7 Olorunfem. 007 Table1: Descrptve Statstcs for Important Varables Varable Obs Mean Std. Dev. Mn Max p p p p p p p p p p expfd w w w w w w w w w w lnp lnp lnp lnp lnp lnp lnp lnp lnp lnp lnexp age hhsze x y l ln pl ln l b pc p, x y xa p The expendture (ncome) elastcty for good s 1 2 y 1 x ln w b p c p x y0 x a p, Compensated prce elastctes are obtaned from the Slutsy equaton as w c Estmaton Methods The use of the quadratc model s ustfed by the quadratc relatonshp between the budget shares and the logarthm of total expendtures. The ncluson of demographc varables s meant to study whether the det of the famly members depends on the age of the ndvdual. Varables related to household s demography are expected to affect the allocaton of household expendtures among goods manly because of economes of scale and because famles of dfferent szes and composton have dfferent needs (Blow, 2003). RESULTS Descrptve Result In an attempt to loo at the expendture pattern for food demand, n Ondo State, ths secton begns by examnng the descrptve statstcs of the data used n the study. These nclude: descrptve statstcs for prces, expendture shares, and total expendture for each household age and household sze for the perod covered n the study. All these are n Table 1. Table 1 shows that P8 has the largest mean followed by P10. Whle P10 has the largest standard devaton, P6 has the smallest standard devaton. The mean and standard devaton for the total expendture are and The mean value for age and household sze are and 4.72 respectvely. Fgure 2a shows the head of household by age group. The Fgure shows that those above the age of 60 years are more n the South Senatoral Dstrct of the State followed by the Central Senatoral Dstrct. Those between the ages of years are less n the Central Senatoral dstrct. Fgure 2b shows the head of household by sex and local government. The mean number of males who are heads of household are more n each of the LGAs n the study area. Fgure 2c shows that the mean household sze for rural area s hgh n both the Ondo Central Senatoral and Southern Senatoral dstrcts. Whle the average household sze for rural and urban n Central and South Senatoral was 3 and 4 respectvely, but for the urban, t was 2 and 3 respectvely. At the North Senatoral area, the average household sze was 5 each for both rural and urban areas. Fgure 2d shows the scatterplot matrces

8 008 E3 J. Bus. Manage. Econ. a above mean of northsenatoral mean of southsenatoral mean of centralsenatoral b AKOKO NE AKURE SOUTH Ese Odo OWO Otpupa Ondo East mean of male mean of female c Central North South mean of rural mean of urban d expfd AGE hhsze Fgure 2. (a) Head of household by age group; (b) Head of household by sex and local government; (c) Household sze; (d) Scatterplot correlaton matrx among age, household sze and expendture between total expendture for food, age and household sze. Ths s used to loo at the relatonshp between all these varables. In each plot, the varable to the sde of the graph s used as the Y varable and the varable above or below the graph s used as the X Varable (Ulrch et al, 2008). In the frst lne of the Fgure 2d are scatter plots of expendture for food aganst age and household sze. Ths shows that there s postve relatonshp between expendture and age and between expendture and household sze. Table 2 shows the results of the estmated parameters of the AIDS model wth demographc varables (age and household sze). The thrd column reports parameter estmates of the AIDS model whle the fourth column reports the value of the standard error. Most of the 55 prce effect are sgnfcantly dfferent from zero at the 5% sgnfcance level, suggestng that there s much quantty response to movement n relatve prces, that s, a change n prce leads to systemc change n the expendture share for each of the commodtes. The coeffcent of the household sze s postvely related to the expendture share ndcatng that as the household sze ncreases, the expendture share for food also ncreases. Ths result s n lne wth Horowtz (2002). However, most of the coeffcents of age are negatve, ndcatng that at a younger age, the rate of consumpton tend to be hgh. Table 3 shows the estmated parameters of the QUAIDS model wth demographc varables (age and household sze) usng data on all of Ondo State. Most of the prces effects are sgnfcantly dfferent from zero at the 5% sgnfcance level, suggestng that there s much quantty response to movement n relatve prces. The expendture squared term on food s sgnfcant for all the food captured n the model. Ths contrasts wth smlar studes le Surabh (2008 ) that the squared terms of expendture on food are sgnfcant only for two of the food tem captured n hs study. The result of the QUAIDS model also show that the demand for food depends on the age and household composton of the household. We nterprete result only for the QUAIDS model. Ths s so because the fndng shows that the QUAIDS test s more relable, as the Wald test{ch2(9)=340.71; Prob Ch2=0.0000} ndcates that lambda coeffcents are ontly sgnfcantly dfferent from zero and that the quadratc ncome terms are mportant showng the

9 Olorunfem. 009 Table 2: Estmated Parameters of the AIDS Food Demand System wth Demographc Varables Usng Data on Ondo State Varable Eq Coeffcent Std. Error Constant α α α α α α α α α α Expendture β β β β β β β β β β Prces Table 2. CONT Age Age Age Age Age Age Age Age Age Age Age Household Sze hhsze 1 1, hhsze hhsze hhsze hhsze hhsze hhsze hhsze hhsze hhsze Sources: Author s Computaton usng Stata 11

10 010 E3 J. Bus. Manage. Econ. Table 3: Estmated Parameters of the QUAIDs Food Demand System wth Demographc Varables Usng Data on All of Ondo State Varable Eq. Coeffcent Std. Error Constant α α α α α α α α α α Expendture Squared β β β β β β β β β β Prces Table 3. Cont Expendture λ λ λ λ λ λ λ λ λ λ Age Age Age Age Age Age

11 Olorunfem. 011 Table 3. Cont. Age Age Age Age Age Household sze hhsze hhsze hhsze hhsze hhsze hhsze hhsze hhsze hhsze hhsze Sources: Author s Computaton usng Stata 11 superorty of QUAIDS model over the AIDS model. That s the quadratc model rather than the AIDS model s good because of the quadratc relatonshp between the budget shares and the logarthm of the total expendture. Ths fndng accords wth that of Luca (2007). Compensated Elastctes Compensated or Hcsan elastctes are reduced to contan only prce effects, and are thus compensated for the effect of a change n the relatve ncome on demand. By usng the parameter estmates n Table 4 for both AIDS and QUAIDS model n all of Ondo State, the compensated own and cross-prce elastctes, were calculated at ther sample means and are shown n Table 4. The compensated own and cross-prce elastctes for both AIDS and QUAIDS model was shown on Tables 5 to 7 for Ondo South, Ondo North and Ondo Central Senatoral Dstrcts. Compensated own prce elastctes of all ten foods are farly relatvely nelastc (see Table 4). For QUAIDS model, most of the food tems carry negatve sgns n accordance wth the a pror expectaton and are statstcally sgnfcant at the 5% level. The compensated own prce elastcty n all of Ondo State for beverages ( ) s the most elastc, followed by the own prce elastcty for beans ( ), rce ( ), and garr ( ). Except for the cross-prce elastcty for few of the foods that are complments, such as, yam flour and gar, yam and gar, rce and plantan, and vce versa all other cross-prce elastctes carry postve sgns as expected for substtute products. Smlar to the own prce elastctes, the cross-prce elastctes are all statstcally sgnfcant at the 5% level. Regardng the cross-prce elastctes for all the state put together usng the QUAIDS model, the consumpton of rce shows the strongest substtuton response for the prce of gar (0.347 ), whereas the consumpton of gar sn t as responsve to the prce of rce (0.04 ). The second strongest substtute response s the consumpton of rce for the prce of beverage (0.217), followed by rce for yam (0.207 ). Ths scenaro s also smlar to what obtaned n each of the senatoral dstrcts of the state. Uncompensated Elastctes Uncompensated or Marshallan prce elastctes contan both the ncome and prce effects. Smlar to the compensated own and cross-prce elastctes, the uncompensated own and cross-prce elastctes were calculated at ther sample means and results are shown n panel 4 of Table 4. As for the case of the compensated own prce elastctes, the uncompensated own prce elastctes possess the expected negatve sgns and are statstcally sgnfcant at the 5% level. The uncompensated own prce elastctes of rce (-0.70), yam (-0.468), beans ( ) and yam ( ) are all sgnfcant. The consumpton of beverages shows the strongest substtuton response for the prce of frut and vegetable (0.256), followed by meat for plantan (0.208). Table 8 shows the expendture elastcty of demand for maor food groups n Ondo State and each of the Senatoral areas as estmated usng the QUAIDS model. The elastctes are presented at the mean level. The expendture elastctes are computed for the food, whch are rce, garr, beans, yam, yam flour, bread, beverages, meat, frut and vegetable and plantan. The estmated expendture elastctes for all Ondo State are all postve and statstcally sgnfcant at the 5% level, ndcatng that all the food tems are normal goods. And that rce, beans, yam flour, meat, and vegetables and fruts are luxury goods snce the coeffcent 1.419, 1.017, 1.385, and 1.618, respectvely whch are all greater than l. However, garr, yam, bread, beverages and plantan are all necessty goods. From ths result, t can be nferred that for the people to be able to get the requred proten sources from meat and enough vtamn from beans, the government must encourage the consumpton of each of these food tems so that people can afford t. The calculated expendture elastctes for each of the Senatoral Dstrct, dffer. The elastctes are all postve and sgnfcant at 5% level for Ondo North, ndcatng normal goods for some of the foods wth the excepton of garr, yam, bread and beverages whch are necessty

12 012 E3 J. Bus. Manage. Econ. Table 4:Prce Elastcty of the AIDs and QUAIDS Food Demand System usng Data on All of Ondo State. Compensated or Hcsan Elastcty (AIDS model) RICE GARI BEANS YAM YAM FLOUR BREAD BEVERAGES MEAT FRUITS AND VEGETABLES PLANTAIN RICE GARI BEANS YAM YAM FLOUR BREAD BEVERAGES MEAT FRUITS & VEGETABLES PLANTAIN Uncompensated or Marshallan Elastcty (AIDS Model) RICE GARI BEANS YAM YAM FLOUR BREAD BEVERAGES MEAT FRUITS AND VEGETABLES PLANTAIN RICE GARI BEANS YAM YAM FLOUR BREAD BEVERAGES MEAT FRUITS & VEGETABLES PLANTAIN Compensated or Hcsan Elastcty (QUAIDS Model) RICE GARI BEANS YAM YAM FLOUR BREAD BEVERAGES MEAT FRUITS AND VEGETABLES PLANTAIN RICE GARI BEANS YAM YAM FLOUR BREAD BEVERAGES MEAT FRUITS & VEGETABLES PLANTAIN

13 Olorunfem. 013 Tabl 4. Cont. Uncompensated or Marshallan Elastcty (QUAIDS Model) RICE GARI BEANS YAM YAM FLOUR BREAD BEVERAGES MEAT FRUITS AND VEGETABLES PLANTAIN RICE GARI BEANS YAM YAM FLOUR BREAD BEVERAGES MEAT FRUITS & VEGETABLES PLANTAIN Sources: Author s Computaton Table 5: Prce Elastcty of the AIDs and QUAIDS Food Demand System usng Data on Ondo South. Compensated or Hcsan Elastcty (AIDS model) RICE GARI BEANS YAM YAM FLOUR BREAD BEVERAGES MEAT FRUITS AND VEGETABLES PLANTAIN RICE GARI BEANS YAM YAM FLOUR BREAD BEVERAGES MEAT FRUITS & VEGETABLES PLANTAIN Uncompensated or Marsallan Eastcty (AIDS Model) RICE GARI BEANS YAM YAM FLOUR

14 014 E3 J. Bus. Manage. Econ. Table 5. Cont. BREAD BEVERAGES MEAT FRUITS & VEGETABLES PLANTAIN Compensated or Hcsan Eastcty (QUAIDS Model) RICE GARI BEANS YAM YAM FLOUR BREAD BEVERAGES MEAT FRUITS & VEGETABLES PLANTAIN Uncompensated or Marsallan Eastcty (QUAIDS Model) RICE GARI BEANS YAM YAM FLOUR BREAD BEVERAGES MEAT FRUITS & VEGETABLES PLANTAIN Sources: Author s Computaton

15 Olorunfem. 015 Table 6: Prce Elastcty of the AIDs and QUAIDS Food Demand System usng Data on Ondo North. Compensated or Hcsan Elastcty (AIDS model) RICE GARI BEANS YAM YAM FLOUR BREAD BEVERAGES MEAT FRUITS & VEGETABLES PLANTAIN Uncompensated or Marshallan Elastcty (AIDS model) RICE GARI BEANS YAM YAM FLOUR BREAD BEVERAGES MEAT FRUITS & VEGETABLES PLANTAIN Compensated or Hcsan Elastcty (QUAIDS model) RICE GARI BEANS YAM YAM FLOUR BREAD BEVERAGES MEAT FRUITS & VEGETABLES PLANTAIN

16 016 E3 J. Bus. Manage. Econ. Table 6. Cont. Uncompensated or Marshallan Elastcty (QUAIDS model) RICE GARI BEANS YAM YAM FLOUR BREAD BEVERAGES MEAT FRUITS & VEGETABLES PLANTAIN Sources: Author s Computaton Table 7: Prce Elastcty of the AIDs and QUAIDS Food Demand System usng Data on Ondo Central. Compensated or Hcsan Elastcty (AIDS model) RICE GARI BEANS YAM YAM FLOUR BREAD BEVERAGES MEAT FRUITS AND VEGETABLES PLANTAIN RICE GARI BEANS YAM YAM FLOUR BREAD BEVERAGES MEAT FRUITS & VEGETABLES PLANTAIN Uncompensated or Marshallan Elastcty (AIDS model) RICE GARI BEANS YAM YAM FLOUR

17 Olorunfem. 017 Table 7. Cont. BREAD BEVERAGES MEAT FRUITS & VEGETABLES PLANTAIN Compensated or Hcsan Elastcty (QUAIDS model) RICE GARI BEANS YAM YAM FLOUR BREAD BEVERAGES MEAT FRUITS & VEGETABLES PLANTAIN Uncompensated or Marshallan Elastcty (QUAIDS model) RICE GARI BEANS YAM YAM FLOUR BREAD BEVERAGES MEAT FRUITS & VEGETABLES PLANTAIN Sources: Author s Computaton

18 018 E3 J. Bus. Manage. Econ. Table 8: Expendture and Own Prce Elastcty from QUAIDS Models Commodty Expendture Elastcty Own Prce Elastcty Ondo South Ondo North Ondo Central All-Ondo Ondo South Ondo North Ondo Central All-Ondo Rce Garr Beans Yam Yam Flour Bread Beverages Meat Frut & Vegetable Plantan Sources: Author s Computaton goods, snce ther coeffcent are less than 1. The result of the Ondo Central s smlar but for the expendture elastcty for frut and vegetable that s now negatve ndcatng t to be an nferor good. For Ondo South, beans, yam, yam flour, bread and plantan are all nferor goods wth the coeffcent of , , , and , respectvely that are all less than 1. Polcy Implcatons and Concluson Ths study looed at food demand n Ondo State, Ngera. The maor food consumed n the area were selected whch nclude rce, garr, beans, yam, yam flour, bread, beverages, meat, frut and vegetables and plantan. The fndng shows some mportant revelatons, some of whch are lsted below: I. The QUAIDS model seems to be more approprate for the data used n the study as a result of the coeffcent of the quadratc term of the estmate. II. The expendture elastcty has the predcted sgn for all the food tems captured n the study for all Ondo State put together. Garr, yam, bread, beverages and plantan are necesstes. Whle rce, beans, yam flour, meat and frut and vegetables are luxury goods, snce the expendture elastcty for them are greater than 1. Ths mples that as expendture ncreases or ncome levels ncrease the proporton of expendture on these products s much hgher than all other food tems. The demand for hgh value food s more ncome elastc as compared to that for staple food. III. IV. Expendture share for food ncreases wth household sze and decreases wth age. Ths s aganst the study of Luca (2007) that food share does not ncrease wth famly sze enlargement. The own prce elastcty s lowest for frut and vegetable, and yam whle hghest for beverages n all Ondo State put together. Thus even a margnal ncrease n the prce of beverages and ts products can lead to a substantal declne n ts consumpton. Ths s, however, not true when looed at each of the senatoral dstrcts. For nstance, n Ondo South, meat has the hghest own prce elastcty. Acnowledgement I wsh to express my sncere thans to Dr Bran Po of the Stata Corporaton USA, for teachng me the A B C of the QUAIDS command n Stata and for the research materals sent to me as well as hs readness at all tmes, to answer my questons. References Abdula A (2002 ). Household Demand for Food n Swtzerland. A Quadratc Almost Local Demand System. Swss J. Econ. Stat. 138(1): Abodun ED, Oorua VO, Aa OIY (2009). Cross Sectonal Analyss of Food Demand n the North Central, Ngera: The Quadratc Almost Ideal Demand System (QUAIDS) Approach 1(2): Ahmad ZB, Zanalahdn M (1993 ). Demand for meat n Malaysa: An applcaton of the Almost Ideal Demand System analyss. Pertana J. Soc. Sc. Hum. 1(1): Bans J, Blundell R, Lewbel A (1997). Quadratc Engel Curves and Consumer Demand. Rev. Econ. Stat. 79(4):