Household Size Economies: Malaysian Evidence

Transcription

1 Economc Analyss & Polcy, Vol. 41 No. 2, september 2011 Household Sze Economes: Malaysan Evdence Thayoong Penny Mok 1 The Treasury, Wellngton 6140, New Zealand (Emal: penny.mok@treasury.govt.nz) and Glls Maclean Lncoln Unversty, PO Box 84, Lncoln 7647, New Zealand (Emal: Glls.Maclean@lncoln.ac.nz) and Paul Dalzel AERU Research Unt, Lncoln Unversty, PO Box 84, Lncoln 7647, New Zealand (Emal: Paul.Dalzel@lncoln.ac.nz) Abstract: People lve n households wth dfferent sze and composton and they consume a varety of goods; categorsed as prvate and publc goods. Wth the exstence of publc goods n the household, doublng the household sze need not ncrease the consumpton expendture twofold to mantan the same standard of lvng. Usng households per capta expendture from the Household Expendture Survey , we estmate the household sze economes ndces for household consumpton goods through the Seemngly Unrelated Regresson. The results suggested that the lower ncome households enjoy savngs from a wder range of publc goods compared to the hgher ncome households. I. Introducton The strong negatve correlaton between household sze and consumpton (or ncome) per capta n developng countres has lead to the concluson that larger famles tend to be poorer. Ths s msleadng as household sze affects the standards of lvng. People lve n households wth 1 Correspondng author: penny.mok@treasury.govt.nz. All vews n ths paper are those of the authors and should not be attrbuted to the Treasury. 203

2 Household Sze Economes: Malaysan Evdence dfferent sze and composton and they consume a varety of goods; categorsed as prvate and publc goods. Publc goods can be shared wthn the members of the households where two or more persons would obtan the same satsfacton as a sngle person consumng the same servces. Prvate goods such as food away from home, clothng and healthcare are attrbuted to ndvduals n the household. The noton of household economes emerged from the exstence of publc goods n the household. Hence, doublng the household sze need not ncrease the consumpton expendture twofold to mantan the same standard of lvng. Lazear and Mchael (1980) have demonstrated that a household of two adults would spend 31-35% lower n comparson wth two households of sngle adult each, holdng ncome constant. Sharng opportuntes are observed n the costs of shelter and energy by sharng common spaces and furnshng, economzng servces such as food preparaton and savngs from bulk purchases of food (see Deaton and Paxson 1998, Grffth, Lebtag, Lecester and Nevo 2009, Kakwan and Son 2005, Nelson 1988, Vernon 2010). The excess resources from sharng would be allocated toward prvate and publc goods consumpton. Many goods have some prvate and some publc characterstcs. Clothng can be shared and passed down amongst famly members (Kakwan and Son 2005). Ths could be vewed as savngs whch mght be essental for the lower ncome households. Thus, a smple comparson of aggregate household consumpton wll not be a good representatve of the welfare n a gven household wthout consderng the possblty of household economes. Despte ts mportance n poverty research, there s no consensus on the approprate method to measure household economes. The estmaton of the economes of scale n consumpton has been developed based manly on two models: Engel s and Barten s model. Engel s method has been domnantly appled n household sze economes estmaton due to ts smplcty, usng food share as welfare ndcator of dfferent szed households (Deaton and Muellbauer 1980, Lanjouw and Ravallon 1995). Under Engel s assumpton and nterpretaton, the exstence of household economes of scale would make a larger household wth the same per capta expendture (PCE) as a smaller household better-off. Hence, ths would yeld a lower food share for the larger household. Holdng PCE constant, ths can only occur when there s a fall n food expendture per capta. Deaton and Paxson (1998) argued that ths contradcts what s expected when welfare ncreases due to ncrease n household sze wth the presence of economes of scale. The ncrease n welfare due to the economes of scale would cause households to consume more food, especally n low ncome countres. Deaton (1997) ndcated that the Engel method works but makes no sense. Deaton and Paxson (1998) (hereafter Deaton-Paxson) draw from Barten s model n ther attempt to estmate the household scale. An ncrease n household sze, at constant PCE, would allow the expendture released by the sharng of publc goods to be spent on both publc and prvate goods. Thus, the food budget share wll ncrease, assumng that t s a normal good. Nonetheless, Deaton-Paxson faled to prove ts valdty. In comparson to Lanjouw and Ravallon (1995) who estmated the sze economes usng the Engel method, Deaton-Paxson showed dfferent conclusons whch are sourced from the underlyng assumptons made. The controversal mplcatons concluded by Deaton-Paxson have nstgated several researchers to further analyse the theoretcal models and ther underlyng assumptons. Gan and Vernon (2003) proved the applcablty of Barten s 204

3 Thayoong Penny Mok, Glls Maclean and Paul Dalzel model n estmatng the household economes through food share n food and other publc goods as opposed to food share n total expendture. Gbson (2002) demonstrated that the measurement errors n household expendture surveys for large households caused Engel estmates of household scale to be overstated. The conventonal method usng Engel s model also assumed that the household elastctes of substtuton are zero, thus all households wll have the same degrees of economes of scale for each good (Lanjouw and Ravallon 1995). Consequently, f all goods ncludng prvate and publc goods have the same degrees of economes of scale, then t wll be constant across all households. Kakwan and Son (hereafter Kakwan-Son) argued that the household elastctes of substtuton are non-zero, as they depend on the household utlty and composton. They postulated that the degree of economes of scale for dfferent goods depends upon household s expendture and household composton. Thus, the economes of scale should dffer across goods and households. The consderaton of the household economes of scale has been lmted n the offcal poverty measurement n Malaysa. The recent poverty lne re-estmaton only consdered the savngs n housng nto the non-food poverty lne estmaton (Unted Natons Development Programme [UNDP] 2007). Lazear and Mchael (1980) have demonstrated that the largest savngs from household consumpton were observed n food and shelter whle smaller n servces such as personal care and medcal. Whle t s agreed that housng would have the hghest degree of savngs, falure n consderng the possblty of other goods savngs would have resulted n naccurate poverty measurement. It s mportant to publc-polcy analysts, to have a relable estmate of household sze economes to address socal-securty ssues across dfferent famly types of the poor. The objectve of ths paper s twofold; theoretcal and emprcal. Ths research tests and extends Kakwan-Son s secondary assumpton that the degrees of economes of scale wll be dfferent for dfferent households, dependng on how well-off the household s and what the household s composton s by usng dfferent percentle PCE households n Malaysa. In partcular, ths paper estmates the household sze economes for the poor, n comparson to the more affluent households. The estmated household sze economes wll be tested for ther mplcatons on headcount rato. Ths paper s organsed as follows: Secton II dscusses the frameworks of the Engel and Barten model whch form the bass of ths paper. Secton III descrbes the data and methodology. The emprcal results and mplcatons of the estmated household scales on the headcount rates are dscussed n Secton IV. Secton V dscusses and concludes. II. Economes of Scale Models 2.1 The Engel Model The most nfluental functonal form of Engel curve parametrc analyss s based on the model ntroduced by Workng (1943), who postulated a lnear relatonshp between the share of the budget on ndvdual goods and the logarthm of total expendture. The model was extended to nclude the household demographc composton. Lanjouw and Ravallon (1995) adopted 205

4 Household Sze Economes: Malaysan Evdence the Engel method n ther estmaton of household economes of scale usng a Workng-Leser model as below: (1) where w f s the budget share for food; x denotes total expendture; n denotes household sze; a r = n r / n s the proporton of persons n household n r demographc group; z s a vector of the household characterstcs (regon, adult employment rate); and u s an error term. Parameters to be estmated are a, b, d, s and h. Lanjouw and Ravallon (1995) proved that the queston of whether large households are poorer depends on the extent of dsperson n famly szes and the sze elastcty of the equvalence scale. Applyng the Engel method mposed several strct assumptons: sze elastcty s ndependent of utlty and prces are ndependent of household sze. Thus, the method would underestmate the sze elastcty once the assumpton of larger households buyng cheaper food through bulk dscounts and prce elastcty of demand for food s less than unty s consdered. The exstence of publc goods would create substtuton effects n favour of prvate goods, other than food. Households could be exactly compensated for an ncrease n household sze. Thus, holdng utlty constant, food share wll fall as household sze ncreases. Consequently, the sze elastcty of welfare would be underestmated. Deaton (1997) tested Engel s method usng a utlty theoretc model; c (u, p, n) through two cost of lvng functons for household sze n that acheve utlty level u at prces p. The same food Engle curve was derved from both the functons but the estmated sze elastctes of cost wth respect to the household sze dffered. The result suggested that the true economes of scale were not captured by the Engel curve estmates, thus ndcatng the lack of dentfcaton The Barten Model Further extenson on household economes based on utlty theoretc model was ntroduced by Barten (1964). Deaton and Paxson (1998) appled a smlar food share model to equaton (1) wth publc and prvate goods wthn the households. An ncrease n household sze, at constant PCE, would allow the expendture released by sharng of publc goods to be spent on both prvate and publc goods. Hence, there s a negatve substtuton effect and a postve ncome effect on the demand for prvate goods such as food. Thus, food shares would ncrease wth household sze due to two reasons. Frstly, as food has lmted substtutes, ts own-prce elastcty would be lower than the ncome elastcty n absolute value. Ths s true especally n lower ncome countres. Secondly, food has smaller economes of scale than housng as shown n equaton (4). Thus, the food budget share wll ncrease, assumng that t s a normal good. Ths model conflcts wth the Engel s Law, whch predcts the food budget share wll fall wth household sze. Deaton and Paxson tested the condtons wth the food share model: w R 1 f + = + x n + n + a b ln( / ) g ln drar + h. z u (2) r = 1 where w f s the budget share for food; x denotes total expendture; n denotes household sze;

5 Thayoong Penny Mok, Glls Maclean and Paul Dalzel a r = n r / n s the rato to household sze of household members who fall n one of r groups defned by age and sex; z s a vector of the household characterstcs (ncludng fracton of workng adults n the household, rural/urban areas and regon of resdence); and u s an error term. Parameters to be estmated are a, b, g, d and h. Notably, equaton (2) s dentcal to equaton (1) as γ = ßσ. Prevous studes estmated the economes of scale for ndvdual goods usng the prces of ndvdual goods that are pad by the households (Lazear and Mchael 1980, Nelson 1988). In the absence of these prces n most household expendture surveys, household surveys have been matched wth the goods market prces. Kakwan-Son argued that ths was problematc due to the complcatons of matchng the goods between the survey and prce data. They also opposed the conventonal assumpton that households face the same prces. Ths s well supported by Broda, Lebtag and Wensten (2009) and Grffth et al. (2009) that showed that poorer households pay dfferent prces by choosng cheaper and lower qualty goods. Aguar and Hurst (2007) suggested that prces people pay are related to the value of tme and the amount of tme that people decde to nvest n shoppng. Generally, the poor are wllng to spend more tme shoppng n order to pay less. In vew of ths complcaton, Kakwan-Son developed a model to estmate the economes of scale ndces for overall and ndvdual goods wthout the need of prce nformaton. Kakwan-Son drew from Barten s model whch ncluded the substtuton effects and made further assumptons pertanng to the nature of goods consumed by households to overcome the under-dentfcaton problem from the models. Kakwan-Son s ntuton of the economes of scale s that an ncrease n λ % of all persons n dfferent demographc categores requres the ncrease of less than λ % of the cost or ncome to mantan the same level of utlty as before for the th good. The varaton of budget shares for dfferent goods depends upon household s expendture and composton. They argued that the assumpton made by the conventonal methods of unform economes of scale for all goods was unrealstc, snce the economes of scale should dffer across goods. They assumed that the famly composton effect on the household consumpton wll be dfferent for dfferent goods, through the functon m (a 1, a 2,,a R ) beng dfferent for each good. The proposed economes of scale ndces for dfferent goods are obtaned from the elastctes of Hcksan demand functons through the Marshallan demand functons, where the latter could be observed from household survey data. The relatonshp between the Hcksan and Marshallan demand elastctes s explored through the Slutsky equaton. The proposed ndex of economes of scale: n f = ε f + q + q ε (3) j= 1 j j where f denotes economes of scale for the th good; ε s the ncome elastcty; f s the overall economes of scale; q s the total elastcty of household composton (m) wth respect to the number of person n the rth demographc (a r ) for the th good; q j s the total elastcty of household composton (m) wth respect to the number of person n the rth demographc (a r ) for the jth good; εj s the Marshallan prce elastcty of the th good wth respect to the prce of the jth good. If f <1, the th good generates economes of scale to the household but f f =1, the th good does not generate economes of scale. If f >1, dseconomes of scale 207

6 Household Sze Economes: Malaysan Evdence n consumpton are ncurred. An ncrease n a r changes all the prces, whch has ncome and substtuton effects on household consumpton. Further dfferentaton of the Marshallan demand wth respect to a r gves: n h = d + ε d (4) r r j= 1 j jr where hr denotes the Marshallan elastcty of demand for the th good wth respect to a r ; dr s the elastcty of m wth respect to a r ; and d s the elastcty of m j wth respect to a r. Thus, n j= 1 jr f = q + q ε (5) where f = h. R j r = 1 j r Substtute equaton (5) nto equaton (3) gves: f = ε f + f (6) The economes of scale ndces for ndvdual goods ( f ) are derved from the estmaton of overall ndex of economes of scale ( f ) and parameters f and ε. The two latter parameters are estmated from the Marshallan demand equatons usng the household expendture data. The estmaton of f s based on assumptons of the nature of goods. Kakwan-Son proposed to assume that healthcare s purely prvate consumpton. Thus, f whch denotes the economes of scale for the th good s unty for expendture for medcal and healthcare. Substtutng the assumpton nto equaton (6) wth the estmates of ε and f for healthcare would enable the estmaton of f. Alternatvely, Kakwan-Son suggested applyng equal economes of scale for housng furnshng and household servces nto equaton (6) for economes of scale estmaton. Hence, f for other ndvdual goods would be estmated usng equaton (6). The dfferng assumptons appled for the economes of scale estmaton yeld dfferent ndces for ndvdual and overall goods but consstent rankngs of goods by ther economes of scale ndces. Kakwan-Son computed the Marshallan elastctes based on the Workng-Leser model: R w = a + b log x + g r ar + µ (7) r = 1 where w s the budget share devoted to the th good; x s the household total expendture; a r s the number of ndvduals wth the rth characterstcs n the household; and µ denotes the error term. Equaton (7) can be estmated usng Zellner s (1963) seemngly unrelated regressons procedure. The ncome elastcty and Marshallan elastcty, respectvely, are derved as follows: b ε = 1 + (8) w g a r r h r = (9) w 208

7 Thayoong Penny Mok, Glls Maclean and Paul Dalzel where w s the weghted average value of the budget share devoted to the th good; and a r s the weghted average number of ndvduals wth the rth characterstc n the household. The calculatons of standard errors are based on bootstrap procedure to test the sgnfcance of the parameters for ndvdual and overall economes of scales. III. Method We argued that the degree of economes of scale for dfferent goods depends upon household expendture and household composton. Thus, the economes of scale should dffer across goods and households. As poorer households face dfferent prces and they mght choose cheaper and lower qualty goods, thus an ncrease n a household member would have dfferent mpact on household scales. We estmate the household sze economes across goods usng dfferent percentles of household PCE. In partcular, the behavour of the poor should be focused when adoptng the household scales n poverty measurement. The selecton of the households follows the common practce for poverty lne estmaton, whch s based on the pror estmates of poverty ncdence for the country (Pradhan, Suryahad, Sumarto & Prtchett, 2001). The offcal poverty rates of the country were 5.9% and 8.7%, usng household-based and ndvdual-based calculaton respectvely n 2004 (UNDP, 2007). The selecton of the 10 th and 20 th percentles PCE households s based on the unweghted average of the PCE to contrast wth the results of the aggregate sample sze. 3.1 Data Ths research uses the Household Expendture Survey (HES) conducted by the government n It s a comprehensve expendture of households ncludng durables, sem-durables and servces for 12 months, from June 2004 to May The survey covers urban and rural areas of Pennsular Malaysa, Sabah and Sarawak except the nteror areas of Sabah, Sarawak and the ndgenous settlements (the Orang Asl). The sample was selected usng stratfed mult-stage desgn. The frst level of stratum comprsed all 16 states of Malaysa whle the second stratum s made up of urban and rural strata wthn the prmary stratum. For ths research, a sample of 4,362 households for the whole of Malaysa has been used. The survey provdes sample weghts but does not provde nformaton on geographcal stratum and stratum dentfers. Total household expendture s measured as expendture on all tems, ncludng durable goods. Expendture on food ncludes food consumed at and away from home. The survey showed that the average monthly consumpton expendture of households n Malaysa was RM 1,953 (equvalent to US$ 513) per month. On average, households spent about 69% of ther monthly expendture on four man groups, namely: housng, water, electrcty, gas and other fuels whch comprsed 22%; food and non-alcoholc beverages (20%); transport; and restaurants and hotels comprsng 16% and 11% respectvely. Households spent the least on healthcare (1%), alcoholc beverages and tobacco, and educaton whch comprsed 2% of ther expendture respectvely. The proporton of expendture on food and non-alcoholc beverages decreases as the household expendture level ncreases. Households n the lowest expendture class (less than RM 500) spent 39% of ther expendture on food and non-alcoholc beverages 209

8 Household Sze Economes: Malaysan Evdence as compared to 9% spent by the households n the expendture class of RM 5,000 and above. Interestngly, the hghest expendture class spent most of ther expendture (28%) on transport. The average household sze n Malaysa s 4.3 persons and about 56% were small sze households (less than 5 person), 37% were medum sze (5-7 persons) and 8% were large (8 or more persons). On average, a sngle member household spent about RM 1,026 as opposed to RM 2,226 and RM 2,500 spent by households of 5 persons and 10 persons and above respectvely. In terms of proporton, a sngle member household spent about 11% on food and non-alcoholc beverages whle a larger household of 10 persons and more spent about 28% of ther expendture on food and non-alcoholc beverages. In contrast, a sngle member household spent about 15% on food away from home as compared to household sze 10 and above who spent about 8%. The survey revealed that the lowest household expendture group was headed by relatvely young householder of 24 years and below. The expendture ncreased wth older head of the household wth the hghest expendture recorded by household head between the ages of 35 and 44. Subsequently, the expendture declned for head of household from the age of 45 wth the largest declne by household head above 65 years old. Ths s consstent wth the vew that households wll smooth ther consumpton n the course of one s lfetme. Households headed by males spent 1.3 tmes more than households headed by females wth each spendng about the same proporton of expendtures on housng; water; electrcty, gas and other fuels; food and non-alcoholc beverages; transport; and restaurants and hotels. Further analyss on the head of the households revealed that the hghest level of expendture (RM 3,552 per month) were headed by household employed n the legslators, senor offcals and managers occupaton category, followed by households headed by those employed n the professonal category (RM 3,361) and techncans and assocate professonals category (RM 2,336). Not surprsngly, households headed by sklled agrcultural and fshery workers recorded the lowest expendture of RM 1,157, spendng about 27% on food and non-alcoholc beverages. In contrast, households headed by those employed n the professonal category allocated 22% of ther expendture on transport. Offcal data on ncome s not avalable due to the senstvty ssue of ncome varaton between races n the country. One of the man concerns n equaton (2) s that the errors n w f and ln(x/n) are correlated. Thus, the standard measurement error n ln(x/n) would bas the estmate of b and g, the parameters of nterest. Note that ln(x/n) s equvalent to ln(pce). Deaton and Paxson (1998) proposed to use the logarthm of per capta ncome as the nstrument for PCE. The Malaysa HES data do not contan the nformaton of household ncome. Smlarly to Gbson (2002), we proposed the use of age of household head and the average adult household years of educaton as nstruments for PCE. The F-tests for the nstruments are hghly sgnfcant at , suggestng that the nstruments are hghly correlated wth the endogenous varable, ln(pce). Over-dentfcaton tests also showed that the two varables do not correlate wth the respectve dependent varables. Thus, both are good predctors of PCEs. The Durbn-Wu- Hausman tests from ths research suggest no sgnfcant dfference between the OLS and the IV estmates for the overall selecton of samples. Thus, OLS estmatons are conducted n all models. 2 The models follow Deaton and Paxson (1998) weghted least squares lnear regresson, 2 IV estmates are sutable for the whole sample as the Durbn-Wu-Hausman test statstc of s hgher than the crtcal value of ch-squared at the 5% sgnfcance level (32.67). For the lower percentles of the household samples, t s found that there s no sgnfcant dfference between the OLS and the IV estmates. 210

9 Thayoong Penny Mok, Glls Maclean and Paul Dalzel wth weghts nversely proportonal to the samplng weght provded by the survey. The standard errors n Kakwan-Son s method are computed from the bootstrap. 3.2 Poverty Lne Ths paper uses PCE as a measure of welfare. The measure ncludes the total values of food and non-food consumpton tems (purchases, home-produced tems, gfts and concessonare lodgng receved), as well as the mputed use-values for owner-occuped housng. Thus, the poverty lne reflects the expendture on food and non-food tems whch are deemed essental for a person to mantan a mnmum acceptable standard of lvng. It s wdely accepted that the developng countres should use household consumpton expendture as an ndcator of lvng standards as ncome vares more sgnfcantly than consumpton. Pror poverty studes n Malaysa showed hgh ncdence of poverty n the rural areas of Sabah and Sarawak (UNDP 2007). Snce most of the households n the rural areas are nvolved n agrcultural sector, t s defensble to apply the consumpton expendture approach n poverty measurement as ncome mght be understated. For the purpose of ths paper, the per capta poverty lne of RM for Malaysa s used as the reference pont to evaluate the mplcatons of dfferent household scales on the headcount rates. The poverty lne s adjusted for economes of scale n household consumpton usng the equaton below: PL hn = kmpl n HS h (qn-1) (10) where q n s the economy of scale; HS h s the sze of the hth household; and k s the parameter to scale up the poverty lne so that the mean of PL hn across households s equal to MPL n to ensure that the adjustment for economes of scale does not change the populaton mean of each of the food and non-food components (see Kakwan and Sajaa, 2004). Dseconomes of scale are not consdered n ths paper for smplcty. IV. Emprcal Results 4.1 Household Sze Elastctes Summary statstcs are reported n Table 1. The poorest households, are below the 10th percentle household PCE spend almost 50% of ther total expendture on food. The expendture on shelter whch s classfed as publc good s about 24% of the total expendture for the poorest two decles. These are represented by (w ) n Table 4 and 5. Table 2 shows the overall results of the negatve relatonshp between the food share and household sze. These corroborate the Deaton-Paxson paradoxcal concluson of Barten s model. A 10% ncrease n the logarthm of household sze ln(n) decreases the food share by the proporton of 5, 2 and 0.007, respectvely for all three household percentles. The effects are less promnent for the hgher decles, whch s consstent wth the Barten model. Accordng to the Engel method, the economes of scale parameter s are estmated from the rato of the coeffcents on ln(n) and ln(pce). The economes of scale s are estmated to be 0.22, 0.21 and 0.43 for the 10 th, 20 th percentles and aggregate households respectvely. 211

10 Household Sze Economes: Malaysan Evdence Table 1: Descrptve Data (Accordng to PCE Percentles) Varables Aggregate sample 20 th percentle 10 th percentle Mean Std. dev Mean Std. dev Mean Std. dev Food share ln food expendture per capta ln non-food expendture per capta ln per capta expendture ln household sze rm rm rm rm rm rm rf rf rf rf rf rf Adult earners rato School years of adults Household head age Notes: rm04 represents the rato of the number of males aged 0-4 to total household numbers. Other varables begnnng wth r are demographc ratos, for ther respectve gender and age group. Means and standard devatons are calculated usng household samplng weghts. Varables ln(n) ln(pce) Table 2: Food Engel Curve (Instrumental Varable) Food n total expendture Aggregate households 20 th percentle 10 th percentle (0.17) (0.19) R Sze economes s Notes: The parameters are estmated usng weghted least squares, wth weghts nversely proportonal to the samplng weght n the survey. Refer to Table A1 n the Appendx for detaled estmates. Parentheses denote standard errors. The estmated sze economes for the lowest two decles are equvalent but the coeffcent for the aggregate sample s twce that for the poorest decles. The sze economes of 0.43 suggest that ten ndvduals, each spendng $1 a day n separate sngle-person households wll acheve the same welfare level as a 10-person household wth total expendtures of $3.72 a day ( = 3.72). The estmated sze economes usng the aggregate household sample dsplay 212

11 Thayoong Penny Mok, Glls Maclean and Paul Dalzel a rather large fall n food spendng per person for households n Malaysa. However, f the sze economes of 0.22 s used, the same welfare level requres total expendtures of $6.03 a day ( = 6.03). If the sze economes estmated from the aggregate sample s used for poverty estmaton nstead of the 10 th percentle PCE, ths would under-estmate the poverty headcount for the country. The Barten model predcts that poor households who have fewer substtutes for some prvate good wll ncrease consumpton of that partcular prvate good more than the hgher ncome households when household sze ncreases. If food s the prvate good that s not easly substtuted, the elastcty of per capta food expendture should be larger for poorer households. Further analyss on the elastcty of per capta food expendture wth respect to household sze s estmated as -0.32, and for the 10 th, 20 th percentle and aggregate households, respectvely. These are estmated usng g /w f, wth the respectve average food shares dsplayed n Table 1. The elastcty of food expendture n absolute terms s hgher for the poorest percentles, as predcted by the Barten model. The results above are estmated on the assumpton that the household sze economes are constant across goods and households. In contrast, Kakwan-Son postulated that the household sze economes vary across goods and households. The estmates of sze economes usng the specfcaton of Kakwan-Son are reported n Table 3. Table 3: Economes of Scale Indces Goods Top 20 th percentle 20 th percentle 10 th percentle Aggregate sample φ φ φ φ φ φ φ φ Food Clothng (0.12) 1.05 (0.17) Housng (0.12) Furnshng 0.30 (0.13) (0.12) (0.18) 0.58 (0.12) Medcal (0.30) 1.00 (0.20) 0.38 (0.30) 1.00 (0.24) 0.36 (0.46) 1.00 (0.39) Transport (0.10) (0.12) (0.18) 1.09 (0.12) Communcaton (0.19) 1.35 (0.15) (0.40) 1.05 (0.27) Educaton (0.45) 1.95 (0.28) 0.02 (0.20) 1.35 (0.16) (0.25) 1.12 (0.19) 1.60 Personal goods (0.19) Mscellaneous (0.1) (0.15) 0.94 (0.14) (0.22) 0.57 (0.14) Total f 0.97 (0.21) 0.81 (2.60) 0.71 (0.71) 0.93 Notes: Standard errors are n parentheses, computed from the bootstrap method. These varables are estmated usng the SUR method wthout weghts. 213

12 Household Sze Economes: Malaysan Evdence The overall ndex of sze economes (φ ) are 0.71, 0.81 and 0.93 for the 10 th, 20 th percentle and aggregate households, respectvely. 3 Ths shows that 29%, 19% and 7% of total expendture can be saved n the larger households of respectve decles wthout affectng ther standards of lvng. As hgh ncome households are ncluded n the estmaton of sze economes, the ndex gets larger. Further analyss of the top 20 th percentles households gve the value of f = 0.97, ndcatng only 3% of savngs obtaned wth an addtonal member n the household. Ths concurs wth the fndngs of Salcedo, Schoellman and Tertlt (2009) that suggest that as households get rcher, the household publc goods become relatvely less mportant. Thus, ths suggests that rcher households devote hgher budget shares on prvate goods. Ths paper shows that the φ and φ 1 vares substantally as postulated by Kakwan-Son, dependng on the household decles used as reference groups. The φ 1 values n the 10 th percentle PCE households ndcate a wder range of savngs n consumpton compared to the hgher ncome households. Economes of scale are present n sx consumpton goods; housng, mscellaneous, furnshng, food, clothng and personal goods for the poorest decles and dsplay larger degrees of savngs than for the top decles PCE. The current housng cost provdes the hghest sze economes for all households, except for the top decles. Although food and clothng are usually regarded as prvately consumed goods, ths ndcates they provde economes of scale. Ths concurs wth Kakwan-Son s fndngs usng Australan households (Kakwan and Son 2005). The value of φ 1 for food s 0.67, whch translates nto savngs of 33% for the poorest households n Malaysa. The household savngs on food decreases wth household expendture. The top decles dsplay a lower savngs of 25% as the household sze ncreases. Ths could be explaned by the fact that the poor mght save more than ther affluent counterparts through the choces of bulk purchases, economy generc food brands and purchase on sale (Grffth et al. 2009). Economes of scale for the aggregate Malaysan households are present for housng, food and mscellaneous expendture. Clothng provdes rather small economes of scale to the poor wth the ndex of Interestngly, the effect s larger for the top decles. Ths corroborates the ntal supposton that clothng could be passed down to famly members. The effect dsappears when the 20 th percentle and aggregate households are used to estmate the sze economes. Clothng s a prvately consumed good, provdng no economes of scale, wth ndces of 1.0 for the 20 th percentle and aggregate households. Dseconomes of scale n consumpton are present when φ 1 >1. For all the households, educaton has the largest dseconomes of scale. The negatve values of φ 1 for educaton suggest that the expendture on educaton wll fall as the household sze ncreases holdng ncome or expendture constant. Further analyss of Marshallan elastctes n Table 4 shows that the ncrease n household members aged 6 to 17 years ncreases the expendture on educaton but not for the other household members of the poorest decles. Educaton s essentally a prvately consumed good and large number of chldren s observed n poor households. Expendture on educaton tends to decrease for the addtonal ncrease of a household member over 17 years old, 3 Ths s estmated usng Seemngly Unrelated Regresson model (unweghted), through natural logarthm specfcaton. The SUR model usng logarthm base 10 produced slghtly hgher ndces: 0.80, 1.37, 0.90 and 0.68 for 10 th, 20 th, top 20 th percentles, respectvely and aggregate sample. The sze economes for the 20 th percentle do not seem robust under ths specfcaton. 214

13 Thayoong Penny Mok, Glls Maclean and Paul Dalzel suggestng that the demand for tertary educaton s low amongst the poor. When the household sze ncreases, the poor wll reallocate ther resources to other prvate consumpton goods such as food and medcaton whch are deemed essental to ther lvelhoods, rather than educaton. A low degree of dseconomes of scale s present n expendture on transport and communcaton for the poorest decles. Both goods could be nterpreted as pure prvately consumed goods as ther ndces are near 1.0. Communcaton expendture s also a pure prvately consumed good for aggregate households. The negatve φ for both goods suggest that the poor wll reduce ther consumpton on these goods when household sze ncreases. Ths could be explaned by the ncluson of goods such as school bus fares, bcycles and other expenses whch do not provde consumpton economes of scale to the larger households. Thus, t s logcal that the poor wll reduce ther consumpton on these goods by seekng alternatves and reallocate ther expendtures to food and clothng whch s more essental. On the contrary, the aggregate households show dseconomes of scale for consumpton on furnshng, transport, educaton and personal goods. The presence of dseconomes of scale n household consumpton contrasts wth the results of Kakwan and Son (2005) usng the Australan Household Expendture survey of 1984, where the latter showed household economes of scale for all the goods consumed. Plausble explanatons for ths dfference could be due to the dfferent level of country development and market nsttutons. Malaysa, as a developng country lackng n socal securty benefts and market lnkages whch lmt the opportuntes for household economes of scale would have a dfferent household consumpton pattern than a developed country such as Australa. Table 4: Income and Marshallan Elastctes, 10 th Percentle Marshallan elastctes wth respect to age Goods w ε Food Clothng (0.13) Housng Furnshng 1.41 (0.15) Medcal 0.91 (0.31) 0.06 (0.23) (0.12) (0.38) Transport (0.14) (0.10) Communcaton (0.27) (0.15) (0.25) 0.05 Educaton (0.22) 0.22 (0.12) (0.13) Personal goods (0.17) Mscellaneous (0.19) (0.14) Notes: Standard errors are n parentheses, computed from the bootstrap method. 215

14 Household Sze Economes: Malaysan Evdence The negatve value of φ for expendture on housng across households mples that households wll decrease ther housng expendture as the household sze ncreases, assumng ncome or expendture s constant. As φ provdes nformaton about the household reallocaton mechansm, the postve values for expendture on food across households confrm Barten s predcton that households wll ncrease expendture on prvate consumpton goods (food) and decrease expendture on publc consumpton goods (housng) as the household sze ncreases. For the 10 th percentle PCE household, postve values of φ are also observed n clothng and medcal expendtures. For the aggregate households, the postve values of φ are observed n food, clothng, furnshng and personal goods expendtures. Thus, for the poorest households, publc sharng wth some economes of scale could be observed from housng, furnshng, personal goods and mscellaneous goods. From the savngs allowed through publc good consumpton, the poorest group chooses to reallocate resources to food, clothng and medcal goods whch are deemed essental. Dfferent estmates of f across households reflect the dfferences n household consumpton patterns where the hgher ncome households shft from publc to prvate consumpton goods when they have more ncome at ther dsposal. Movng from the poorest to rchest decles, hgher ncome (or expendture) households are spendng more (φ > 0) on furnshng, communcaton and personal goods whch do not yeld economes of scale (hgh f ) wth respect to household sze. These are regarded as prvately consumed goods by the rchest decles as f 1 but not by the poorest decles. Housng and mscellaneous goods are regarded as publcly consumed goods by all households. All households face dseconomes of scale n transportaton and reducton n expendture wth respect to household sze. Tables 4 and 5 show the ncome and the Marshallan elastctes wth respect to household sze and age for the poorest decles and the aggregate households. Refer to Table A2 and A3 n the Appendx for the estmates usng the 20 th percentle and top 20 th percentles. The ncome elastctes ( ε ) supported the above concluson that households at dfferent ncomes have dfferent consumpton behavour, whch wll result n dfferent household sze economes across households. Goods are classfed as luxury f ε >1. For the poorest two decles, goods such as food, housng and medcaton are vewed as necesstes (0< ε <1). For the top decles, necessty goods encompass a wder range. They are observed n consumpton on food, housng, clothng and communcaton. One possble explanaton for the dfferences would be that the poor who normally consume less food calores are more vulnerable to sckness. Hence, expendture on medcaton for the poor would be less responsve to ncome than the wealther households. Further deductons can be made from these estmates. For the poorest decles, goods whch are regarded as luxures are normally shared amongst household members. Ths can be observed n goods such as clothng, furnshng, personal goods and mscellaneous goods where certan degrees of economes of scale occurred. Goods whch are regarded as necesstes by the poor such as food, medcaton and housng are consumed prvately and publcly. On the contrary, goods whch are regarded as luxures and necesstes by the rchest decles are consumed prvately amongst household members, except housng and mscellaneous goods. The f ndces dsplay the choce of goods amongst households. The savngs from housng, furnshng, food, mscellaneous and personal consumpton by the poor are usually obtaned through bulk purchases, lower qualty of goods and possbly over-crowdng n housng 216

15 Thayoong Penny Mok, Glls Maclean and Paul Dalzel Table 5: Income and Marshallan Elastctes, Aggregate Sample Marshallan elastctes wth respect to age Goods w ε Food Clothng Housng Furnshng (0.32) Medcal Transport (0.13) Communcaton (0.16) Educaton (0.18) Personal goods (0.21) Mscellaneous (0.56) (0.17) Notes: Standard errors are n parentheses, computed from the bootstrap method. (Grffth et al. 2009). The choce made by the poor ndcates the actual mnmum expendture on each good for a decent lvelhood. In contrast to the poorest decles, the rchest decles dsplay postve reallocaton of resources to goods such as furnshng and personal goods as the household sze ncreases. For statstcal sgnfcance checkng of f, the standard errors of the parameters of the economes of scale are computed through a bootstrap method usng 1000 replcatons (see Kakwan and Son 2005). Households wll have sgnfcant economes of scale f the value of f s sgnfcantly dfferent from one. Thus, to test the hypothess, t values of (1 f ) are computed. The t value for the 10 th percentle and aggregate sample of (1 f ) were computed as equal to 0.41 and 1.02, respectvely whch are not sgnfcant at the 5% level of sgnfcance. 4 However, the f are statstcally sgnfcant at the 5% level of sgnfcance for the 10 th percentle and aggregate sample households. We queston the applcablty of the assumpton of a unty ndex of economes of scale for medcal and healthcare expendture n the Malaysan household context. The bootstrapped standard error s derved from the assumpton that the medcal expendture s purely prvate consumpton. The bootstrap samples are drawn repeatedly from the sample. However, not all households have sgnfcant expendture on 4 OLS usng weghted-least squares and nstrumental varables produced unrelable economes of scale ndces for each percentle; 1.56, 1.65 and 0.90 respectvely for 10th, 20th percentle and aggregate sample. OLS usng weghted-least squares wthout nstrumental varables produced lower economes of scale: 0.53, 0.34 and 0.43 respectvely for the 10th, 20th percentle and aggregate sample. These ndces are hgher than the ndces estmated usng Engel method. 217

16 Household Sze Economes: Malaysan Evdence medcal goods as t s provded free by the government, especally to the poor. The medcal expendture for the households s low, whch s about RM26 per household per month or 1% of the total household expendture. The ncome elastcty of medcal expendture s 1.02 for the entre sample, n contrast to 0.71 from Kakwan-Son s fndngs. Thus, usng medcal and healthcare expendture may not be a good base for the economes of scale ndex estmaton for Malaysa; ths n turn would affect the sgnfcance test of the ndex. 4.2 Poverty Measurements The household sze economes estmatons were appled to the poverty measurements usng headcount rates and are dsplayed n Table 6. For all reference groups, the average per capta poverty lnes n Table 6 declne monotoncally wth household sze. Arguably, ths mght be due to two reasons. Frst, larger households have more chldren and the food poverty wll declne wth household sze due to the lower food poverty lne for chldren. Secondly, larger households wll experence savngs n publc good consumpton such as housng and food preparaton. We also compare our results wth the Malaysa s current method whch only consdered the household sze economes n housng. Table 6: Poverty Lne Per Capta by Household Sze for Dfferent Methods Hh sze Kak- Son a Headcount No EOS Headcount Engel method b Headcount Engel method c Headcount M sa method d Headcount ³ Mean Notes: Headcount rates are calculated usng the populaton weghts of the survey. a estmates are based on the φ from the 10th percentle PCE. The sze economes are ncorporated n the food and non-food poverty lne for dfferent household szes. b estmates are based on the σ from the 10th percentle PCE. c estmates are based on the σ from the aggregate households. d estmates are based on the Malaysa s estmates of household economes of scale for housng (0.474), usng the authors estmated poverty lnes. The per capta poverty lnes show a decreasng trend wth household sze but the headcount rates ncrease wth household sze. The poverty measurements appear to be senstve to the methods used to estmate the economes of scale, as shown n Table 6 and Fgure 1. When no allowance s made for sze economes, the poverty rate ncreases rapdly wth household sze. Households wth 8 or more members have a 27% poverty rate. When the sze economes estmated from the 10 th percentle group wth the Deaton-Paxson specfcaton s used (s = 0.22), 218

17 Thayoong Penny Mok, Glls Maclean and Paul Dalzel the smallest households have 1% poverty rate but the 8-person households have a poverty rate of 18%. The household sze economes estmated from the 10 th percentle PCE wth the Kakwan-Son method produce a 2% poverty rate for the smallest households and a 17% poverty rate for the largest households. Usng the sze economes estmated from the 10 th percentle group, the headcount rates calculated from the Kakwan-Son and the Deaton-Paxson are smlar. The headcount rates for the Deaton-Paxson specfcaton usng the aggregate sample are the lowest amongst all methods, suggestng that t would under-estmate the poverty rate. The Malaysan government estmated the household sze economes of housng at (UNDP 2007). The headcount rates estmated from the offcal household sze economes dsplay a smlar trend to the headcount rates wthout household sze economes. Both headcount rates ncrease rapdly wth household sze. For the 10 th percentle household, the method proposed by Kakwan-Son whch ncludes household sze economes for all ndvdual goods produce lower headcount rates, as opposed to the offcal method. Thus, the offcal sze economes n poverty measurement mght have over-estmated the poverty rate n the country. Fgure 1: Poverty and Household Sze Poverty and household sze Headcount rate K-S 10th No EOS Engel_10th Engel_pop Msa Household sze V. Conclusons Ths research utlzed comprehensve expendture of household data (HES) whch ncluded durables and sem-durables and servces n The survey revealed that households n dfferent expendture groups behave dfferently. For example, households n the lowest expendture group spent most of ther expendture (39%) on food and non-alcoholc beverages whereas households n the hghest expendture group allocate most of ther expendture (28%) on transport. 219

18 Household Sze Economes: Malaysan Evdence We confrm our earler supposton that the degree of economes of scale vary across goods and households. The estmatons of sze economes dffer dependng on the decles and methods used. Assumng that households n smlar per capta expendture percentles share the same preferences, the estmated household sze economes for the lower ncome households are larger than the hgher ncome households usng a common benchmark of analyss. Ths could best be explaned by the choce of the rcher households who consume relatvely more prvate goods as opposed to poorer households. The overall economes of scale ndces proposed by Kakwan-Son produce smlar sze economes to the Deaton-Paxson specfcaton for the poorest two decles reference groups, whch result n a smlar trend for headcount ratos. The poverty measurements for dfferent reference groups used to estmate the household sze economes show trends consstent wth the poverty measurements produced n the poverty lnes estmaton. The offcal household sze economes whch only consdered household savngs n housng expendture had over-estmated the headcount rato n larger households. The results shown n the 10 th and 20 th percentle PCE household are robust, provde a better alternatve to estmate the household economes of scale ndex for poverty measurement n Malaysa s context. The detaled economes of scale nformaton on every consumpton good of the household s well represented by the expendture system derved by Kakwan-Son. The method proved the valdty of the Barten model for food expendture. The postve values f for expendture on food for all the percentles usng the Kakwan-Son specfcaton show that household expendture on food ncreases when the household sze ncreases, holdng ncome or expendture constant. Ths method proved to be a good alternatve to the conventonal economes of scale estmaton usng the Engel method whch was regarded as not sensble by Deaton-Paxson. The f ndces offer rch nformaton on the allocaton of resources and the choce of goods amongst poor households. It could be used as an alternatve ndcator to complement poverty measurement. The economes of scale for consumpton of ndvdual goods are sgnfcant but the overall sze economes ( f ) s not. The bootstrapped standard errors are derved from the assumpton that medcal expendture s pure prvate consumpton. Ths paper questons the applcablty of the assumpton of the unty ndex of economes of scale for healthcare expendture as proposed by Kakwan-Son when the ncome elastcty of medcal goods s hgh and the budget share for the good s low. The 10 th percentle PCE shows the presence of household sze economes for food, housng, clothng, furnshng, personal goods and mscellaneous goods. The results suggest that the household economes of scale from food preparaton and food bulk purchase are rather hgh for the lower ncome households. It also shows the presence of dseconomes of scale manly n educaton consumpton. Adoptng the specfcaton to the entre sample ndcates the presence of sze economes n food, housng and mscellaneous expendtures. In nterpretng these results, the presence of measurement errors n expendture surveys needs to be acknowledged. Gbson (2002) found that the Engel estmates of household sze economes are senstve to the method used to collect household expendture data. Gbson found that the household sze economes estmated by Lanjouw and Ravallon for Pakstan was based upwards by the use of recall data. Ths was due to the measurement errors n expendtures beng correlated wth household sze. Most household expendture surveys, ncludng the Malaysan HES, are based on the combnaton of dary and recall methods. 220