Spatial differences in poverty : the case of Peru

World Bank Reprint Series: Number 153 Vinod Thomas Spatial lDifferences in Poverty: The Case of Peru Reprinted with permission from Journal of Developinent Economtiics, vol. 7 (1980), pp. 85-98.  Journal of Development E.conomics 7 (1980) 85 48. ? North-Holland Publishing ( omipan SPATIAL DI0FFIRENCES IN POV'ERTY \ The Case of Peru Vinod THOMAS* IT f IOrd BtIiti, / s.lsliiingo. n)( C 20(43. C'S I Recei%ed October 1975, final Ne-ooi receied Mlarch lTN0 This paper examines the implications of spatial dliltei iens in liiis costs l'oi Ineludse to poverty. Taking PerLu as a caIse Wdtud,. spatial price indices are used to ealci te 1ca.cu ii 'i poverty lines, based on the local cost if a basket o' basic nieedts. Applied to nconie di,,sti ibluton data, these poxerty lines yield measures of the extent and location ol' poxi lx thc paper shoA, that these measures are significantlN dilTerent from, and mclLel more accurate thanll illse obthalled using a single countr\ s% idc poxerty line: the latter can gixe a misleading pictture of po%crty bx oxer' slatini spatial differences, in general oxerestimatin, rural and underestimaitinig urban pox r0 1. Introduction It is generally accepled that livingz costs vary beli' ' cell d illereill Ollace\ within countries anId that a given incomlc miay . have (iifl'ecit Ii real al aes iII different places. Despite this rccogiiilioii. it is comImIon in the :dtiulilltll of economic policy to use the same monev income level as a reference Point across a whole country (e.g.. to assess income tax liabilities or eli'ibilit\ for welfare pavimients, and determinie the size of publicly administered old age pensions). for while it may be povsible to at-rx icoit)ine dlrcsllolds depen2I' d1'ting. on local costs of living, and wouild be inuklCe CLtl t. 'le oll a1n nilerpet'I snl basis, doing so would clearl\ create administrative complications. Spatial differences in the costs of lixingT. ho%\xcer, have seriOtlu nlenpliolmi-.0 for the design of policies an(d prog,ramsi, to alleviate poNertN. For I\aInplc. in 11ea1 u rill the extent of the poverty problem. a n.acgle mnon income po%ertv line applied across a wV11oe CCtnlltl. mraN in fact rCepr'so1l 'd`idClx (liffereill levels of purchasing poxwer. Some of those designated as poor iheingg below the poverty line) in an area wlhere lixing, costs are loxt- will in real terms, be *This paper is part of a larger studiy I did at the WoilId Bank (10"X ). in \-Npetion sitil Peru's Ministry of Economics antid I lnance. The Nt | xould ntot h1axe bleenl 1oible xithollut tile support of ('arlos Amat x 1Leon ('ha1e, and his res,ll colup at tlhe iiiist1i Indl ti ou la's-h Keare, Jolhn ng lisli nd I I,\i ('Chaparro att the .World Biaiik I x ould like to .lkos\ l0delee assistance receixed from Nelson Valerde, Johii 1 isk and Join Shiilnt aind helpful coiullnenPlt made by Enlriqtue Lerdau, Ci;e.o,ie Tollex and a Illaot X. Inlel. ' lele\ i tit al ealrhit dflialt hk Richiard \Webb. Any remaining err rs are. ot cou-e. m. ren poiisibililf. 1lie ',exss and interpretations in this paper are iho'. o' the authot anid should not be attributed tot the Wor ltd Banik. to its :iflihaicd organiiiationiis or to an, illdliulial inlle in their bleall.  85 1 Thomov, Sptatial dii vrnce, In poretrtY better off thai sotiex. li irio in a high cost area, who are excluded from the target group becautlse their incomes fall above the poverty line. Thus, th.> leasurle will tend to overestimate the tnunmher, of poor in low cost areas, and vice xersa. Anid. ats a result, it wvili ngie a iniisleadinL impression of the l ,ca tu a)nd extent of poverty. Frxctlk how tnisle;iding. will not normally be initiihNle obvious. To thIIroV liht on this .I.esti n. this paper takes the casc of Peru anid describes the use of spatial dilfferences in the costs or basiSC rireCmLIL-nlents in the ;csu 'enwii t ipox i lt'.. First, an cenpirical discussion is presented of the sPai;A! dfiFL'r cie' in the prices of the 'hasic' food aIud non-food items in f'c. u1. Sectionl 2 of the p!Pp: II,(" the estimates made by Thomas (1978) of the price _trationi ('l ti[e two catcumi ei,. in deriving i\ crall cOnIsumller price indic c for thc .mittiernt locations. In '&ctioil 3, these prices indices are applticel to a money intcome level thWit correspond to what may be consi'dere(d as ani :alVluc' ,overtN lexel. This enables us to derive poverty linc'v that are specific to the different parts of the country. In section 4 these povCrty linies are arpplied to awtual incone and its diistribLution in the different parts (Ol the ecmililt x to es,tilIa;te \ W'i,; indices of poveirty. The restilts thitis derlxed ire mnpLal1111l1tC vre , those oh,'ined bN LISiuig a single nalikonal potcrty line, to show how ,. lead ic the latter can 'be. I lhe analak s dra%tx, otn a 1971 '-2 country-vide household survey undertaken by thie \zoi'"or ( of AuLricLultni e. IThe resalts or this stIrt CV called FN(C'A were l1lllislei!.i ftrl'Y'. Ihe ENCA classification of the eCCOnonly 11to thiee ditillct regiolns C at.l Sierra and Selva appcaris to be an excellenlt basis trsr examining Peru's regional differences. We shall further dist irtcuizl thlee air;cw of the coutntrv differing shariply in their degree of ulrhallization. Lima. the lart.eost iiirhani ceniter, U rba (oast, renresenltini, all the cities of the ('o,ist, ind iR L1111 S.i al.l. eleselntell11lW all locations with less than 200)() people in Siicrra. 2. Spatial price indicEs To obtain location-specific ptcrt\ linie that reflect comparable levels of coniilller expenditure, regional CL 'usiilerI pi-ice indices are required. Ideally, cOnsullmIlelr price ind(lices should allow tus to conipare the reionl;dl differences in theC cost Of ILcluet1 in; a certain level ol' titilitv. If' people antd loca tions were idIelnticall, a g'ien basket of goods aniid ser\ices couldL he aissumicd to pr-ovide thile saie lex el olf uttilitv. Realis.ically,i howvexer, peoples tieed,s and tastes, as well as the lulalli t ofi ,Okl)Lk and ser-vice-., xarv fr0lor place to place atnd it is '-T0e tlatt u gewn InI tills paper were obt.ined brom tihe i IC ' tape by kinid courtesy of the Mtiistrx Lio Economics and I inauwe and ale g'.en In tTie World Bank W-ii\\ ' in Paper (273). The b1siC 11,i il l.Llil ha3s nlo' beeti publiAsied th ilti Ninvtry of Agrctiltiure andt tte Mtinistry of cononicNs and F inance, I iialt, Plerul.  V 7'Thonmtzs, Spatial dilicrenceV in povert l 87 thus difficult to define baskets of goods and services that arc ippropriate across a whole country, or to argue that such baskets provide the same level of utility. Some of these problems may not arise in the case of food, since the level of nutrition can be defined in terms of calories anid proteins. One can calculatc a food price index that reflects diffSerences in the cost of achieving a certain level of nutrition 'required' for each location. Of course, a Narictt of food baskets, differing in their compositions and hence prices, caln provide the 'required' level of nutrition. Ideally, perhaps, a basket sholuld be chosen for each location that reflects the availahilitN of food items anic th" revealed pireference of the people in that locaitioni. And since the price index beinig c:lcdulated is that of achieving the 'minimum' requiremenits, the preferences or tastes of the poor should be focussed upon, In the actual estimations presented in this paper, a single basket of food iten.s is used for all regions, assuming that these items are widely available throughout the country. This basket consists of the items consumed by the Rural Sierra's people at the twentieth percentile of the income range, the overall quantity of food in the basket. however, is adjusted to mweet the nutritional requirements for each location as reconmllmlendiedL by Pertu's National Planninig Institute (1975). A different food basket for the twenitietlh percenitile in e.icll region was not used, because data were aivailable only for m.ina. I Urban Coast and Rural Sierra. Since Rural Sicrra is the poorest of these tlhree locations, its data at the tw entieth percei tile were used to giN e the composition of a poor personi's diet. To the extent that this particular baisKct used is not widely available and or the items in it are not revealed preferre(d by the poor uniformly across locations, the cost differences derived on its basis in this paper will be exaggerated M-Teasuring and pricing the Cons0Umption of ser% ices and coinnioditie. other than food raises problems that will be met in most aitteinps to compare levels of living within countries. Data onl iin-food expenditures are frequenitly available from household budget sui\'eys fror a Iulilber of locationit , but the qualltitiCs coinsumnied may not be reported, or the co-nmodity specifications mav be poor, or not consistent with the availablc price data. Even if some quantity estimates are available, 'miiimum reqLuireml1enCts' of non-food items are hard to define and measuire, and as a result, regionall variaition in needs is difficult to assess Qualitv diffecrenices or nlon-food items are similarly hard to acCOunt1 for. If price data are a',6aliablc for at least some of the main non-food catcgorics like heousilg. clothigli and transportaition, one may attempt to definie 'comnparlable' LILuan lit ullits ;and(l build a non-foodl price index directlv on this basis. Peruvian data on1 nion- food prices do not permliit this. In the face of these difficulties Thoinam. 11978) sUggests a nmetlhod of calculating a noni-food price indiex fotr Perui firo(m data oni non-food  8$ i: Thomas, Spatial ddl?-) v'mu,' in potrertv expenditlue. In that approach it is asis,umed that regionial CxpCelditure data at the mean refer to equivalent baskets of goods and services." In reality, ho'wever, considerable quality differenices exist; because of this, it would have been better, had the data perm,,itted, to construct the price in(lices on the basis of exncr t- ire data for groups at similar po.itioll in the income distributiotn. I approach, lhow ever, is to thinlk of mean differences in expenldLituLreH in aniy location rclatiN e to the countlxN average as tIhe I)r0dL'ut of a price differenice and as qLuantity differeice. The quaLnltity (diffrlence is thenl explainied in terms of a price difference and ani incomf diffelrelnce het'.cen locations. \VrVitini them ill their price and incom;e elasticity forms and usinlg the relations given by the Slutsky equations [see McClosley (foirthficomingo)] the price in any location is xplresSe( aS anl illnLdX With a'INeragu price in the counitrv as the base. In airticular, the npproclch uises the ela t onsips between food and noni-food elisticities for a two-good world. which permit the use of food elaiticities to alpproxiinalte the relltliie3d non-food clasticities. The price indices as presented in this paper are tllse calcdculatcd by Thomas (1978) usinlg the following steps. The prices of food C;ategorics in the food basket is I aken fro m the ENCA survey and Coln 1elteLl into relative prices, with niationa.l a'eage pr-ices taken as tas1 for each comninoditN. The relati\e. prie-e of the Nariollu food c0mmno11(dtile. in the haskel tire '\eiglh ted according to the inport:i nce of the coilrmioditics in the nationlll a'.eragcc budget, to give a pmi-e index of food items. For iipficit\, the nationl; average expenditure '.eilght are assumed folr all regions: the fitlnal IrSlt.1s do not appear to be xerv .ensiti.e to the tise of repional expenditture weights, nstead. A noi-food price index, is calculated based oni data on national non- food expenditulre. The non-food expelndittre (eiffeerenice of each loca tion from Peru's national a'e. crage expend itiire are con erted into noll-rood price differences uisinag esiiatMed values of incomec and price elasticities of food demrand for the nation of respectively, ().7 and -- 0.4. The results are not very sensitiNe to altcriiati\ e \ alue, of these elasticities. Using the \\.eihlts of food and no1-foo0d caltegor)ies in budget of the natioiial a'. rag-e family of 0.5 each, the two price iindices, for food antid non-food, are coimbiined into an overall price index for eachi regilon. The use of nationzl e\xpenditure wcights as opposed to regional N%eigohts similplifies the proc0edur trenmendot.lsl) While not ItTecting the resuLlts significantly. The uise of a naltioiiiil a'.er.1igc ilncoimie clkitici ty indicates tlhe qLaLn6tities that w\N-ould be consurmed in a l%rpothetic;al 'average' loca tion at diffeenil incomee lexels. It will inot fullv identify (liffeirencs in the Lqimani1tit% consumnied in a particular place thlazt arie d to locationl-pLeific nleeds. 'I'le )0Ced tiLrle usecd in thlis pa per for iitarlice, will nIot idemtit\ that part of urbail peoples iiigler conllsu mnpioln that talkes place purely (dtue to the fact that the\ are city- d'.'ellcIs lor examiple. larger conumipition of traliusporlliol. cIlltes safety dev-ic>es. Sch.l nan t ire beyond those ini the la'.crg'It a b tion. will  V. Tlwonuzs, Spatial difIP,renIce, in porerty8 instead become part of the price differences. This feature of our methiod is reasonable insofar as this type of quiantity differences does ne1t4 enhance welfare (e.g., the urbani dwellers are not better off because of thecir larger consumption of safety devices); if on the contrary, it does contribute to welfare, the price index as calcuilated in this paper for the urban areas will be biased upwards. TIable I Interregional prize inidices Peru (1971 1. LUrbani Rural Peru Lima C'oast Sierra Selva Coast Sierra 1. Food 10 125 106 87 97 100 84 2. Non-Food 10 157 1(12 72 97 125 56 3. Ov~erall lOt) 141 103 79 97 118 70 4. Based on minimum wage 100 140 106 79 99 1(14 72 aSoure: Tliomas (1978) Table 1 presents the estimated price NI-rat ion betwveen the maj,~or regions and the three choseni areas. The food price index as giveni in row I reflects the cost differences of 'the typical diet' of the poor. The actuial cost of this diet varies between 3,943 soles per capita ppr year in Lima-, 3,470 soles in UJrban Coast, ancd 2,650 soles in Rural Sierra. Among thle thiree regions", the Coast shows the highest cost for this food basket 3,344 soles per capita pci- year, compared to 2,745 soles in Sierra and 3,060 soles in the Selva. The national average cost is 3,155 soles per capita per year. Row 2 in table 1 shows the cost differences in buying the non-food requirIements in thle v-arious locationis. Non-food prices are highest in Lima and the Coast, Ibllmved by Selxva and Sierra. They increase with the degrece Of l1rha,IiZI6011n non-food, pr-ices in Lima appear to be over 25, I highier thian in otheri bigy cities in the Coa.st anid about three times these in the villages of Sierra. The overall price inidex shown in row 3 is a wveigghted a%erace of rows I anid 2. There are conisider-able price differences, betwecen the Coast, Sierra and Selva, and, not ~.upriingy,urban areas in giener-al seem to be more ;expIensive to live in. In anl alternative attempt to Constr'Uct a pr.'ce index, infrormaiitioni on the mllliinimu wage est:iblished b% the Ministry of Labor, Perui, v% as uised, Row 4 in table I shows esuiiimles of minimiium wages for- the regions and areas con' rted inito ani index withi a national average of 100 as base. Thlis index shows dikcrgeciec, betw\een Lima and Ruiral Siei-ra, anid between C'oiat. Sierr-a anid Sek\a, "%\hichi are;cniearkably simiilari to the previouis rc,stil ts. TIo the e Uen t that mlinlimn in1 wage differentials ICCuIra telN reflect thle inicomei IexelS :-CqUired to achiec~ comiparable le\ els of Ii ving. they strengthen the pjresent results.  90 r: Uwioina(s, Spatial dif,'C renct . in potertY 3. Poverty levels Delinitions of absolute poverty are based on an individtual's (or household's) ability to afford some specr.-d basket of goods and services. Here, we define the absollute po% erty tbaket on criteria similar to those adopted by the World Bank in 1976 for the estimation of income cut-off points for- piroject ide1itification0 pUrposes. The mCetho0d lised was hasud on Orshansky's approach whiclh, althoughi rather cruide, is still uised as the hasis for estimnatiln po\ertv incomiie levels in the U.S. According to Orshansky (1965, 1969) the poVerty income level is determinied by costing a hypothetical adeqLuLa.te diet and ad juhtMinc this cost to allok% f(or non -foo(d consumptlion according to the proportions of food and nion-food expenditures in the buLdlget of the average family. The ii\eraue U.S. famnily spends a third of its inconme on food. The poverty line is therefore takeni as three times the cost of the hypothetically adequate diet. This multiplier is clealdy inaplpropriate where the percentage of food expenditure in average hiousehold budgets varies widely but is usually far above one-third. The work on Bank member countries thus comnhinL'd elements o f both absolute and relative definitionns of poverty: (i) the cost of the food conmponiient of the po%erty level income was calculated onI the basis of the food expen3dituLres Of thle we%'n1tieth11 p-erencCtile in the income distribuitoin of the countw r in LuestionC.adjutedJ upwa rds if niecessarv to erisni e nitritional adeqLMac (ii) thle il L11tipl iCr Used to arrixe at the poverty level income w-as the ratio of non-flrood Cxpnelditrilce of the twentieth percenitile. In conistru1ctinig the abs,Olute poverty expenditure levels for the different parts of Peru, the food element is based on the cost of a basket consunmed by people at the twentieth percentile in the income di1tribultioll in Rural Sierra, which was the basis for the food price inidex. This cost, of 2,650 soles per capita-year, provides a lo\%eri bound on food colts. This basket satisfies the nuLtritional requirements of those who ConsuTmle it in Rural Sierra, and its contenits need only small adjIustments to meet the nutritionial requirements typical in other parts of the country. The costs of the basket in other regions, derived by applyinig the food price indices (table 1, row 1) are given in row I of table 2. As regards the non-food comnponlent of 1i'ing costs, it would not be appropriate simply to use tl e national wNeragc ratio of food,' non-food expeniditures as is donie in the U.S.: natiomnaly, average per capita noln-food expenditule in Peru is just (1 ( greater than food exlenditLure, bu, the average ratio of non-food to food( cxpeinditure varies from 0.5:1 in Rural Sierra to 1.93:1 in Lima. (At the tweintietlh perceintile in lima. food and non- food expenditules are about equal. like the a%r.'rage for Peru as a whole.) For the population of Rtural SiCera as a w%hole, and at the twentieth pereentile in Urban Coast, expetnditures on noni-food are oinl) half those on food. This  1 Thoinas, Spattial ,1cY% in porerty 91 may be typical of large parts of the comitry. For the present study, the low ratio of non-food expenditures of 0.3:1 is adopted as a minimum Figure: this is the non-foodffood ratio at the fiftiletl percentile in Rural Sierra. Es.tinmites made on this basis are referred to as 'low' in the tables that follow. timate were also made usinig a ratio of 0.5:1: these are referred to as 'medium'. Table 2 Poverty expenditure levels Pertu (1971) (soles per capita-wear) Regio Areas Urban Rural Peru t.imi ('oast Sierra Selva Coast Sierra 1. Food cost 3155 3943 3344 2745 3(06(0 347(0 265(1 2. Non-food cost (a) low (NF F 0.3) 142(0 2229 1448 1(22 137' 1775 795 (b) medium (NF F=0.51 2366 3715 2413 1704 2295 2958 1325 3. Absolute pmeCrl expenditure (a) low 1.v F=0.3) 4575 6172 4792 3767 4437 5245 3445 (b) medium tNF F=t).5) '21 7658 5757 4449 5355 6428 3975 4. Minimum wage 4 67 6658 51(10 3765 4753 4956 3445 The cost of non-fOOd reqLuirementk that is implied by the 0.3:1 ratio [given by row 2(a)] is added to the minimlulll food costs shown in the First row of table 2. The non-food reqlulirernci-irs for the other parts of Peru are estimated by applying the non-food price index to the estimated non-Foo(d expenditure for Rural Sierra. Row 3(a) perhaps representis a lower bolulnd on absoltute poverty expenditure levels. Row 3(b) slhows the somnewhalt hig her estimates of poverty levels made using a hiigher non-Food Cost 2(b) based on a non-food food expenditure raItio of 0.5: 1. Botlh the poverty levels show considerable differmences in expeniditLur-es across regions and areas, needed to buy. what may be considered the 'basic' requirements. The required expenditure, according the 'low' estimate in Lima, is 35 C() higher than the national averae, wlhile that in Rural Sierra is 25 "O below the national average. Row 4 of table 2 shows estimates of annual per capita minimumii wages. Data on minimum wages, estimlaltcd by Peru's Ministry of LabOr, were multiplied by 1.9 the national a\erl.ge number of earners per family and then divided by 6 the national average nuImlhber of earners per family - and then divided by 6 the nationa.il average family size. 4. Poverty indices To derive poverty indices, we need to comnpare the poverty expenditure  92 1: 7Thlzomas, Spatial dillTIc . ifl p0'aert le\el1s eiven in rows 3 and 4 of ?able 2, with the actual distribution of expenditure. But since data oni ex\pendituLre distributiion were not readily a. ilable at the time of this study. income diStriblution estilllmates gi\Cen by Peru's Ministry of Ecoiionoics and Finance (1977) were used instead. It was fouiid, hkw\%\cr, that mean i -,ome stimatels were well below mean expenditures, particldarly fori Sierra anid Selva and the rura1 areas, This might he due to under-iepor'ting of incon-., in tlhese areas and or the inability (f the samplingg nmethod used to fullly captLure the NuaNo;anaily of income, Therefore to make the po\erty e,\pendituirc levels compai able with the data on income diistriblution thc fFormer were adjiwited dow1n1wVa,rds, where necessary, using ratios of mean incomnes to e\penditUres. This section compares estimates of poverty obtained uisinig a single poverty linie with those based on the region specific po.crty lines. Table 3 comnlpares the percentage and num:lbers of poor below the alternative poverty thresholds. Table 3 shows only the poxerty C.Npellditure leCels as estimiiated in table 2 and not the adjusted poveitv 'income' levels (previous paragraphI) to simplify the exposition. It may be noted howe\er. that the percentages anid nUmbers of poor in that table were derived conmbiininl adjUsted po%ertv income lexels with the incoime tribLtilon data. 'Tables 4 and 5, how- e;-er, exclusively showx the adjusted poxertv 'income' le \els becae.SC sonme of the remaininig rows of lhese tables ha\e direct ariilithmetic relationships to 'hem. Row I of table 3 shows a single po'e cty thil-Cr1old of 4,575 soles 'obtailled by appl% ing a eqirLIce1d n110n-ood cxpenduiire of only 0.3 of the expeniditure needeCd to satisfy nutritiOrial nieeds. Rows 2 and 3 show the 'low' and 'medium' values of the poverty expendituire thresholds after adjusting for regional cost of living differenices, while row 4 shows the per capita miilimum wage. Based on the low' pov rty thrcshold, 28"',, oif lerui's pOPula1tion., or 3.84 million people, cannot satisfy the 'basic re'luimemens. About 2.28 million, or 59",, of them, live in Sierra. Withini the reieons and areas, the proportions of populILtion who are below the minimumLiiii threslhold range frfii 8% in Lima to 36", in Sierra and 12.3 ",, in Urban Coast to 41 ",, in Rural Sierra. Thus, Peru's poor are concentratted in Sierra and Sel\u. rather than the Coast, and in rural aireas rather thtani uirban center.>, An index of po.ertN. I. [Senl (1973) anid A\nand (1977)] is the product Of (il the percentage of popuilation helom the poverty line, and (ii) the poverty gap, or the extenit to. x hich the mneai income of the poor nleieds to be raised to bring them up to thc po\erty line. N, Y'*- Y'(  Table 3 Regional distribution of poor: Comparison of a national with alternative regional poverty levels. Regions Areas Urban Rural Peru Lima Coast Sierra Selva Coast Sierra 1. Norional absolute po%erty Expenditure level 4575 4575 4575 4575 4575 4575 4575