The New Palgrave Dictionary of Economics, 2nd edition, Larry Blume and Steven Durlauf (eds) London: Palgrave Macmillan, forthcoming.

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1 The New Palgrave Dctonary of Economcs, 2nd edton, Larry Blume and Steven Durlauf (eds) London: Palgrave Macmllan, forthcomng. Poverty Lnes Martn Ravallon The artcle provdes welfare-economc defntons of poverty lnes and crtcally assesses the man methods of settng poverty lnes found n practce. These can be nterpreted as ways of expandng the nformaton set used n appled work to address some longstandng problems n measurng welfare. Objectve methods draw on nformaton from outsde economcs on the commodtes needed for normatve actvty levels. Subjectve methods extend the nformaton base by drawng on self-reported perceptons of consumpton adequacy, allowng estmaton of an endogenous socal subjectve poverty lne. Knowng how many people lve n households wth ncome or consumpton expendture below the poverty lne has helped focus attenton on the extent of poverty and has nformed polcymakng for fghtng poverty. But how are poverty lnes defned and calculated? Ths artcle frst provdes a theoretcal defnton, and then descrbes the man methods found n practce. Poverty lnes n theory People n dfferent crcumstances wth dfferent household szes or demographc compostons or lvng n dfferent places naturally have dfferent levels of economc welfare at the same level of ncome. They have dfferent needs. A poverty lne should reflect these dfferences. But how should that be done? To answer ths queston we must frst defne the conceptual deal aganst whch the methods found n practce are to be judged. 1

2 The poverty lne for a gven ndvdual can be defned as the money the ndvdual needs to acheve the mnmum level of welfare to not be deemed poor, gven ts crcumstances. Everyone at the poverty lne s taken to be equally badly off, and all those below the lne are worse off than all above t. The next queston s: what concept of welfare should serve as the anchor for the poverty lne? For economsts the obvous answer s utlty. A justfcaton for utlty-consstent poverty lnes can be found by applyng standard welfare-economc prncples to poverty measurement (Ravallon, 1994). These prncples are that assessments of socal welfare should depend solely on utltes, that people wth the same ntal utlty should be treated the same way, and that socal welfare should not be decreasng n any utlty. To formalze ths defnton, consder ndvdual wth characterstcs x (a vector). The nterpersonally comparable utlty functon s u q, x ) (. The quantty vector q s utlty maxmzng, gvng demand functons q ( p, y, x ) at total expendture y and correspondng utlty maxmum, v p, y, x ). The utlty-consstent poverty lne s the pont on the consumer s ( expendture functon correspondng to a common reference utlty level. (As always, the monetary measurement of welfare requres a reference utlty level.) The consumer s expendture functon s e( p, x, u), gvng the mnmum cost of utlty u n sub-group j when facng the prce vector p. Let u z denote the mnmum utlty deemed necessary to escape poverty. Consstency requres that ths s a constant across all. The money metrc of u z defnes the utlty-consstent poverty lnes: u z = e p, x, u ) for all = 1,..n (1) ( z Ths s closely related to a number of other economc concepts. Eq. (1) s money-metrc utlty at a specfc reference utlty, nterpretable as the poverty lne n utlty space. (Textbook treatments of money-metrc utlty functons sometmes called equvalent ncome functons u / r r z can be found n Varan, 1978, and Deaton and Muellbauer, 1980.) The value of z e( p, x, u ) for reference ndvdual r gves the true cost-of-lvng ndex (see, for example, Deaton and Muellbauer, 1980). The value of u y / z s the welfare rato (Blackorby and Donaldson, 1987). 2

3 On explotng the propertes of the expendture functon (see, for example, Varan, 1978), eq. (1) can be wrtten n a more nstructve form: u z = p q p, x, u ) (2) ( z Thus, the poverty lne s the cost of a bundle of goods, namely, the vector of utlty-compensated (Hcksan) demands, q p, x, u ). Ths bundle can be nterpreted as basc consumpton needs. ( z Note that an absolute poverty lne n terms of utlty can have the propertes of a relatve poverty lne n the ncome space, n that t rses wth the mean ncome of a relevant reference group. Ths s possble f ndvdual utlty depends on both own ncome and ncome relatve to others n that reference group. In other words, the ndrect utlty functon has the form, r v p, y, y / y, x ) where ( r y s the mean ncome of the reference group(s); the poverty lne r r takes the form z = z p, y, x, u ) (whch solves u = v p, z, z / y, x ) ). Thus, there s no ( z z ( nconsstency between vewng poverty as absolute n the space of welfare, but relatve n the space of commodtes (paraphrasng Sen, 1983). However, the extreme case n whch the poverty lne s a constant proporton of the mean (as used by poverty measures derved by Eurostat, for the European Commsson) requres the seemngly mplausble assumpton that utlty depends solely on relatve ncome, gven by the rato of own ncome to the country s mean ncome. By ths measure, f all ncomes ncrease by the same proporton then the proporton of people lvng below the poverty lne wll be unchanged. Cross-country comparsons of poverty lnes suggest that relatve ncome s valued more hghly as mean ncome rses; n the poorest countres, absolute ncome levels are the domnant consderaton, so then the poverty lnes tend to have a low elastcty to the mean; Ravallon (1994; 1998). There s mcro emprcal evdence supportng ths vew, based on self-assessed welfare (Ravallon and Lokshn, 2005). For economsts, utlty s the obvous anchor for settng poverty lnes, but t s not the only approach. Functonng-based concepts of welfare offer an alternatve foundaton for poverty lnes. The approach can be characterzed n the terms of Sen s (1985) argument that well-beng should be thought of n terms of a person s capabltes, that s, the functonngs ( bengs and dongs ) that a person s able to acheve. On ths vew, poverty means not havng an 3

4 ncome suffcent to support specfc normatve functonngs. Utlty as the attanment of personal satsfacton can be vewed as one such functonng relevant to well-beng (Sen, 1992, ch. 3). But t s possbly only one of the functonngs that matter. Independently of utlty, one mght say that a person s better off f she s able to partcpate fully n socal and economc actvty. From ths startng pont, a more general theoretcal formalzaton of the defnton of a poverty lne can be proposed as follows. Let a person s functonngs be determned by the goods she consumes and her characterstcs, gvng the vector of functonngs: f = f q, x ) (3) ( where f s a vector-valued functon. One can postulate that a person derves utlty drectly from her functonngs. We can then nterpret u q, x ) as a derved utlty functon, obtaned by ( substtutng (3) nto the (prmal) utlty functon defned over functonngs. Functonng consstency for a set of poverty lnes requres that certan normatve functonngs are reached at the poverty lne. Let f z denote the vector of crtcal functonngs deemed to be needed to be not poor. These are normatve judgments, just as u z s a normatve judgment. Assume that there s a bundle c ( c q such that no functonng s below ts crtcal value: f f q, x ) (4) z Ths yelds the poverty lnes: c c z = p q. There can be multple solutons for c q. Two ways to pck a unque poverty lne can be dentfed. The frst s to defne 4 c z as the mnmum y such that: f f q ( p, y, x ), x ] (5) z j[ j j j j Notce that one (or more) specfc functonngs wll be decsve n determnng c z j, that s, the functonng that s the last to reach ts crtcal value as ncome rses. In ths sense, the lowest prorty functonng for the ndvdual wll be decsve. The alternatve approach s to treat attanments as a random varable (that s, wth a probablty dstrbuton) and take a mean condtonal on ncome and other dentfed covarates, ncludng group membershp. Then poverty lnes are deemed to be functonng consstent f f z s reached n expectaton.

5 Implementng these concepts emprcally requres that we solve two problems. The frst can be called the referencng problem: what s the reference level of utlty that anchors the poverty lne ( uz n eq. 1)? It s temptng to say ths choce s arbtrary, and to hope that t s nnocuous. But the choce of the reference s far from arbtrary, and (n general) t affects the resultng poverty measure. Ths speaks to the mportance of testng the senstvty of poverty comparsons (such as between groups or over tme) to the choce of reference, as t determnes the level of the poverty lne. Tests exst for the robustness of ordnal comparsons usng stochastc domnance crtera; on ths approach see Atknson (1987) and Ravallon (1994). The second problem s the dentfcaton problem. Even f we can readly agree on what the poverty lne s n welfare space, there s a further problem n dentfyng the expendture functon n eq. (1). Standard practce s to calbrate the parameters of the cost functon from consumer demand behavour. The problem s that ndvduals vary n characterstcs, such as ther sze and demographc composton, whch nfluence welfare n ways that may not be evdent n consumer demand behavour. Then there s a fundamental problem of dentfcaton (Pollak and Wales, 1979; Pollak, 1991). Poverty lnes n practce The methods of settng poverty lnes found n practce fall under two headngs: objectve poverty lnes and subjectve poverty lnes. Objectve poverty lnes The man methods found n practce are the food-energy-ntake (FEI) method and the cost-of-basc needs (CBN) method. It s known that these methods gve radcally dfferent results; usng data for Indonesa, Ravallon and Bdan (1994) found vrtually zero correlaton between the regonal poverty profles (gven the poverty rates across geographc areas) produced by these two methods. Snce polcy choces (such as n regonal targetng) could depend crtcally on whch method s used, t s mportant to probe carefully nto the choce. 5

6 The FEI method can be nterpreted as a specal case of the functonng-based approach descrbed above. The specalzaton s to focus on just one functonng, namely food-energy ntake. The method fnds the consumpton expendture or ncome level at whch food-energy ntake s just suffcent to meet predetermned food-energy requrements for good health and normal actvty levels. (Such calorc requrements are gven n WHO, 1985, for example.) To deal wth the fact that food-energy ntakes naturally vary at a gven ncome level, the FEI method typcally calculates an expected value of ntake at gven ncome. Fgure 1 llustrates the method. The vertcal axs s food-energy ntake, plotted aganst ncome (or expendture) on the horzontal axs. A lne of best ft s ndcated; ths s the expected value of calorc ntake at gven ncome (that s, the nonlnear regresson functon). By smply nvertng ths lne, one fnds the ncome z at whch a person typcally attans the stpulated food-energy requrement. Ths method, or somethng smlar, has been used often, ncludng by Dandekar and Rath (1971), Osman (1982), Greer and Thorbecke (1986), and Paul (1989), and by numerous governmental statstcs offces. It s often found n practce n developng countres. One concern about ths method s that the resultng poverty lnes need not be consstent n terms of utlty or capabltes more generally (Ravallon, 1994; Ravallon and Lokshn, 2006). Consder frst how FEI poverty lnes respond to dfferences n relatve prces, whch can of course dffer across the subgroups (such as regons) beng compared n the poverty profle and over tme. For example, the prces of many non-food goods relatve to food are lkely to be lower n urban than n rural areas. Ths wll probably mean that the demand for food and (hence) food-energy ntake wll be lower n urban than n rural areas, at any gven real ncome. But ths does not, of course, mean that urban households are poorer. The relatonshp between foodenergy ntake and ncome wll shft accordng to dfferences n tastes, actvty levels and publcly provded goods. There s nothng n the FEI method to guarantee that these dfferences are ones that would normally be consdered relevant to assessng welfare. Indeed, t s qute possble to fnd that the rcher sector (by the agreed metrc of utlty) tends to spend so much more on each calore that t s deemed to be the poorer sector. That has been found to be the case n studes of the propertes of FEI poverty profles for Indonesa (Ravallon and Bdan, 1994) and Bangladesh (Ravallon and Sen, 1996; Wodon, 1997). 6

7 Problems also arse n comparsons over tme. Suppose that all prces ncrease, so the cost of a gven utlty must rse. There s nothng to guarantee that the FEI-based poverty lne wll ncrease. That wll depend on how relatve prces and tastes change; the prce changes may well encourage people to consume cheaper calores, and so the FEI poverty lne wll fall. Wodon (1997) gves an example of ths problem n data for Bangladesh. The FEI poverty lne fell over tme even though prces generally ncreased. The potental utlty nconsstences n FEI poverty lnes are worryng when there s moblty across the subgroups of the poverty profle, such as due to nter-regonal mgraton. For example, t s possble that a process of economc development through urban sector enlargement, n whch none of the poor are any worse off and at least some are better off, would result n a measured ncrease n poverty. The CBN method stpulates a consumpton bundle deemed to be adequate for basc consumpton needs, and then estmates ts cost for each of the subgroups beng compared n the poverty profle. Ths s the approach of Rowntree (1901) n hs semnal study of poverty n York, England, n 1899, and there have been numerous examples snce, ncludng the offcal poverty lnes for the Unted States (Orshansky, 1965; Ctro and Mchael, 1995). Some form of functonng consstency s assured by constructon, snce varous valued functonngs are essentally the startng pont for defnng basc consumpton needs. The poverty bundle s typcally anchored to food-energy requrements consstent wth common dets n the specfc context. However, allowances for non-food goods are also ncluded, to assure that basc nonnutrtonal functonngs are assured. The CBN method s utlty consstent f the rght bundle s used, correspondng to the relevant ponts on the utlty-compensated demand functons (eq. 2). However, there s nothng to guarantee that the bundles of goods bult nto CBN poverty lnes le on the compensated demand functons, at the (common) reference level of utlty. Thus t s mportant to have some way of assessng a set of CBN poverty bundles. Ravallon and Lokshn (2006) propose an approach to testng the utlty consstency of CBN poverty lnes across households wth common preferences usng Samuelson s (1938) theory of revealed preference. However, ths can be 7

8 appled only wthn subgroups deemed to have common preferences. In practce utlty functons can vary, due to dfferences n clmate, for example. In some cases a complete vector of normatve (food and non-food) goods s set, as n Russa s poverty lnes (Ravallon and Loskhn, 2004). However, t s more often the case that only food needs are set, based on nutrtonal requrements. To nclude an allowance for nonfood needs, a common practce s to dvde the food poverty lne by some budget share for food. For example, the US poverty lne assumes a food share of one thrd, so the total poverty lne s three tmes the food lne (Orshansky, 1963). However, the bass for settng a food share s rarely transparent. Why use the average share, as n the US lne? Whose food share should be used? Arguably, a more appealng approach s to set an allowance for non-food goods that s consstent wth demand behavour at (or n a regon of) the food poverty lne. Ravallon (1994) proposes two methods. The frst dvdes the food component of the poverty lne by the mean food share of households whose actual food spendng s n a neghbourhood of the food poverty lne. The second method uses mean non-food spendng of households whose total sendng s n a neghbourhood of the food poverty lne. Ravallon argues the frst method gves a reasonable upper bound to the allowance for non-food needs whle the second gves a lower bound. Subjectve poverty lnes There s an nherent subjectvty and socal specfcty to any noton of basc needs, ncludng nutrtonal requrements. Psychologsts, socologsts and others have argued that the crcumstances of the ndvdual relatve to others nfluence perceptons of well-beng at any gven level of ndvdual command over commodtes. (Runcman, 1966, provded an nfluental exposton, and supportve evdence. Also see the dscussons n Easterln, 1995, and Oswald, 1997.) By ths vew, the dvdng lne... between necesstes and luxures turns out to be not objectve and mmutable, but socally determned and ever changng (Sctovsky, 1978, p. 108). 8

9 Subjectve poverty lnes have been based on answers to the mnmum ncome queston (MIQ), such as the followng (paraphrased from Kapteyn, Kooreman and Wllemse, 1988): What ncome level do you personally consder to be absolutely mnmal? That s to say that wth less you could not make ends meet. (Ths can be thought of as a specal case of Van Praag s, 1968, ncome evaluaton queston, whch asks what ncome s consdered very bad, bad, not good, not bad, good, very good.) One mght defne as poor all whose actual ncome s less than the amount they gve as an answer to ths queston. However, ths would almost certanly lead to nconsstences n the resultng poverty measures, n that people wth the same ncome, or some other agreed measure of economc welfare, wll be treated dfferently. Clearly an allowance must be made for heterogenety, such that people at the same standard of lvng may well gve dfferent answers to the MIQ, but must be consdered equally poor for consstency. Past emprcal work has found that the expected value of the answer to the MIQ condtonal on actual ncome tends to be an ncreasng functon of actual ncome. (Contrbutons nclude Groedhart et al., 1977; Danzger et al., 1984; and Kapteyn, Kooreman and Wllemse, 1988.) Furthermore, past studes have tended to fnd a relatonshp such as that depcted n Fgure 2, whch gves a stylzed representaton of the regresson functon on ncome for answers to the MIQ. The pont z * n the fgure s an obvous canddate for a poverty lne; people wth ncome above z * tend to feel that ther ncome s adequate, whle those below z * tend to feel that t s not. We can call z * the socal subjectve poverty lne (SSPL). It s recognzed n the lterature that there are other determnants of economc welfare whch should shft the SSPL, such as famly sze and demographc composton. Indeed, the answers to the MIQ are nterpretable as ponts on the consumer s expendture functon at a pont of mnmum utlty (eq.1). Under ths nterpretaton, subjectve welfare assessments provde a means of overcomng the well-known problem of dentfyng utlty from demand behavor alone when household attrbutes vary (Kapteyn, 1994). Whle the MIQ has been appled n a number of OECD countres, there have been few attempts to apply t n a developng country. There are a number of potental ptfalls. Income s not a well-defned concept n most developng countres, partcularly (but not only) n rural 9

10 areas. It s not at all clear whether one could get sensble answers to the MIQ. The qualtatve dea of the adequacy of consumpton s a more promsng one n a developng-country settng, and (arguably) many developed countes. Pradhan and Ravallon (2000) propose a method for estmatng the SSPL based on qualtatve data on consumpton adequacy, as gven by responses to approprate survey questons. Instead of askng respondents what the precse mnmum consumpton s that they need, one smply asks whether ther current consumptons are adequate. Ths provdes a multdmensonal extenson to the one-dmensonal MIQ. The SSPL s the level of total spendng above whch respondents say (on average) that ther expendtures are adequate for ther needs. For emprcal mplementaton, the probablty that a sampled household wll respond that ts actual consumpton of each type of commodty s adequate can be modelled as a probt regresson. Under certan techncal condtons, a unque soluton for the subjectve poverty lne can then be obtaned from the estmated parameters of the probt regressons for consumpton adequacy. Pradhan and Ravallon provde emprcal examples for Jamaca and Nepal; the SSPL gave a smlar overall poverty rate to pre-exstng objectve poverty lnes for both countres, though the structure of the poverty profle was dfferent n some respects: for example, whle the objectve poverty lnes mpled that larger households tended to be poorer, ths was not the case wth the subjectve approach. Subjectve data also offer a test of objectve poverty lnes, by regressng self-rated welfare on ncome normalzed by the poverty lne plus the varables that went nto the constructon of the poverty lne, whch should be jontly nsgnfcant f those lnes accord wth subjectve welfare. Ths approach s outlned n Ravallon and Lokshn (2002) and llustrated usng Russa s poverty lnes. 10

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12 Paul, S A model of constructng the poverty lne. Journal of Development Economcs 30, Pollak, R Welfare comparsons and stuaton comparsons. Journal of Econometrcs 50, Pollak, R. and Wales, T Welfare comparson and equvalence scale. Amercan Economc Revew 69, Pradhan, M. and Ravallon, M measurng poverty usng qualtatve perceptons of consumpton adequacy. Revew of Economcs and Statstcs 82, Ravallon, M Poverty Comparsons. Chur, Swtzerland: Harwood Academc Press. Ravallon, M Poverty lnes n theory and practce. Lvng Standards Measurement Study Workng Paper No Washngton, DC: World Bank. Ravallon, M. and Bdan, B How robust s a poverty profle? World Bank Economc Revew 8, Ravallon, M. and Lokshn, M Self-rated economc welfare n Russa. European Economc Revew 46, Ravallon, M. and Lokshn, M On the consstency of poverty lnes. In Poverty, Inequalty and Development: Essays n Honor of Erk Thorbecke, ed. A. de Janvry and R. Kanbur. Amsterdam: Kluwer Academc Publshers. Ravallon, M. and Lokshn, M Who cares about relatve deprvaton? Polcy Research Workng Paper World Bank, Washngton, D.C. Ravallon, M. and Sen, B When method matters: montorng poverty n Bangladesh. Economc Development and Cultural Change 44, Runcman, W Relatve Deprvaton and Socal Justce. London: Routledge and Kegan Paul. Rowntree, B Poverty: A Study of Town Lfe. London: Macmllan. Samuelson, P A note on the pure theory of consumer behavour. Economca 5, Sctovsky, T The Joyless Economy. Oxford: Oxford Unversty Press. Sen, A Poor, relatvely speakng. Oxford Economc Papers 35, Sen, A Commodtes and Capabltes. Amsterdam: North-Holland. Sen, A Inequalty Re-examned. Oxford: Oxford Unversty Press. 12

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14 Fgure 1 The food-energy ntake method of settng poverty lnes Food-energy ntake (calores per day) 2100 z Income or expendture Fgure 2 The socal subjectve poverty lne (z * ) Subjectve mnmum ncome 45 z * Actual ncome 14