Weakly Relative Poverty

Transcription

1 Polcy Research Workng Paper 4844 WPS4844 Weakly Relatve Poverty Martn Ravallon Shaohua Chen Publc Dsclosure Authorzed Publc Dsclosure Authorzed Publc Dsclosure Authorzed Publc Dsclosure Authorzed The World Bank Development Research Group Drector's offce and the Poverty and Inequalty Team February 2009

2 Polcy Research Workng Paper 4844 Abstract Prevalng measures of relatve poverty put an mplausbly hgh weght on relatve deprvaton, such that measured poverty does not fall when all ncomes grow at the same rate. Ths stems from the (mplct) assumpton n past measures that very poor people ncur a neglgble cost of socal ncluson. That assumpton s nconsstent wth evdence on the socal roles of certan prvate expendtures n poor settngs and wth data on natonal poverty lnes. The authors propose a new schedule of weakly relatve lnes that relax ths assumpton and estmate the mpled poverty measures for 116 developng countres. The authors fnd that there s more relatve poverty than past estmates have suggested. In 2005, one half of the populaton of the developng world lved n relatve poverty, half of whom were absolutely poor. The total number of relatvely poor rose over , despte fallng numbers of absolutely poor. Wth sustaned economc growth, the ncdence of relatve poverty becomes less responsve to further growth. Slower progress aganst relatve poverty can thus be seen as the other sde of the con to success aganst absolute poverty. Ths paper a product of the Drector's offce and the Poverty and Inequalty Team, Development Research Group s part of a larger effort n the department to montor progress aganst poverty n the developng world. Polcy Research Workng Papers are also posted on the Web at The authors may be contacted at schen@worldbank.org and mravallon@worldbank.org. The Polcy Research Workng Paper Seres dssemnates the fndngs of work n progress to encourage the exchange of deas about development ssues. An objectve of the seres s to get the fndngs out quckly, even f the presentatons are less than fully polshed. The papers carry the names of the authors and should be cted accordngly. The fndngs, nterpretatons, and conclusons expressed n ths paper are entrely those of the authors. They do not necessarly represent the vews of the Internatonal Bank for Reconstructon and Development/World Bank and ts afflated organzatons, or those of the Executve Drectors of the World Bank or the governments they represent. Produced by the Research Support Team

3 Weakly Relatve Poverty Martn Ravallon and Shaohua Chen 1 Development Research Group, World Bank 1818 H Street NW, Washngton DC, 20433, USA 1 These are the vews of the authors and should not be attrbuted to the World Bank or any afflated organzaton. For helpful comments the author s grateful to Rebecca Blank, Francos Bourgugnon, Stefan Klasen, Peter Lambert, Mchael Lpton, Lous de Mesnard, Domnque van de Walle and semnar partcpants at the Pars School of Economcs and partcpants at the OECD/Unversty of Maryland Conference Measurng Poverty, Income Inequalty, and Socal Excluson: Lessons from Europe, Pars 2009, and the World Bank. Addresses: mravallon@worldbank.org, schen@worldbank.org.

4 1. Introducton The methods used to set poverty lnes have dffered radcally between rch and poor countres. Poverty n the developng world s typcally measured usng absolute lnes, whch am to have the same real value at dfferent dates and places. Vrtually all developng countres use such lnes and, at the global level, the World Bank s $1-a-day lne s an absolute lne, amng to have the same purchasng power n dfferent countres and at dfferent dates. 2 By contrast, the more common practce n OECD countres s to use what we shall call strongly relatve poverty lnes, whch are set at a constant proporton typcally 40-60% of the (date and countryspecfc) mean or medan ncome. 3 Ths dfference n how poverty lnes are set matters greatly to the propertes of the resultng poverty measures. The bulk of the lterature has confned attenton to measures that are homogeneous of degree zero between the mean and the poverty lne for any gven Lorenz curve. 4 Usng an absolute lne, such a poverty measure automatcally falls when all ncomes grow at the same rate, whle any measure based on strongly relatve lnes wll be unchanged. 5 So t s hardly surprsng that ths choce has been found to matter greatly to assessments of how poverty s changng over tme, 6 as well as to cross-sectonal poverty comparsons. 7 2 The orgnal $1-a-day was proposed by Ravallon et al. (1991) n a background paper for World Bank (1990); the latest update s Ravallon et al. (2008). 3 Examples for OECD countres nclude Smeedng et al. (1990), Atknson (1998), Saunders and Smeedng (2002), Fouarge and Layte (2005), Eurostat (2005), Nolan (2007) and OECD (2008, Chapter 5). An excepton s the offcal poverty lne for the US, whch s three tmes the cost of a subsstence food basket, as frst proposed by Orshansky (1963). However, there has been consderable dssatsfacton wth ths lne; for a revew of the debates see Blank (2008). There has been some debate about whether the poverty measure should be anchored to the mean or the medan (Saunders and Smeedng, 2002; Easton, 2002; de Mesnard, 2007); poverty lnes set as a constant proporton of the medan can have perverse propertes when the Lorenz curve shfts (as shown by de Mesnard, 2007). Ths s a legtmate concern but s not central to the present paper. 4 Ths holds for the headcount ndex, poverty gap ndex, and ndeed the entre class of Foster-Greer- Thorbecke (1984) measures, as well as the Watts ndex and many other measures. Note that the two types of measures are typcally calculated on the same dstrbuton of relatve ncomes,.e., the same Lorenz curve. 5 Note also that, for a gven Lorenz curve, the medan s drectly proportonal to the mean. Thus ths strong relatvty property also holds when the poverty lne s a fxed proporton of the medan. 6 For example, the UNDP (2005, Box 3) (based on Nolan et al., 2005) showed how relatve poverty measures for Ireland were rsng despte hgher absolute lvng standards for the poor; thus the UNDP (p. 334) warns that: when economc condtons change rapdly, relatve poverty measures do not always present a complete pcture of the ways that economc change affects people s lves. In another example, Easton (2002) argued that relatve measures for New Zealand were deceptve n showed fallng poverty despte lower levels of lvng for the poor. 7 For example, OECD (2008, Chapter 5) reports the same poverty rate for the US as Mexco. In another example, the urban poverty lne proposed by Osberg and Xu (2008) for Chna (set at half the medan) s 2.4 tmes ther rural lne, or 1.7 tmes when deflated by the Ravallon and Chen (2007) absolute lnes. The Osberg-Xu method suggests lttle dfference n poverty ncdence between urban and rural Chna, whle the Ravallon-Chen method ndcates far hgher poverty measures n rural Chna. 2

5 Usng an absolute lne, any two people wth the same purchasng power over commodtes, but lvng n dfferent countres, are treated the same way, n that both are ether poor or not poor. However, relatve poverty measures only treat them the same way f the two countres have the same mean ncome. Two man arguments can be dentfed n support of the use of relatve lnes. 8 The frst vews poverty lnes as money-metrcs of utlty and clams that people attach value to ther ncome relatve to the mean n ther country of resdence. Snce ths presumes that relatve ncome s a source of utlty t can be descrbed as welfarst. Whle the dea that utlty anchors poverty lnes s not common n appled work, t s consstent wth a strand of the lterature on welfare measurement n economcs whereby cost-of-lvng ndces and equvalence scales are anchored to some reference level of utlty. 9 The second ( non-welfarst ) argument s more common n practce. Essentally ths says that poverty lnes should allow for dfferences n the cost of socal ncluson, whch can be defned as the expendture needed to cover certan commodtes that are deemed to have a role n assurng that a person can partcpate wth dgnty n customary socal and economc actvtes. 10 Ths argument does not rest on the vew that socal ncluson s a (drect or ndrect) source of utlty. Rather t s seen as a desred capablty for not beng deemed poor n a specfc context. The most nfluental exponent of ths lne of argument has clearly been Sen (1983, 1985), who argued that t s a person s capabltes that should be seen as absolute; n the context of poverty measurement, ths means that an absolute approach n the space of capabltes translates nto a relatve approach n the space of commodtes (Sen, 1983, p. 168). Relatve poverty n the ncome space s then seen as the logcal mplcaton of absolute poverty n the capablty space. If, addtonally, the cost of socal ncluson s drectly proportonal to mean ncome n the country of resdence then one can justfy a strongly relatve poverty lne. 8 A thrd justfcaton sometmes heard s that strongly relatve measures remove the effects of cross-country dfferences n survey methods and measurement practces; see, for example, UNDP (2005, Box 3). Ths only holds for dstrbuton-neutral dfferences and f one accepts the followng welfare justfcatons for strongly relatve measures; f they are not accepted then t s unclear n what sense strongly relatve lnes are comparable across countres, gven that ther real values are lkely to vary so much. The data justfcaton s thus secondary. 9 On the welfarst nterpretaton of a poverty lne as a pont on the consumer s cost functon correspondng to a reference level of utlty see Blackorby and Donaldson (1987). For a broader overvew of economc approaches to welfare measurement see Slesnck (1998). 10 It can be granted that socal ncluson s a broader concept than ths defnton allows, and may well requre more than commodtes, ncludng, for example, freedom from dscrmnaton accordng to gender or ethncty. However, the concern here s wth the measurement of poverty n terms of command over commodtes. 3

6 Both the welfarst and non-welfarst arguments can clam some support from past thnkng and evdence. The dea that people care about relatve ncome has a long hstory. It s sometmes called the theory of relatve deprvaton (RD), followng Runcman (1966), although economsts often refer to t as the relatve ncome hypothess, followng Duesenberry (1949). Some verson of RD has often been nvoked to explan observed behavor. 11 Whle early dscussons lacked evdence on the exstence of RD effects, there s now a body of supportve evdence from both observatonal studes and experments, though manly n developed-country settngs. Experments have suggested that relatve poston matters to behavor. 12 Regressons for self-reported satsfacton wth lfe or perceved economc welfare have also found results broadly consstent wth the dea of RD. 13 There has been much less research on whether very poor people care about RD; n one of the few studes, Ravallon and Lokshn (2007) found evdence for Malaw that, for very poor people, the postve externaltes from havng better-off frends and neghbors outweghed the negatve externaltes through RD, although ths pattern reversed at hgher ncome levels. The dea that certan socally-specfc expendtures can be deemed essental for socal ncluson s also long-standng. Famously, Adam Smth (1776, Book 5, Chapter 2, Artcle 4) ponted to the socal-ncluson role of a lnen shrt n eghteenth century Europe: A lnen shrt, for example, s, strctly speakng, not a necessary of lfe. The Greeks and Romans lved, I suppose, very comfortably though they had no lnen. But n the present tmes, through the greater part of Europe, a credtable day-labourer would be ashamed to appear n publc wthout a lnen shrt, the want of whch would be supposed to denote that dsgraceful degree of poverty whch, t s presumed, nobody can well fall nto wthout extreme bad conduct. The socal roles of certan forms of consumpton have also been noted from research n poor countres. Anthropologsts have ponted to the socal roles played by festvals, celebratons and communal feasts; see, for example, Geertz (1976) and Fuller (1999, Chapter 6). Rao (2002) documents the mportance of celebratons to mantanng the socal networks that are crucal to copng wth poverty n rural Inda. Banerjee and Duflo (2007) report seemngly hgh expendtures on celebratons and festvals by very poor people n survey data for a number of 11 Easterln (1974) used RD to explan why economc growth n the US has had lttle effect on the proporton of people who thnk they are happy. Other examples of the use of relatvsm to explan behavor can be found n Frank (1997), Oswald (1997), Fehr and Schmdt (1999), Walker and Smth (2001) and Hopkns (2008). 12 See, for example, Fehr and Schmdt (1999) and Alpzar et al (2005). 13 Examples nclude van de Stadt et al., (1985), Clark and Oswald (1996), Solnck and Hemenway (1998), Pradhan and Ravallon (2000), Ravallon and Lokshn (2002, 2007), McBrde (2001), Blanchflower and Oswald (2004), Kngdon and Knght (2007), Ferrer--Carbonell (2005), Luttmer (2005) and Fafchamps and Shlp (2009). 4

7 developng countres. In Yemen, partcpants at qat sessons dscuss local economc and socal affars whle chewng ths mld stmulant; these sessons serve an mportant socal role and no less so for poor people such that refusng to take qat s tantamount to acceptng ostracsaton (Mlanovc, 2008, p.684). Clothng can also serve a socal role. Fredman (1990) descrbes how poor Congolese acqured clothng wth a conspcuous desgner label, whch he nterpreted as status-seekng behavor. A feld experment by van Kempen (2004) revealed that poor people n Bolva were wllng to pay a premum for a desgner label, whch (he argues) serves as a symbolc expresson of socal dentty for the poor (van Kempen, 2004, p.222). 14 In the lght of such observatons there s a case for askng what a global relatve poverty measure for the developng world mght look lke, analogous to the wdely cted $1-a-day absolute measures. The purpose of ths paper s to provde such a poverty measure. However, we argue that nether the welfarst nor capabltes-based arguments above are fully convncng as justfcatons for strongly relatve lnes. We argue that the welfarst justfcaton requres an mplausbly hgh weght on relatve poston and the non-welfarst, capablty-based, justfcaton makes the mplausble assumpton that the cost of ncluson goes to zero n the lmt as a person becomes very poor. We propose nstead that poverty measures should satsfy the followng weak relatvty axom (WRA): If all ncomes ncrease (decrease) by the same proporton then an aggregate poverty measure must fall (rse). In any standard poverty measure ths wll be satsfed as long as the elastcty of the poverty lne to the mean does not exceed unty. One can fnd antecedents to ths dea n the lterature. Research on socal-subjectve poverty lnes poverty lnes based on responses to survey questons concernng the mnmum ncome to make ends meet or perceved consumpton adequacy 15 has ponted to mean-ncome elastctes of the poverty lne less than unty. 16 The proposals made by the 1995 panel of the Natonal Research Councl (NRC) for revsng the offcal poverty lne of the US would also be lkely to generate poverty lnes wth a postve (though nter-temporally varable) elastcty less For a more general dscusson of the socal-symbolc roles that consumpton can play see Khall (2000). See Groedhart et al. (1977), Kapteyn, Kooreman and Wllemse (1988) and Pradhan and Ravallon (2000). Hagenaars and van Praag (1985) estmate an elastcty of 0.51 for eght European countres. Klpatrck (1973) estmated an elastcty of about 0.6 for subjectve poverty lnes n the US. 5

8 than unty. 17 Each of these approaches can be questoned. 18 However, most mportantly for the present paper, these approaches are not operatonal for global poverty measurement. We need a schedule of weakly relatve poverty lnes wth global applcablty. Past global poverty measures have been anchored to natonal poverty lnes converted to nternatonal $ s at purchasng power party (PPP). The orgnal $1-a-day lne was an average for low-ncome countres (Ravallon et al., 1991). Atknson and Bourgugnon (AB) (2001) proposed a schedule of global poverty lnes also calbrated to natonal lnes. These were hybrd lnes, beng absolute for low-ncome countres (set at the $1-a-day lne) and strongly relatve for mddle ncome and developed countres. 19 We follow the same approach of usng natonal poverty lnes to dentfy our proposed schedule of weakly relatve poverty lnes. The followng secton proposes our new measures of weakly relatve poverty. Secton 3 dscusses the dentfcaton assumptons, whle secton 4 descrbes key features of the data. Secton 5 calbrates the parameters of our poverty lnes to the observed relatonshp across countres between natonal poverty lnes and mean consumpton. Secton 6 presents our estmates of the new measures of relatve poverty. Secton 7 concludes. 2. Revstng the theory of relatve poverty lnes An exclusve focus on absolute poverty s justfed f one accepts two axoms: subgroup addtvty and subgroup anonymty (Ravallon, 2008). The frst says that aggregate poverty s the sum of all ndvdual levels of poverty n the populaton, mplyng that f poverty ncreases n any subgroup, and does not change for any other group, then aggregate poverty must ncrease. 20 The practce of poverty measurement has largely been confned to such addtve measures. 21 Less attenton has been pad to subgroup anonymty, whch says that movng a person between 17 The panel recommended that US poverty lnes should be anchored to medan expendtures on food, clothng and shelter (Ctro and Mchael, 1995). Gven that these goods tend to be necesstes, they wll have an elastcty wth respect to mean ncome less than unty. 18 For example, n the case of the proposal by the NRC panel t s unclear why concerns about relatve poverty would apply only to necesstes; t would seem more natural to assume that the ncome gradent n a poverty lne stems from socal ncluson needs that go beyond necesstes n a country such as the US. 19 Chen and Ravallon (2001, 2004) mplemented a slght varaton on the AB lnes but ther lnes were stll strongly relatve above a crtcal level of consumpton. 20 Ths s the subgroup monotoncty axom of Foster and Shorrocks (1991). 21 Examples nclude the wdely used Foster-Greer-Thorbecke (1984) class of measures. Atknson (1987) revews other addtve measures n the lterature. Addtvty s not unversally accepted; see the dscusson n Foster and Sen (1997); Sen s (1976) poverty measure s an example of a not addtve. 6

9 groups, wth no absolute loss to own consumpton, cannot ncrease aggregate poverty. Ths precludes the possblty that a person s poverty depends on her ncome relatve to her group. As dscussed n the ntroducton, both welfarst and non-welfarst arguments can be made for relaxng anonymty. The followng dscusson wll show how weakly relatve poverty lnes can be derved consstently wth both approaches. The welfarst nterpretaton argues that poverty should be seen as absolute n the space of welfare, rather than n the consumpton or ncome space, and that welfare depends (postvely) on both own ncome and relatve ncome own ncome relatve to mean ncome n the country of resdence. 22 It follows that for a poverty lne to be a money-metrc of welfare t must be an ncreasng functon of mean ncome. To see ths more formally, suppose that welfare depends on own ncome, Y, and relatve ncome, Y/M, where M s the mean for the country of resdence. Welfare s V(Y, Y/M), whch s taken to be smoothly non-decreasng n both Y and Y/M. The poverty lne n ncome space s denoted Z and s defned mplctly by: V = V ( Z, Z / M ) (1) where V s the fxed poverty lne n the welfare space. Lettng η denote the elastcty of Z wth respect to M, t s readly verfed that: 1 η = ( 0 η 1) (2) 1 + M. MRS where MRS s the margnal rate of substtuton of relatve ncome for own ncome ( MRS V V Y / Y / M = ), nterpretable as the weght on own ncome dvded by that on relatve ncome. If η=0 then relatve ncome does not matter (ts weght s zero and so the MRS goes to nfnty), whle η=1 mples that only relatve ncome matters (zero weght on own ncome). Thus we can state the followng result: Proposton 1: Welfarst poverty lnes satsfy the Weak Relatvty Axom as long as both own ncome and relatve ncome are valued postvely. Notce that the elastcty of the poverty lne (η) wll only rse wth the mean f the weght attached to relatve ncome rses suffcently. More precsely, η wll be ncreasng n M f (and only f) the elastcty of the MRS wth respect to M s less than One can certanly queston whether ths s the approprate reference group for relatvst comparsons at the ndvdual level; see, for example, the dscusson of reference groups n Ravallon and Lokshn (2007) and references theren. However, t s the relevant group for the problem at hand of measurng global poverty. 7

10 The utlty of relatve ncome has not, however, been the man argument made for relatve poverty lnes. Rather, the case has been seen to rest on the vew that there are certan demands on ncome that are socally determned and that a person s absolutely deprved f those demands cannot be met n a specfc socal context. Atknson and Bourgugnon (2001) proposed a neat way of mplementng ths dea for the purpose of measurng global poverty. They postulated two key capabltes: physcal survval and socal ncluson. The former s the capablty of beng adequately nourshed and clothed for meetng the physcal needs of survval and normal actvtes. On top of ths, a person must also satsfy certan socal ncluson needs, whch are assumed to be drectly proportonal to mean consumpton n the country of resdence. Each capablty has a correspondng poverty lne, gvng the absolute and relatve lnes. The AB proposal s that one should only be deemed not * poor f one s nether absolutely poor nor relatvely poor. Lettng Z be the mnmum expendture needed to assure that basc consumpton needs are met, measured at purchasng power party (PPP), the AB poverty lne for country s: AB * Z = max( Z, km ) ( 0 < k < 1) (3) * * There are two unknown parameters n (3), Z and k. AB proposed that Z should be set at the World Bank s $1-a-day lne, on the grounds that ths can be consdered a reasonably lower bound, snce t s anchored to the poverty lnes found n the poorest countres (Ravallon et al., 1991). AB then argued that the value of k could also be based on natonal poverty lnes above those found n the poorest countres, by studyng how those lnes vary wth man consumpton n the orgnal data base of poverty lnes used by Ravallon et al. (1991) to set the $1-a-day lne. By vsual nspecton of the Ravallon et al. (1991) data set on natonal poverty lnes at 1985 PPP, Atknson and Bourgugnon set k=0.37. Subsequently, Chen and Ravallon (2001) found that k=1/3 gave a better ft wth the Ravallon et al. (1991) data set at 1993 PPP. However, the AB lne fals the WRA n that t has an elastcty of unty for all countres * wth M > Z / k. Ths s surely mplausble. The dea that dstrbuton-neutral growth has no mpact on the extent of poverty n new mddle-ncome countres such as Chna would surely be very hard to accept (not least, we would conjecture, n Chna). The volaton of the WEA stems from the seemngly mplausble assumpton that the cost of socal ncluson s drectly 8

11 proportonal to the mean. Whle the costs of socal-ncluson may be very low for very poor people, they are unlkely to vansh n the lmt. To address ths concern, whle preservng the neatness of the AB soluton, we propose the followng generalzed AB poverty lne : * Z = max( Z, α + km ) (4) Ths adds a thrd parameter, α 0, whch s the lower bound to socal-ncluson needs. The elastcty s strctly less than unty for α > 0. We can thus state: Proposton 2: The generalzed Atknson-Bourgugnon poverty lnes satsfy the Weak Relatvty Axom as long as the cost of socal ncluson has a postve lower bound. 3. Identfcaton from natonal poverty lnes The orgnal $1-a-day lne was chosen to be representatve of the natonal poverty lnes found n the poorest countres (Ravallon, et al., 1991), and ths prncple has guded subsequent updates (Chen and Ravallon, 2001; Ravallon et al., 2009). We follow Atknson and Bourgugnon (2001) and Chen and Ravallon (2001) n also calbratng the whole schedule of relatve poverty lnes to data on how natonal poverty lnes vary across countres. In other words, we assume that the dfferences n the real value of poverty lnes between countres at dfferent levels of mean consumpton reflect dfferences n ether the value attached to relatve deprvaton (followng the welfarst approach outlned above) or dfferences n the costs of socal ncluson needs (followng the non-welfarst approach). Our emprcal mplementaton makes the further assumpton that our global (weakly) relatve poverty lnes change over tme consstently wth the cross-sectonal varaton seen between countres. Ths secton revews the arguments that can be made for and aganst these dentfyng assumptons. From a welfarst perspectve, t s plausble that absolute consumpton needs domnate subjectve welfare at very low levels of consumpton but that, as countres become rcher, people attach hgher value to relatve poston, and there are both theoretcal and emprcal arguments that can be used to support that vew (Ravallon and Lokshn, 2007; Ravallon, 2008). Smlarly, t s plausble that perceptons of what t means to be socally excluded evolve wth the overall level of economc development. 9

12 The ssue here s whether these dfferences wll be reflected n natonal poverty lnes. Such lnes must nvarably pass a test of ther socal relevance n the specfc country context. 23 A poverty lne that s too frugal by the standards of socety wll no doubt be seen as such by those constructng that lne, and so be rejected. Smlarly, a lne that s too generous wll not be easly accepted ether. As argued by Ravallon (1998, 2008b), the very process of settng a natonal poverty lne entals enumerable choces that appear to be guded n large part by a desre for the lne to be accepted n the specfc context. Ths argument would seem more plausble for the capabltes-based approach than the welfarst approach based on relatve deprvaton. Some set of capabltes s an (mplct or explct) foundaton for most poverty lnes used n practce. Nutrtonal needs for good health and normal actvtes are commonly dentfed, although there s consderable dscreton n terms of how such needs are mapped nto the consumpton space. In a poor country, t s socally acceptable, and common, to allow a poverty lne to attan almost all of the stpulated nutrtonal requrements (2100 calores per day, say) wth one or two starchy food staples, whle n a mddle-ncome or rch country the stpulated det s far more dverse (and palatable). Allowances for non-food consumpton ntroduce even more dscreton, and t seems plausble that deas about socal ncluson needs n specfc socetes would come to play an mportant role, partcularly (but not only) for the non-food allowances. It would hardly seem credble that the natonal poverty lnes that emerge from the choces made n ther calbraton would not come to reflect prevalng vews about what poverty means n the specfc context. The apparent stckness of real natonal poverty lnes over tme sts uncomfortably wth ths vew. Whle relatve poverty lnes used n OECD countres and by Eurostat are automatcally adjusted over tme n lne wth the changes n the mean (or medan), t does not appear to be common to see offcal poverty lnes n growng developng economes beng revsed upwards n real terms. However, t s not necessarly nconsstent wth our approach to fnd that the real level of the poverty lne s resstant to change n some growng economes. For one thng, t may well be the case that a (postve) mnmum aggregate ncome gan to a low-ncome country s needed before upward pressure on the poverty lne emerges; n fact that s mpled by our weakly relatve poverty lnes based on equaton (4). It must also be acknowledged that there can be a strong 23 Ths s no less true of the poverty lnes constructed for World Bank Poverty Assessments, whch emerge out of close collaboraton between the techncal team (often ncludng local statstcal staff and academcs) and the government of the country concerned. 10

13 poltcal resstance to revsng the poverty lne. 24 The fact that actual poverty lnes n practce are stcky s not a compellng reason aganst allowng them to vary for the purposes of measurng global relatve poverty. There are, of course, random dfferences n natonal lnes at gven mean consumpton or ncome that one would not want to attach any normatve sgnfcance to n measurng global poverty. The fact that there s poltcal resstance to revsng real poverty lnes upwards, and that they are set at dfferent tmes n dfferent countres, wll create random dfferences n the poverty lnes found at gven current mean consumpton. There are also dfferences n methodologes used to set poverty lnes n practce (as dscussed n Ravallon et al., 2009). The ssue here s whether there s a systematc pattern n the condtonal mean natonal poverty lne (condtonal on mean consumpton), such that t has a very low gradent amongst poor countres but then rses wth mean consumpton. Such a pattern was frst found n natonal poverty lnes by Ravallon et al. (1991) and we wll confrm below that t s also evdent n new data on natonal lnes. 4. Data for measurng global relatve poverty In measurng relatve poverty n the developng world we shall draw on three new data sources. The frst s a new complaton of natonal poverty lnes documented n Ravallon, Chen and Sangraula (RCS) (2009). Ths explots the new analytc work on poverty at country level that has been done snce 1990, when Ravallon et al. (1991) collected the data on natonal poverty lnes used for settng the $1-a-day lne (and by AB for settng ther encompassng lne). Much of the new work has been done under the World Bank s program of country Poverty Assessments and the program of Poverty Reducton Strategy Papers by natonal governments, often wth assstance from the Bank or other governments or nternatonal agences. There were very few of these studes avalable n 1990, but they have now been done for some 100 developng countres. Almost all nclude estmates of natonal poverty lnes. Second, we use the PPP of ndvdual consumpton by households from the latest (2005) round of the Internatonal Comparson Program (ICP) (World Bank, 2008). Ths s the most 24 See, for example, the dscusson n Blank (2008) on why the offcal poverty lne n the US has not been updated, despte consderable dssatsfacton wth the old lne, proposed n 1963 and only updated for nflaton snce. Smlarly, the poverty lne n Chna has not been revsed upwards n real terms for over 20 years, despte a four-fold ncrease n mean ncome. Ths has led many observers to queston the relevance of ther poverty lnes to current condtons; see, for example, Osberg and Xu (2008). The government of Chna s n the process of revsng upwards the country s offcal poverty lnes. The Plannng Commsson of the Government of Inda s also revstng the country s offcal poverty lne. 11

14 ambtous round to date of the ICP and entaled a substantal mprovement n data qualty for estmatng PPP s. For the purpose of measurng global poverty, an mportant feature of the 2005 ICP s that t dd a much better job of collectng the prces needed to measure lvng costs. Relable prce surveys are qute dffcult to do, partcularly n poor countres where non-traded goods are a large share of spendng. The new surveys done for the 2005 ICP used far more elaborate product descrptons to help dentfy comparable goods, so that we do not make the mstake of judgng people to be better off because they consume lower qualty (and hence cheaper) goods. However, there are also a number of concerns about the 2005 ICP round n ths context. 25 These nclude a lkely urban bas n the prce surveys for some countres and the fact that the ICP s desgned for comparng natonal accounts aggregates rather than poverty measurement. 26 Thrd, we use our own complaton of 675 household surveys for 115 countres; the latest survey rounds cover a total of 1.23 mllon randomly sampled households. Chen and Ravallon (2008a) provde a lstng of the countres and years; further detals can be found n the PovcalNet ste. The surveys were mostly done by governmental statstcs offces. We have estmated all poverty measures from the prmary (unt record or specally commssoned tabulatons) survey data. Households are ranked by ether consumpton or ncome per person; we have preferred consumpton, whch s avalable for about 60% of the surveys. The dstrbutons are weghted by household sze and sample expanson factors. Thus our poverty counts gve the number of people lvng n households wth per capta consumpton or ncome below the poverty lne. Interpolaton methods (descrbed n Chen and Ravallon, 2004, 2008) are used to lne up the survey-based estmates wth the reference years at three-yearly ntervals over Fgure 1 plots the natonal poverty lnes for developng countres aganst prvate consumpton per capta from the Natonal Accounts, both converted to nternatonal $ s usng the 2005 household consumpton PPP from the ICP. We see that the natonal poverty lne tends to rse wth mean consumpton, whch we call the economc gradent. The least squares estmate of the elastcty of Z to M s (wth a t-rato of 13.68, based on a robust standard error). 27 Ths s sgnfcantly less than unty (t=7.21). So these data are not consstent wth strongly 25 For an overvew of the ssues n constructng PPPs see Deaton and Heston (2008). On the mpacts of some of the methodologcal choces on global poverty measures see Ackland et al. (2008). 26 Chna s an mportant example of ths urban bas; for further dscusson and a descrpton of how we have attempted to correct for ths bas see Chen and Ravallon (2008b). 27 The estmate s also robust to outlers; a medan quantle regresson gave (t=9.57). 12

15 relatve poverty n developng countres, but they are consstent wth the weakly-relatve poverty a natonal poverty lne that rses wth mean consumpton, but wth an elastcty less than unty. However, Fgure 1 also suggests that the economc gradent only emerges once mean consumpton s above a crtcal level. Fgure 1 gves a nonparametrc regresson of the natonal poverty lnes aganst log mean consumpton. 28 So the same pattern found by Ravallon et al. (1991) usng ther complatons of natonal poverty lnes for the 1980s s evdent n Fgure 1, wth the poverty lne rsng wth mean consumpton, but wth a low elastcty ntally. The data n Fgure 1 wll be used n the followng secton to calbrate our proposed schedule of weakly relatve poverty lnes. 5. Emprcal mplementaton and mplcatons namely Recall that there are three parameters to our schedule of relatve poverty lnes n (4), * Z, α and k. We set these to $1.25 a day, $0.60 a day and 1/3 respectvely, gvng the followng schedule of relatve poverty lnes (n $ s per day at the 2005 PPP for household consumpton): Z max[$ 1.25, $ M / 3] = $ max[$0.65, M / 3] (5) * The value of Ẑ =$1.25 a day s the nternatonal poverty lne proposed by RCS, whch s the average poverty lne amongst the poorest 15 countres (although the lne s qute robust to small changes n the number of countres, as shown by RCS). A vsual nspecton of the scatter plot n Fgure 1 suggests that a postve slope starts to emerge at a log of monthly consumpton of around 4, correspondng to about $2 a day, and that the gradent s about one-n-three. The parameter choces n (5) were confrmed econometrcally, usng a sutably constraned verson of Hansen s (2002) method for estmatng a pece-wse lnear ( threshold ) model. (The varaton on Hansen s model s that, n our case, the slope of the lower lnear segment s constraned to be zero and there s no potental dscontnuty at the threshold.) Ths gave k ˆ = (t=12.70). 29 * Ẑ =$1.23 (t=6.36) and We use STATA s Locally Weghted Scatter Plot Smoothng method wth the default bandwdth (0.8). By ths method one essentally estmates (1) for each possble value of consumpton n the data and pcks the value that mnmzes the resdual sum of squares The varaton on Hansen s model s that, n our case, the slope of the lower lnear segment s constraned to be zero and there s no potental dscontnuty at the threshold. We are grateful to Mchael Lokshn for programmng Hansen s method. 13

16 We can also provde a number of other statstcal tests that confrm ths choce. There s a hgh correlaton between the poverty lnes mpled by (5) for our sample and the nonparametrc regresson functon n Fgure 1 (r=0.994) as well as wth the data on natonal poverty lnes (r=0.836). Equaton (5) also outperforms a wde range of smooth parametrc functonal forms. Indeed, remarkably, the standard error n predctng the natonal lnes s actually lower usng equaton (5) than the nonparametrc regresson n Fgure 1; the standard devaton of the error s $1.19 for our poverty lnes versus $1.20 for the ftted values usng the smoothness parameter for the regresson n Fgure 1. (Of course, a suffcently less smooth nonparametrc regresson would do better than our pece-wse lnear model.) There s no correlaton between the errors n predctng the natonal poverty lnes usng (5) and the ftted values of the nonparametrc regresson n Fgure 1 (the correlaton coeffcent s 0.02). As a further test, nether the ftted values from the nonparametrc regresson n Fgure 1 nor a cubc polynomal n M were sgnfcant when added to a regresson of the natonal poverty lnes on Z gven by (5). 30 The bold unbroken lne n Fgure 2 gves our weakly-relatve schedule n (5). In our data set of natonal poverty lnes, Z vares from $1.25 a day to $8 a day. 31 The fact that the rsng porton of our poverty lnes n (5) s not homogeneous mmedately mples that the elastcty of the poverty lne to mean consumpton s below unty throughout (the elastcty goes to unty n the lmt, as consumpton goes to nfnty). The elastcty s zero at M < $1.95 and then rses from 0.5 to close to 1.0 over the sample range. The consumpton level at whch the knk (above whch the poverty lne rses wth the mean) occurred n the Chen Ravallon (2001) verson of the AB schedule of relatve poverty lnes s apprecably hgher than for our new schedule. For the Chen and Ravallon (2001) relatve lnes the knk was at a consumpton level of $3.24 per day at 1993 PPP, whle the new schedule of relatve poverty lnes n equaton (5) has a knk at $1.95 a day at 2005 PPP. If we had nstead chosen max($ 1.25, M / 3) as the relatve poverty lne at 2005 PPP, the knk would be at a consumpton level of $3.75 a day nstead of $1.95. Ths reflects 30 The jont F test of the null that the three parameters n the cubc functon of M are all zero n the regresson of natonal poverty lnes on Z gven by equaton (5) gave F(3,69)=0.14 (prob.=0.93) whle the t-test on the coeffcent on the ftted values when added to the same regresson was t= There are three specal cases: Chna, Inda and Indonesa. For these countres, we have separate rural and urban dstrbuton data from 1981 to In addton, for Chna and Inda we have separate rural and urban CPI over tme. We treat the relatve poverty lne based on (5) as the natonal lne for Inda and Indonesa, and then back out the rural and urban poverty lnes usng the urban-rural dfferentals n natonal lnes. For Chna, the 2005 PPP s an urban PPP, so we set the urban relatve poverty lne as the natonal lne, and adjust the rural relatve poverty lne down accordng to the rato of urban to rural poverty lnes (followng Chen and Ravallon 2008b). 14

17 the fact that our weakly relatve measures allow α > 0, thus shftng up the schedule (Fgure 2). There are 18 countres wth M n the nterval ($1.95, $3.75),.e., there are an extra 18 countres n the segment where the absolute lne s no longer bndng. So our new data on natonal poverty lnes suggest that relatve poverty s a more promnent concern than past work ndcated. Ths echoes our fndng that the overall elastcty of the poverty lne to the mean n our sample s qute hgh less than unty but smlar to some past estmates for developed countres. What mght we expect on a pror grounds about the trends over tme n weakly relatve poverty, as compared to absolute poverty? That wll depend n part on how the dstrbuton of relatve ncomes evolves. As a stylzed fact, there s no correlaton across countres between rates of growth and rates of change n a standard measure of relatve nequalty. 32 In other words, amongst developng countres, economc growth tends to be dstrbuton-neutral on average. 33 Ths motvates a consderaton of dstrbuton-neutral growth as a benchmark case. To see how the trend rates of reducton n the poverty rate wll dffer usng our relatve poverty measure under dstrbuton-neutral growth, let F ( Z ) denote the proporton of the populaton of country * lvng below our weakly relatve poverty lne, whle F ( Z ) s the correspondng poverty rate usng the absolute lne. Under a dstrbuton-neutral growth process t s readly verfed that the proportonate rates of poverty reducton are: 34 d ln F ( Z ) dt d ln F ( Z dt * ) d ln Z ln F ( Z ) d ln M = 1.. (for * Z > Z ) (6.1) d ln M ln M dt * ln F ( Z ) d ln M =. (6.2) ln M dt * Here the partal elastctes, ln F ( Z ) / ln M < 0 and ln F ( Z ) / ln M < 0, hold both Z and the Lorenz curve constant. Snce our relatve poverty measures satsfy the WRA, the relatve poverty rate wll fall as long as the growth rate ( d ln M / dt ) s postve. The absolute poverty rate wll also fall wth postve growth. Whether or not the relatve poverty measure falls more Ferrera and Ravallon (2009) provde an overvew of the evdence on ths stylzed fact. Growth can be dstrbuton neutral wthn all countres, but not dstrbuton neutral n the world as a whole, dependng on how the rates of growth vary wth ntal mean ncomes. Ravallon (2009) shows that the overall growth process n the developng world has not been dstrbuton-neutral. 34 We explot the fact that L ( F ( Z )) = Z / M where L s the Lorenz curve. Thus F ( Z ) s homogeneous of degree zero n Z and M, holdng constant the Lorenz curve (and hence the functon L (.) ). 15

18 slowly than the absolute measure depends on the relatve sze of the partal elastctes. Ths s an emprcal ssue. Ravallon (2009) shows that, for the developng world as a whole, the (absolute) elastcty falls monotoncally as the poverty lne ncreases over the range $0.75 to $13 a day, certanly encompassng the range of our relatve poverty lnes. Then relatve poverty wll fall at a slower rate than absolute poverty. Furthermore, as absolute poverty falls wth economc growth the elastcty of the poverty lne wth respect to the mean ( d ln Z / d ln M ) ncreases whle the partal elastcty ( ln F ( Z ) / ln M < 0 ) tends to fall. Thus the rate of reducton n relatve poverty wll tend to fall as the level of absolute poverty falls. Wth populaton growth, after some pont, the numbers of relatvely poor wll be rsng, whle the numbers of absolutely poor are fallng. As we wll see, ths predcton s confrmed by our estmates. 6. Poverty measures for the developng world We present our results for at three yearly ntervals. Table 1 gve our estmates of the absolute poverty measures for the $1.25 a day lne at 2005 PPP for the developng world as a whole and the largest regons n terms of the number of poor. 35 We fnd that 25 percent of the populaton of the developng world, 1.4 bllon people, lved below $1.25 a day n Twenty-fve years earler (n 1981) the percentage was 52%. Ths rate of progress was suffcent to brng the count of the number of poor down from 1.9 bllon to 1.4 bllon. However, progress was hghly uneven across regons, wth dramatc declnes n the poverty count for East Asa, but wth much less progress n other regons, and rsng numbers of absolutely poor n Sub-Saharan Afrca (though wth some sgn of progress n the late 1990s). 36 The correspondng relatve measures are found n Table 2. The top panel gves the mean poverty lnes by regon. (The mean lnes do not fgure n the analyss but are stll of nterest.) In all regons and all years, the mean s above $38 per month ($1.25 a day), mplyng that the relatve poverty lne s generally domnant. (The $1.25 lne s bndng for about 20% of countres and years.) In 2005, the nter-regonal dfferences n relatve poverty lnes range from $47 per month n Sub-Saharan Afrca to $151 per month n Latn Amerca. The relatve poverty lnes rse over tme wth economc growth; n East Asa the average lne goes from about $40 per month n 1981 to over $60 per month n We exclude the Mddle East, North Afrca, Eastern Europe and Central Asa. These account for only 2.1% of the absolute poverty count (and 10.4% of the relatve poverty count). 36 For further dscusson see Chen and Ravallon (2008a). 16

19 The next two panels of Table 2 gve the percentages below the lne and numbers of poor. Through most of the 1990s, about half of the populaton of the developng world was relatvely poor. The proporton fell over tme, from 63% n 1981 to 53% n 1990 and 47% n But the declne was not contnual; the aggregate ncdence of relatve poverty rose slghtly n both the late 1980s and late 1990s. The trend rate of declne over the perod as a whole s percentage ponts per year (wth a standard error of 0.10). Projectng ths trend rate of declne over forward to 2015, the proporton lvng n relatve poverty would be 40.5% (standard error=2.4%). The trend declne n the ncdence of relatve poverty has not been suffcent to reduce the number of poor by ths measure, whch rose from 2.3 bllon to 2.6 bllon over (Table 2). The turnng pont appears to be around Fgure 3 shows the smultaneous rse n relatve poverty and fall n absolute poverty. As one would expect, the proporton of the relatvely poor that are also absolutely poor has fallen over tme, gven economc growth. In 1981, 82% of the relatvely poor were absolutely poor; by 2005 the proporton had fallen to 53%. South Asa saw the largest absolute ncrease n the number of relatvely poor. East Asa experenced a fallng count of both the absolutely poor and the relatvely poor (though wth a more rapd pace of progress aganst absolute poverty). Comparng Tables 1 and 2, we see changes n the regonal profle of poverty, although t s notable that the two regons wth the hghest ncdence of absolute poverty also have the hghest relatve poverty rate. In 2005, Sub- Saharan Afrca (SSA) had the hghest ncdence of absolute poverty, wth South Asa n second place (Table 1), but South Asa emerges as the regon wth the hghest ncdence of relatve poverty (Table 2), wth SSA second. Latn Amerca and the Carbbean (LAC) had the thrd hghest relatve poverty ncdence, but came fourth n absolute poverty. As expected, the share of global poverty n LAC rses from 3.3% to 9.6%. The largest declne n share s for SSA, whch falls from 28.4% to 16.4%; South Asa s share falls from 43.3% to 36.1%. Also comparng Tables 1 and 2, we fnd that the aggregate headcount ndex of relatve poverty for 2005 s 1.88 tmes the aggregate ndex of absolute poverty; n 2002, the rato was It s of nterest to compare these numbers to the correspondng ratos from Chen and Ravallon (2004), usng ther parameterzaton of the Atknson-Bourgugnon relatve poverty lnes. For the latest year n the Chen-Ravallon seres (2001) the aggregate measure of relatve 17

20 poverty was 1.36 tmes the aggregate measure of absolute poverty. Ths upward revson n the extent of poverty reflects the aforementoned fact that our weakly relatve measures mply that the economc gradent n poverty lnes emerges at a lower level than was found usng the AB poverty lnes calbrated on the Ravallon et al. (1991) data set. 7. Conclusons Whle we can accept that people care about ther relatve poston n socety (at least above some level of lvng) t s very hard to accept that they only care about relatve ncome. And whle one can agree that certan goods have a socal role t s hard to accept that the expendture requred to attan those goods s neglgbly small for very poor people; recallng Adam Smth s example of the role of a lnen shrt n eghteenth century Europe, a socallyadequate shrt would not presumably have cost any less to the poorest person than the rchest. Whle poor people may be hghly constraned n ther spendng on thngs that facltate ther ncluson, and so be more socally excluded, that does not mean that ther socal ncluson needs are neglgble. Thus, the prevalng justfcatons for strongly relatve poverty measures are hard to accept on theoretcal grounds. Our weakly relatve poverty lnes relax these assumptons. From a welfarst perspectve, our measures place a natural upper bound on the weght attached to relatve deprvaton, namely that t cannot matter so much that measured poverty does not fall when all ncomes ncrease by the same proporton. From a non-welfarst perspectve, we mpose a postve lower bound on the cost of socal ncluson. Our poverty lnes are calbrated to a new complaton of natonal poverty lnes, drawng on a vast amount of new poverty studes done snce the 1980s. A smple, dataconsstent, schedule of relatve poverty lnes s shown to provde an excellent ft to these data on natonal lnes, but wth an elastcty that rses from zero to unty, but never reaches unty. On mplementng our weakly relatve poverty lnes usng almost 700 surveys for 115 countres we fnd that there s more relatve poverty n the developng world than has been thought and that the pace of progress aganst relatve poverty over s less encouragng than that aganst absolute poverty. We fnd that 47% of the populaton of the developng world lved n relatve poverty n 2005, down from 53% n 1990 and 63% n Ths was not a suffcent rate of declne n the ncdence of poverty to prevent a rse n the number of poor, n contrast to our absolute poverty measures that show fallng poverty counts n the aggregate. Wth 18

21 economc growth, the relatve poverty lne tends to rse, and proportonately more as average ncome rses. Both the drect mpact on the poverty lne and the effect on the responsveness of the poverty rate to economc growth tend to brng down the trend rate of declne n relatve poverty. Slower progress aganst relatve poverty s thus the other sde of the con to success aganst absolute poverty. 19

22 References Ackland, Robert, Steve Dowrck and Benot Freyens, 2008, Measurng Global Poverty: Why PPP Methods Matter, Workng Paper, Australan Natonal Unversty. Alpzar, Francsco, Fredrk Carlsson and Olof Johansson-Stenman, 2005, How Much Do We Care About Absolute versus Relatve Income and Consumpton? Journal of Economc Behavor and Organzaton 56: Atknson, Anthony B., 1987, On the Measurement of Poverty, Econometrca 55: , 1998, Poverty n Europe, Oxford: Blackwell Press. Atknson, Anthony B., and Francos Bourgugnon, 2001, Poverty and Incluson from a World Perspectve. In Joseph Stgltz and Perre-Alan Muet (eds) Governance, Equty and Global Markets, Oxford: Oxford Unversty Press. Banerjee, Abhjt and Esther Duflo, 2007, The Economc Lves of the Poor, Journal of Economc Perspectves 21(2): Blackorby, Charles and Donaldson, D., 1987, Welfare Ratos and Dstrbutonally Senstve Cost-Beneft Analyss, Journal of Publc Economcs 34, Blanchflower, D. and A. Oswald, 2004, Well-Beng over Tme n Brtan and the U.S.A. Journal of Publc Economcs 88: Blank, Rebecca M., 2008, How to Improve Poverty Measurement n the Unted States, Journal of Polcy Analyss and Management 27(2): Chen, Shaohua and Martn Ravallon, 2001, How Dd the World s Poor Fare n the 1990s?, Revew of Income and Wealth 47(3): and, 2004, How Have the World s Poorest Fared Snce the Early 1980s? World Bank Research Observer 19(2): and, 2008a, The Developng World s Poorer than we Thought, but no less Successful n the Fght aganst Poverty, Polcy Research Workng Paper 4703, World Bank. and, 2008b, Chna s Poorer than we Thought, but no Less Successful n the Fght Aganst Poverty, n Sudhr Anand, Paul Segal, and Joseph Stgltz (ed), Debates on the Measurement of Poverty, Oxford Unversty Press. Ctro, Constance and Robert Mchael, 1995, Measurng Poverty: A New Approach. Washngton, DC: Natonal Academy Press. 20