1 Dollar a Day Revsted Martn Ravallon, Shaohua Chen, and Prem Sangraula The artcle presents the frst major update of the nternatonal $1 a day poverty lne, proposed n World Development Report 1990: Poverty for measurng absolute poverty by the standards of the world s poorest countres. In a new and more representatve data set of natonal poverty lnes, a marked economc gradent emerges only when consumpton per person s above about $2.00 a day at 2005 purchasng power party. Below ths, the average poverty lne s $1.25, whch s proposed as the new nternatonal poverty lne. The artcle tests the robustness of ths lne to alternatve estmaton methods and explans how t dffers from the old $1 a day lne. JEL codes: I32, E31, O10 The wdely used $1 a day poverty lne was set for World Development Report 1990: Poverty (World Bank 1990) based on research for that report documented n Ravallon, Datt, and van de Walle (1991). The am was to set a global poverty lne that defned poverty n the developng world as a whole by the standards of what poverty means n the world s poorest countres, recognzng that rcher countres naturally have hgher standards. Ths (ntentonally) frugal bass for measurng global poverty gves the $1 a day lne a salence n focusng nternatonal attenton on the world s poorest a salence that a hgher lne would not have. 1 A consensus emerged n the nternatonal development communty on ths standard for measurng extreme poverty n the world, and t became the bass of the frst Mllennum Development Goal, to halve the 1990s $1 a day poverty rate by Ths artcle provdes the frst major revson of the orgnal $1 a day lne. Understandng why ths revson s necessary requres understandng how the orgnal nternatonal poverty lne was set n 1990 and what new data have become avalable snce then. Martn Ravallon (correspondng author) s a drector of the Development Research Group at the World Bank; hs emal address s Shaohua Chen s a senor statstcan n the Development Economcs Research Group at the World Bank; her emal address s Prem Sangraula s an economst n the Development Research Group at the World Bank; hs emal address s 1. For example, Prtchett (2006) proposes a poverty lne of around $10 a day. Calculatons usng the World Bank s PovcalNet ( ndcate that 95 percent of people n developng countres lve below ths lne. THE WORLD BANK ECONOMIC REVIEW, VOL. 23, NO. 2, pp do: /wber/lhp007 Advance Access Publcaton June 26, 2009 # The Author Publshed by Oxford Unversty Press on behalf of the Internatonal Bank for Reconstructon and Development / THE WORLD BANK. All rghts reserved. For permssons, please e-mal: 163
2 164 THE WORLD BANK ECONOMIC REVIEW Ravallon, Datt, and van de Walle (1991) studed how poverty lnes vared wth mean consumpton when both were converted to a common currency at purchasng power party (PPP, meanng a currency converson rate that s ntended to ensure a common purchasng power over commodtes). They found that natonal poverty lnes have a postve economc gradent above some crtcal level. The elastcty rses wth average consumpton, approachng unty n rch countres. It can thus be argued that absolute poverty (measured usng a poverty lne wth a constant real value) s the more relevant concept n poor countres, whle relatve poverty (n whch the poverty lne rses wth the mean) s more salent n mddle- and hgh-ncome countres. The poverty lnes that preval n each country (or that would be expected gven the country s mean consumpton) could be used n assessng global poverty. But then the resultng aggregate poverty measures would not be treatng people at the same level of real consumpton the same way. And by treatng absolutely poor people smlarly to relatvely poor people such a measure of global poverty would rsk dvertng the focus from what s surely the hghest prorty: rasng the lvng standards of the poorest people n the world. But what absolute lne should be used? Ravallon, Datt, and van de Walle (1991) proposed measurng global poverty by the standards of the poorest countres, based on a survey of natonal poverty lnes. 2 Drawng on 33 natonal poverty lnes for the 1970s and 1980s (for both developed and developng economes), Ravallon, Datt, and van de Walle proposed a lne of $23 a month ($0.76 a day) at 1985 consumpton PPP. That value was the predcted poverty lne for the poorest country n the sample, based on a regresson model. A hgher lne of $31 a month ($1.02 a day) that was more representatve of the poverty lnes n low-ncome countres. Subsequently, the hgher lne became more accepted n the World Bank and nternatonally, and t became known as the $1 a day lne. The PPPs used by Ravallon, Datt, and van de Walle were from the Penn World Table (Summers and Heston 1991) and were based on the prce surveys for 1985 done by the Internatonal Comparson Program (ICP). New prce surveys were done n 1993, and the World Bank started estmatng ts own PPPs, usng methods that were consdered more approprate for measurng poverty. 3 The changes n ICP benchmark years create comparablty problems, due to dfferng estmaton methods for the PPPs and dfferences n the ICP prce surveys. Recognzng these problems, Chen and Ravallon (2001) revsed past estmates of poverty measures to ensure consstency wth new data avalable when the ICP benchmark round changed from 1985 to Chen and Ravallon (2001) appled the new PPPs to the orgnal Ravallon, Datt, and 2. Pror to Ravallon, Datt, and van de Walle (1991), the World Bank had used explctly arbtrary lnes; see Ahluwala (1974). 3. Ackland, Dowrck, and Freyens (2006) and Deaton and Heston (2008) dscuss alternatve approaches to measurng PPPs and ther approprateness for dfferent applcatons.
3 Ravallon, Chen, and Sangraula 165 van de Walle (1991) data set of 33 natonal lnes n local currency unts. Employng the same regresson method as n Ravallon, Datt, and van de Walle, Chen and Ravallon found the predcted poverty lne for the poorest country to be $31.96 a month ($1.05 a day). However, a slghtly hgher lne was consdered more representatve; the new $1 a day lne was set at $32.74 a month, or $1.08 a day, at 1993 PPPs. In 2004, about one n fve people n the developng world (1 bllon people) were deemed to be poor by ths standard (Chen and Ravallon 2007). These estmates all reled on the orgnal Ravallon, Datt, and van de Walle (1991) complaton of poverty lnes. However, much new analytc work on poverty at the country level has been done snce 1990, notably under the World Bank s program of country poverty assessments and the Poverty Reducton Strategy Papers prepared by natonal governments, often wth assstance from the World Bank, other governments, or nternatonal agences. Few of these studes were avalable n 1990, but they have snce been completed for about 100 developng economes. They provde a rch source of data on poverty at the country level, and almost all nclude estmates of natonal poverty lnes. The poverty studes done snce 1990 also allow us to correct for the samplng bases n the orgnal Ravallon, Datt, and van de Walle (1991) complaton of natonal poverty lnes bases that could not be avoded n the orgnal complaton gven the data avalable at the tme. Another mportant new source of data s the 2005 round of the ICP (World Bank 2008). As the most ambtous round of the ICP (whch began n 1968), t s expected to ental substantal mprovements n data qualty for estmatng PPPs. These new data prompt a reassessment of the nternatonal poverty lne. The analyss n ths artcle leads to a proposed new nternatonal poverty lne of $1.25 a day at 2005 PPP for household consumpton. Secton I presents the new complaton of natonal poverty lnes, whch are shown to rse wth mean consumpton but wth a low elastcty at low consumpton. Based on these emprcal results, secton II dscusses the proposed new nternatonal poverty lne. Secton III compares the proposed new lne to the old $1 a day lne. Secton IV concludes. I. NATIONAL P OVERTY L INES ACROSS D EVELOPING E CONOMIES The two most obvous ways of updatng the old $1 a day poverty lne have serous drawbacks. Frst, one mght smply apply the U.S. consumer prce ndex (CPI). Ths assumes that the old $1 a day lne, based on an old sample of natonal poverty lnes and an old set of PPPs, s stll vald; that assumpton gnores possble bases n past data sets bases the new data can go at least some way toward addressng. Second, one mght keep the rato of the poverty lne to (say) the developng world s mean ncome the same. Wth growth, ths would mply a hgher real poverty lne over tme. Indeed, the poverty lne would have an elastcty of unty wth respect to mean ncome, mplyng that
4 166 THE WORLD BANK ECONOMIC REVIEW dstrbuton-neutral growth (all ncomes grow at the same rate) would leave poverty measures unchanged, even though the poor ganed n absolute terms. An elastcty of unty would seem hard to defend, especally for poor countres. 4 The approach taken here returns to the logc of the orgnal $1 a day lne, armed wth new data. The set of natonal poverty lnes collected by Ravallon, Datt, and van de Walle (1991) covered 33 countres and drew on specalzed, country-specfc, mostly academc studes of poverty spannng Clearly, ths data set s now rather old. Snce then there has been consderable expanson n research and analyss on poverty n developng economes, notably through the World Bank s country-level poverty assessments, whch have now been completed for many developng economes. These are core reports wthn the World Bank s program of analytc work at the country level; each report descrbes the extent of poverty and ts causes n a gven country. The poverty assessment s conducted n consultaton wth the government, and most poverty assessments clam government ownershp. Most low-ncome countres have also prepared Poverty Reducton Strategy Papers, whch are prepared by the government, often wth some fnancal support from ad donors. A large share of the work on poverty assessments and Poverty Reducton Strategy Papers typcally goes nto poverty measurement and both typcally lay out what s known about poverty n each country, ncludng a detaled poverty profle as well as aggregate poverty statstcs and how they have changed over tme. Both reports are mportant sources of nformaton on the accepted natonal poverty lnes. For the purpose of ths artcle, a new data set of 88 natonal poverty lnes was compled from the most recent poverty assessments and Poverty Reducton Strategy Papers over In the source documents, each poverty lne s gven n the prces for a specfc survey year (for whch the subsequent poverty measures are calculated). In most cases, the poverty lne was also calculated from the same survey (though there are some exceptons, for whch pre-exstng natonal poverty lnes were updated usng the CPI). Sometmes the natonal poverty lnes were old lnes updated over tme for nflaton, and sometmes the poverty lne was calculated afresh at each survey, though typcally anchored to a common food bundle. Such recalculated poverty lnes would not generally have the same real value over tme when assessed accordng to a reasonable prce ndex, snce the Engel curve may shft for other reasons and thus change the real value of the nonfood component of the poverty lne. When a choce had to be made, the most recent natonal poverty lne avalable was selected. The new data set on natonal poverty lnes dffers from the old (Ravallon, Datt, and van de Walle 1991) data set n four man respects. Frst, whle the old data were drawn from sources for the 1980s (wth a mean year of 1984), 4. For further dscusson, see Ravallon (2008b) and Ravallon and Chen (2009).
5 Ravallon, Chen, and Sangraula 167 the new data are all post-1990 (mean of 1999), such that n no case do the proxmate sources overlap. Second, the new data set covers 88 developng economes (74 wth complete data for the subsequent analyss), whle the old data set ncluded only 22 developng economes ( plus 11 developed countres). Thrd, the old data set used rural poverty lnes when there was a choce, whereas the new one estmates natonal average lnes. Fourth, the old data set was unrepresentatve of Sub-Saharan Afrca, wth only fve countres from that regon (Burund, Kenya, South Afrca, Tanzana, and Zamba), whereas the new data set has a good spread across regons, ncludng 25 countres n Sub-Saharan Afrca. The proporton of Afrcan countres n the old sample was about half what t should have been to be consdered representatve of poor countres. The sample bas n the Ravallon, Datt, and van de Walle data set was unavodable at the tme (1990), but t can now be corrected. The fact that the poverty assessments are World Bank reports rases two concerns. Frst, t mght be conjectured that these are external poverty lnes, rather than poverty lnes accepted by the country. However, the process of producng a poverty assessment entals (often extensve) consultaton wth the government, ncludng dscusson about the most approprate poverty lne. Thus, ths new set of poverty lnes has a stronger clam to beng natonal poverty lnes than those used by Ravallon, Datt, and van de Walle (1991), whch were based largely on academc studes. Second, t mght be thought that the poverty lnes used n the World Bank poverty assessments reports and n governments Poverty Reducton Strategy Papers are based toward the World Bank s old nternatonal poverty lne. Ths does not appear to be a serous concern. The poverty assessments (and the Poverty Reducton Strategy Papers) typcally ether use a pre-exstng natonal poverty lne or derve a new lne, and n both cases the lne has no obvous orgns n the World Bank s $1 a day poverty lne. The am s to use a poverty lne approprate to the country. Some 80 percent of these reports use a verson of the cost of basc needs method n whch the food component of the poverty lne s the expendture needed to purchase a food bundle specfc to each country (or regon) that yelds a stpulated food energy requrement. 5 To ths amount an allowance s added for nonfood spendng, whch s typcally anchored to the nonfood spendng of people whose food spendng (or sometmes total spendng) s near the food poverty lne. There s consderable scope for dscreton n settng such a poverty lne. Although the stpulated food-energy requrements are smlar, the food bundles that can yeld a gven food energy ntake can vary enormously, and some wll be preferable to others n any gven context. The nonfood spendng that s deemed adequate wll also vary. The judgments made n settng the varous parameters of a poverty lne are lkely to reflect prevalng notons of what poverty means n each country settng. 5. Ths method, and alternatves, are dscussed n detal n Ravallon (1994, 1998, 2008a).
6 168 THE WORLD BANK ECONOMIC REVIEW These poverty lnes are converted to a common currency usng the PPP for ndvdual consumpton expendture by households from the 2005 ICP, as documented n World Bank (2008). 6 The 2005 ICP s clearly the most complete assessment to date of how the cost of lvng vares across countres. The ICP collected prmary data on a regon-specfc lst of prces for 600 1,000 (dependng on the regon) goods and servces. The prces were obtaned from a large sample of outlets n each country. All regons partcpated, but the partcpaton rate was markedly lower for Latn Amerca. The 2005 ICP ntroduced several mprovements over prevous ICP rounds. The number of countres partcpatng rose from 117 n 1993 to 146 countres. The new countres nclude Chna, whch had not prevously partcpated n the ICP. The surveys have been mplemented on a more scentfc bass. New methods were used for measurng government compensaton and housng. Adjustments were made for the lower average productvty of publc sector workers n developng economes (lowerng the mputed value of the servces derved from publc admnstraton, educaton, and health). Rng comparsons (lnkng regonal PPP estmates through global prces) were done for more countres (18 n all). The 2005 data were also subject to more rgorous supervson and valdaton methods than was the 1993 round, ncludng strcter standards n defnng nternatonally comparable qualty standards for the goods dentfed n the ICP prce surveys. Otherwse, the PPPs calculated from the ICP data (and n World Bank 2008) follow standard methods; as n the past, the World Bank uses a multlateral extenson of the blateral Fsher prce ndex. 7 Whle these are clearly mprovements, the new PPPs stll have some lmtatons. The ICP amed to survey prces that were natonally representatve. Ths was not the case n Chna, where the ICP survey was confned to 11 ctes. Although the survey ncluded some surroundng rural areas, t cannot be consdered representatve of rural Chna, where the cost of lvng s lower than n urban areas. The correcton method descrbed n Chen and Ravallon (2008a) was used to derve a PPP for rural areas based on a pror estmate of the 6. The ICP started n Before 2000, the Penn World Table (Summers and Heston 1991) was the man source of the PPP rates for consumpton derved from the ICP, as used n the Bank s global poverty measures. In 2000, there was a swtch to the 1993 PPPs estmated by the World Bank s Development Data Group; the most recent results are reported n World Bank (2008). There are methodologcal dfferences n these two sets of PPPs. The Penn World Table used the Geary-Khams (GK) method, whle the Bank used the Elteto-Koves-Szulc (EKS) method, whch s the multlateral extenson of the blateral Fsher ndex. On the dfferences between the GK and EKS methods and mplcatons for global poverty measures, see Ackland, Dowrck, and Freyens (2006). There were also mprovements n country coverage and data qualty n the 1993 PPPs as compared wth the Penn World Table. 7. As argued n Ravallon, Datt, and de Walle (1991), the weghts attached to dfferent commodtes n the conventonal PPP rate may not be approprate for the poor. Results reported n Deaton and Duprez (2008) do not suggest that the reweghtng needed to derve a PPP for the poor wll have much mpact on the aggregate consumpton PPP. The workng paper verson of ths artcle reports tests of senstvty to usng the Deaton-Duprez PPP (Ravallon, Chen, and Sangraula 2008).
7 Ravallon, Chen, and Sangraula 169 urban rural dfferental n absolute poverty lnes. However, there are other concerns that were not addressed. The weghts attached to dfferent commodtes n the conventonal PPP rate are not approprate for the poor (Ravallon, Datt, and van de Walle 1991), though t s not clear that usng those weghts entals a sgnfcant bas. 8 Yet another lmtaton s that the PPP s a natonal average; just as the cost of lvng tends to be lower n poorer countres, the PPP can be expected to be lower n poorer regons wthn a country, especally n rural areas. 9 For each country, the natonal poverty lne was converted to 2005 nternatonal dollars usng the ndvdual consumpton PPP from World Bank (2008). The 2005 PPP was not avalable for 11 of the 88 countres (manly due to the poor ICP coverage n Latn Amerca) and was deemed unrelable for one country (Zmbabwe). 10 Allowng for mssng PPPs and other data problems gave 75 lnes. 11 Appendx table A-1 gves the precse poverty lnes for each country; detals on the sources are n the workng paper verson of ths artcle (Ravallon, Chen, and Sangraula 2008). In no case do the sources overlap wth Ravallon, Datt, and van de Walle (1991). The densty functon s gven n fgure 1. The poverty lnes range from $19.05 to $ a month, wth a mean of $87.59 and medan of $60.81 (fgure 1). (The standard devaton s $66.22.) The mode s slghtly under $50 a month. Ths artcle follows Ravallon, Datt, and van de Walle (1991) n usng prvate consumpton expendture per capta from the natonal accounts as the measure of economc welfare (or, more precsely, household fnal consumpton expendture). The sample mean for prvate consumpton expendture s $ a month ($6.89 a day) at 2005 PPP; 15 of the sample countres have consumpton per capta of less than $60 per month, or about $2.00 a day. The poorest country by ths measure s Malaw, at $1.03 a day. The mode of the natonal poverty lnes s qute close to the mode of prvate consumpton 8. Deaton and Duprez (2009) estmated PPPs for the poor for a subset of countres wth the requred data. The results do not suggest that the mpled reweghtng has much mpact on the consumpton PPP. The workng paper verson dscusses senstvty of the nternatonal poverty lne to the choce of PPPs (Ravallon, Chen, and Sangraula 2008). The Asan Development Bank (2008) has taken the further step of mplementng specal prce surveys for Asan countres to collect prces on explctly lower qualtes of selected tems than those dentfed n the standard ICP. Usng lower qualty goods essentally means lowerng the poverty lne. In terms of the mpact on the poverty counts for Asa n 2005, the Asan Development Bank s method s equvalent to usng a poverty lne of about $1.20 a day by the methods descrbed here; ths calculaton s based on a log-lnear nterpolaton between the relevant poverty lnes. 9. Ravallon, Chen, and Sangraula (2007) allow for urban rural cost of lvng dfferences facng the poor and provde an urban rural breakdown of the pror global poverty measures usng the 1993 PPP. These estmates wll be updated n the future work. 10. The 2005 consumpton PPP mples a poverty lne of $6 a month, whch s very hard to beleve. 11. One country, Madagascar, was dropped because of large nconsstences n the data from varous sources (natonal accounts aggregates reported by the World Bank and the Internatonal Monetary Fund). Usng the World Bank s estmate of prvate consumpton expendture gves a poverty lne almost three tmes mean consumpton.
8 170 THE WORLD BANK ECONOMIC REVIEW FIGURE 1. Densty Functons of Poverty Lnes and Prvate Consumpton per Capta at 2005 PPP Source: Authors analyss based on data n appendx table A-1. expendture per capta, but otherwse the dstrbutons are very dfferent, wth consumpton showng a far greater spread (fgure 1). The alternatve to prvate consumpton expendture from the natonal accounts s mean household consumpton or ncome from household surveys. However, n many cases the poverty lne was calculated from such surveys, so any relatonshps between the natonal poverty lnes and the survey means may well be spurous, beng drven by common measurement errors. Consder, for example, the most popular method of settng a natonal poverty lne, whch values a predetermned food bundle and adds an allowance for nonfood spendng based on the food Engel curve. Underestmaton of nonfood spendng n the survey wll shft the Engel curve and automatcally adjust the poverty lne downward. The measurement error alone wll generate a postve correlaton between the poverty lne and the survey mean. 12 (The overall drecton of bas s ambguous n theory, gven that there wll also be the usual attenuaton bas when a regressor s measured wth error.) Under the assumpton that the measurement errors n the natonal accounts are largely ndependent of those n the surveys, prvate consumpton expendture s probably a better ndcator. 12. The same would happen f the poverty lne were derved by the alternatve method of fndng the total consumpton expendture level at whch predetermned food-energy requrements are met on average. If nonfood spendng s underestmated by the survey, the poverty lne s automatcally adjusted downward, reflectng the measurement error. A spurous correlaton results.
9 Ravallon, Chen, and Sangraula 171 FIGURE 2. Natonal Poverty Lnes and Log Prvate Consumpton per Person for the Survey Year Note: Ftted values use a lowess smoother wth bandwdth ¼ 0.8. Source: Authors analyss based on data n appendx table A-1. Fgure 2 plots the poverty lnes aganst log consumpton for the survey year. The least squares estmate of the elastcty of the poverty lne to prvate consumpton expendture s (wth a t-rato of 13.68, based on a robust standard error). 13 Ths elastcty estmate s sgnfcantly less than unty (t ¼ 7.21), as used n relatve poverty lnes for many developed countres (see, for example, Eurostat 2005), although t s smlar to some past estmates based on subjectve poverty lnes for developed countres. 14 However, fgure 2 suggests that the economc gradent emerges strongly only once mean consumpton s above a crtcal level. In a nonparametrc regresson of the natonal poverty lnes aganst log mean consumpton, 15 the elastcty of the poverty lne to mean consumpton rses from zero to around 0.7 at the hghest level of mean consumpton (see fgure 2) The estmate s qute robust to outlers; a medan quantle regresson gves (t ¼ 9.57). 14. Hagenaars and van Praag (1985) estmated an elastcty of 0.51 for eght European countres. Klpatrck (1973) estmated an elastcty of about 0.6 for subjectve poverty lnes n the Unted States. 15. The nonparametrc regresson s Stata s locally weghted scatter plot smoothng method wth the default bandwdth (0.8). Alternatve bandwdths n the nterval (0.2, 0.9) were also tested. The mean of the predcted values n the poorest 15 countres ranged from $37.52 to $38.11 (although the regresson lne was clearly undersmoothed at bandwdths below about 0.5). 16. Ths elastcty was estmated by takng a smple movng average of the left- and rght-sde dscrete dfferentals n logs at each data pont along the nonparametrc regresson functon n fgure 2.
10 172 THE WORLD BANK ECONOMIC REVIEW The same pattern found by Ravallon, Datt, and van de Walle (1991) usng the older complatons of natonal poverty lnes s evdent n fgure 2, wth the poverty lne rsng wth mean consumpton, but wth a low ntal elastcty. By nterpretaton, absolute poverty appears to be the domnant concern n poor countres, wth relatve poverty emergng at hgher consumpton levels. However, t s notable how hgh the overall elastcty s for developng economes. The economc gradent n the poverty lnes comprses a component for food needs and one for nonfood needs, although ths dfference can be quantfed only for a subset of the natonal poverty lnes. For a subsample of 28 countres, complete data are also avalable for separatng the food and nonfood components of the natonal poverty lnes. The mean food share at the poverty lne s (wth a range of ). The elastcty of the food component of the poverty lne to mean consumpton s (t ¼ 9.55), whereas the elastcty of the nonfood component s almost twce as hgh, at (t ¼ 8.97). (The overall elastcty s (t ¼ 11.02) for ths subsample and for the full sample.) So, the economc gradent n natonal poverty lnes evdent n fgure 2 s drven more by the gradent n the nonfood component of the poverty lnes (whch accounts for about 60 percent of the overall elastcty), although an apprecable share s attrbutable to the economc gradent n food poverty lnes. II. SETTING AN I NTERNATIONAL P OVERTY L INE B ASED ON THE N ATIONAL L INES Armed wth the new complaton of natonal poverty lnes, consder agan the basc dea behnd the $1 a day poverty lne, whch was chosen to be representatve of poverty lnes n poor countres. There are several ways of settng a new nternatonal poverty lne consstent wth ths dea. The sample medan poverty lne s $60.81 a month, or almost exactly $2.00 a day; the sample mean s hgher, at about $2.90 a day. However, the marked economc gradent shown n fgure 2 mples that the mean or medan wll be well above the poverty lnes found for the poorest countres. The poverty lne for Malaw wth the lowest personal consumpton expendture per capta n the sample s $26.11 a month. However, lke all specfc data ponts n a sample, ths one s susceptble to measurement error, and the country-specfc error term could be large. It s notable that even though the relatonshp n fgure 2 s qute flat at low consumpton, there s stll a szable varance. No doubt, dosyncratc dfferences n the data and methods used n settng natonal poverty lnes have a role; there are measurement errors and methodologcal dfferences between countres n how poverty lnes are constructed, whch can be nterpreted as nose n the mappng from the underlyng welfare space nto the ncome space. Some averagng s clearly called for, as s normal n economc measurement. A better method s to use the expected
11 Ravallon, Chen, and Sangraula 173 TABLE 1. Estmated Poverty Lne for the Poorest Country for Varous Parametrc Models Specfcaton Predcted poverty lne for the poorest country n 2005 PPP dollars per month (C mn ¼ $31.34 for Malaw) Z ¼ aþ bc þ 1 $31.04 (8.53) Z ¼ aþ b 1 C þ b 1 C 2 þ 1 $29.32 (6.59) Z ¼ aþ b 1 ln C þ b 1 ln C 2 þ 1 $44.22 (6.89) a ln Z ¼ aþ b 1 ln C þ b 1 ln C 2 þ 1 $33.76; ln Ẑ ¼ 3.52 (33.51) ln Z ¼ aþ b 1 C þ b 1 C 2 þ 1 $32.63; ln Ẑ ¼ 3.49 (47.16) Note: Numbers n parentheses are t-ratos based on robust standard errors. a The turnng pont ln C ¼ 4.04 above the lowest consumpton. The predcted value of Z at the turnng pont s $36.05 (t ¼ 13.61). Source: Authors analyss based on sources descrbed n Ravallon, Chen, and Sangraula (2008). value of the poverty lne n the poorest country, based on how the poverty lnes vary wth mean consumpton. Table 1 gves a number of parametrc specfcatons (ncludng those used by Ravallon, Datt, and van de Walle 1991; Ravallon 1994; Chen and Ravallon 2001) and the mpled estmates of the poverty lne for the poorest country. The estmates n table 1 rase three concerns. Frst, the results may be drven by the specfc parametrc form. Sgns of ths possblty nclude the much hgher predcted natonal poverty lne Z for the poorest country n the sem-log model poverty lne Z regressed on a quadratc functon of the log of personal consumpton expendture (ln C ). But ths s deceptve, snce the turnng pont of the quadratc functon s above the lowest consumpton. Ths s clearly an artfact of the parametrc form, snce there s no sgn n fgure 2 of a negatvely sloped segment at low prvate consumpton expendture per capta. If ths specfcaton s gnored, the results n table 1 suggest that a poverty lne of around $1 a day at 2005 PPP s defensble f poverty n the world s measured by the standards of the poorest country n the world. Second, a parametrc model need not estmate well at all levels of consumpton. For example, the lnear regresson of Z on C has a very good overall ft, wth a correlaton of wth the ftted values n fgure 2 and a correlaton of wth the data. However, the lnear projecton based on ths regresson underpredcts the poverty lnes for the poorest dozen or so countres. 17 The nonparametrc regresson n fgure 2 provdes a more flexble method of averagng, gven that the regresson s ensured to have reasonably good ft over the full range of the data, ncludng among the poorest countres. The predcted value of Malaw s prvate consumpton expendture per capta s $37.16 a month ($1.22 a day). 17. Based on the lnear projecton, the mean predcted Z for the poorest 15 countres (ranked by C) s $ By contrast, the mean poverty lne for the poorest 15 countres s $37.98, whle the mean of the predcted values from the nonparametrc regresson s $37.89.