When Is Growth Pro-Poor? Evidence from a Panel of Countries

Transcription

1 Forhcoming, Journal of Developmen Economics When Is Growh Pro-Poor? Evidence from a Panel of Counries Aar Kraay The World Bank Firs Draf: December 2003 Revised: December 2004 Absrac: Growh is pro-poor if he povery measure of ineres falls. According o his definiion here are hree poenial sources of pro-poor growh: (a) a high growh rae of average incomes; (b) a high sensiiviy of povery o growh in average incomes; and (c) a povery-reducing paern of growh in relaive incomes. I empirically decompose changes in povery in a sample of developing counries during he 1980s and 1990s ino hese hree componens. In he medium- o long-run, mos of he variaion in changes in povery can be aribued o growh in average incomes, suggesing ha policies and insiuions ha promoe broad-based growh should be cenral o he pro-poor growh agenda. Mos of he remainder of he variaion in changes in povery is due o poveryreducing paerns of growh in relaive incomes, raher han differences in he sensiiviy of povery o growh in average incomes. Cross-counry evidence provides relaively lile guidance as o he policies and insiuions ha promoe hese oher sources of propoor growh. The World Bank, 1818 H Sree N.W., Washingon, DC, 20433, [email protected]. This paper has been prepared in he conex of he pro-poor growh program sponsored by he World Bank s PREM-Povery group. I am graeful o Louise Cord, Robera Gai, Francisco Ferreira, Tamar Manuelyan-Ainc, Marin Ravallion, and an anonymous referee for helpful commens; and o Shaohua Chen and Diane Seele for providing daa. I would also like o hank he research deparmen a he Inernaional Moneary Fund for is hospialiy while pars of his paper were wrien. The opinions expressed here are he auhor s, and do no reflec hose of he World Bank or he IMF, heir Execuive Direcors, or he counries hey represen.

2 1. Inroducion The erm pro-poor growh has recenly become pervasive in discussions of developmen policy. Despie widespread use of he erm, here is much less consensus as o wha exacly pro-poor growh means, le alone wha is deerminans are. According o one view, growh is pro-poor if he accompanying change in income disribuion by iself reduces povery (Kakwani and Pernia (2000)). However, his definiion is raher resricive, as i implies ha, for example, China s very rapid growh and dramaic povery reducion during he 1980s and 1990s was no pro-poor because he poor gained relaively less han he non-poor. A broader and more inuiive definiion is ha growh is pro-poor if he povery measure of ineres falls. Ravallion and Chen (2003) propose his definiion and apply i o a paricular povery measure, he Was index. In his paper, I adop he broader definiion, and hen apply sandard povery decomposiion echniques o idenify hree poenial sources of pro-poor growh: (a) a high growh rae of average incomes; (b) a high sensiiviy of povery o growh in average incomes; and (c) a povery-reducing paern of growh in relaive incomes. I implemen his decomposiion for several povery measures, using household survey daa for a large sample of developing counries in he 1980s and he 1990s. I hen use variance decomposiions o summarize he relaive imporance of hese differen sources of pro-poor growh. Finally, I invesigae he correlaes of he sources of pro-poor growh in his panel of observaions on changes in povery. The main resuls of his paper are he following. Firs, regarding he relaive imporance of he hree poenial sources of pro-poor growh, I find ha mos of he variaion in changes in povery is due o growh in average incomes. In conras, changes in relaive incomes accoun for only 30 percen of he variance of changes in he headcoun measure of povery in he shor run, and only hree percen in long run. Growh in average incomes accouns for virually all of he remaining 70 percen of he variance in he shor run, and 97 percen of he variance in he long run, while crosscounry differences in he sensiiviy of povery o growh are very small. The share of he variance of changes in povery due o relaive income changes in somewha larger 1

3 for more boom-sensiive povery measures, reflecing he fac ha changes in hese measures place less weigh on growh in average incomes. Second, I find some evidence ha growh in average household survey incomes is correlaed wih several of he usual deerminans of growh from he empirical growh lieraure, including insiuional qualiy, openness o inernaional rade, and size of governmen. The evidence documened here for he cross-counry correlaes of growh in household survey incomes is no especially compelling, given various limiaions of he daase. However, I find almos no evidence ha povery-reducing paerns of growh in relaive incomes are significanly correlaed wih a se of explanaory variables ha he empirical growh lieraure has idenified as significan deerminans of growh in per capia GDP. The same is rue for a number of oher variables, ha while no generally significan for growh, have been suggesed in he lieraure as poenially reducing inequaliy. Taken ogeher, hese resuls underscore he imporance of growh in average incomes for povery reducion. This in urn suggess ha a policy package focusing on deerminans of growh in average incomes, such as he proecion of propery righs, sound macroeconomic policies, and openness o inernaional rade should be a he hear of pro-poor growh sraegies. Moreover, he absence of compelling cross-counry evidence ha hese facors are sysemaically correlaed wih he changes in income disribuion ha maer mos for povery reducion suggess ha here are no obvious radeoffs policies ha lead o growh in average incomes are unlikely o sysemaically resul in adverse effecs on povery hrough heir effecs on relaive incomes. This does no mean ha growh in average incomes is sufficien for povery reducion. Raher, he resuls presened here sugges ha cross-counry evidence is unlikely o be very informaive abou he policies and insiuions ha are likely o lead o povery-reducing paerns of growh in relaive incomes. This suggess ha more micro-level and casesudy research may be useful in shedding ligh on he deerminans of povery-reducing disribuional change. This paper is relaed o a growing empirical lieraure on growh, inequaliy, and povery. Mos immediaely, his paper builds on Dollar and Kraay (2002). In ha paper, we defined he poor as hose in he boom quinile of he income disribuion, and 2

4 empirically invesigaed he deerminans of growh in incomes of he poores quinile. In a large panel of counries, we found ha growh in incomes of he poor racked growh in average incomes roughly one-for-one. Since he growh rae of average incomes of he poor is he sum of he growh rae of average incomes and he growh rae of he firs quinile share, our paper showed ha neiher average incomes, nor a large se of oher conrol variables, were significanly correlaed wih changes in he firs quinile share. Tha paper conribued o a growing lieraure on he deerminans of inequaliy, including Li, Squire and Zhou (1998), Gallup, Radele and Warner (1998), Spilimbergo, Londono and Szekely (1999), Leamer, Maul, Rodriguez and Scho (1999), Easerly (1999), Barro (2000), Foser and Szekely (2001), and Lundberg and Squire (2003). This paper differs from Dollar and Kraay (2002), as well as much of he exising lieraure on deerminans of inequaliy, in wo respecs. Firs, insead of looking a relaive povery measures or inequaliy, here I focus on changes in absolue povery measures as he dependen variable. 1 As is well undersood, changes in absolue povery measures are complicaed non-linear funcions of underlying changes in average income and measures of income inequaliy. The second conribuion of his paper is o empirically consruc he exac measures of disribuional change ha maer for changes in various povery measures for a large sample of counries, raher han simply looking a common summary saisics of inequaliy such as he Gini coefficien or quinile shares. This means ha I can empirically sudy he conribuions of growh and disribuional change o changes in povery, wih less resricive assumpions abou he shape of he underlying income disribuion. 2 Despie hese differences, he main conclusions of his paper are similar o hose in Dollar and Kraay (2002). In paricular, boh papers find ha growh in average incomes maers a grea deal for reducions in boh relaive and absolue povery. Boh papers also find lile evidence ha common deerminans of growh, as well as a 1 A noable early excepion is Ravallion and Chen (1997), who esimae regressions of changes in absolue povery on changes in mean incomes using a panel of household surveys from developing counries. 2 For example, Lopez (2003) invesigaes he deerminans of growh and change in he Gini coefficien, and hen draws conclusions regarding he likely effecs on povery by assuming ha he disribuion of income is lognormal, so ha here is a one-o-one mapping beween he Gini coefficien and he Lorenz curve. In his paper I use a more flexible hree-parameer approximaion o he Lorenz curve, raher han he one-parameer approximaion implici in he lognormal assumpion. 3

5 number of oher variables, are robusly correlaed wih paerns of disribuional change ha maer for povery reducion. The res of his paper proceeds as follows. Secion 2 reviews sandard povery decomposiion echniques and uses hem o illusrae he channels hrough which growh and disribuional change maer for changes in a number of povery measures. Secion 3 describes he daase of changes in povery in a large sample of developing counries on which he empirical analysis is based. Secion 4 provides evidence on he relaive imporance of he sources of pro-poor growh, as well as evidence on some of he correlaes of hese sources. Secion 5 concludes. 4

6 2. Empirical Framework In his secion I use sandard echniques o decompose changes in povery ino hree componens: (a) growh in average incomes; (b) he sensiiviy of povery o growh in average incomes; and (c) changes relaive incomes. Le y (p) denoe he income of he p h percenile of he income disribuion a ime. This can be wrien as a funcion of average income, µ, and he Lorenz curve, L (p), i.e. y P denoe he following generic addiive povery measure: dl (p) (p) = µ. Le dp H (1) P = f(y (p)) dp 0 1 where H = y (z) denoes he fracion of he populaion below he povery line, z. This noaion capures a number of differen povery measures. For example, if θ z y (p) f( y (p), θ) = we have he Foser-Greer-Thorbecke class which includes he z headcoun (θ=0), he povery gap (θ=1), and he squared povery gap (θ=2). If f ( y ) (p) = ln y (p) z, we have he Was povery index. Nex, differeniae his povery measure wih respec o ime o obain he following expression for he proporionae change in povery: 3 dp 1 (2) = η (p) g (p) dp d P H 0 Equaion (2) expresses he proporional change in povery as he average across all perceniles of he income disribuion of he growh rae of each percenile muliplied by he sensiiviy of he povery measure o growh in ha percenile. In paricular, 3 Differeniaing under he inegral sign in Equaion (1) requires he applicaion of Leibniz s rule. Noe ha he erm involving he derivaive of he upper limi of inegraion is zero, since he povery measures are zero when evaluaed a he povery line. 5

7 df(y (p)) y (p) η ( p) is he elasiciy of he povery measure wih respec o he dy (p) P income of he p h percenile. This erm capures he effec on povery of a small change in incomes of individuals a he p h percenile of he income disribuion. This sensiiviy dy (p) 1 is muliplied by he growh rae of each percenile, g (p), which d y (p) Ravallion and Chen (2003) refer o as he growh incidence curve. The overall proporional change in povery hen consiss of he average across all perceniles of he produc of hese wo erms. In order o separae ou he effecs of growh in average incomes, re-wrie Equaion (2) as: H H dp µ 1 d 1 dµ (3) = η (p) dp + η (p) g (p) d P d µ 0 d 0 1 dp µ Equaion (3) idenifies he hree sources of pro-poor growh discussed above: (a) growh in average incomes; (b) he sensiiviy of povery o growh in average incomes; and (c) growh in relaive incomes. The firs erm in Equaion (3) capures he firs wo sources dµ 1 of pro-poor growh. I consiss of growh in average incomes,, muliplied by a d µ erm summarizing he sensiiviy of he povery measure o changes in average incomes, H η 0 ( p) dp. This is simply he average across all perceniles of he sensiiviy of povery o growh in each percenile of he income disribuion. The second erm in Equaion (3) capures he remaining source of pro-poor growh: changes in relaive incomes. This hird source of pro-poor growh is he average across all perceniles of he income disribuion of he produc of (a) he growh rae of income in he p h percenile relaive o average income growh, and (b) he sensiiviy of povery o growh in ha percenile. For example, if he povery measure of ineres is very sensiive o growh among he poores, and if he income of he poores grows faser han average incomes, hen povery will fall faser. 6

8 Equaion (3) is useful for hinking abou he various definiions and sources of pro-poor growh. The Kakwani and Pernia (2000) definiion of pro-poor growh saes ha growh is pro-poor if and only if he second erm in Equaion (3) is negaive, i.e. he paern of growh in relaive incomes is such ha he povery measure falls. A broader definiion of pro-poor growh suggesed by Ravallion and Chen (2003) is ha growh is pro-poor if he povery measure of ineres falls. According o his definiion, here are hree poenial sources of pro-poor growh: (a) rapid growh in average incomes; (b) a high sensiiviy of povery o growh in average incomes; and (c) a povery-reducing paern of growh in relaive incomes. In he empirical secion of his paper, I will use daa on income disribuions and average incomes for a large sample of developing counries o consruc hese hree sources of pro-poor growh, documen heir relaive imporance, and invesigae heir deerminans. Before doing so, however, i is useful o examine he key ingrediens in Equaion (3) in more deail: he paern of growh in relaive incomes, dµ g (p) d povery o growh in each percenile, η (p). 1, and he funcion summarizing he sensiiviy of µ Figure 1 graphs wo examples of he paern of growh in relaive incomes, for China over he period , and for Indonesia over he period In China, according o he household survey average incomes grew a 14 percen per year, and he dollar-a-day headcoun measure of povery fell from 51 percen o 33 percen of he populaion. However, here was also a sharp increase in inequaliy during his period, wih he Gini coefficien rising from 34 o 40. The paern of relaive income growh raes shown in he relaive growh incidence curve highlighs his paern of increased inequaliy. Growh in he poores 80 perceniles of he populaion was below average, while only he riches 20 percen of he populaion saw above-average growh. In Indonesia, survey mean income fell dramaically beween 1996 and 1999 a nearly 9 percen per year during he Eas Asian financial crisis. Ye during his period, he paern of growh in relaive incomes was povery-reducing. Inequaliy as measured by he Gini coefficien fell from 36.5 o The relaive growh incidence curve is downward sloping, indicaing ha incomes of he richer perceniles of he income disribuion fell faser han incomes of poorer perceniles. In fac, below-average growh was recorded only for he riches 20 percen of he populaion. Despie his pro-poor paern of relaive 7

9 income growh, he headcoun measure of povery increased from 8 percen o 13 percen of he populaion, driven by he large negaive growh effec. 4 Consider nex he sensiiviy of povery o growh in differen perceniles of he income disribuion. In he case of he Foser-Greer-Thorbecke class, θ 1 θ y (p) y (p) 1 η (p) = 1, while for he Was index, η ( p) =. Noe ha P z z P hese sensiivies in general depend no only on he povery measure of ineres, bu also on he enire disribuion of income as summarized by y (p). Figure 2 graphs hese sensiiviies, using he acual disribuion of income in China in 1990 as an example, o show how differen povery measures are sensiive o growh in differen perceniles of he income disribuion. In he case of he headcoun, his sensiiviy is zero everywhere excep jus below he povery line where i spikes down o minus infiniy. This is because he headcoun simply adds up he number of people below he povery line small increases in he incomes of inframarginal poor people ha do no bring hem above he povery line will no reduce he headcoun. The same is rue for increases in incomes of hose above he povery line, including he near-poor jus above he povery line. The case of he headcoun already illusraes he broader poin of Figure 2: he exen o which a given paern of growh is pro-poor depends crucially on he povery measure of ineres. In paricular, if he objecive of pro-poor growh is o reduce he headcoun measure of povery, hen a pro-poor growh sraegy should focus exclusively on raising he incomes of hose jus a he povery line, and should ignore everyone else. This srong -- and well-undersood o be absurd -- conclusion is driven by he choice of he headcoun as he povery measure of ineres. Consider nex he povery gap and he squared povery gap. The povery gap is mos sensiive o growh in incomes of hose a he povery line, bu is also sensiive o growh in incomes of everyone below he povery line. The inuiion for his is he following: he povery gap 4 I is imporan o noe ha he growh incidence curves here adjus only for average inflaion. In he case of Indonesia food price inflaion during he crisis was much higher han non-food price inflaion (see Suryahadi e. al. (2003) for deails). To he exen ha food represens a larger share of he consumpion baske of he poor, he paern of growh in real incomes was less propoor han depiced in Figure 1. 8

10 reflecs a social welfare funcion which is indifferen o he disribuion of income among poor people. In his case a given rae of average growh resuls in a larger absolue increase in income for a person near he povery line, and so he povery measure is mos sensiive o hose neares he povery line, bu is non-zero for all poor people. The squared povery gap is also sensiive o growh in he incomes of all hose below he povery line, bu he sensiiviy is now U-shaped. Growh in incomes of he riches and poores of hose below he povery line maers leas, and he squared povery gap is mos sensiive o growh in incomes of poor people somewhere in beween hese wo exremes. The inuiion for his again depends on he underlying social welfare funcion, which now values absolue ransfers from richer o poorer poor people. This however is offse by he fac ha a given average growh rae resuls in a larger absolue increase in income for richer poor people. This is why he sensiiviy of he povery measure o growh is a non-monoonic funcion of he income percenile. The Was index has he propery ha i is equally sensiive o growh in all perceniles below he povery line. This is why Ravallion and Chen (2003) argue ha a good measure of pro-poor growh is he average (across all perceniles) growh rae of hose below he povery line, i.e. he average growh rae of incomes of he poor. In his paper I go furher and decompose he average growh rae of incomes of he poor ino growh in average incomes and he average growh rae of he poor relaive o growh in average incomes. This allows me o disinguish beween he effecs of growh in average incomes and growh in relaive incomes on he Was measure, and all he oher measures considered here. This disincion is no rivial, as we will see in he empirical secion of he paper ha, across counries, growh in average incomes accouns for a much greaer share of he variaion in changes in povery han do changes in relaive incomes. Finally consider he average across all perceniles of he sensiiviy of povery o growh in he incomes of percenile p, η (p). Recall from Equaion (3) ha his average sensiiviy measures he effec of growh in average incomes on he povery measure. High values of his average sensiiviy of povery o growh in average incomes are one of he hree poenial sources of pro-poor growh. For he Foser-Greer-Thorbecke class of povery measures, his average sensiiviy can be expressed in erms of he povery 9

11 measure iself when θ is no equal o zero, H P ( θ 1) η =θ (p) dp 1, where P (θ) P ( θ) 0 denoes he FGT measure wih parameer θ. 5 In he case where θ is zero, he sensiiviy of he headcoun o growh in average incomes is: H 1 L '(H) η (p) dp = which can be expressed as he slope of he densiy of P ( θ) µ L ''(H) 0 income a he povery line. For he Was measure, he average elasiciy is simply minus one imes he raio of he headcoun index o he Was index. While hese resuls are useful for analyically characerizing he sensiiviy of he differen povery measures o growh in average incomes, we will see shorly ha cross-counry differences in he sensiiviy of povery o growh in average incomes are no empirically very imporan, in he sense ha hey explain lile of he cross-counry variaion in he firs erm in Equaion (3). 5 This resul can be found in Kakwani (1993). 10

12 3. Daa In he res of his paper I use he analyic framework of he previous secion o decompose observed changes in povery ino he hree erms discussed above: (a) growh in average incomes; (b) he sensiiviy of povery o growh in average incomes; and (c) changes in relaive incomes. Afer consrucing hese hree erms for a large sample of developing counries, I use hem o idenify he relaive imporance of, and facors correlaed wih, hese sources of pro-poor growh. I use household survey daa on average incomes and en poins on he Lorenz curve for a large number of surveys, as compiled by Marin Ravallion and Shaohua Chen a he World Bank. Their daa comes direcly from primary sources, and is available a hp:// 6 Depending on he counry, he surveys measure eiher he disribuion of income or he disribuion of consumpion. Average income or consumpion is measured in 1993 dollars and is adjused for crosscounry differences in purchasing power pariy. Since I am ineresed in changes in povery over ime, I ake only counries wih a leas wo household surveys. This resuls in a oal of 285 surveys covering 80 developing counries. Mos of he survey daes are in he 1990s, wih some counries exending back o he 1980s. I use he World Bank s dollar-a-day povery line which in 1993 dollars is $1.08 per day, or $393 per year. Using hese surveys, I consruc wo daases of spells of changes in povery. In he firs daase, I consider all possible spells for each counry, discarding only hose few cases where he survey changes from an income o an expendiure survey or vice versa wihin a counry. This resuls in 185 spells of povery changes. The lengh of hese spells is quie shor, averaging 3.4 years and ranging from one o 13 years. In order o be able o look a changes over longer horizons, I also consruc a daase consising of one spell per counry, where he iniial and final years are chosen so as o maximize he lengh of he spell given available daa. This resuls in a se of 77 spells, wih an average lengh of 8 years, and ranging from wo o 19 years. I eliminae all spells where he headcoun measure of povery is negligible in eiher he iniial or final period, i.e. below wo percen. I also discard a small proporion of spells for which he average 6 I am graeful o Shaohua Chen for kindly providing key daa from all of he household surveys, including some ha was no a he ime available on he povery monioring websie. 11

13 annual growh rae of mean income exceeds 15 percen in absolue value, or for which he average annual growh rae of he headcoun exceeds 30 percen in absolue value. 7 Finally, for he daase of long spells, I discard hose counries for which he longes possible spell is shorer han five years. This reduces he firs daase o 110 spells covering 49 counries wih an average lengh of 3.5 years, and he second daase o 41 spells wih an average lengh of 9.6 years. These spells are lised in Appendix 1. In order o consruc he differen povery measures and heir decomposiions discussed in he previous secion, I need he full Lorenz curve and no jus he 10 poins provided in he Ravallion-Chen daa. To obain his, I assume ha he Lorenz curve has he following funcional form: α (4) L(p) = p ( 1 (1 p) ), α 0, 0 < β 1, γ 1 β γ This paricular parameerizaion is a member of a family of ordered Lorenz curves proposed by Sarabia, Casillo, and Sloje (1999). In Appendix 2, I discuss in more deail he qualiy of his parameric approximaion o he Lorenz curve, using record-level daa from Ghana as an example. The appendix shows ha his approximaion o he Lorenz curve is quie good, bu ha he associaed quanile funcion ends o undersae incomes of he poores. This means ha povery measures based on his approximaion are likely o be biased upwards, and more so for more boom-sensiive povery measures. I also show ha hese biases will lead o an underesimaion of he sensiiviy of povery o growh in average incomes. I esimae he hree parameers of he Lorenz curve for each survey using an algorihm suggesed by he same auhors. This involves selecing all possible combinaions of hree poins on he Lorenz curve, and hen for each combinaion finding values of α, β, and γ such ha he Lorenz curve passes hrough hese hree poins. The final esimaes of α, β, and γ are hen found by averaging across all he resuling esimaes of hese parameers, discarding hose for which he parameer resricions 7 This cuoffs roughly correspond o he 5 h and 95 h perceniles of he disribuion of growh raes of mean income and he headcoun. In a leas some of hese cases growh raes of variables are sufficienly exreme as o be implausible, and likely reflec problems of comparabiliy in surveys over ime. Appendix 1 liss he discarded observaions and summarizes some of he key resuls including hese exreme observaions. 12

14 indicaed in Equaion (4) ha are required for he Lorenz curve o have posiive firs and second derivaives do no hold. I hen obain he quanile funcion by analyically differeniaing he Lorenz curve and muliplying by average income. Using his, I can consruc η (p) for each povery measure of ineres, as well as he growh incidence y (p) curve over he observed discree inerval, g (p) = 1. y (p) 1 13

15 4. Resuls I begin by consrucing four povery measures of ineres (he headcoun, he povery gap, he squared povery gap, he Was index) for he iniial and final years of each spell. I hen compue he average annual growh raes of each of hese measures over each spell. Table 1 repors he simple correlaions of he levels and average annual growh raes in hese povery measures wih he corresponding log-levels and growh raes of survey mean income. These simple correlaions are all negaive, and are large in absolue value, especially hose in levels and hose for he long spells. Figure 3 graphs he proporional change in he headcoun agains he growh rae of average incomes, using he sample of long spells. There is a srong and highly significan negaive relaionship beween changes in povery and change in average incomes. Table 1 and Figure 3 confirm he widely-undersood empirical regulariy ha povery on average falls as average incomes increase. In he res of his secion I go beyond his basic observaion o documen he relaive imporance of he differen sources of pro-poor growh discussed above, and heir correlaes. The Relaive Imporance of Sources of Pro-Poor Growh I firs decompose he change in povery in each spell ino a growh componen and a disribuion componen using he decomposiion suggesed by Da and Ravallion (1992), which is he discree analog of he infiniesmal decomposiion in Equaion (3). Le (, ) P µ denoe a povery measure based on mean income a ime, µ, and he L Lorenz curve a ime, L. The proporional change in he povery measure over he discree inerval beween ime and -1 is: (5) P ( µ,l ) P( µ 1,L 1 ) P( µ,l ) 1 1 P = ( µ,l 1 ) P( µ 1,L 1 ) P( µ,l ) 1 1 P + ( µ 1,L ) P( µ 1,L 1 ) + ε P( µ,l ) 1 1 The firs erm on he righ-had side is he growh componen of he change in povery, and is consruced as he proporional difference beween he iniial povery measure and a hypoheical povery measure compued using he second period mean bu he firs period Lorenz curve. The second erm is he disribuion componen which is compued as he proporional difference beween he iniial povery measure and a 14

16 hypoheical povery measure consruced using he firs period mean bu he second period Lorenz curve. These wo componens are he discree-ime analogs of he wo erms in Equaion (3). Unlike Equaion (3), however, here is also a residual erm because he decomposiion is done over a non-infiniesmal inerval. Empirically however hese residuals will urn ou o be unimporan on average. I measure he proporional changes on he lef- and righ-hand side of Equaion (5) as log differences and normalize by he lengh of he inerval o obain average annual percen changes in povery and he growh and disribuion componens for each spell. I also divide he firs erm in Equaion (5) by growh in average incomes o obain he sensiiviy of povery o growh in average incomes. Tables 2 and 3 repor he resuls of applying his decomposiion o he wo daases of spells. Throughou hese wo ables, I use he following variance decomposiion o summarize he relaive imporance of he various sources of pro-poor growh. For wo correlaed random variables X and Y, I define he share of he variance of X+Y due o variaion in X as VAR(X) + COV(X, Y). 8 The op panel of VAR(X) + VAR(Y) + 2 COV(X, Y) each able documens he imporance of he residual relaive o he sum of he growh and disribuion componens of he change in povery. The firs column shows he variance of he sum of he growh and disribuion componens, he second column he variance of he residual, and he hird he covariance beween he wo. The final column repors he share of he variance of changes in povery due o he growh and disribuion componens, which is virually one for all povery measures. This simply reflecs he fac ha he variance of he residual erm is iny relaive o he variance in measured changes in povery. This can also be verified visually from he op panel of Figure 4, which graphs he change in he headcoun measure of povery on he horizonal axis, and he sum of he growh and disribuion componens on he verical axis, using he daase of long spells. The slope of he OLS regression line is he share of he variance in povery changes due o he growh and disribuion componens, and one minus he slope is he share due o he residual erm. I is clear from his graph ha changes in povery are 8 When X and Y are normally disribued, his variance decomposiion has a very naural inerpreaion. I measures how much he condiional expecaion of X increases for each uni ha he sum (X+Y) is above is mean value. See Klenow and Rodriguez (1997) for deails. 15

17 largely accouned for by he sum of he growh and disribuion componens, wih very lile of he variaion due o he residual. The middle panels of Tables 2 and 3 repor he same variance decomposiion, bu now o assess he imporance of he growh componen relaive o he disribuion componen of changes in povery. For he sample of all spells, beween 43 and 70 percen of he variaion in changes in povery is due o he growh componen, wih he remainder due o changes in relaive incomes. For he long spells, beween 69 and 97 percen of he variaion in changes in povery is aribuable o he growh componen, depending on he povery measure of ineres. In boh ables, he growh componen is relaively less imporan for boom-sensiive povery measures such as he povery gap and he squared povery gap. The middle panel in Figure 4 graphically summarizes his second decomposiion for he long spells sample, ploing he growh componen of changes in he headcoun on he verical axis, and he sum of he growh and disribuion componens on he horizonal axis. Again, he slope of he OLS regression line can be inerpreed as he share of he variaion on he horizonal axis due o he growh componen. Visually inspecing his graph, i is clear ha if he headcoun declines subsanially, i is mosly because he growh componen of povery reducion is large. The boom panels of Tables 2 and 3 furher disenangle he growh componen ino growh in average incomes, and he sensiiviy of povery o growh in average incomes, i.e. hey separae he firs erm in Equaion (3) ino is wo componens. Since he variance decomposiion used here applies o sums of random variables, I ake he logarihm of he absolue value of he growh componen, which hen becomes he sum of he logarihm of he absolue value of growh, and he logarihm of he absolue value of he average sensiiviy of povery o growh, and apply he decomposiion o his sum. Tables 2 and 3 show ha around 90 percen of he variaion in he growh componen of changes in povery is due o differences in average income growh, and very lile is due o differences in he sensiiviy of povery o average income growh. The boom panel of Figure 4 illusraes his, bu wihou he log ransform required o do he variance decomposiion. On he horizonal axis I graph he growh componen of he change in povery, while on he verical axis I graph growh in average incomes. While he slope of his regression canno be inerpreed as a variance share, i neverheless is very clear ha cross-counry differences in he growh componen of changes in povery are 16

18 overwhelmingly accouned for by cross-counry differences in growh iself. Pu differenly, i is clear from his graph ha if he growh componen of povery reducion is large, i is mos likely ha growh iself was large, raher han ha he sensiiviy of povery o growh was large. 9 Two sriking feaures of Tables 2 and 3 meri furher discussion: (a) he share of he variaion in povery measures due o growh declines as he povery measures become more boom-sensiive, i.e. when we move from he headcoun o he povery gap o he squared povery gap; and (b) he share of he variance due o growh is smaller over he shor horizons represened in he daase of all spells, and is larger in he daase of long spells. Consider firs he observaion ha he variaion in changes in povery due o growh declines as he povery measures become more boom-sensiive. This finding should no be inerpreed as evidence ha he poores perceniles of he income disribuion are more likely o experience slower-han-average growh. Raher, i primarily reflecs he fac ha more boom-sensiive povery measures place relaively less weigh on changes in average incomes han hey do on changes in relaive incomes. 10 Recall ha he sensiiviy of povery o growh in average incomes is H P ( θ 1) η =θ (p) dp 1 P ( θ) 0 for he FGT family of povery measures. Differeniaing P ( ) his sensiiviy wih respec o θ and using he fac ha θ P < ( θ) 0 and < 0, i is 2 θ θ sraighforward o see ha he sensiiviy of povery o growh in average incomes is sricly declining (in absolue value) as he povery measure becomes more boomsensiive, i.e. as θ increases. This means ha when relaive incomes do no change, he proporional change in povery associaed wih a given average growh rae will be 2 9 A firs glance his resul seems inconsisen wih Ravallion (1997), who documens ha he sensiiviy of povery o growh varies significanly wih iniial inequaliy. However, using eiher sample of spells I can replicae he resul ha he ineracion of growh wih he iniial Gini coefficien is significanly correlaed wih he change in headcoun measures of povery. Alhough here are cross-counry differences in he sensiiviy of povery o growh which are significanly correlaed wih iniial inequaliy, in he daa hese differences are dominaed by he much larger cross-counry differences in growh iself, and his is wha he variance decomposiions show. 10 In Appendix 2 I also show ha he approximaion errors associaed wih he parameerizaion of he Lorenz curve reduce he sensiiviy of povery o growh in average incomes for more boomsensiive povery measures. 17

19 smaller he more boom-sensiive is he povery measure. In oher words, even for a purely disribuion-neural growh process, growh will appear o be less pro-poor (in he sense ha he proporionae change in povery is smaller) he more boom-sensiive is he povery measure. When relaive incomes also change, i is no longer possible o sign he derivaive of he change in povery wih respec o θ for an arbirary shif in he Lorenz curve. Empirically, however, in he majoriy of spells in his daase, proporional changes in povery are larger in absolue value he more boom-sensiive are he povery measures. This is rue even hough he growh componen of changes in povery is unambiguously smaller in absolue value in all spells, implying ha, on average, he disribuion componen of changes in povery becomes larger in absolue value he more boom-sensiive are he povery measures. This in urn accouns for a smaller share of he variance of changes in povery due o growh for more boom-sensiive povery measures. 11 I is also possible o documen direcly ha he incomes of he very poores on average do no grow more slowly han average incomes, using he esimaed growh incidence curves for each spell. In he daase of long spells, I calculae he average annual growh rae of incomes relaive o he survey mean, a he perceniles corresponding o 100 percen, 50 percen, and 25 percen of he iniial-period headcoun, using only he 22 spells for which he iniial headcoun is more han 10 percen. The average across spells of hese growh raes are 1.2 percen, -1.4 percen, and 1.5 percen respecively, bu wih very large sandard deviaions of 3.6 percen, 5.0 percen, and 6.6 percen respecively. Based on his I canno rejec he null hypohesis ha he growh rae of incomes a and below he povery line do no differ significanly from growh in average incomes. 11 For he paricular case of equiproporionae shifs in he Lorenz curve, Kakwani (1993) shows ha he elasiciy of povery wih respec o he Gini coefficien is µ P ( θ 1) θ 1+ 1 I is z P ( θ) sraighforward o verify by simple differeniaion ha his elasiciy is sricly increasing in θ when he povery line is below he mean, i.e. z<µ.. Thus for his special case we can unambiguously show ha he more boom-sensiive he povery measure, he growh componen of changes in povery will be smaller and he disribuion componen of changes in povery will be larger. 18

20 The second sriking feaure of Tables 3 and 4 is ha he share of he variance of changes in povery due o growh is larger in he sample of long spells. In order o undersand his finding i is useful o examine in more deail he sources of variaion in he growh and disribuion componens of changes in povery. In he long spells, he sandard deviaion of he growh componen of he headcoun is 0.88 percen, which reflecs purely cross-counry variaion in he long-run average growh componen of changes in povery. In he sample of all spells, he sandard deviaion of he growh componen rises o 1.04 percen, reflecing he addiion of he wihin-counry variaion in he growh componen. This fairly modes increase indicaes ha mos of he variaion in he growh componen of changes in povery in he sample of all spells is due o crosscounry variaion, and relaively lile reflecs wihin-counry variaion. Since we have already seen ha cross-counry differences in he sensiiviy of povery o growh are small, i is also he case in his daase ha average income growh iself varies relaively more across counries han i does wihin counries over ime. The disribuion componen of changes in povery is a weighed average of he growh raes of each percenile of he income disribuion relaive o average growh. In boh he long spells and he full sample of all spells, he relaive growh raes of each percenile are on average near zero. However, in he sample of all spells, he relaive growh raes of each percenile vary much more across spells han hey do in he sample of long spells. This is shown in Figure 5, which repors he average (across spells) of he growh rae of percenile p relaive o average growh, as well as he sandard deviaion (across spells) of his relaive growh rae. In boh samples he relaive growh raes of all perceniles are close o zero on average across spells, consisen wih he well-documened fac ha growh ends o be disribuion-neural on average. However, he variaion around his average is nearly wice as large in he sample of all spells as i is in he sample of long spells, reflecing subsanial addiional wihin-counry variaion over ime in relaive income growh raes. Puing ogeher hese observaions, we can now accoun for he difference in he relaive imporance of he growh and disribuion componens of changes in povery in he sample of long spells and he sample of all spells. In he long spells sample, relaive income changes over long periods are fairly closely clusered around zero for all perceniles of he income disribuion. The weighed average of hese relaive growh 19

21 raes, i.e. he disribuion componen of changes in povery, is herefore also near zero on average wih relaively lile dispersion across counries, and conribues relaively lile o he cross-counry variaion in changes in povery. In he sample of all spells, he variance of he growh componen increases only modesly, since growh in average incomes ends o vary much more across counries han i does wihin counries over ime. However, he variance of relaive income changes increases much more, reflecing he much greaer wihin-counry variaion over ime in relaive income growh raes. As a resul, he disribuion componen of changes in povery varies more across spells and accouns for a greaer share of he overall variaion in changes in povery. In summary, he resuls in his subsecion ell us ha, over longer horizons, beween 69 and 97 percen of cross-counry differences in povery changes can be accouned for by growh. The relaive imporance of he growh componen of changes in povery is smaller for more boom-sensiive povery measures. This does no mean ha he poores on average experience slower growh. Raher, i simply reflecs he fac ha more boom-sensiive povery measures assign a smaller weigh o changes in average incomes. The relaive imporance of he growh componen is also smaller in he sample of shorer spells han in he sample of long spells. This reflecs he fac ha, in his daase, here are non-rivial flucuaions in relaive incomes from one survey dae o he nex, bu hese end o average o zero boh across counries and over ime. Finally, cross-counry differences in he sensiiviy of povery o growh in average incomes are empirically relaively unimporan in accouning for cross-counry differences in raes of povery reducion. Wha Drives he Sources of Pro-Poor Growh? I now urn o he quesion of wha drives he various sources of pro-poor growh. In ligh of he resuls of he previous secion ha cross-counry differences in he sensiiviy of povery o growh in average incomes are relaively unimporan, I focus primarily on he firs and hird sources of pro-poor growh: growh in average incomes, and changes in relaive incomes. I measure growh in average incomes as he average annual growh rae over he spell of household average income or consumpion. I use wo differen summary measures of changes in relaive incomes. The firs is simply he average annual proporional change in he Gini index, for comparabiliy wih exising 20

22 resuls on he deerminans of changes in summary saisics of inequaliy. I also use he discree-ime disribuion componen of he change in he headcoun measure of povery. Resuls for he disribuion componen of he oher hree povery measures are very similar o hose for he headcoun, and are no repored o save space. There are many limiaions o his daase which complicae he idenificaion of causal deerminans of growh or change in relaive incomes. The sample of observaions is quie small, especially when we consider he long spells daase where he deerminans of longer-erm growh and disribuional change are more likely o be apparen. There is also subsanial measuremen error in he daa on growh in survey means, and for measures of disribuional change. While classical measuremen error in hese dependen variables will no necessarily lead o biases in coefficien esimaes, i will inflae sandard errors and reduce he significance of esimaed coefficiens. Because here are relaively few spells per counry in he daase consising of all spells, and only one per counry in he long spells daase, i is no possible o meaningfully base idenificaion on he wihin-counry variaion in he daa. This raises he possibiliy ha any observed parial correlaions may be driven by unobserved counry-specific characerisics excluded from he regressions. The small number of spells per counry also means ha i is no possible o rely on inernal insrumens o achieve idenificaion. 12 In ligh of hese difficulies, my more modes objecive here is o simply documen some parial correlaions beween hese sources of pro-poor growh and a number of righ-hand-side variables of ineres, and o inerpre hem wih an appropriae abundance of cauion. I consider he same lis of righ-hand-side variables as in Dollar and Kraay (2002). In ha paper, we considered a small number of variables ha are frequenly found o be robusly correlaed wih real GDP growh in he cross-counry growh lieraure: insiuional qualiy as proxied by a measure of propery righs proecion (he rule of law indicaor from Kaufmann, Kraay and Masruzzi (2003)) as well as he World Bank s Counry Policy and Insiuional Assessmen (CPIA) indicaor; 12 This is of course especially problemaic for he regressions below ha involve a lagged dependen variable, which, ogeher wih unobserved counry-specific effecs, will make esimaes of he coefficien on he lagged dependen variable inconsisen, and can bias he coefficiens on he oher variables in differen direcions depending on heir correlaion wih he lagged dependen variable. See Caselli, Esquivel, and Lefor (1996) for deails. 21

23 openness o inernaional rade (he consan-price local currency raio of expors plus impors o GDP); inflaion as a proxy for sable moneary policy (measured as he logarihm of one plus he CPI inflaion rae); he size of governmen (measured as he share of governmen consumpion in GDP in local currency unis); and a measure of financial developmen (he raio of M2 o GDP in local currency unis). We also considered a number of variables ha are generally less robusly correlaed wih growh, bu ha some sudies have found o be correlaed wih inequaliy, eiher in levels or in differences. These include a measure of democracy (he voice and accounabiliy indicaor from Kaufmann, Kraay and Masruzzi (2003)); relaive produciviy in agriculure (measured as he raio of value added per worker in agriculure relaive o overall value added per worker, boh in curren local currency unis); and primary educaional aainmen. In ha paper we found lile evidence ha any of hese variables were robusly correlaed wih changes in a paricular measure of inequaliy, he firs quinile share. The resuls for he oher measures of relaive income change considered here will be quie similar. This lis of variables is clearly no an exhausive lis of he poenial deerminans of growh in average incomes or changes in relaive incomes. However, i is a useful saring poin in he search for he correlaes of growh and disribuional change ha maer for povery reducion. I begin by esimaing a number of very parsimonious regressions for each of he dependen variables of ineres. I regress growh in average incomes on he log-level of iniial period income (o pick up convergence effecs) plus each of he conrol variables described above, one a a ime. I do he same for he change in he Gini coefficien, insead including he iniial level of he Gini coefficien o pick up convergence in his variable. For he disribuion componen of he change in he headcoun, I simply esimae univariae regressions on each of he righ-hand-side variables. 13 Table 4 repors he resuls, wih each enry corresponding o a differen regression. The rows correspond o each of he indicaed righ-hand-side variables. 13 Ravallion (2001) documens he empirical imporance of inequaliy convergence using he Gini coefficien. I have experimened wih alernaive iniial inequaliy measures in he regressions involving he disribuional change componens of he various povery measures, bu I find ha none are robusly significan. 22

24 The columns correspond o he differen dependen variables and differen samples. For he regressions including eiher iniial log income or he iniial Gini, I do no repor he coefficiens on hese variables o save space, bu hey generally ener negaively and usually significanly in all specificiaions, consisen wih available evidence on convergence in boh of hese variables. Remember also ha he disribuion componen of he change in he headcoun is oriened such ha a reducion corresponds o a reducion in povery. A firs glance a Table 4 shows ha very few of he explanaory variables of ineres are significanly correlaed wih he dependen variable of ineres a convenional significance levels. In fac, in he 54 regressions in hese wo ables, here are only wo coefficiens ha are significan a he 5 percen level, and only wo ohers a he 10 percen level. One possible explanaion for he lack of significan resuls is ha he measures of growh and disribuional change on he righ-hand-side are conaminaed by subsanial measuremen error. I is difficul o judge however by how much sandard errors should be adjused o reflec his measuremen error. 14 Raher han ry o judge he saisical significance of he parial correlaions documened in Table 4, I simply describe some of he qualiaive paerns ha emerge. Consider firs insiuional qualiy, as proxied by he rule of law indicaor. This ends o be posiively correlaed wih growh, bu also posiively correlaed he measures of disribuional change, suggesing ha disribuional change ends o raise povery in counries wih good insiuional qualiy. The voice and accounabiliy measure follows he same paern, alhough less srongly so, likely because i is quie highly correlaed wih rule of law in his sample. Openess o inernaional rade, is posiively correlaed wih growh, bu negaively correlaed wih he Gini coefficien, indicaing ha disribuional change ends o be povery-increasing in counries ha rade more. Inflaion and financial developmen end o be exremely weakly correlaed wih boh growh and disribuional change in his sample, and wih differing signs across specificaions. Governmen consumpion is 14 There is an addiional facor which likely biases sandard errors upward in he sample of all spells. For counries wih muliple spells of growh or disribuional change, here is likely o be by consrucion a negaive correlaion beween he errors of successive spells. Correcing for his will likely reduce sandard errors somewha. 23

25 negaively correlaed wih growh, bu ineresingly is also associaed wih reducions in inequaliy in hree of he four specificaions. Relaive produciviy in agriculure is essenially uncorrelaed wih growh, bu ends o be posiively correlaed wih disribuional change measures. Somewha surprisingly he sign of he correlaion suggess ha counries wih higher relaive produciviy in agriculure are more likely o experience povery-increasing changes in relaive incomes. Finally, primary educaion is also virually uncorrelaed wih growh, and also is essenially uncorrelaed wih mos of he disribuional change measures, wih he excepion of he Gini in he long spells regression. Somewha surprisingly, he correlaion is posiive, suggesing increases in inequaliy are more likely in counries wih higher educaion. Overall, while mos of he parial correlaions documened in Table 4 are no saisically significan, he qualiaive paern suggess ha here may be some radeoffs. For example, rule of law and rade are posiively correlaed wih growh bu also wih povery-increasing shifs in relaive incomes, while he opposie is rue for governmen consumpion. Table 5 explores hese possible radeoffs in a slighly richer empirical specificaion, using he daase of long spells. The firs column repors a more fullyspecified growh regression wih iniial income, and iniial values of insiuional qualiy, rade openness, and size of governmen as righ-hand-side variables. Despie he likely noise in he daa, i is encouraging ha i is possible o find a plausible specificaion in which some of he deerminans of growh from he growh lieraure are also reasonably significanly correlaed wih growh in he household survey mean. These variables ener wih signs consisen wih he broader growh lieraure. Iniial income eners negaively, picking up convergence effecs, alhough no significanly. Insiuional qualiy and rade are boh significanly posiively correlaed wih growh, and larger governmen size is significanly associaed wih slower growh. I do no wan o claim ha hese resuls are a robus feaure of his paricular daase. However, he resuls are broadly consisen wih he findings of he empirical growh lieraure, which uses per capia GDP growh raes for a much larger sample of counries, and so i seems reasonable o consider his paricular specificaion. 24

26 In he second column of Table 5, I show he same regression, bu insead using he change in he Gini coefficien as he dependen variable. None of he correlaes of growh are significanly correlaed wih changes in his summary saisic of inequaliy. I is however difficul o move from he resuls in hese firs wo columns o conclusions abou he effecs on povery, wihou making paricular assumpions on he shape of income disribuions. Since I have already consruced he growh and disribuion componens of changes in povery, I can simply use hese as dependen variables o invesigae how hese correlaes of growh maer for changes in povery. The remaining wo columns of Table 5 do his for he headcoun index. Given he high correlaion beween he growh componen of povery changes and average income growh documened above, i is no surprising ha he regressions for he growh componens of povery are very similar o he growh regression in he firs column. The signs, however, are swiched, because he sensiiviy of povery o growh is negaive. Insiuional qualiy, rade, and governmen size are all correlaed wih he growh componen of he change in he headcoun in he expeced direcion, alhough he significance is slighly less han before. In conras, only rade appears o be significanly associaed wih increases in povery hrough changes in relaive incomes, a he 10 percen level. The las wo regressions permi quanifying he poenially offseing impacs of hese variables on povery hrough he growh and disribuion channels. Since he observed change in povery is essenially equal o he sum of he growh and disribuion componens (wih a relaively unimporan residual as we have seen), he overall effec on povery of each of hese variables is jus he sum of he wo coefficiens. The esimaes in Table 5 sugges ha he magniude of he growh effecs of hese hree variables is subsanially larger (in absolue value) han he disribuion effecs. For Rule of Law, he growh effec lowers povery, while he disribuion effec raises i, bu he growh effec is an order of magniude larger han he disribuion effec. For rade, he growh effec is povery-reducing while he disribuion effec is povery-increasing, bu again he former dominaes he laer. Finally, he growh and disribuion effecs work in opposie direcions for governmen size, bu wih he adverse growh effec more han wice as large as he povery-reducing disribuion effec. 25

27 Conclusions In his paper I have used sandard decomposiion echniques o idenify hree poenial sources of pro-poor growh: (a) a high rae of growh of average incomes; (b) a high sensiiviy of povery o growh in average incomes; and (c) a povery-reducing paern of growh in relaive incomes. Empirically implemening hese decomposiions for a large sample of changes in povery, we have seen ha only he firs and hird sources of pro-poor growh are empirically relevan. Moreover, especially in he medium- o long run, cross-counry differences in growh in average incomes are he dominan facor explaining changes in povery. Togeher, hese decomposiion resuls indicae ha he search for pro-poor growh should begin by focusing on deerminans of growh in average incomes. A some level, his is an encouraging conclusion, because by now a large body of empirical resuls exiss on he policies and insiuions ha drive growh in average incomes. Neverheless, he empirical resuls shown here on he correlaes of growh and disribuional change are raher unsaisfacory. Mos of he simple correlaions beween hese dependen variables and a number of righ-hand-side variables of ineres are far from significan a convenional levels. I is possible o find mulivariae specificaions for growh in survey means over longer horizons ha yield sensible resuls consisen wih he empirical growh lieraure. A mos, his provides some comfor ha he resuls on parial correlaes of growh in survey mean income documened here are more broadly robus and may even have causal inerpreaions. However, here is much more o be learned abou why per capia GDP growh, whose deerminans are well-documened, ranslaes so imperfecly ino growh in survey means. 15 In conras, in his sample i is difficul o find significan correlaes of eiher changes in summary saisics of inequaliy such as he Gini, or disribuional shifs ha maer for a variey of povery measures of ineres such as he ones I have consruced here. Moreover, some of he parial correlaions wih disribuional change documened here do no appear o be consisen wih hose uncovered in oher papers. The wide range of signs and significance of resuls from he cross-counry lieraure should cauion us agains drawing paricularly srong conclusions abou he deerminans of pro-poor 15 See for example Deaon (2003) for a discussion of some of he relevan issues. 26

28 changes in relaive incomes from any one cross-counry sudy. Counry-specific research using household level daa is likely o shed more ligh on he forces driving relaive income changes ha maer for povery reducion. 27

29 References Barro, Rober J. (2000). Inequaliy and Growh in a Panel of Counries. Journal of Economic Growh. 5:5-32. Caselli, Francesco, Gerardo Esquivel and Fernando Lefor (1996). Reopening he Convergence Debae: A New Look a Cross-Counry Growh Empirics. Journal of Economic Growh 1: Chen, Shaohua and Marin Ravallion (1997). Wha Can New Survey Daa Tell Us abou Recen Changes in Disribuion and Povery? The World Bank Economic Review, 11(2): Deaon, Angus (2003). Measuring Povery in a Growing World, or Measuring Growh in a Poor World. NBER Working Paper No Dollar, David and Aar Kraay (2002). Growh is Good for he Poor. Journal of Economic Growh. 7: Easerly, William (1999). Life During Growh. Journal of Economic Growh, 4: Foser, James and Miguel Székely (2001). Is Economic Growh Good for he Poor? Tracking Low Incomes Using General Means. Ineramerican Developmen Bank Research Deparmen Working Paper No Gallup, John Luke, Seven Radele and Andrew Warner (1998). Economic Growh and he Income of he Poor. Manuscrip, Harvard Insiue for Inernaional Developmen. Kakwani, Nanak (1993). Povery and Economic Growh, Wih Applicaion o Coe d Ivoire. Review of Income and Wealh. 39(2): Kakwani, Nanak (2000). Wha Is Pro-Poor Growh?. Asian Developmen Review. 18(1): Klenow, Peer J. and Andrés Rodríguez-Clare (1997), The Neoclassical Revival in Growh Economics; Has I Gone Too far? in Ben S. Bernanke and Julio Roemberg eds. NBER Macroeconomics Annual Cambridge, MIT Press. Leamer, Edward, Hugo Maul, Sergio Rodriguez, and Peer Scho (1999). Does Naural Resource Abundance Increase Lain American Income Inequaliy?. Journal of Developmen Economics. 59:3-42. Li, Hongyi, Lyn Squire and Heng-fu Zou (1998). Explaining Inernaional and Ineremporal Variaions in Income Inequaliy. The Economic Journal, 108: Lopez, Humbero (2003). Pro Growh, Pro Poor: Is There a Tradeoff. Manuscrip, The World Bank. 28

30 Lundberg, Maias and Lyn Squire (2000). The Simulaneous Evoluion of Growh and Inequaliy. Economic Journal. 113: Milanovic, Branko (2003). Can We Discern he Effec of Globalizaion on Income Disribuion? Evidence from Household Surveys. Manuscrip, The World Bank. Ravallion, Marin (1997). Can High-Inequaliy Developing Counries Escape Absolue Povery?. Economics Leers. 56(1): Ravallion, Marin (2001). Inequaliy Convergence. World Bank Policy Research Deparmen Working Paper No Ravallion, Marin and Shaohua Chen (2003). Measuring Pro-Poor Growh. Economics Leers. 78: Sarabia, J-M, Enrique Casillo, and Daniel Sloje (1999). An Ordered Family of Lorenz Curves. Journal of Economerics. 91: Spilimbergo, Anonio, Juan Luis Londono, and Miguel Szekely (1999). Income Disribuion, Facor Endowmens, and Trade Openness. Journal of Developmen Economics. 59: Suryahadi, Asep, Sudarno Sumaro, and Lan Priche (2003). The Evoluion of Povery During he Crisis in Indonesia. SMERU Research Insiue Working Paper. 29

31 Table 1: Correlaions of Povery Measures and Survey Mean Income or Consumpion Correlaions wih Survey Mean Levels Growh Raes All Spells (110 Observaions) Headcoun Povery Gap Squared Povery Gap Was Long Spells (41 Observaions) Headcoun Povery Gap Squared Povery Gap Was

32 Table 2: Decomposing Changes in Povery: All Spells Growh, Disribuion and Residual Componens of Change in Povery: dp = G + D + R Growh and Disribuion Componens vs Residual (G+D vs R) V(G+D) V(R) COV(G+D,R) Share of Variance Due o G+D Headcoun Povery Gap Squared Povery Gap Was Growh vs Disribuion Componens (G vs D) V(G) V(D) COV(G,D) Share of Variance Due o G Headcoun Povery Gap Squared Povery Gap Was Average Growh and Sensiiviy o Average Growh in Growh Componen: ln G = ln dlnµ + ln η V( dlnµ ) V( η ) COV( dlnµ, η ) Share of Variance Due o dlnµ Headcoun Povery Gap Squared Povery Gap Was

33 Table 3: Decomposing Changes in Povery: Long Spells Growh, Disribuion and Residual Componens of Change in Povery: dp = G + D + R Growh and Disribuion Componens vs Residual (G+D vs R) V(G+D) V(R) COV(G+D,R) Share of Variance Due o G+D Headcoun Povery Gap Squared Povery Gap Was Growh vs Disribuion Componens (G vs D) V(G) V(D) COV(G,D) Share of Variance Due o G Headcoun Povery Gap Squared Povery Gap Was Average Growh and Sensiiviy o Average Growh in Growh Componen: ln G = ln dlnµ + ln η V( dlnµ ) V( η ) COV( dlnµ, η ) Share of Variance Due o dlnµ Headcoun Povery Gap Squared Povery Gap Was

34 Table 4: Correlaes of Pro-Poor Growh RHS Variable is: All Spells Dependen Variable Is: Percen Change in Growh Gini Long Spells Dependen Variable Is: Disribuion Percen Componen Change in of Headcoun # Obs Growh Gini Disribuion Componen of Headcoun # Obs CPIA (1.23) (0.07) (0.68) (0.48) (0.21) (0.04) KK Rule of Law (1.76)* (0.06) (0.83) (1.73)* (1.06) (2.00)** Trade/GDP (1.21) (1.55) (0.20) (1.68) (0.18) (0.28) ln(1+inflaion) (0.09) (0.12) (0.38) (0.06) (0.07) (0.61) Governmen Consumpion/GDP (1.04) (0.02) (0.46) (0.72) (0.28) (1.16) M2/GDP (0.64) (0.40) (0.23) (0.63) (0.44) (0.71) KK Voice and Accounabiliy (0.88) (0.75) (0.55) (1.68) (1.51) (1.56) Relaive Produciviy in Agriculure (0.33) (1.24) (1.21) (0.53) (1.38) (1.52) Average Years of Primary Educaion (1.42) (1.01) (0.10) (0.02) (3.08)*** (1.00) Noe: -saisics repored below coefficien esimaes. * (**) (***) denoe significance a he 1 (5) (10) percen levels. 33

35 Table 5: Mulivariae Growh and Disribuional Change Regressions Annual Percen Change in: Annual Percen Change in Headcoun Survey Mean Gini Growh Disribuion Componen Componen Iniial Income (1.36) (1.29) (1.66) (1.17) KK Rule of Law (1.98)* (0.66) (1.55) (0.31) Trade/GDP (2.08)** (0.95) (2.23)** (1.89)* Governmen Consumpion (2.23)** (0.40) (2.10)** (1.06) R-Squared # Observaions Noe: Heeroskedasiciy-consisen -saisics repored below coefficien esimaes. 34

36 Figure 1: Relaive Growh Incidence Curves Growh Rae of Percenile p Relaive o Average Indonesia China Percenile of Income Disribuion, p 35

37 Figure 2: Sensiiviy of Povery o Growh in Percenile p 0 Percenile of Income Disribuion, p Sensiiviy of Povery Measure o Growh in Percenile p P(1) Was P(2) -6 P(0) 36

38 Figure 3: Growh and Povery Reducion (Long Spells, Headcoun) 0.2 ETH PER Average Annual Growh in Headcoun YEM CIV y = -1.15x R = 0.54 COL PRY BDI RUS BGD VEN ZMB GHA MDG NGA LSO IND MAR BWA EGY LKA SLV CRI TUN MYS PAN ECU MRT CHN HND THA M EX UGA GTM KEN IDN BRA PHL PAK GM B AZE Average Annual Growh in Survey Mean VNM

39 Figure 4: Decomposing Changes in he Headcoun (Long Spells) Sum of Growh and Disribuion Componens Growh and Disribuion Componens vs. Residual ETH9500 PER YEM9298 COL8898 BDI9298 VEN8198 ZMB9198 RUS9398 MDG8099 NGA8597 GHA8799 BGD8400 CIV UGA8996 TUN8590 MRT8895 SLV8998 MAR8599 IND8397 ECU8895 PAN9196 MYS8497 CRI8696 EGY9199 LKA8595 BWA8593 LSO PRY IDN8700 BRA8598 MEX8998 GTM8700 THA8800 HND8998 CHN9098 AZE9501 PAK8798 KEN GMB9298 PHL8500 VNM Average Annual Growh in Headcoun y = 0.96x R 2 = 0.91 Growh Componen Growh Componen vs. Disribuion Componen CIV8595 YEM9298 ETH9500 PER8594 VEN8198 KEN9297 MDG8099 RUS9398 BDI9298 COL8898 ZMB9198 UGA8996 PAN9196 NGA8597 TUN8590 MYS8497 EGY IND8397BGD8400 ECU8895 MRT8895 LKA8595 SLV8998 MAR8599 GHA BRA8598 IDN8700 HND8998 MEX AZE9501 THA8800 LSO8695 CRI8696 GTM8700 CHN9098 BWA8593 PAK GMB9298 PHL8500 PRY9098 y = 0.97x VNM R 2 = Sum of Growh and Disribuion Componens Growh in Mean vs. Sensiiviy of Povery o Growh 0.15 GMB PRY9098 GTM8700 VNM9398PHL8500 LSO8695 HND8998 CHN9098 BWA8593 PAK8798 CRI MEX8998 THA8800 AZE9501 BRA8598 MRT8895 SLV8998 IDN8700 ECU8895 TUN8590 UGA8996 MYS8497 PAN9196 LKA8595 MAR8599 GHA8799 IND8397 0EGY9199 NGA8597 BGD8400 ZMB9198 MDG8099 COL8898 BDI9298 RUS9398 KEN VEN CIV8595 PER8594 y = -0.52x R 2 = YEM9298 Growh in Survey Mean Growh Componen ETH

40 Figure 5: Relaive Income Growh Raes, Long and Shor Spells (Average and Sandard Deviaion Across Spells for Indicaed Perceniles) 10% 8% 6% Average, Long Spells SdDev, Long Spells Average, All Spells SdDev, All Spells 4% 2% 0% % Percenile of Iniial Income Disribuion 39

41 Appendix 1: Sample of Spells Table A1.1 liss he sample of spells used in he variance decomposiions in Tables 2 and 3. Table A1.2 liss he observaions excluded from he sample due o exreme values of growh in he survey mean or growh in he headcoun measure of povery. My assumpion is ha hese exreme observaions have a higher noise-osignal raio han he res of he daase. However, i should be noed ha some of he excluded observaions in Table A1.2 likely reflec acual changes in living sandards, and he convenien shorcu of simply eliminaing exreme observaions will end up discarding boh legiimae as well as problemaic daa poins. Alhough he main conclusions of his paper are no sensiive o he exclusion of hese daapoins, hey do maer for he precise magniudes of he resuls. To illusrae his Table A1.3 repors he variance decomposiions for he headcoun measure, for he unresriced sample and for he sample used in he main body of he paper dropping exreme observaions. In he sample of all spells, he main consequence of dropping ouliers is o slighly lower he share of he variance of changes in povery due o he growh componen, from 81 percen o 70 percen. In he sample of long spells, dropping jus wo ouliers (for Zimbabwe and Mali) raises he share of he variance of changes in povery due o growh from 86 percen o 97 percen. In his sample he share of he variance in he growh componen due o growh in he survey mean also falls slighly from 93 percen o 89 percen. 40

42 Table A1.1 Sample of Spells All Long All Long All Long Azerbaijan Ghana Niger Burundi Gambia Nigeria Burkina Faso Guaemala Bangladesh Pakisan Honduras Panama Brazil Indonesia Peru Philippines India Paraguay Boswana Chile Russian Fed China Senegal El Salvador Jamaica Thailand Kenya Coe d'ivoire Sri Lanka Trinidad & Tob Tunisia Colombia Lesoho Turkey Madagascar Uganda Cosa Rica Mexico Venezuela Mauriania Dominican Rep Malaysia Ecuador Vienam Egyp Yemen Esonia Zambia Ehiopia

43 Table A1.2 Discarded Spells Average Annual Growh in: Survey Mean Headcoun All Spells Armenia Brazil Chile Coe d'ivoire Coe d'ivoire Colombia Ecuador Ghana Ghana Ghana Ghana Honduras Honduras Indonesia Jamaica Kyrgyz Republic Lesoho Lihuania Mexico Mali Mongolia Pakisan Philippines Tanzania Venezuela Venezuela Souh Africa Zambia Zimbabwe Long Spells Mali Zimbabwe

44 Table A1.3 Consequences of Discarding Spells for Variance Decomposiions Share of Variance of dlnp due o G+D Share of Variance of G+D Due o G Share of Variance of ln G due o dlnm Number of Observaions All Spells Full Sample Resriced Sample Long Spells Full Sample Resriced Sample

45 Appendix 2: Qualiy of Parameric Approximaion o Lorenz Curve This appendix discusses he qualiy of he parameric approximaion o he Lorenz curve used in he paper, and he consequences for he resuls, using record-level household survey daa from Ghana as an illusraion. I is imporan o noe a he ouse ha using parameric Lorenz curves fied o grouped daa is unavoidable in a large cross-counry exercise such as his one. This is because i is difficul if no impossible o obain access o record-level household survey daa for a large se of counries. 16 Neverheless, i is useful o invesigae he exen o which errors inroduced by lowdimensional paramerizaions fo he income disribuion may influence he resuls presened here. There is a large lieraure on esimaing Lorenz curves, and checking he qualiy of various parameric approximaions o empirical Lorenz cuves. The Sarabia e. al. (1999) paper is ypical of his lieraure in ha i finds ha one- o hree-parameer Lorenz curves fi acual disribuions quie well on average, alhough he qualiy of he approximaion is generally worse a he upper and lower ends of he income disribuion. There is less sysemaic evidence on he consequences of hese approximaions for povery measuremen. Since povery measures depend on he quanile funcion, he key issue is he exen o which firs derivaive of he Lorenz curve is well approximaed, raher han he Lorenz curve iself. Ravallion e. al. (1991) use record-level daa from Indonesia in 1984 o documen ha povery esimaes based on hree-parameer Lorenz curves fied o grouped daa provide fairly good approximaions o he headcoun and povery gap for ha counry and year, and ha he qualiy of he approximaion varies lile wih he number of groups. Here I use daa from he Ghana 1998/99 Living Sandards Measuremen Survey o perform a similar exercise. I exrac from his survey he household-level consumpion aggregae, household size, and he sampling weighs, for he 5998 households covered by he survey. To capure inra-household scale economies I consruc per capia consumpion as household consumpion divided by he square roo of household size. I hen apply he sampling weighs o each per capia consumpion observaion o arrive a 16 The larges cross-counry daase on povery and inequaliy is he Global Povery Monioring daase mainained by he World Bank. The compilers of his daase have obained access o record-level daa for only abou half of he surveys covered. 44

46 he disribuion of consumpion across individuals. To assess he qualiy of parameric approximaions o he Lorenz curve based on a small number of observaions on grouped daa, I exrac jus he decile shares from he rue Lorenz curve, and hen fi he parameric Lorenz curve o hese nine daa poins as described in he ex. The op-lef panel of Figure A2 repors he acual and esimaed Lorenz curves obained in his way, and he op-righ panel plos he difference beween he acual and esimaed Lorenz curves. These figures are consisen wih exising evidence: he parameric Lorenz curve races he acual one quie well. The discrepancy beween he esimaed and acual Lorenz curve is less han one-half of one percen over mos of he range, wih a maximum error of one percen near he upper end of he disribuion. The mean absolue error is 0.3 percen, which is comparable o he errors repored in Sarabia e. al. (1999) for Sweden, Brazil, and he Unied Saes. The boom panels of Figure A2 show repor he logarihm of he acual and esimaed quanile funcions, and he difference beween he wo. The quanile funcion based on he parameric Lorenz curve racks he acual quanile funcion quie well around he middle of he income disribuion, bu here are subsanial discrepancies a he upper and lower ails of he disribuion. The gap beween esimaed and acual consumpion is less han wo percen for he middle hree quiniles of he disribuion, bu he parameric quanile funcion subsanially underesimaes (overesimaes) consumpion in he boom (op) quinile. I is no hard o see his paern is no specific o he case of Ghana: he parameric quanile funcion goes o zero (infiniy) as he populaion share goes o zero (one), while acual consumpion is never zero or infinie. As a resul, his parameric approximaion will always end o undersae consumpion a he boom end of he disribuion, and oversae i a he upper end. This paern of approximaion errors in he quanile funcion has sraighforward implicaions for povery esimaes. The op wo panels of Table A2 repor he four povery indices considered in his paper, for wo povery lines, based on he acual daa and on he esimaed quanile funcion. In he op panel, he povery line is se a he mean, resuling in a povery headcoun 59.7 percen. For his high povery line, all four povery measures are quie well approximaed using he esimaed quanile funcion: he difference beween he acual and esimaed povery indices varies beween 0.4 percen 45

47 and 4.1 percen. However, when he povery line is se a half he mean, in he middle panel of Table A2, he approximaion errors are signficanly larger, wih he esimaed povery measures consisenly subsanially larger han he acual ones. This is no surprising, since wih a lower povery line a greaer proporion of poor individuals have heir consumpion undersaed by he parameric quanile funcion. For he same reason, in boh panels he povery esimaes based on he parameric quanile funcion oversae povery more he more boom-sensiive is he povery index. A furher ineresing observaion is ha he povery measures based on esimaed Lorenz curves underesimae he sensiiviy of povery o growh. This can be seen in he boom panel, which repors he log change beween he firs and second panels of he esimaed and acual povery measures. Since shifing he povery line down is equivalen o shifing he mean of he disribuion up, his can be inerpreed as he proporionae change in povery ha would occur if incomes doubled, holding consan he Lorenz curve. The hird colum shows ha he esimaed povery measures fall less han he acual ones (excep for he headcoun), and ha his discrepancy is larger for increasingly boom-sensiive measures. To see why, recall from he main ex of he paper ha he sensiiviy of povery o growh in average incomes is P ( θ 1) θ 1. Since P(θ) based on he parameric approximaion is biased down by P ( θ) more han P(θ-1), he sensiiviy of povery o growh will also be biased down (in absolue value). 46

48 Figure A2: Acual and Parameerized Lorenz Curves for Ghana 1998/99 Lorenz Curve Acual Parameerized Acual-Parameerized Logarihm of Quanile Funcion Acual Paramerized 0.3 Acual-Parameerized

49 Table A2: Acual and Esimaed Povery Measures for Ghana 1998/99 Acual Esimaed (Acual- Esimaed)/Acual Povery Line = 100% of Mean Headcoun Povery Gap Squared Povery Gap Was Index Povery Line = 50% of Mean Headcoun Povery Gap Squared Povery Gap Was Index Log Change in Povery/Log Change in Mean Headcoun Povery Gap Squared Povery Gap Was Index