When Is Growth ProPoor? Evidence from a Panel of Countries


 Gregory Garrison
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1 Forhcoming, Journal of Developmen Economics When Is Growh ProPoor? Evidence from a Panel of Counries Aar Kraay The World Bank Firs Draf: December 2003 Revised: December 2004 Absrac: Growh is propoor if he povery measure of ineres falls. According o his definiion here are hree poenial sources of propoor growh: (a) a high growh rae of average incomes; (b) a high sensiiviy of povery o growh in average incomes; and (c) a poveryreducing 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 longrun, mos of he variaion in changes in povery can be aribued o growh in average incomes, suggesing ha policies and insiuions ha promoe broadbased growh should be cenral o he propoor 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. Crosscounry 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, This paper has been prepared in he conex of he propoor growh program sponsored by he World Bank s PREMPovery group. I am graeful o Louise Cord, Robera Gai, Francisco Ferreira, Tamar ManuelyanAinc, 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 propoor 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 propoor growh means, le alone wha is deerminans are. According o one view, growh is propoor 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 propoor because he poor gained relaively less han he nonpoor. A broader and more inuiive definiion is ha growh is propoor 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 propoor growh: (a) a high growh rae of average incomes; (b) a high sensiiviy of povery o growh in average incomes; and (c) a poveryreducing 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 propoor growh. Finally, I invesigae he correlaes of he sources of propoor 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 propoor 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 boomsensiive 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 crosscounry correlaes of growh in household survey incomes is no especially compelling, given various limiaions of he daase. However, I find almos no evidence ha poveryreducing 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 propoor growh sraegies. Moreover, he absence of compelling crosscounry 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 crosscounry evidence is unlikely o be very informaive abou he policies and insiuions ha are likely o lead o poveryreducing paerns of growh in relaive incomes. This suggess ha more microlevel and casesudy research may be useful in shedding ligh on he deerminans of poveryreducing 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 oneforone. 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 nonlinear 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 oneoone mapping beween he Gini coefficien and he Lorenz curve. In his paper I use a more flexible hreeparameer approximaion o he Lorenz curve, raher han he oneparameer 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 propoor 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 FoserGreerThorbecke 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, rewrie 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 propoor 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 propoor 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 propoor growh: changes in relaive incomes. This hird source of propoor 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 propoor growh. The Kakwani and Pernia (2000) definiion of propoor growh saes ha growh is propoor 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 propoor growh suggesed by Ravallion and Chen (2003) is ha growh is propoor if he povery measure of ineres falls. According o his definiion, here are hree poenial sources of propoor growh: (a) rapid growh in average incomes; (b) a high sensiiviy of povery o growh in average incomes; and (c) a poveryreducing 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 propoor 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 dollaraday 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 aboveaverage 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 poveryreducing. 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, belowaverage growh was recorded only for he riches 20 percen of he populaion. Despie his propoor 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 FoserGreerThorbecke 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 nearpoor 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 propoor depends crucially on he povery measure of ineres. In paricular, if he objecive of propoor growh is o reduce he headcoun measure of povery, hen a propoor growh sraegy should focus exclusively on raising he incomes of hose jus a he povery line, and should ignore everyone else. This srong  and wellundersood 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 nonfood 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 nonzero 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 Ushaped. 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 nonmonoonic 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 propoor 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 propoor growh. For he FoserGreerThorbecke 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 crosscounry 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 crosscounry 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 propoor 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://www.worldbank.org/research/povmonior. 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 dollaraday 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 RavallionChen 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 recordlevel 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 boomsensiive 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 loglevels 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 widelyundersood 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 propoor growh discussed above, and heir correlaes. The Relaive Imporance of Sources of ProPoor 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 righhad 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 discreeime 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 noninfiniesmal inerval. Empirically however hese residuals will urn ou o be unimporan on average. I measure he proporional changes on he lef and righhand 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 propoor 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 boomsensiive 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 crosscounry differences in he growh componen of changes in povery are 16
18 overwhelmingly accouned for by crosscounry 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 boomsensiive, 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 boomsensiive. This finding should no be inerpreed as evidence ha he poores perceniles of he income disribuion are more likely o experience slowerhanaverage growh. Raher, i primarily reflecs he fac ha more boomsensiive 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 crosscounry 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 crosscounry 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 boomsensiive is he povery measure. In oher words, even for a purely disribuionneural growh process, growh will appear o be less propoor (in he sense ha he proporionae change in povery is smaller) he more boomsensiive 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 boomsensiive 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 boomsensiive are he povery measures. This in urn accouns for a smaller share of he variance of changes in povery due o growh for more boomsensiive 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 iniialperiod 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 boomsensiive 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 crosscounry variaion in he longrun 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 wihincounry 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 wihincounry variaion. Since we have already seen ha crosscounry 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 welldocumened fac ha growh ends o be disribuionneural 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 wihincounry 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
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