Why Don t We See Poverty Convergence?

Transcription

1 Ref: Amercan Economc Revew, forthcomng Why Don t We See Poverty Convergence? Martn Ravallon 1 Development Research Group, World Bank 1818 H Street NW, Washngton DC, 20433, USA mravallon@worldbank.org Abstract: Average lvng standards are convergng amongst developng countres and faster growng economes see more progress aganst poverty. Yet we do not fnd poverty convergence; countres startng wh hgher poverty rates do not see hgher proportonate rates of poverty reducton. The paper tres to explan why. A new data set reveals an adverse effect on consumpton growth of hgh nal poverty at a gven nal mean. A hgh poverty rate also makes economc growth less effectve n reducng poverty. For many poor countres, the growth advantage of startng out wh a low mean s lost due to a hgh ncdence of poverty. Keywords: Poverty trap, mddle class, nequaly, economc growth JEL: D31, I32, O15 1 The author s grateful to Shaohua Chen and Prem Sangraula for help n settng up the data set used here. Helpful comments were receved from Sebastan Galan, Karla Hoff, Aart Kraay, Kalle Moene, Lus Servén, Domnque van de Walle, partcpants at presentatons at the World Bank, the Courant Research Center, Göttngen, the 2009 meetng n Buenos Ares of the Network on Inequaly and Poverty, Cornell Unversy, the Center for Global Development, the Unversy of Calforna Berkeley, the Unversy of Oslo, and the Revew s edor and anonymous referees. These are the vews of the author and should not be attrbuted to the World Bank or any afflated organzaton.

2 1. Introducton Two promnent stylzed facts about economc development are that there s an advantage of backwardness, such that on comparng two otherwse smlar countres the one wh the lower nal mean ncome wll tend to see the hgher rate of economc growth, and that there s an advantage of growth, whereby a hgher mean ncome tends to come wh a lower ncdence of absolute poverty. Past emprcal support for both stylzed facts has almost nvarably assumed that the dynamc processes for growth and poverty reducton do not depend drectly on the nal level of poverty. Under that assumpton, the two stylzed facts mply that we should see poverty convergence: countres startng out wh a hgh ncdence of absolute poverty should enjoy a hgher subsequent growth rate n mean consumpton and (hence) a hgher proportonate rate of poverty reducton. That poses a puzzle. The data on poverty measures over tme for about 90 developng countres assembled for ths paper reveal ltle or no sgn of poverty convergence. For example, Fgure 1 plots the proportonate rate of change n poverty specfcally the annualzed log dfference between household surveys n the percentage of each country s populaton lvng below $2 a day at 2005 purchasng power pary aganst s nal level. (The data are descrbed later.) There s no sgn of convergence; the regresson lne has a slope of (wh a robust standard that s about twce that fgure). The overall poverty rate of the developng world has been fallng snce at least 1980 (Chen and Ravallon, 2010), but the proportonate rate of declne has been no hgher n s poorest countres. Clearly somethng mportant s mssng from the story. Intuvely, one hypothess s that eher the growth rate n the mean, or the mpact of growth on poverty, depends drectly on the nal poverty rate, n a way that nullfes the advantage of backwardness. To test ths hypothess, the paper estmates a model n whch the proportonate rate of progress aganst poverty depends on the rate of growth n mean consumpton and the poverty rate, whle the rate of growth n the mean depends n turn on the nal poverty rate as well as the nal mean. The results suggest that mean-convergence s counteracted by two dstnct poverty effects. Frst, there s an adverse drect effect of hgh nal poverty on growth workng aganst convergence n mean consumpton. Second, hgh nal poverty dulls the mpact of growth on poverty. On balance there s ltle or no systematc effect of startng out poor on the proportonate rate of poverty reducton. 2

3 In the process of documentng these fndngs the paper also explores the role played by other aspects of the nal dstrbuton dscussed n the lerature, ncludng nequaly. These are found to play no more than a subsdary role. For example, hgh nal nequaly only matters to growth and poverty reducton n so far as entals a hgh nal ncdence of poverty relatve to the mean. And the paper confrms that countres startng out wh a small mddle class judged by developng country rather than Western standards face a handcap n promotng growth and poverty reducton, but ths too s largely accountable to dfferences n the ncdence of poverty. After revewng the lerature n the next secton, the data are descrbed n secton 3 whle secton 4 tests for convergence n both the mean and the poverty rate. The man results, ncludng varous tests of ther robustness, are then presented n sectons 5 (on how poverty affects growth) and 6 (on how affects the elastcy of poverty to growth). Secton 7 brngs these elements together to calbrate a decomposon of the speed of convergence n poverty, whch answers the queston n the paper s tle. 2. Past theores and evdence A number of papers have demonstrated that an economy s growth path can depend on parameters of the nal dstrbuton of ncome. The parameter that has receved most attenton s nequaly. One way that hgh nequaly can reduce an economy s aggregate output s when borrowng constrants stemmng from cred market falures leave unexploed opportunes for nvestment n physcal and human capal (Galor and Zera, 1993, Bénabou, 1996; Aghon and Bolton, 1997). 2 Wh dmnshng margnal products of capal, mean future wealth wll be a quas-concave functon of the dstrbuton of current wealth. Thus hgher current nequaly mples lower future mean wealth at a gven current mean wealth. A smlar result can be obtaned when hgh nequaly prompts dstortonary polcy responses (as n Alesna amd Rodrk, 1994) or restrcts effcency-enhancng cooperaton, such that key publc goods are underprovded or effcency-enhancng reforms are blocked (as n the models revewed n Bardhan et al., 2000). Motvated by these theoretcal arguments, a subset of the (large) emprcal lerature on the determnants of economc growth has ncluded explc measures of nequaly as regressors for growth, although nferences are clouded by the fact that the regressons often also nclude 2 Also see the dscussons n Perott (1996), Hoff (1996), Aghon et al. (1999), Bardhan et al. (2000), Banerjee and Duflo (2003), Azarads (2006) and World Bank (2006, Chapter 5). 3

4 varables that are mplcly functons of nequaly, such as human development attanments, aggregate nvestment shares and measures of fnancal-sector development. 3 A number of emprcal papers have reported adverse effects of nequaly on growth. 4 The precse measure that has receved most attenton n the emprcal lerature s ncome or consumpton nequaly, as typcally measured by the Gn ndex. 5 Another strand of the lerature has argued that the sze of a country s mddle class matters to economc growth, by fosterng entrepreneurshp, or shftng the composon of consumer demand, or makng more polcally feasble to attan polcy reforms and nstutonal changes conducng to growth. 6 Whle ths lerature has focused on nequaly or the mddle class, arguments can also be made suggestng that poverty may well be the more relevant parameter of the nal dstrbuton. In a model of growth wh borrowng constrants (based on Banerjee and Duflo, 2003), Ravallon (2009) shows that hgher current poverty ncdence defned by any poverty lne up to the mnmum level of nal wealth needed to not be lqudy constraned n nvestment choces yelds lower growth at a gven level of mean current wealth. Another way ths can happen s llustrated by Lopez and Servén (2009) who ntroduce a subsstence consumpton requrement nto the utly functon n the model of Aghon et al. (1999) and show that hgher poverty ncdence (falure to meet the subsstence requrement) mples lower growth. 3 Basc schoolng and health attanments (often sgnfcant n growth regressons) are one of the potental channels lnkng nal dstrbuton to growth, as n Galor and Zera (1993). Smlarly, whle the share of nvestment n GDP has often been used as a predctor of growth rates (Levne and Renelt, 1992), ths s one of the channels dentfed n the theoretcal lerature lnkng nequaly to growth. The same argument can be made about prvate cred (as a share of GDP) as a measure of fnancal sector development (Beck et al., 2007); growth theores based on borrowng constrants suggest that the aggregate flow of cred depends on the nal dstrbuton. 4 Support for the vew that hgher nal nequaly mpedes growth has been reported by Alesna and Rodrk (1994), Persson and Tabelln (1994), Brdsall et al., (1995), Clarke (1995), Perott (1996), Dennger and Squre (1998), Ravallon (1998), Knowles (2005) and Vochovsky (2005) (amongst others). Not all the evdence has been supportve; also see L and Zou (1999), Barro (2000) and Forbes (2000). The man reason why the latter studes have been less supportve appears to be that they have allowed for addve country-level fxed effects n growth rates; I wll return to ths pont. 5 Wealth nequaly s arguably more relevant though ths has rarely been used due to data lmatons. An excepton s Ravallon (1998), who studes the effect of geographc dfferences n the dstrbuton of wealth on growth n Chna and fnds evdence that hgh wealth-nequaly mpedes growth. 6 Analyses of the role of the mddle class n promotng entrepreneurshp and growth nclude Acemoglu and Zlbott (1997) and Doepke and Zlbott (2005). Mddle-class demand for hgher qualy goods plays a role n the model of Murphy et al. (1989). Brdsall et al. (2000) conjecture that support from the mddle class s crucal to reform. Srdharan (2004) descrbes the role of the Indan mddle class n promotng reform. Easterly (2001) fnds evdence that a larger ncome share controlled by the mddle three quntles promotes economc growth. 4

5 Ths s also suggested by models of poverty traps based on mpatence for consumpton hgh tme preference rates assocated wh low lfe expectancy leadng to low savngs and nvestment rates by the poor. 7 Here too, whle the theoretcal lerature has focused on nal nequaly, can also be argued that a hgher nal ncdence of poverty mples a hgher proporton of mpatent consumers and hence lower growth. Yet another example s found n how work productvy s affected by past nutronal and health status. Only when past nutronal ntakes have been hgh enough (above basal metabolc rate) wll be possble to do any work, but dmnshng returns wll set n later; see the model n Dasgupta and Ray (1986). Followng Cunha and Heckman (2007), ths type of argument can be broadened to nclude other aspects of chld development that have lastng mpacts on learnng ably and earnngs as an adult. By mplcaton, havng a larger share of the populaton who grew up n poverty wll have a lastng negatve mpact on an economy s aggregate output. These arguments pont to the mportance of poverty as a constrant on growth, whch s our frst clue as to why we do not fnd poverty convergence. However, whle all these arguments suggest that the growth rate may depend on parameters of the nal dstrbuton, s unclear whether nequaly, poverty or the sze of the mddle class s the most relevant parameter. The fact that very few encompassng tests are found n the lerature, 8 and that these dfferent measures of dstrbuton are clearly not ndependent, leaves one n doubt about what aspect of dstrbuton really matters. For example, when the nal value of mean ncome s ncluded n a growth regresson alongsde nal nequaly, but nal poverty s an excluded but relevant varable, the nequaly measure may pck up the effect of poverty rather than nequaly per se. A second clue to the puzzle of why we do not see poverty convergence can be found n the lerature on the effects of growth on poverty n developng countres. The consensus n that lerature s that hgher growth rates tend to yeld more rapd rates of absolute poverty reducton. 9 There s also evdence that nequaly matters to how much mpact a gven growth rate n the 7 See, for example, Azarads (2006), though Kraay and Raddatz (2007) argue that poverty traps arsng from low savngs (hgh tme preference rates) n poor countres are hard to reconcle wh the data. 8 By an encompassng test I mean that a nested test of the competng hypotheses s employed. In ths nstance, the encompassng test entals puttng all the parameters of the nal dstrbuton n the growth regresson. 9 See World Bank (1990, 2000), Ravallon (1995, 2001, 2007), Felds (2001) and Kraay (2006). Also see the revew of the arguments and evdence on ths pont n Ferrera and Ravallon (2009). (Relatve poverty measures are less responsve to growth snce the poverty lnes rses wh the mean.) 5

6 mean has on poverty. 10 Intuvely, n hgh nequaly countres the poor wll tend to have a lower share of the gans from growth n the mean. Ravallon (1997, 2007) examnes ths ssue emprcally usng household surveys for multple countres over tme and fnds evdence of a strong nteracton effect between nal nequaly and the growth rate n the mean when explanng the proportonate rate of poverty reducton. In the most parsmonous specfcaton, whch also fs the data for developng countres well, the expected value of the log dfference n the poverty rate over tme s drectly proportonal to the dstrbuton-corrected growth rate, gven by the ordnary growth rate n the mean tmes one mnus an ndex of nequaly. Easterly (2009) conjectures that the nal poverty rate s lkely to be a better predctor of the elastcy than the nal level of nequaly, though no evdence s provded. The rest of the paper presents new evdence consstent wh both clues from the lerature. 3. Data and descrptve statstcs In keepng wh the bulk of the lerature, the country s the un of observaton. 11 However, unlke past data sets n the lerature on growth emprcs, ths one s frmly anchored to the household surveys, n keepng wh the focus on the role played by poverty and nequaly, whch s measured from surveys. By calculatng the poverty and nequaly statstcs drectly from the prmary data, at least some of the comparably problems found n exstng data complatons from secondary sources can be elmnated. However, there s no choce but to use household consumpton or ncome, rather than the theoretcally preferable concept of wealth. I found 99 developng and transon countres wh at least two suable household surveys snce about (For about 70 of these countres there are three or more surveys.) Vrtually all of the surveys are natonally representatve. 12 For the bulk of the analyss I restrct the sample to the 92 countres n whch the earlest avalable survey fnds that at least some households lved below the average poverty lne for developng countres (descrbed below). 13 Ths happens mechancally gven that log transformatons are used. However, also has the defensble effect of droppng a number of the countres of Eastern Europe and Central Asa 10 See Ravallon (1997, 2007); World Bank (2000, 2006); Bourgugnon (2003) and Lopez and Servén (2006). 11 It s known that aggregaton can hde the true relatonshps between the nal dstrbuton and growth, gven the nonlneares nvolved at the mcro level (Ravallon, 1998); dentfyng the deeper structural relatonshps would requre mcro data, and even then the dentfcaton problems can be formdable. 12 The only excepton was that urban surveys were also used (for both the frst and last survey) for Uruguay where over 90% of the populaton lves n urban areas. Results were robust to droppng these urban surveys. 13 The data set was constructed from PovcalNet n December

7 (EECA) (ncludng the former Sovet Unon); ndeed, all of the countres wh an nal poverty rate (by developng country standards) of zero are n EECA. As s well known, these countres started ther transons from socalst command economes to market economes wh very low poverty rates, but poverty measures then rose sharply n the transon. 14 The earlest avalable surveys pck up these low poverty rates, wh a number of countres havng no sampled household lvng below the poverty lnes typcal of developng countres. Wh the subsequent rse n poverty ncdence, ths looks lke convergence, but has ltle or nothng to do wh neoclasscal growth processes rather s a polcy convergence effect assocated wh the transon. The experence of these countres s clearly not typcal of the developng world. The longest avalable spell between two surveys s used for each country. Both surveys use the same welfare ndcator, eher consumpton or ncome per person, followng standard measurement practces. When both are avalable, consumpton s preferred, n the expectaton that s both a better measure of current economc welfare and that s lkely to be measured wh less error than ncomes. 15 Three-quarters of the spells use consumpton. Naturally the tme perods between surveys are not unform. The medan year of the frst survey s 1991 whle the medan for the second s The medan nterval between surveys s 13 years and vares from three to 27 years. All changes between the surveys are annualzed. Gven the most recent survey for date t n country and the earlest avalable survey for date t, the growth rate for the varable x s g x ) ln( x / x ) (droppng the subscrpt on t ( / and for brevy). Natonal accounts and socal ndcators are also used, matched as closely as possble to survey dates. All monetary measures are n constant 2005 prces (usng countryspecfc Consumer Prce Indces) and are at Purchasng Power Pary (PPP) usng the ndvdual consumpton PPPs from the 2005 Internatonal Comparson Program (World Bank, 2008). Poverty s manly measured by the headcount ndex ( H ), gven by the proporton of the populaton lvng n households wh consumpton per capa (or ncome when consumpton s not avalable) below the poverty lne. For the bulk of the analyss the poverty lne s set at $2.00 per person per day at 2005 PPP, whch s the medan poverty lne amongst developng countres based on the complaton of natonal poverty lnes n Ravallon et al. (2009). $2 a day s also very 14 Pror to the global fnancal crss there were sgns that poverty measures were fnally fallng n the regon, snce the later 1990s; see Chen and Ravallon (2010). 15 The only excepton was Peru, for whch ncomes allowed a much longer tme perod. 7

8 close to the medan consumpton per person n the developng world for 2005; see Chen and Ravallon (2010) whch also descrbes the methods used here n measurng poverty and nequaly. The (unweghted) mean poverty rate for the $2 lne fell from 46.4% n the earlest round of surveys to 39.8% n the latest rounds. Ths lne s clearly somewhat arbrary; for example, there s no good reason to suppose that $2 a day corresponds to the pont where cred constrants cease to be, but nor s there any obvously better bass for settng a threshold. I wll also consder a lower lne of $1.25 a day and a much hgher lne of $13 a day n 2005, correspondng to the US poverty lne. The $1.25 lne s the mean of the poorest 15 countres n terms of consumpton per person (Ravallon et al., 2009) whle $13 per person per day s the offcal poverty lne n the US for a famly of four n Inequaly s measured by the usual Gn ndex ( G ).The nal ndex ranged from 19.4% (Czech Republc) to 62.9% (Serra Leone), both around 1990, and about one quarter of the sample had a Gn ndex below 30% whle one quarter had an ndex above 50%. Between the earlest and latest surveys, the mean Gn ndex stayed roughly unchanged at about 42%. 17 Four measures of the mddle class are used. The frst s the populaton share lvng between $2 and $13 a day, denoted MC F 13) F (2) where (z) s the dstrbuton ( functon for country at date t (so H (2) ). Ths s nterpreted as the mddle class by F developng-country standards; whle the bounds are somewhat arbrary, ths defnon appears to accord roughly wh the dea of what means to be mddle class n Chna and Inda (Ravallon, 2010). By contrast, those lvng above $13 a day can be thought of as the mddle class and rch by Western standards. These are absolute measures. The thrd measure uses a relatve defnon of the mddle class, namely the consumpton or ncome share controlled by the mddle three quntles, denoted MQ, as used by Easterly (2001). Fnally, I wll also consder the mser ndex proposed by Lnd and Moene (2010); ths s a measure of polarzaton between the rch and poor, and so can be thought of as an nverse measure of the sze of the mddle H class. More precsely, the mser ndex s H ( ) where s the overall mean and the mean below the poverty lne. Thus the mser ndex s hgher when there s a hgh poverty rate and mean ncome of the poor s low relatve to the overall mean. F H s See Department of Health and Human Servces. Summary statstcs for all varables are reported n the workng paper verson (Ravallon, 2009). 8

9 mean The average sze of the mddle class (by developng-country standards) ncreased, from a MC of 48% to a mean MC of 53%. The mddle-class expanded n 64 countres and contracted n 35. There s also a bmodaly n the dstrbuton of countres by the sze of ther mddle class, as s seen n Fgure 2, whch plots the kernel denses of MC and MC. Takng 40% as the cut-off pont, 30 countres are n the lower mode and 69 are n the upper one for the most recent survey; the correspondng counts for the earlest surveys are 42 and The relatve measure of the mddle class behaves dfferently, wh ltle change n the mean MQ over tme and the densy functon s unmodal n both the earlest and latest surveys. There are some strong correlatons amongst these parameters of the nal dstrbuton. The Gn ndex s hghly correlated wh MQ (r= for the earlest surveys and for the latest). 19 The poverty measures are also strongly correlated wh the survey means; ln H ln have a correlaton of (whle s for ln F (1.25) and ln ). The leastsquares elastcy of of ln H on ln H wh respect to the nal survey mean (.e., the regresson coeffcent ) s (t=13.340). (All t-ratos n ths paper are based on Whe standard errors.) There s a very hgh correlaton between the poverty measures usng $1.25 a day and $2.00 a day (r=0.974). There are weaker correlatons between the two poverty measures and the nal Gn ndex (r= and for z=1.25 and z=2.00). However, there s also a strong multple correlaton between the poverty measures (on the one hand) and the log mean and log nequaly (on the other); for example, regressng ln H on ln and ln G one obtans R 2 = The log Gn ndex also has a strong partal correlaton wh the log of the poverty rates holdng the log mean constant (t=4.329 for ln H ). The sze of the mddle class s also hghly correlated wh the poverty rate; the correlaton coeffcent between MC and H s ; 95% of the varance n the nal sze of the mddle class s accountable to dfferences n the nal poverty rate. (The bmodaly n terms of the sze of the mddle class n Fgure 2 reflects a smlar bmodaly n terms of the $2 a day poverty rate.) Across countres, 80% of the varance n the changes over tme n and MC can also be 18 For further dscusson of the developng world s rapdly expandng mddle class, and the countres left behnd n ths process, see Ravallon (2009). 19 The workng paper verson gves a complete correlaton matrx (Ravallon, 2009). 9

10 attrbuted to the changes n H. 20 The absolute and relatve measures of the sze of the mddle class are posvely correlated but not strongly so. The mser ndex s more strongly correlated wh the relatve measure of the mddle class (r= for the mser ndex for the frst survey wh MQ ) than the absolute measure (r=0.218 wh MC ). There s a strong correlaton between the proportonate rate of change n poverty g ( H )) and the ordnary growth rate n the survey mean g ( )). The regresson coeffcent s ( (t=-5.948) wh R 2 = ( Snce the tme perod between surveys ( ) fgures n the calculaton of the growth rates mght be conjectured that poorer countres have longer perods between surveys, basng ths paper s results. However, the correlaton coeffcents between and the varous measures of nal dstrbuton are all small (most well under 0.2 n absolute value); see Ravallon (2009). Whle ths paper focuses manly on the developng world as a whole, one regon stands out: Sub-Saharan Afrca (SSA). By the $2.00 a day lne, the mean of H for SSA s 76.04% as compared to 29.51% for non-ssa countres; the dfference s sgnfcant (t=8.84). Smlarly, n terms of the sze of s mddle class, SSA s concentrated n the lower mode n Fgure 2. Twothrds (20 out of 29) of SSA countres are n the lower mode for the earler survey round; the correspondng means of MC are 22.9% (s.e.=3.6%) and 59.1% (3.0%) for SSA and non-ssa countres and the dfference s sgnfcant at the 1% level. Inequaly too s hgher n SSA; the mean Gn ndex n the earlest surveys s 47.4% (1.8%) for SSA versus 39.0% (1.7%) n non- SSA countres, and the dfference s sgnfcant (t=7.68). There s clearly a SSA effect n both growth and poverty reducton. 4. Testng for convergence n both mean consumpton and poverty Intuvely, the twn stylzed facts that there s convergence n mean consumpton and that growth n the latter reduces the ncdence of absolute poverty mply that we should see poverty convergence, as dscussed n the ntroducton. Indeed, an even stronger result s mpled by the standard log-lnear models for growth and poverty reducton found n the lerature, wh parameters ndependent of the nal level of poverty. Then the speed of convergence wll be the 20 R 2 =0.826 for the regresson of MC MC on F ( 2) F (2) ; the regresson coeffcent s (t= ; n=92), whch s sgnfcantly dfferent from -1 (t=2.946). 10

11 same for the mean as the poverty measure. To see ths, consder the most common emprcal specfcaton for the growth process n the mean: ln ln (1) where s a country-specfc effect, 1 s a country-specfc convergence parameter and s a zero-mean error term. (To smplfy notaton I assume evenly spaced data for now.) Next let the headcount ndex of poverty be a log-lnear functon of the mean: ln H ln (2) Where s a country-specfc effect, s nterpretable as the (country-specfc) elastcy of poverty to the mean (wh the expectaton that 0) and s a zero-mean error term. The mpled model of the growth rate n poverty s then: * * 1 * ln H ln H (3) * for whch s readly verfed that * and ( 1 ) 1. *, The parameters of (1) and (2) (,,, ) can vary across countes but (for the sake of ths argument) suppose they do so ndependently of H the speed of convergence for the poverty measures, that for the mean, ln / ln. 1. Comparng (1) and (3) can be seen that ln H / ln H 1, s the same as However, ths predcton s not borne out by the data, as we saw n Fgure 1. Table 1 gves standard convergence tests for mean consumpton based on the regresson coeffcent of g ) on ln, wh and whout controls. 21 The controls ncluded nal consumpton per ( capa from the natonal accounts, prmary school enrollment rate, lfe expectancy at brth, and the prce ndex of nvestment goods from Penn World Tables (6.2), whch s a wdely-used measure of market dstortons; all three varables are matched as closely as possble to the date of the earlest survey. It can be seen from Table 1 that the survey means exhb convergence; the coeffcent s (t=-3.412) whout the controls and (t=-7.435) wh them. 21 Alternatvely one can estmate the convergence parameter usng a nonlnear regresson g ( ) [(1 e )/ ]ln (as n Barro and Sala--Martn, 1992). Ths gave a very smlar result to (1) n Table 1, namely ˆ (t=-2.865). Clearly, the approxmaton that e 1 (lnearzng the nonlnear regresson specfcaton) works well. 11

12 Uncondonal convergence s weaker usng means from consumpton surveys only (Column 2) or natonal accounts (Column 3), though condonal convergence s stll evdent. However, as can be seen from Table 2, there s no sgn of convergence for the poverty measures, wh or whout the controls. 22 The proportonate rates of poverty reducton are roughly orthogonal to nal levels, as we saw n Fgure One can also form a subsample of about 70 countres wh at least three surveys. 24 Ths extra round of surveys can be used to test for convergence more robustly to measurement errors. 25 One way of dong ths s to calculate the trend over the three surveys and test f ths s correlated wh the startng value. On estmatng the trend for each country by regressng the logs of the three (date-specfc) means for that country on tme and smlarly for the headcount ndces, convergence n the mean s stll evdent; the regresson coeffcent of the estmated trend on the log mean from the earlest survey s (t=-2.052), whch s sgnfcant at the 4% level. And agan there s no sgnfcant correlaton between these trends n poverty reducton and the nal poverty measures; the regresson coeffcent of the estmated trend on the log headcount ndex from the earlest survey s (t=0.805). Another method of testng for convergence n these data s to form means from the frst two surveys and look at ther relatonshp wh the changes observed between the last survey and the mddle one. Defne the mean from the frst two surveys as M x ) ( x x ) / 2 ( whle the growth rate s g ( x ) ln( x / x ) / 2 2. Usng ths method, I found that the uncondonal mean convergence s no longer evdent (though condonal convergence s stll found) but there s an ndcaton of poverty dvergence; regressng g H ) (the proportonate ( change n the poverty measure between the mddle and fnal rounds) on M ) ; the ( 2 H 22 Ths was also true for the $13 lne, for whch the convergence parameter was (t=-0.480). Agan, the nonlnear specfcaton gave a very smlar result n all cases. 23 Recall that poverty convergence s defned n proportonate rather than absolute terms. The absence of poverty convergence by ths defnon mples that poorer countres tend to see larger absolute reductons n ther poverty rate. 24 When there were more than three surveys I pcked the one closest to the mdpont of the nterval between the latest survey and the earlest. 25 As s well known, measurement errors can create spurous sgns of convergence; f the nal mean s over- (under-) estmated then the subsequent growth rate wll be lower (hgher).clearly stems n part at least from ths problem. It s notable that the coeffcent drops usng only the consumpton surveys (Table 4) or natonal accounts consumpton. However, sgnfcant condonal convergence n the means (ncludng those only from consumpton surveys) and natonal accounts consumpton s stll evdent. 12

13 coeffcent s 0.029, whch s sgnfcant at the 6% level (t=1.901). There s stll some contamnaton due to measurement error n these tests. Yet another method s to regress g x ) on the correspondng measure from the earlest ( survey ( ln x 1 ); the result s smlar, namely ltle sgn of (uncondonal) mean convergence 2 but mld dvergence for poverty (a coeffcent of wh t=1.819). In summary, there are no sgns of poverty convergence and even some sgns of dvergence. The rest of ths paper wll try to explan why. It wll be argued that the nal poverty rate matters to the subsequent rate of poverty reducton through two dstnct channels, namely the growth rate n mean consumpton and the elastcy of poverty to the mean. Frst, wll be shown n the followng secton that the parameter (n equaton 1) s a decreasng functon of the nal poverty rate. Second, secton 6 wll be shown that the elastcy of poverty to the mean, (equaton 2), s a decreasng functon of the nal level of poverty. Secton 7 wll brng these two elements together to answer the queston posed n the tle to ths paper. 5. The relevance of nal poverty to the growth rate n the mean The secton begns wh benchmark regressons for growth. A causal nterpretaton of these regressons requres that the nal dstrbuton (n the earlest survey used to construct each spell) s exogenous to the subsequent rate of growth. Ths can be questoned. I shall test encompassng models wh controls for other factors. I also provde results for an nstrumental varables estmator under wdely-used (though stll questonable) excluson restrctons. 5.1 Growth regressons wh poverty as an nal condon Table 3 gves estmates of the followng benchmark regresson: 26 g ( ) ln ln H (4) The result usng the full sample s gven n column (1) of Table 3. Ths suggests that dfferences n the nal poverty rate have szeable negatve mpacts on the growth rate n the mean at a gven nal mean. A one standard devaton ncrease n ln H would come wh (2% ponts) declne n the growth rate for the survey mean. Columns (2) and (3) gve the 26 The regressons are consstent wh a dervatve of ln wh respect to ln that s less than uny, but fades toward zero at suffcently long gaps between survey rounds; for example, column (1) n Table 2 mples a dervatve that s less than uny for 29 years; the largest value of n the data s 27 years. 13

14 correspondng estmates usng consumpton surveys only (droppng the 22 surveys for whch only ncome was avalable) and usng growth rates n natonal-accounts consumpton respectvely. (I wll return to dscuss the alternatve estmates n columns (4)-(6).) Estmatng the regresson solely on consumpton surveys strengthens the result; the condonal convergence effect s even stronger, as s the poverty effect. The results are robust to usng consumpton from the natonal accounts. The notable dfferences are that the convergence parameter n (4) s lower, ˆ 0.02 (column 3, Table 3) and that the headcount ndex based on the $1.25 lne s a slghtly stronger predctor of the natonal accounts consumpton growth rate. (The results usng natonal accounts consumpton are less sensve to the poverty lne between $2.00 and $1.25 a day.) It mght be conjectured that the poverty measure (at gven nal mean) s pckng up some other aspect of the nal dstrbuton, such as nequaly (the varable dentfed n much of the emprcal lerature referred to n secton 2). Indeed, f we magne functon of ln and ln G ln H to be a lnear (whch fs the data que well as noted n secton 3) then one can re-wre (4) n a reduced form smlar to the past papers n the lerature whch fnd that nequaly mpedes growth at a gven mean (secton 2). An encompassng test s needed. Addng the log of the nal Gn ndex to equaton (4) does not change the result; the coeffcent on the Gn ndex s not sgnfcantly dfferent from zero and the coeffcent on ln H remans (hghly) sgnfcant n the augmented verson of (4). It s poverty not nequaly that s dong the work. To nvestgate ths further, I added nequaly ( ln G ), the ncome share of the mddle three quntles ( ln ), the share of the Western mddle class and rch ( F (13) ), the MQ 1 mser ndex, prmary school enrollment rate, lfe expectancy at brth, and the relatve prce ndex of nvestment goods. 27 Table 4 gves the augmented models usng both survey means and consumpton from natonal accounts. The table also gves restrcted forms that pass comfortably. The nal poverty rate remans a strong and sgnfcant predctor of growth n these encompassng models. The sze of the Western mddle class, lfe expectancy and the prce of nvestment are also sgnfcant predctors. The relatve share of the mddle quntles s sgnfcant for the growth rates n the survey means (but not natonal accounts consumpton), though wh a 27 Ths s a common measure of polcy dstortons, derved from Penn World Tables (followng Lopez and Servén, 2009). As noted n secton 2, schoolng and health attanments can also be nterpreted as channels lnkng nal dstrbuton to growth rather than as ndependent effects, so the nterpretaton of the poverty coeffcent n these augmented regressons s not strctly the same as for the benchmark regresson. 14

15 negatve sgn. The mser ndex has no sgnfcant effect on growth (as also found by Lnd and Moene, 2010). The two regonal effects that have been dentfed n the lerature on growth emprcs are for Sub-Saharan Afrca (negatvely) and East Asa (posvely). In testng augmented versons of the regressons n Table 4, wh dummy varables for these two regons, I fnd no sgn of an SSA effect n any specfcaton and a negatve East Asa effect though only mldly sgnfcant (at the 8% level). Of course (as noted), there are uncondonal effects on growth n both regons. But these are largely captured whn the model. I also tred addng two nteracton effects. In the frst, I added an nteracton effect between nequaly and the nal mean; ths s hghly nsgnfcant (t-rato of ). Second, addng ln G. ln H I fnd that has a posve coeffcent though not sgnfcantly dfferent from zero at even the 15% level. Whle nequaly and the ncome share of the mddle quntles are nsgnfcant when one controls for nal poverty (though, of course, nequaly can be one factor leadng to hgher poverty), the populaton share of the Western mddle class and rch emerges wh a sgnfcant negatve coeffcent (Table 4). The jontly negatve coeffcents on the poverty rate and the share of the Western mddle class mply that a hgher populaton share n the developng-world mddle class s growth enhancng. Thus the data can also be well descrbed by a model relatng growth to the populaton share of the developng world s mddle class. (As one would expect, replacng ln and F (13) by ln[ F (13) / H ] gave a very smlar overall f, though not que as H 1 t good as Table 4.) The negatve (condonal) effect of the poverty rate may well be transmted through dfferences n the sze of the mddle class. Whle the above results appear to be convncng n suggestng that s hgh poverty not nequaly that retards growth, s mportant to recall that the poverty effect only emerges when one controls for the nal mean. The between-country dfferences n the ncdence of poverty at a gven mean reflect dfferences n relatve dstrbuton. Whle those dfferences are not smply a matter of nequaly as normally defned, they are correlated wh nequaly. The predcted values of the growth rates from the regresson n column (1) of Table 3 are sgnfcantly correlated wh nequaly; r= Snce hgher nequaly tends to mply hgher poverty at a gven mean (secton 3), also mples lower growth prospects. 5.2 Robustness tests 15

16 It mght be conjectured that the effect of ln H n (4) reflects a msspecfcaton of the functonal form for the convergence effect, notng that the poverty measure s a nonlnear functon of mean ncome. To test for ths, I re-estmated (4) usng cubc functons of control for the nal mean. Whle I found some sgn of hgher-order effects of ln ln to, these made very ltle dfference to the regresson coeffcent on the poverty rate n the augmented regresson; the coeffcent on ln H n column (1) n Table 3 becomes (t=-3.547). There s, however, a marked nonlneary n the relatonshp, whch s beng captured by the log transformaton of H n (4). If one uses H rather than ln H on the same sample, the negatve effects are stll evdent but they are much less precsely estmated, wh substantally lower t-ratos a t-rato of for the coeffcent on H come out somewhat more strongly f one adds a squared term n though n both cases the effects H to pck up the nonlneary, wh both the lnear and squared terms sgnfcant at the 10% level or better. As a smple graphcal test for msspecfcaton of the functonal form n (4) I plotted (from column (1) n Table 3) aganst ln H rate. 28 The log transformaton appears to be the rght functonal form. g ( ) 0.035ln. The relatonshp s close to lnear n the log poverty In terms of goodness-of-f, the more relevant poverty lne s that usng the $2.00 a day lne. On replacng ln by ln F (1.25) n (4) the poverty rate stll has a negatve coeffcent H but s not sgnfcant at the 5% level. I also estmated the followng specfcaton: g ( ) ln 1 [ln H ln F (1.25)] 2 ln F (1.25)) (5) The estmate of 1 2 s , but s not sgnfcantly dfferent from zero (t=-0.801), suggestng that (4) s the correct specfcaton. The results are also robust to usng the poverty gap ndex nstead of the headcount ndex; the correspondng verson of (4) s smlar, wh a coeffcent on the log of the poverty gap ndex of , wh t-rato of However, the f s better usng the headcount ndex. The subsample of 70 countres wh at least three surveys can be used to form ntertemporal averages, to reduce the attenuaton bases n the benchmark regresson due to measurement error; equaton (4) can be re-estmated n the form: 28 The workng paper verson gves the graph (Ravallon, 2009). 16

17 g ( ) ln M( ) ln M( H ) 2 2 (6) (It wll be recalled that M x ) ( x x ) / 2.) Column (4) of Table 3 gves the results. ( The regresson coeffcents are larger (n absolute value), consstent wh the presence of attenuaton bas n the earler regressons. The standard errors also fall notceably. Ths strengthens the earler results based on the benchmark regresson (equaton (4)). Another way of usng the extra survey rounds s as a source of nstrumental varables (IVs). Growth rates between the mddle and last survey rounds were regressed on the mean and dstrbutonal varables for the mddle round but treatng the latter as endogenous and retanng the data for the earlest survey round as a source of IVs. Lettng now denote the length of spell (=1,2), the model becomes: g( ) ln ln H 2 2 (7) The nstrumental varables are ln 1 2 ln C, ln G 1, ln F ( ) 2 z 1 (z=1.25, 2.00) 2, 1 2 and 1. The frst-stage regressons for ln and ln H 2 had R 2 =0.884 (F=61.06) and 2 R 2 =0.796 (F=31.30) respectvely. The correspondng Generalzed Methods of Moments (GMM) estmates of (9) are found n Table 3, Column (5). (I also gve the correspondng result usng natonal accounts consumpton n column (6).) We see that the fndng that a hgher nal poverty rate mples a lower subsequent growth rate n the mean (at gven nal mean) s robust to allowng for the possble endogeney of the nal mean and nal poverty rate, subject to the usual assumpton that the above nstrumental varables are excludable from the man regresson. One can also use the subsample to allow for country-fxed effects, whch sweep up any confoundng latent heterogeney n growth rates at country level. The man results are not robust to ths change. Regressng g ( ) g ( ) on ln( / ) and ln( H / ) 2 H 2 1, the 2 coeffcent on the former remans sgnfcant but the poverty rate ceases to be so. However, s hard to take fxed-effects growth regressons serously wh these data. Whle ths specfcaton addresses the problem of tme-nvarant latent heterogeney s unlkely to have much power for detectng the true relatonshps gven that the changes over tme n growth rates wll almost certanly have a low sgnal-to-nose rato. Smulaton studes have found that the coeffcents on growth determnants are heavly based toward zero n fxed- 17

18 effects growth regressons (Hauk and Waczarg, 2009). 29 I suspect that the problem of tmevaryng measurement errors n both growth rates and nal dstrbuton s even greater n the present data set, possbly reflectng survey comparably problems over tme. The problem of nose n the changes n growth rates can be llustrated f we consder the relatonshp between the two measures of the mean used n ths study, namely that from the surveys ( ) and that from the prvate consumpton component of domestc absorpton n the natonal accounts ( C ). Usng a log-log regresson n the levels gves an elastcy of toc of 0.75 (R 2 =0.82) for the latest survey rounds. Usng a country-fxed effects specfcaton n the levels, the elastcy drops to 0.51 (R 2 =0.21). However, when one also ncludes fxed-effects n the growth rates n the mean (usng the subsample wh at least three surveys) the elastcy drops to 0.09 (R 2 =0.07), whch must be consdered an mplausbly low fgure, undoubtedly reflectng substantal attenuaton bas due to measurement error n the changes n growth rates. 6. Inal poverty and the growth elastcy of poverty reducton We have seen that countres startng wh a hgher poverty rate tend to see slower growth at a gven nal mean consumpton. Now I turn to the second channel how the growth elastcy of poverty reducton depends on nal dstrbuton. Ths can be thought of as the drect effect of the nal dstrbuton on the pace of poverty reducton, as dstnct from the ndrect effect va the rate of growth n the mean. Agan I focus on the $2 lne, although the $1.25 lne gves smlar results. For any gven relatve dstrbuton, the elastcy of the poverty rate to mean consumpton s smply (one mnus) the elastcy of the poverty rate wh respect to the poverty lne. 30 Ths can be calculated at any gven poverty lne. The nteracton effect between ths elastcy and the growth rate n the mean s then an obvous predctor of the rate of poverty reducton. 31 On calculatng the elastcy for the $2 a day poverty lne usng the nal survey for each country, and denotng that elastcy by, one fnds that the regresson coeffcent of ln( H / H ) on 29 Ths pont s llustrated well by the Monte Carlo smulatons found n Hauk and Waczarg (2009). 30 Ths follows mmedately from the aforementoned fact that the poverty rate s homogeneous of degree zero n the poverty lne and the mean for a gven Lorenz curve. 31 On explong ths fact n a decomposon analyss for a panel of countres (usng an earler verson of the same data set used here) Kraay (2006) concludes that the bulk of the varance n rates of poverty reducton s due rates of growth. Note that ths can be true and yet there s a large dfference n the rates of poverty reducton at a gven rate of growth between countres wh dfferent nal dstrbutons; see Ravallon (2007). 18

19 ln( / ) s not sgnfcantly dfferent from uny; the coeffcent s wh a standard error of and R 2 = Of course there are also changes n relatve dstrbuton, whch presumably account for the bulk of the remanng varance n rates of poverty reducton. Consstently wh past fndngs n the lerature, 32 the changes n relatve dstrbuton are vrtually orthogonal to rates of growth and (hence) the above regresson coeffcent s very close to uny. (If hgher growth s systematcally assocated wh worsenng dstrbuton then the regresson coeffcent would be based downward, and so below uny.) However, there may well be relevant correlatons wh the propertes of the nal dstrbuton. Addonally, the elastcy s self a functon of the nal mean and nal dstrbuton. These observatons motvate a reduced form model n whch the rate of poverty reducton depends on both the rate of growth and s nteracton effects wh relevant aspects of the nal dstrbuton. Table 5 gves regressons of the annualzed change n the log of the $2 a day poverty rate aganst both the annualzed growth rate n the mean and s nteracton wh the nal poverty rate. Columns (1) and (2) gve unrestrcted estmates of an encompassng test: g ( H) 0 1 ln H ( H ) g( ) (8) Results are gven for both OLS and IVE; the IVE method uses the growth rate n prvate consumpton per capa from the natonal accounts as the nstrument for the growth rate n the survey mean. Followng Ravallon (2001), ths IV allows for the possbly that a spurous negatve correlaton exsts due to common measurement errors (gven that the poverty measure and the mean are calculated from the same surveys). The results n Table 5 ndcate that the (absolute) growth elastcy of poverty reducton tends to be lower n countres wh a hgher nal poverty rate. There s no sgn of condonal convergence n poverty; the null that 1 0 s easly accepted. Table 5 also gves homogeney tests for the null 0; the tests pass comfortably, ndcatng that the relevant growth rate s 0 1 the poverty-adjusted rate, as gven by the growth rate n the mean tmes one mnus the poverty rate. At an nal poverty rate of 10% (about one standard devaton below the mean) the elastcy s about -3 whle falls to about -0.7 at a poverty rate of 80% (about one standard devaton above the mean). I also used the subsample wh three survey rounds to mplement an IVE usng the same nstruments as before. Agan, the homogeney restrcton s easly accepted 32 For a recent overvew see Ferrera and Ravallon (2009). 19

20 (t=-0.447). The IVE of the regresson coeffcent of g H ) on 1 H ) ( ) s (t= ). ( ( g 2 There s also a strong nteracton effect wh the sze of the mddle-class: At the lower mode for g ( H ) ( MC ( 1.749) (0.221) ( 4.818) ) g ( ) ˆ R 2 =0.539, n=91 (9) MC of around 15% (Fgure 2), equaton (9) mples a growth elastcy of (t=-3.13) whle at the upper mode, around 75%, s (t=-7.15). However, ths nteracton effect s largely attrbutable to H. Lettng H and F (13) enter separately (recallng that MC F ) ( 13 H ) only H s sgnfcant: g ( H ) ( F ( 1.939) (0.039) ( 0.631) (13) 0.029H (3.638) ) g ( ) ˆ R 2 =0.539, n=91 (10) One cannot reject the null hypotheses that the nteracton effect wh F (13) has no mpact, though nor can one reject the null that the coeffcents on the two nteracton effects add up to zero (F=0.001), mplyng agan that s the populaton share of the mddle class (by developng country standards) that matters. Statstcally s a dead heat then between a model n whch s a larger mddle class that determnes how much mpact a gven rate of growth has on poverty and a model n whch s the nal poverty rate that matters. However, gven that the man way people n developng countres enter the mddle class s by escapng poverty recall that 80% of the varance n changes n the sze of the mddle class s accountable to changes n the poverty rate seems more reasonable to thnk of poverty as the relevant prmary factor. I also dd an encompassng test wh extra nteracton effects wh G elastcy of poverty reducton (, the partal ), the prmary school enrollment rate, lfe expectancy, the prce of nvestment goods and regonal dummy varables for SSA and East Asa. (Growth elastces of poverty reducton are sgnfcantly lower n SSA, but ths s entrely due to the regon s above-average poverty ncdence.) These are ndvdually and jontly nsgnfcant (the jont F-test accepted the null wh prob.=0.199). Does the relatonshp dffer accordng to whether growth s posve or negatve? The survey mean decreased over tme for about 30% of the spells; the mean I[ ( )] where I[x] s the ndcator functon ( I [ x] 1 f x>0 and I [ x] 0 otherwse). On stratfyng the g 20

21 parameters accordng to whether the mean s ncreasng or not, and re-estmatng specfcaton (3) n Table 5 one obtans: g( H ) (2.869 H 3.117) I[ g( )] g( ) ( 1.628) (4.246) ( 5.046) R 2 =0.552, n=91 (11) (2.218H 1.984)(1 I[ g ( )]) g ( ) ˆ (3.709) ( 5.717) The posve nteracton effect s found durng spells of contracton n the mean ( I[ ( )] 0 ) as well as expansons ( I[ ( )] 1); the homogeney restrcton passes n both cases (the t-test g for contractons s 1.143, versus for expansons). Nor can one reject the null that the coeffcents are the same for expansons versus contractons (F=2.978, prob.=0.062). So the key proxmate determnant of the rate of poverty reducton s the poverty adjusted growth rate ( 1 H ) ( ) ) rather than the ordnary growth rate ( g ) ). The regresson ( g ( coeffcent of the rate of poverty reducton ( g H ) ) aganst the poverty-adjusted growth rate n ( the survey mean s almost twce as hgh as for the ordnary growth rate. 33 Allowng for nal poverty rate adds 17 percentage ponts to the share of the varance n the rate of poverty reducton that can be explaned by the rate of growth n the mean. g 7. So why don t we see poverty convergence? Recall that the speed of poverty convergence, g ( H ) / ln H, s close to zero (secton 4). We can now combne the man results from the last two sectons to explan why. Based on the varous encompassng tests n sectons 5 and 6, my emprcally-preferred model takes the form: g ( H ) (1 H ) g ( ) (12.1) g ( ) ln ln H (12.2) The regressors n (12.2) are not, of course, ndependent; as we also saw n Secton 3, countres wh a hgher nal mean tend to have a lower poverty rate. 34 I shall allow for ths by assumng that ln H vares lnearly as a functon of ln consstently wh the data. We can then derve the followng three-way decomposon of the poverty convergence elastcy: 33 Recall that the regresson coeffcent of g H ) on g ) s (t=-5.948; R 2 =0.363). The regresson ( ( coeffcent of g H ) on 1 H ) ( ) s (t=-7.273; R 2 =0.535). 34 and lnh ( ( g Nonetheless, as we have also seen, the dfferences across countres n nal dstrbutons ental that are not so hghly correlated as to prevent dsentanglng ther effects. ln 21