Why Don t We See Poverty Convergence?

Why Don t We See Poverty Convergence? Martn Ravallon 1 Development Research Group, World Bank 1818 H Street NW, Washngton DC, 20433, USA Abstract: We see sgns of convergence n average lvng standards amongst developng countres and of greater progress aganst poverty n faster growng economes. Yet we do not see poverty convergence; the poorest countres are not enjoyng hgher rates of poverty reducton. The paper tres to explan why. Consstently wh some growth theores, analyss of a new data set for 100 developng countres reveals an adverse effect on consumpton growth of hgh nal poverty ncdence at a gven nal mean. Startng wh a hgh ncdence of poverty also entals a lower rate of progress aganst poverty at any gven growth rate (and conversely poor countres tend to experence less steep ncreases n poverty durng recessons). Thus, for many poor countres, the growth advantage of startng out wh a low mean s lost due to ther hgh poverty rates. The sze of the mddle class measured by developng-country, not Western, standards appears to be an mportant channel lnkng current poverty to subsequent growth and poverty reducton. However, hgh current nequaly s only a handcap f entals a hgh ncdence of poverty relatve to mean consumpton. Keywords: Poverty trap, mddle class, nequaly, economc growth JEL: D31, I32, O15 1 These are the vews of the author and should not be attrbuted to the World Bank or any afflated organzaton. Address: mravallon@worldbank.org. 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 Karla Hoff, Aart Kraay, 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 and the Instute of Socal Scences, Cornell Unversy.

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 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 (reflectng a lower mean) should enjoy a hgher subsequent growth rate and (hence) hgher proportonate rate of poverty reducton. Indeed, as wll be demonstrated later, the mean and the poverty rate wll have the same speed of convergence n wdely-used log-lnear models. That poses a puzzle. As ths paper wll also show, there s no sgn of poverty convergence amongst developng countres, let alone a smlar speed of convergence to that found for the mean. The overall ncdence of poverty s fallng n the developng world, but no faster (n proportonate terms) n s poorest countres. 2 Clearly somethng s mssng from the story. Intuvely, one hypothess s that eher the growth process 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. Later I wll pont to a number of theoretcal arguments as to how ths can happen. To test ths hypothess, a new data set was constructed for ths paper from household surveys for almost 100 developng countres, each wh two or more surveys over tme. These data are used to estmate a model n whch the rate of progress aganst poverty depends on the rate of growth n the mean and varous parameters of the nal dstrbuton encompassng those dentfed n the lerature whle the rate of growth depends n turn on nal dstrbuton as well as the nal mean. The model s subjected to a number of tests, ncludng alternatve functonal forms, sample selecton by type of survey, and alternatve measures are used for the key varables. A sub-sample wh three or more surveys s also used to test robustness to 2 Note that poverty convergence s defned n proportonate rather than absolute terms, n keepng wh usage the n the growth lerature. The absence of poverty convergence by ths defnon mples that poorer countres tend to see larger absolute reductons n ther poverty rate. 2

dfferent specfcaton choces, ncludng treatng nal dstrbuton as endogenous by treatng lagged nal dstrbuton as excludable. 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 ncomes. Second, hgh nal poverty dulls the mpact of growth on poverty; the poor enjoy a lower share of the gans from growth n poorer countres. On balance there s ltle or no systematc effect of startng out poor on the rate of poverty reducton. Other aspects of the nal dstrbuton play no more than a secondary role. 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. 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 though ths too s largely accountable to dfferences n the ncdence of poverty. 2. Past theores and evdence Growth theores ncorporatng cred-market falure suggest that hgh nequaly reduces an economy s aggregate effcency and (hence) growth rate. 3 The market falure s typcally attrbuted to nformaton asymmetres that lenders are poorly nformed about borrowers. The key analytc feature of such models s a suably nonlnear relatonshp between an ndvdual s nal wealth and her future wealth (the recurson dagram ). The economc ratonale for a nonlnear recurson dagram s that the cred market falure leaves unexploed opportunes for nvestment n physcal and human capal and that there are dmnshng margnal products of capal. Then 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 value of current mean wealth. Models wh such features nclude Galor and Zera (1993), Benabou (1996), Aghon and Bolton (1997) and Banerjee and Duflo (2003). But s nequaly that matters, or somethng else, such as poverty or the sze of the mddle class? Inequaly s obvously not the same thng as poverty; nequaly can be reduced 3 There are a number of surveys ncludng Perott (1996), Hoff (1996), Aghon et al. (1999), Bardhan et al. (2000), Banerjee and Duflo (2003), Azarads (2006) and World Bank (2006, Chapter 5). Borrowng constrants are not the only way that nequaly can matter to growth. Another class of models s based on the dea that hgh nequaly restrcts effcency-enhancng cooperaton, such that key publc goods are underprovded or effcencyenhancng polcy reforms are blocked (Bardhan et al., 2000). Other models argue that hgh nequaly leads democratc governments to mplement dstortonary redstrbutve polces, as n Alesna and Rodrk (1994). 3

whout a lower poverty measure by redstrbutng ncome amongst the non-poor, and poverty can be reduced whout lower nequaly. (Smlarly, efforts to help the mddle-class may do ltle to releve current poverty.) In fact there s another mplcaton of cred market falures that has receved very ltle attenton. 4 The followng secton studes one theoretcal model from the lerature more closely and shows that the smple fact of a cred constrant mples that unambguously 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 yelds lower growth at a gven level of mean current wealth. Ths s not the only argument suggestng that poverty s a relevant parameter of the nal dstrbuton. Lopez and Servén (2009) 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. Another example can be found n the theores that have postulated mpatence for consumpton (hgh tme preference rates possbly assocated wh low lfe expectancy) and hence low savngs and nvestment rates by the poor (see, for example, Azarads, 2006). Here too, whle the theoretcal lerature has focused on nal nequaly, can also be argued that a hgher nal ncdence of poverty means a hgher proporton of mpatent consumers and hence lower growth. Yet another example s found by consderng how work productvy s lkely to be 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 to work 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. There are also theoretcal arguments nvolvng market and nstutonal development, though ths s not a topc that has so far receved as much attenton n ths lerature. Whle past theores have often taken cred-market falures to be exogenous, poverty may well be a deeper causatve factor n fnancal development (as well as an outcome of the lack of fnancal 4 Ravallon (2001, 2007) argues ntuvely that poverty retards growth when there are cred market falures. 4

development). For example, gven fxed cost of lendng (both for each loan and for settng up the lendng nstuton), lqudy constrants can readly emerge as the norm n very poor socetes. A strand of the theoretcal lerature has also ponted to the possbles for multple equlbra n nonlnear dynamc models, whereby the lowest equlbrum s a poverty trap ( lowlevel attractor ). Essentally, the recurson dagram now has a low-level non-convexy, whereby a mnmum level of current wealth s essental before any posve level of future wealth can be reached. In poor countres, the nutronal requrements for work can readly generate such dynamcs, as llustrated by the model of Dasgupta and Ray (1986). Such a model predcts that a large exogenous ncome gan may be needed to attan a permanently hgher ncome and that seemngly smlar aggregate shocks can have dssmlar outcomes; growth models wh such features are also dscussed n Day (1992) and Azarades (1996, 2006) amongst others. Sachs (2005) has nvoked such models to argue that a large expanson of development ad would be needed to assure a permanently hgher average ncome n currently poor countres. 2.1 A model of aggregate growth wh mcro borrowng constrants I now explore one of these models more fully. Banerjee and Duflo (2003) provde a smple but nsghtful growth model wh borrowng constrants. Someone who starts her productve lfe wh suffcent wealth s able to nvest her unconstraned optmal amount, equatng the (declnng) margnal product of her capal wh the nterest rate. But the wealth poor, for whom the borrowng constrant s bndng, are unable to do so. Banerjee and Duflo show that hgher nequaly n such an economy mples lower growth. However, they do not observe that ther model also mples that hgher current wealth poverty for a gven mean wealth also mples lower growth. The followng dscusson uses the Banerjee-Duflo model to llustrate ths hypothess, whch wll be tested later n the paper. The basc set up of the Banerjee-Duflo model s as follows. Current wealth, w t, s dstrbuted across ndvduals accordng to the cumulatve dstrbuton functon, p F (w), gvng the populaton proporton p wh wealth lower than w at date t. It wll be analytcally easer to work wh the quantle functon, w t ( p) (the nverse of (w) ). The cred market s mperfect, such that ndvduals can only borrow up to tmes ther wealth. Each person has a strctly concave producton functon yeldng output h (k) from a capal stock k. Gven the rate F t t 5

of nterest r (taken to be fxed) the desred capal stock s k, such that h ( k ) r. Those wh nal wealth less than k /( 1) are cred constraned n that, after nvestng all they can, they stll fnd that h ( k t ) r, whle the rest are free to mplement k. A share 1 (0,1 ) of current wealth s consumed, leavng for the next perod. Under these assumptons, the recurson dagram takes the form: wt 1 ( wt ) [ h(( 1) wt ) rwt ] for w t k /( 1) (1.1) [ h( k ) ( w k ) r] for w t k /( 1) (1.2) t Planly, w ) s strctly concave up to k /( 1) and lnear above that. Mean future wealth s: ( t 0 t 1 [ w t ( p)] dp (2) By standard propertes of concave functons, we have: Proposon 1: (Banerjee and Duflo, 2003, p.277): An exogenous mean-preservng spread n the wealth dstrbuton n ths economy wll reduce future wealth and by mplcaton the growth rate. However, the Banerjee-Duflo model has a further mplcaton concernng poverty, as another aspect of the nal dstrbuton. Let Ht F t(z) denote the headcount ndex of poverty ( poverty rate ) n ths economy when the poverty lne s z. I assume that z k /( 1) and let H F [ k /( 1)]. Usng (1.1) and (1.2) we can re-wre (2) as: t t [ h(( 1) w ( p)) rw ( p)] dp [ h( k ) ( w ( p) k ) r] dp (3) t1 Ht 0 t t Now consder the growth effect of a mean-preservng ncrease n the poverty rate. I assume that H ncreases and that no ndvdual wh wealth less than k /( 1) becomes better off, t mplyng that w ( p) / H 0 for all t unambguously hgher. It s readly verfed that: 5 t 1 Ht p H t. If ths holds then I wll say that poverty s t H t H 1 ( ) t t wt p wt ( p) [ h(( 1) w ( ))( 1) ] t p r dp r Ht H 0 t H 0 t dp (4) 5 Note that the functon defned by equatons (1.1) and (1.2) s contnuous at k /( 1). 6

The sgn of (4) cannot be determned under the assumptons so far. 6 However, on mposng a constant nal mean H Thus we also have: t, equaton (4) smplfes to: H t t 1 wt ( p) [ (( 1) ( )) ]( 1) h wt p r dp t H 0 t t Proposon 2: In the Banerjee-Duflo model an unambguously hgher nal headcount ndex of poverty holdng the nal mean constant mples a lower growth rate. Ths model mples an aggregate effcency cost of a hgh ncdence of poverty. But a number of ponts should be noted. An nequaly effect s stll present separately to the poverty effect. And the less poverty there s, the less mportant overall nequaly s to subsequent growth prospects. Also note that the theoretcal predcton concerns the level of poverty at a gven nal value of mean wealth. Whout controllng for the nal mean, the sgn of the effect of hgher poverty on growth s ambguous. Two opposng effects can be dentfed. The frst s the usual condonal convergence property, whereby countres wh a lower nal mean (and hence hgher nal poverty) tend to have hgher subsequent growth. Aganst ths, there s an adverse dstrbutonal effect of hgher poverty (Proposon 2). Whch effect domnates s an emprcal queston. 2.2 Past evdence on growth and the nal dstrbuton Followng Barro and Sala--Martn (1992), cross-country regressons for GDP growth rates have found a sgnfcant negatve coeffcent on nal GDP once one controls for nal condons. A subset of the lerature has used nequaly as one such nal condon. 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), Knowles (2005) and Vochovsky (2005). 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. 0 (5) 6 If there s (unrestrcted) frst-order domnance, whereby w ( p)/ H 0 for all p [0, 1], then t 1 / H t 0. However, frst-order domnance s ruled out by the fact that the mean s held constant n ths though experment; there s a redstrbuton from the wealth poor to the wealth nonpoor. t t 7

There are a number of unresolved specfcaton ssues n ths lerature. The aspect of nal dstrbuton that has receved almost all the attenton n the emprcal lerature s nequaly, as typcally measured by the Gn ndex. Wealth nequaly s arguably more relevant though ths has rarely been used due to data lmatons. 7 The populary of the Gn ndex appears to owe more to s avalably n secondary data complatons than any ntrnsc relevance to the economc arguments. 8 In the only paper I know of n whch a poverty measure was used as a regressor for aggregate growth across countres, Lopez and Servén (2009) fnd evdence that a hgher nal poverty rate retards growth. As Lopez and Servén observe, the sgnfcance of the Gn ndex n past studes may reflect an omted varable bas, gven that one expects (and I wll later verfy emprcally) that nequaly wll be hghly correlated wh poverty at a gven mean. There are also ssues about the relevant control varables when studyng the effect of nal dstrbuton on growth. The specfcaton choces n past work testng for effects of nal dstrbuton have lacked clear justfcaton n terms of the theores predctng such effects. Consder three popular predctors of growth, namely human development, the nvestment share, and fnancal development. On the frst, basc schoolng and health attanments (often sgnfcant n growth regressons) are arguably one of the channels lnkng nal dstrbuton to growth. Indeed, that s the lnk n the orgnal Galor and Zera (1993) model. 9 Turnng to the second, one of the most robust predctors of growth rates s the share of nvestment n GDP (Levne and Renelt, 1992); yet arguably one of the man channels through whch dstrbuton affects growth s va aggregate nvestment and ths s one of the channels dentfed n the theoretcal lerature. Fnally, consder prvate cred (as a share of GDP), whch has been used as a measure of fnancal sector development n explanng growth and poverty reducton (Beck et al., 2000, 2007). The theores dscussed above based on borrowng constrants suggest that the aggregate flow of cred n the economy depends on the nal dstrbuton. Another set of specfcaton ssues concerns nteracton effects. As Banerjee and Duflo (2003) pont out, whle lqudy constrants stemmng from cred-market falures mply that the 7 An excepton s Ravallon (1998), who studes the effect of geographc dfferences n the dstrbuton of wealth on growth n Chna. 8 The complaton of Gn ndces from secondary sources (and not usng consstent assumptons) n Dennger and Squre (1996) led to almost all the tests n the lerature snce that paper was publshed. 9 More recently, Gutérrez and Tanaka (2009) show how hgh nal nequaly n a developng country can yeld a polcal-economy equlbrum n whch there s ltle or no publc nvestment n basc schoolng; the poorest famles send ther kds to work, and the rchest turn to prvate schoolng. 8

growth rate depends on the extent of nequaly n the nal dstrbuton, they also suggest that there wll be an nteracton effect between the nal mean and nequaly. However, as the further analyss of the Banerjee-Duflo model n the last secton suggests, the more relevant nteracton effect may well be that between poverty and nequaly. Some of the lerature has focused nstead on testng the assumptons of these theores. The emprcal evdence on poverty traps s mxed. At least some of the theoretcal models of poverty traps appear to be hard to reconcle wh the aggregate data; see, n partcular, the dscusson n Kraay and Raddatz (2007) of poverty traps that mght arse from low savngs (hgh tme preference rates) n poor countres. There are also testable mplcatons for mcro data. An mplcaton of a number of the models based on cred-market falures s that ndvdual ncome or wealth at one date should be an ncreasng concave functon of s own past value. Ths can be tested on mcro panel data. Lokshn and Ravallon (2004) provde supportve evdence n panel data for Hungary and Russa whle Jalan and Ravallon (2004) do so usng panel data for Chna. These mcro studes suggest seemngly szeable effcency costs of nequaly. The same studes do not, however, fnd the propertes n the emprcal ncome dynamcs that would be needed for a poverty trap. There s also evdence of nonlnear wealth effects on new busness start ups n developng countres, though wh ltle sgn of a non-convexy at low levels due to lumpness n capal requrements (Mesnard and Ravallon, 2006). Smlarly, McKenze and Woodruff (2006) fnd no sgn of non-convexes n producton at low levels amongst Mexcan mcroenterprses. However, Hoddnott (2006) and Barrett et al (2006) fnd evdence of wealth-dfferentated behavors n addressng rsk n rural Zmbabwe and Kenya (respectvely) that are consstent wh the dea of poverty traps. Mcro-emprcal support for the clam that there are effcency costs of poor nutron and health care for chldren n poor famles has come from a number of studes. In a recent example, an mpact evaluaton by Macours et al. (2008) of a condonal cash transfer scheme n Ncaragua found that randomly assgned cash transfers to poor famles mproved the cognve outcomes of chldren through hgher ntakes of nutron-rch foods and better health care. Ths echoes a number of fndngs on the benefs to dsadvantaged chldren of efforts to compensate for famly poverty; for a revew see Curre (2001). Whle the theores and evdence revewed above pont to nequaly and/or poverty as the relevant parameters of the nal dstrbuton, yet another strand of the lerature has ponted to 9

varous reasons why the sze of a country s mddle class can matter to the fortunes of those not (yet) so lucky to be mddle class. It has been argued that a larger mddle class promotes economc growth, such as by fosterng entrepreneurshp, shftng the composon of consumer demand, and makng more polcally feasble to attan polcy reforms and nstutonal changes conducng to growth. 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. So we have three contenders for the dstrbutonal parameter most relevant to growth: nequaly, poverty and the sze of the mddle class. The fact that very few encompassng tests are found n the lerature, and that these dfferent measures of dstrbuton are not ndependent, leaves one n doubt about what aspect of dstrbuton really matters. As already noted, 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. Smlarly, the man way the mddle class expands n a developng country s probably through poverty reducton, so s unclear whether s a hgh ncdence of poverty or a small mddle class that mpedes growth. Smlarly, a relatve concept of the mddle class, such as the ncome share of mddle quntles, wll probably be hghly correlated wh a relatve nequaly measure, cloudng the nterpretaton. 2.3 Growth and poverty reducton The consensus n the lerature s that hgher growth rates tend to yeld more rapd rates of absolute poverty reducton; see World Bank (1990, 2000), Ravallon (1995, 2001, 2007), Felds (2001) and Kraay (2006). 10 Ths s mpled by another common fndng n the lerature, namely that growth n developng countres tends to be dstrbuton-neutral on average, meanng that changes n nequaly are roughly orthogonal to growth rates n the mean (Ravallon, 1995, 2001; Ferrera and Ravallon, 2009). Dstrbuton-neutraly n the growth process mples that the 10 Also see the revew of the arguments and evdence on ths pont n Ferrera and Ravallon (2009). 10

changes n any standard measure of absolute poverty (meanng that the poverty lne s fxed n real terms) wll be negatvely correlated wh growth rates n the mean. There s also evdence that nequaly matters to how much a gven growth rate reduces poverty (Ravallon, 1997, 2007; World Bank, 2000, 2006; Bourgugnon, 2003; Lopez and Servén, 2006). Intuvely, n hgh nequaly countres the poor wll tend to have a lower share of the gans from growth. Ravallon (1997, 2007) examned ths ssue emprcally usng household survey data over tme (earler versons of the data set used here). Ravallon (1997) found that the followng parsmonous specfcaton fs the data for developng countres well: where H, ln H (1 1 ) ln (6) G and G are the headcount ndex, the Gn ndex and the mean respectvely for country at date t, 0 s the elastcy of poverty reducton to the dstrbuton-corrected growth rate ( 1 1 G ) ln and s a zero mean error term (uncorrelated wh the growth rates). At mnmum nequaly ( G 1 0 ) growth has s maxmum effect on poverty (n expectaton) whle the elastcy reaches zero at maxmum nequaly ( G 1 1). Ravallon (1997) dd not fnd that the elastcy vared systematcally wh the mean, although Lopez and Servén (2006) showed that f ncomes are log-normally dstrbuted then such a varaton s mpled theoretcally. Easterly (2009) conjectured that the nal poverty rate s lkely to be the better predctor of the elastcy than nal nequaly, though no evdence was provded. 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 the nal dstrbuton, whch s measured from surveys. By calculatng the dstrbutonal statstcs drectly from the prmary data, some of the nconsstences and 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. 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. 11

I found 99 developng and transon countres wh at least two suable household surveys snce about 1980. (For about 70 of these countres there are three or more surveys.) 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). 12 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 (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. 13 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 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; 14 three-quarters of the spells use consumpton. Naturally the tme perods between surveys are not unform across countres. The medan year of the frst survey s 1991 whle the medan for the second s 2004. 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 household survey for date t n country and the earlest avalable survey for date t, the proportonate annualzed dfference ( growth rate ) for the varable x s denoted g x ) ln( x / x ) (droppng the subscrpt on t and for brevy). ( / Natonal accounts (NAS) data and socal ndcators are also used, matched as closely as possble 12 The data set was constructed from PovcalNet n December 2008. Seven countres were dropped because the poverty rate was zero n the earlest surveys. 13 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 (2008). 14 The only excepton was Peru, for whch ncomes allowed a much longer tme perod. 12

to survey dates. All monetary measures are n constant 2005 prces (usng country-specfc 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 $2.00 per day at 2005 PPP, whch s the medan poverty lne amongst developng countres. 15 Let F (z) denote the dstrbuton functon for country at date t; then H F (2). In 2005, $2 a day was also very close to the medan consumpton per person n the developng world. 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. 16 Inequaly s measured by the usual Gn ndex ( G ) half the mean absolute dfference between all pars of ncomes normalzed by the overall mean. The sze of the mddle class ( MC ) s measured by the proporton of the populaton lvng between $2 and $13 a day (followng Ravallon, 2009); so MC F 13) F (2). 17 ( These bounds are also somewhat arbrary, although ths defnon appears to accord roughly wh the dea of what means to be mddle class n Chna and Inda (Ravallon, 2009). By contrast, those lvng above $13 a day can be thought of as the mddle class by Western standards; the share of the Western mddle class s F (13). These are nterpretable as 1 absolute measures of the mddle class. I also calculated a relatve defnon of the mddle class, namely the consumpton or ncome share controlled by the mddle three quntles ( MQ ), as used by Easterly (2001). Table 1 provdes summary statstcs for both the earlest and latest survey rounds. The mean Gn ndex stayed roughly unchanged at about 42%. The nal ndex ranged from 19.4% 15 Ths s based on the complaton of natonal poverty lnes presented n Ravallon et al. (2009). The methods used n measurng poverty and nequaly usng these data are descrbed n Chen and Ravallon (2008). 16 The $1.25 lne s the mean of the poorest 15 countres n terma of consumpton per person. $13 per person per day corresponds to the offcal poverty lne n the US for a famly of four; see Department of Health and Human Servces. 17 Smlarly Banerjee and Duflo (2008) used the nterval $2 to $10 a day to defne the mddle class. 13

(Czech Republc) to 62.9% (Serra Leone), both around 1990. In the earlest surveys, about one quarter of the sample had a Gn ndex below 30% whle one quarter had an ndex above 50%. The average sze of the mddle class ncreased, from a mean MC of 48% to a mean MC of 53%. The mddle-class expanded n 64 countres and contracted n 35. There s also a marked bmodaly n the dstrbuton of countres by the sze of ther mddle class, as s evdent n Fgure 1, 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 57. 18 The relatve measure of the sze of the mddle class behaved dfferently; there was ltle change n the mean MQ over tme (Table 1) and the densy functon was unmodal n both the earlest and latest surveys. Table 2 gves the correlaton coeffcents, focusng on the man regressors used later. The correlatons pont to a number of potental concerns about the nferences drawn from past research. The Gn ndex s hghly (negatvely) correlated wh the ncome share of the mddle three quntles (r=-0.971 for the earlest surveys and -0.968 for the latest). The poverty measures are also strongly correlated wh the survey means; ln H and ln have a correlaton of - 0.851 (whle s -0.836 for ln F (1.25) and ln ). The least-squares elastcy of ln H wh respect to the nal survey mean (.e., the regresson coeffcent of ln H on ln ) s - 1.305 (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= 0.241 and 0.099 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 =0.802. 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 -0.975; 95% of the varance n the nal sze of the 18 For further dscusson of the developng world s rapdly expandng mddle class, and the countres left behnd n ths process, see Ravallon (2009). 14

mddle class s accountable to dfferences n the nal poverty rate. (The bmodaly n terms of the sze of the mddle class n Fgure 1 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 MC can also be attrbuted to the changes n H. 19 The absolute and relatve measures of the sze of the mddle class are posvely correlated but not strongly so. There s a strong correlaton between the rate of poverty reducton and the ordnary growth rate n the survey mean (confrmng the studes revewed n secton 2). Fgure 2 plots the rate of poverty reducton ( g H ) ) aganst g ). The regresson lne n Fgure 2 has a slope of ( -1.372 (t=-5.948) wh R 2 =0.363. ( 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 the later results. Table 2 also gves the correlaton coeffcents between and the varous measures of nal dstrbuton. The correlatons are all small. 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 more concentrated n the lower mode n Fgure 1. Two-thrds (20 out of 29) of SSA countres are n the lower mode for the earler survey round; the correspondng means of MC were 22.89% (s.e.=3.62%) and 59.07% (3.01%) for SSA and non-ssa countres respectvely and the dfference s statstcally sgnfcant at the 1% level. Inequaly too s hgher n SSA; the mean Gn ndex n the earlest surveys s 0.474 (0.018) for SSA versus 0.390 (0.017) n non-ssa countres, and the dfference s sgnfcant (t=7.68). There s clearly a SSA effect n both growth and poverty reducton, though we wll see that ths s accountable to the other varables n the estmated models. 4. Convergence? Vrtually all of the papers n the emprcal lerature revewed n secton 2 have assumed that the parameters of the dynamc processes for growth and poverty reducton are ndependent 19 R 2 =0.826 for the regresson of MC MC on F ( 2) F (2) ; the regresson coeffcent s -0.896 (t=-25.496;n=92), whch s sgnfcantly dfferent from -1 (t=2.946). 15

of the nal level of poverty. The easest way to see that ths assumpton cannot be rght s to show that the standard models mply somethng that s not supported by the data. Consder the most common emprcal specfcaton for the growth process n the mean: ln ln (7) 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 (8) where 0 and s a zero-mean error term. Ths assumes that relatve dstrbuton fluctuates around a statonary mean, wh changes n dstrbuton orthogonal to growth rates n the mean. The mpled growth model for poverty s then: ln H ln H (9) 1 for whch s readly verfed that and ( 1 ) 1. The parameters of (7) and (8) (,,, ) can vary across countes but (for the sake of ths argument) suppose they do so ndependently of H mean, have:. Then the speed of convergence for the ln / ln 1, s the same as that for poverty: ln H / ln H 1. Thus we Proposon 3: In standard log-lnear models for growth and poverty reducton, wh parameters ndependent of the nal level of poverty, the speed of convergence wll be the same for the mean as the poverty measure. However, ths s not borne out by the data. Table 3 gves convergence tests for both the mean and the poverty measures, wh and whout controls. 20 The controls ncluded nal consumpton per capa from the NAS, 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. The survey means exhb convergence wh a coeffcent of -0.013 (t=- 20 The test s the regresson coeffcent of g ( ) on ln. Alternatvely one can estmate the nonlnear regresson g ( ) [(1 e )/ ]ln. Ths gave a very smlar result to (1) n Table 4, namely ˆ 0.012. (t=-2.865). Clearly, the approxmaton that e 1 works well. 16

3.412) whout the controls and -0.042 (t=-7.435) wh them. But ths not true of the poverty measures. Indeed the proportonate rates of poverty reducton are orthogonal to nal levels. 21 Fgure 3 plots the data, and gves a non-parametrc regresson lne. Clearly these results do not support the dea that the mean and the poverty measure have the same speed of convergence; ndeed, there s no convncng sgn of poverty convergence. The rest of ths paper wll try to explan why. In terms of the model above, wll be shown that the parameter s a decreasng functon of the nal poverty rate whle the elastcy of poverty to the mean,, s a decreasng functon of the nal level of poverty. 5. The relevance of nal poverty to growth n the mean As dscussed n secton 2, nal dstrbuton can matter to the rate of poverty reducton through two dstnct channels, namely the growth rate and the elastcy of poverty to the mean. I postulate a smple trangular model n whch rate of growth depends n turn on nal dstrbuton whle the rate of progress aganst poverty depends on the nteracton between the growth rate and the nal dstrbuton. Ths secton focuses on the frst relatonshp; secton 6 turns to the second. The secton begns wh benchmark regressons of growth on the nal mean and nal poverty rate. 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 pace 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 Benchmark regresson for growth Table 4 gves estmates of the followng regresson: 22 g ( ) ln ln H (10) 21 For the $1.25 lne the correspondng regresson coeffcent was -0.005 wh t=-0.393; at the other extreme, for the $13 lne was -0.009 (t=-0.480). Agan, the nonlnear specfcaton gave a very smlar result. 22 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 4 mples a dervatve that s less than uny for 29 years; the largest value of n the data s 27 years. 17

The estmates n column (1) suggest that dfferences n the nal poverty rate have szeable negatve mpacts on the growth rate at a gven nal mean. A one standard devaton ncrease n ln H would come wh 0.021 (2% ponts) declne n the growth rate for the survey mean. The fact that a sgnfcant (partal) correlaton wh the nal poverty rate only emerges when one controls for the nal mean s suggestve of an adverse dstrbutonal effect of hgh poverty. However, s not smply a relatve poverty effect, stemmng from the varance n absolute poverty attrbutable to dfferences n relatve dstrbuton. Ths s evdent n the fact that the convergence parameter ncreases consderably when one adds the nal poverty measure as a regressor. Droppng ln H from (10) the coeffcent on ln falls to -0.013 (t=-3.413). The presence of the poverty rate as a regressor magnfes the convergence parameter, suggestng that the fact that the absolute poverty rate depends on the mean s also playng a crucal role n determnng s sgnfcance n these regressons workng aganst the convergence effect. It mght be conjectured that the effect of ln H n (10) 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 (10) 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 4 became -0.018 (t=-3.547). There s, however, a marked nonlneary n the relatonshp, whch s beng captured by the log transformaton of H n (10). 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 -1.292 for the coeffcent on H come out somewhat more strongly f one adds a squared term n wh both the lnear and squared terms sgnfcant at the 10% level or better. though n both cases the effects H to pck up the nonlneary, A smple graphcal test for msspecfcaton of the functonal form n (10) s to plot g( ) 0.035ln (from column (1) n Table 4) aganst ln H. Fgure 4 gves the results, 18

along wh a locally-smoothed (non-parametrc) regresson lne. The relatonshp s close to lnear n the log poverty rate. 23 The log transformaton appears to be the rght functonal form. The more relevant poverty lne s that usng the $2.00 a day lne. On replacng ln H ln F (1.25) n (10) the poverty rate stll had a negatve coeffcent but was 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)) (11) The estmate of 1 2 was -0.010, but was not sgnfcantly dfferent from zero (t=-0.801), suggestng that (10) s the correct specfcaton. The results were also robust to usng the poverty gap ndex nstead of the headcount ndex; the correspondng verson of (10) was smlar, wh a coeffcent on the log of the poverty gap ndex of -0.011, wh t-rato of -2.338. However, the f s better usng the headcount ndex. Recall that the sample n estmatng (10) used both consumpton and ncome surveys, and that the latter may have more measurement error. Estmatng the regresson solely on consumpton surveys strengthened the result; analogously to (10) one obtans column (2) of Table 4. The condonal convergence effect s even stronger, as s the poverty effect. The results are robust to usng NAS consumpton growth nstead (Table 4). The notable dfferences are that the convergence parameter n (10) s lower, ˆ 0. 02 (column 3, Table 4) and that the headcount ndex based on the $1.25 lne s a slghtly stronger predctor of the NAS consumpton growth. (The results usng NAS consumpton growth were less sensve to the choce of poverty lne between $2.00 and $1.25 a day.) Another way to use NAS consumpton s as a control for other nal condons nfluencng the long-run value of the survey mean. Augmentng (10) wh ths extra control varable gves, for the full sample: g ( ) 0.181 0.050ln (3.942) ( 6.817) 0.011ln H ( 2.382) And for the sample of consumpton surveys: g ( ) 0.232 0.061ln (4.868) ( 6.507) 0.017 ln H ( 3.624) The results are consstent wh the expectaton that 0.022lnC (3.682) 0.025ln C (3.346) The poverty effect remans evdent, though wh a lower coeffcent. 23 ˆ R 2 =0.288; n=87 (12) ˆ R 2 =0.317; n=66 (13) ln C s pckng up long-run dfferences. In both cases I have scaled the vertcal axs to accord wh the sample mean growth rate by usng the devaton of the log nal mean from s sample mean value. by 19

5.2 Further tests on the subsample wh three surveys One can form a subsample of about 70 countres wh at least three household surveys. 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. There are at least four ways one can explo the extra round of surveys. The frst s to test for convergence more robustly to measurement errors. 24 One way of dong ths s to calculate the trend over the three surveys and test f ths s correlated wh the startng value. I estmated 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 was stll evdent; the regresson coeffcent of the estmated trend on the log mean from the earlest survey was -0.009 (t=-2.052), whch s sgnfcant at the 4% level. And agan there was 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 was 0.007 (t=0.805). Another method 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 2 ( 2 2 1 2 g ( x ) ln( x / x ) /. Usng ths method, uncondonal mean convergence was no longer 2 evdent (though condonal convergence was stll found) but there was an ndcaton of poverty dvergence; regressng g H ) (the proportonate change n the poverty measure between the ( mddle and fnal rounds) on M ) ; the coeffcent was 0.029, whch s sgnfcant at the 6% ( 2 H 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 measure from the earlest survey ( ln 1 ); the 2 result was smlar, namely ltle sgn of (uncondonal) mean convergence but mld dvergence for poverty (a coeffcent of 0.027 wh t=1.819). 24 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 NAS consumpton. However, sgnfcant condonal convergence n the means (ncludng those only from consumpton surveys) and NAS consumpton s stll evdent (Table 4). 20

Secondly, the subsample can be used to form nter-temporal averages, to reduce the attenuaton bases n the benchmark regresson due to measurement error; equaton (10) can be re-estmated n the form: g ( ) ln M( ) ln M( H ) 2 2 (14) Column (4) of Table 4 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 equaton (10). The thrd 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 (15) The nstrumental varables were 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 Generalzed Methods of Moments (GMM) estmates of (15) are found n Table 4, Column (5). (I also gve the correspondng result usng NAS consumpton n column (6).) We see that the fndng that a hgher nal poverty rate mples a lower subsequent growth rate (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. Analogously to equaton (12.1), on addng ln C to specfcaton (5) n Table 4, and treated as exogenous, one obtans 2 (usng the same set of nstruments): g ( ) 0.235 0.066 ln (3.731) ( 4.407) 0.022 ln H ( 3.954) 0.035ln C (4.481) ˆ (16) Droppng ln C from the set of IVs gves nstead: 2 g ( ) 0.144 0.041ln (1.815) ( 2.206) 0.016 ln H ( 2.634) 0.025ln C (3.288) ˆ (17) Fnally, one can use the subsample s to estmate a specfcaton wh country-fxed effects, whch sweep up any confoundng latent heterogeney n growth rates at country level. 21

The man results were not robust to ths change. Regressng the change n annualzed growth rates ( g ( ) g ( ) ) on ln( / ) 2 2 1 and ln( H / ) 2 H 2 1, the coeffcent on the 2 former remaned sgnfcant but the poverty rate ceased 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 fxedeffects growth regressons (Hauk and Waczarg, 2009). 25 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 a low sgnal-to-nose rato 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 ). Table 5 gves the levels regresson n logs, whch mples an elastcy of toc of 0.75 (R 2 =0.82) for the latest survey rounds. 26 Usng a country-fxed effects specfcaton n the levels, the elastcy drops to 0.46 whle wh fxedeffects n the growth rates (usng the subsample wh at least three surveys) 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. 5.3 Encompassng regressons It mght be conjectured that the poverty measures (at gven nal means) are pckng up other aspects of the nal dstrbuton, such as nequaly (the varable dentfed n almost all the emprcal lerature, as dscussed n secton 2). Smply addng the log of the nal Gn ndex to equaton (10) does not change the result; the coeffcent on the Gn ndex s not sgnfcantly dfferent from zero; the coeffcent on ln H verson of (10). To nvestgate ths further, I added nequaly ( ln remans (hghly) sgnfcant n the augmented G ), the ncome share of the 25 26 Ths pont s llustrated well by the Monte Carlo smulatons found n Hauk and Waczarg (2009). Includng the seven developng countres wh zero nal poverty ( F ( 2) 0 ) ncreases the elastcy n the levels to 0.750 (t=21.543) but makes ltle dfference to the fxed effects estmates. 22

mddle three quntles ( ln MQ ), the share of the Western mddle class ( 1 F (13) ) and three commonly used varables from the lerature on growth emprcs mentoned above, namely the prmary school enrollment rate, lfe expectancy at brth, and the prce ndex of nvestment goods. The populaton share of the developng world s mddle class was not ncluded gven that s value s nearly lnearly determned by the poverty rate and share of the Western mddle class. Table 6 gves the encompassng regressons usng both survey means and consumpton from the NAS. The table also gves restrcted forms that passed comfortably. The nal poverty rate remans a (hghly) sgnfcant predctor of growth n these encompassng models. Furthermore, s coeffcent falls only modestly n the encompassng regressons (comparng columns (1) and (3) n Table 4 wh (1) and (2) respectvely n Table 6); ths suggests that a large share of s explanatory power s ndependent of these extra varables. 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 also sgnfcant for the growth rates n the survey means (but not NAS consumpton), though wh a negatve sgn. (That was also true f one replaced MQ wh ln G.) The two regonal effects that have been dentfed n the lerature on growth emprcs are for Sub-Saharan Afrca (negatvely) and East Asa (posvely). I tested augmented versons of the regressons n Table 6 wh dummy varables for these two regons. There was no sgn of an SSA effect n any specfcaton. There was a negatve East Asa effect though only (mldly sgnfcant (at the 8% level). Of course, there are uncondonal effects on growth n both regons. But these are largely captured whn the model, partcularly for Afrca. I also tred addng two nteracton effects. In the frst, I added an nteracton effect between nequaly and the nal mean, as dscussed above; ths was hghly nsgnfcant (t-rato of -0.063). Second, addng ln G. ln H I found that had a posve coeffcent (contrary to the theoretcal expectaton dscussed n secton 2) though was not sgnfcantly dfferent from zero at even the 15% level. Inequaly and the ncome share of the mddle quntles are nsgnfcant when one controls for nal poverty (though, of course, nequaly s one factor leadng to hgher poverty), but the populaton share of the Western mddle class emerges wh a sgnfcant negatve coeffcent. The jontly negatve coeffcents on the poverty rate and the share of the Western 23

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 share of the developng world s mddle class. (As one would expect, replacng ln and F (13) H 1 by ln[ F (13) / H ] gave very smlar overall f, though not que as good as Table 6.) The t negatve (condonal) effect of the poverty rate may well be transmted through dfferences n the sze of the mddle class. The subsample wh three surveys also allows one to test for the dstrbutonal effect reported by Banerjee and Duflo (2003), who argued that s not the level of nal nequaly that matters to growth but past changes n nequaly and that ths has an nverted-u effect, whereby changes n nequaly n eher drecton tend to reduce the growth rate. To test for ths, I repeated the regressons above usng the annualzed growth rates between the most recent and the mddle survey and replacng the Gn ndex for the earlest survey by a quadratc functon of the change n the Gn ndex between the earlest survey and the mddle survey. (Other varables were the same except for the mddle survey.) The coeffcents on the nal poverty rate (now the poverty rate for the mddle survey) remaned sgnfcant at the 1% level and the Western mddle class effect remaned evdent but wh reduced sgnfcance. However, the coeffcents for the quadratc functon of the change n the lagged Gn ndex were ndvdually and jontly nsgnfcant n the regressons for both growth rates. Nor was there any sgn of an nverted U relatonshp wh the lagged changes n the poverty rate. Whle the above results appear to be convncng 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. As already noted, 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 4 are sgnfcantly correlated wh nequaly; r=-0.442. Snce hgher nequaly tends to mply hgher poverty at a gven mean (secton 3), also mples lower growth prospects. 6. Inal poverty and the growth elastcy of poverty reducton I turn now 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 24

dstrbuton on the rate of poverty reducton, as dstnct from the ndrect effect va the rate of growth. Agan I focus on the $2 lne, although the $1.25 lne gave smlar results. For any gven relatve dstrbuton the elastcy of the poverty rate to the mean s smply gven by (one mnus) the elastcy of the poverty rate wh respect to the poverty lne. 27 Ths can be calculated at any gven poverty lne. The nteracton effect between ths elastcy and the growth rate s then an obvous predctor of the rate of poverty reducton. 28 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 ln( / ) s not sgnfcantly dfferent from uny; the coeffcent s 1.062 wh a standard error of 0.198 and R 2 =0.389. 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, 29 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 was 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 7 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 regresson: g ( H) 0 1 ln H ( H ) g( ) 2 0 1 2 (18) Results are gven for both OLS and IVE; the IVE method uses the growth rate n prvate consumpton per capa from the NAS 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 27 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. 28 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). 29 For a recent overvew see Ferrera and Ravallon (2009). 25

exsts due to common measurement errors (gven that the poverty measure and the mean are calculated from the same surveys). The results n Table 7 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 0 s easly accepted. Table 7 also gves homogeney 1 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 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 for (15). The homogeney restrcton was (agan) easly accepted (t=-0.447). The IVE of the regresson coeffcent of g H ) on 1 H ) ( ) was -3.478 (t=-3.092). ( ( g 2 There s also a strong nteracton effect wh the sze of the mddle-class: At the lower mode for g ( H ) 0.011 (0.043 0.029MC ( 1.749) (0.221) ( 4.818) ) g ( ) ˆ R 2 =0.539, n=91 (19) MC of around 15% (Fgure 1), equaton (19) mples a growth elastcy of -0.39 (t=-3.13) whle at the upper mode, around 75%, s -2.13 (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 ) 0.011 (0.167 0.030F ( 1.939) (0.039) ( 0.631) (13) 0.029H (3.638) ) g ( ) ˆ R 2 =0.539, n=91 (20) 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 that s the mddle-class share that matters, as n equaton (19). 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. 26

I also tested an encompassng model wh extra nteracton effects wh G, the partal elastcy of poverty reducton ( ), 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 were 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[ ( )] 0. 687 where I[x] s the ndcator functon ( I [ x] 1 f x>0 and I [ x] 0 otherwse). On stratfyng the parameters accordng to whether the mean s ncreasng or not, and re-estmatng specfcaton (3) n Table 7 one obtans: g( H ) 0.013 (2.869 H 3.117) I[ g( )] g( ) ( 1.628) (4.246) ( 5.046) R 2 =0.552, n=91 (21) (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 1.425 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 elastcy s the nal poverty rate. Fgure 5 plots the rate of poverty reducton aganst the poverty-adjusted growth rate n the survey mean (analogous to Fgure 2, whch used the ordnary growth rate). The slope of the regresson lne s almost twce as hgh (a coeffcent of -2.613, t=-7.273) and R 2 =0.535, as compared to 0.363 for the regresson n Fgure 2. So allowng for nal dstrbuton, as measured by the $2 a day poverty rate, adds 17% ponts to the share of the varance n the rate of poverty reducton that can be explaned by the rate of growth n the survey mean. g g 7. So why don t we see poverty convergence? Recall that the speed of poverty convergence, g ( H ) / ln H, s very close to zero. We can now combne the man results to help explan why. Based on the varous encompassng tests above, my emprcally-preferred model takes the form: 27

g ( H ) (1 H ) g ( ) (22.1) g ( ) ln ln H (22.2) The regressors n (22.2) 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. 30 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: g ( H ln H ) (1 H ln H ) ln (Mean convergence effect) 1 (1 H (Drect effect of poverty) ) g ( ) H (Poverty elastcy effect) (23) On evaluatng all varables at ther sample means and usng the estmates n column (1) of Table 4 and column (5) from Table 7, and usng the OLS elastcy of elastcy of the nal headcount ndex wh respect to the nal survey mean of -1.305, one fnds that the mean convergence effect s -0.038, whle the drect effect of poverty s 0.024 and the poverty elastcy effect s 0.0195. The mean convergence effect s almost exactly cancelled by the combnaton of the two poverty effects,, whch are roughly equal n sze. Naturally, dfferent data ponts and parameter estmates gve dfferent magnudes for ths decomposon, though all share the feature that the two poverty effects work n opposon to the (condonal) mean convergence effect. Evaluatng the decomposon at a hgher nal headcount ndex ncreases the poverty elastcy effect whle reducng the other two components. The estmates usng only the consumpton surveys gve a hgher drect effect of poverty, as do the estmates from the subsample wh three surveys; n the latter case the poverty convergence elastcy s larger due to both a lower mean convergence component and the hgher drect effect. 8. Conclusons Arguably the most nterestng thng about the fact that we do not see poverty convergence n the developng s what tells us about the underlyng process of economc growth and s mpact on poverty. The lack of poverty convergence despe mean convergence and that 30 and ln Nonetheless, as we have also seen, the varance across countres n nal dstrbuton entals that H are not so correlated to prevent dsentanglng ther effects. ln 28

growth reduces poverty suggests that somethng about the nal dstrbuton s offsettng the advantage of backwardness. That somethng turns out to be poverty self. The paper s fndngs pont to three dstnct consequences of beng a poor country for subsequent progress aganst poverty. The usual neoclasscal convergence effect entals that countres wh a lower nal mean, and so (typcally) a hgher poverty rate, grow faster and (hence) enjoy faster poverty reducton than otherwse smlar countres. Aganst ths, there s an adverse drect effect of poverty on growth, such that countres wh a hgher nal ncdence of poverty tend to experence a lower rate of growth, controllng for the nal mean (as well as other controls). Addonally a hgh poverty rate makes harder to acheve a gven proportonate mpact on poverty through growth n the mean. (By the same token, the poverty mpact of economc contracton tends to be smaller n countres wh a hgher poverty rate.) The two poverty effects work aganst the mean convergence effect, leavng ltle or no correlaton between the nal ncdence of poverty and the subsequent rate of progress aganst poverty. In terms of the pace of poverty reducton, the advantage of backwardness for countres startng wh a low capal endowment (gven dmnshng returns to aggregate capal) s largely wped out by the hgh level of poverty that tends to accompany a low nal mean. Ths dynamc dsadvantage of poverty appears to exst ndependently of other factors mpedng growth and poverty reducton, such as human underdevelopment and polcy dstortons. The evdence s mxed on the role played by other aspects of dstrbuton. A larger mddle class by developng-country (but not Western) standards makes growth more povertyreducng. But ths effect s largely attrbutable to the lower poverty rate assocated wh a larger mddle class. Controllng for the nal ncdence of poverty, there s no sgn that a hgher overall level of nal nequaly, as measured by the Gn ndex, nhbs the pace of poverty reducton va eher the rate of growth or the growth elastcy. Nonetheless, nal nequaly s emprcally mportant, va s bearng on the extent of poverty. Ths s plan f one calculates the predcted rate of poverty reducton for each country, gven s nal condons. 31 The fve countres wh the hghest (most negatve) predcted rates of poverty reducton are Lhuana (32), Estona (30), Jordan (36), Belarus (30) and Hungary (25); the numbers n parentheses are ther nal Gn 31 For the followng calculaton I substuted equaton (1) n Table 4 (though other specfcatons gve smlar results) nto the regressons wh homogeney mposed n Table 7. 29

ndces n %, so s clear that most of these are relatvely low-nequaly countres. By contrast, the fve countres wh the lowest predcted values were all hgh nequaly countres, namely: Venezuela (56), Chle (56), Brazl (57), Colomba (57) and South Afrca (59). Whle these fndngs confrm that nal nequaly matters to subsequent progress aganst poverty, they also reveal that the man way matters s va s bearng on the nal ncdence of poverty. There s no sgn n ths paper s results that lower nequaly amongst the non-poor, leavng the ncdence of absolute poverty unchanged, brngs any longer-term payoff n terms of growth and poverty reducton. And n the mnory of cases n whch hgh nequaly comes wh low absolute poverty at a gven mean, does not mply worse longer-term prospects for growth and poverty reducton. Knowng more about the reduced form emprcal relatonshp between growth, poverty reducton and the parameters of the nal dstrbuton wll not, of course, resolve the polcy ssues at stake. The polcy mplcatons of dstrbuton-dependent poverty reducton depend on why countres startng out wh a hgher ncdence of poverty tend to face worse growth prospects and enjoy less poverty reducton from a gven rate of growth. The nal level of poverty may well be pckng up other factors, such as the dstrbuton of human and physcal capal; ndeed, the underlyng theores pont more to wealth poverty than consumpton or ncome poverty. The control varables used here for schoolng, lfe-expectancy and the prce of nvestment goods do not knock out the effect of poverty, eher on growth or poverty reducton at a gven rate of growth. However, the cross-country emprcal relatonshps reported here do pont to the mportance n future work of better understandng the handcaps faced by poor countres n ther efforts to become less poor. 30

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Annualzed proportonate rate of poverty reducton Fgure 1: Denses of mddle-class populaton shares.020 Kernel densy.016.012.008.004.000 0 20 40 60 80 100 Frst survey's $2-$13 populaton share (%) Second survey's $2-$13 populaton share (%) Fgure 2: Rate of poverty reducton plotted aganst rate of growth n survey mean.3.2.1.0 -.1 -.2 -.3 -.4 -.15 -.10 -.05.00.05.10.15 Annualzed growth rate n survey mean 36

Annualzed log dfference n headcount ndex Growth rate n survey mean Fgure 3: Growth rates plotted aganst nal values 1(a): Survey means.15.10.05.00 -.05 -.10 -.15 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 Log mean n earlest survey 1(b): Headcount ndces of poverty.2.1.0 -.1 -.2 -.3 -.4 -.5 -.6 0 1 2 3 4 5 Log headcount ndex n earlest survey 37

Annualzed proportonate rate of poverty reducton Annualzed growth rate controllng for nal mean Fgure 4: Growth rate wh a control for the nal mean plotted aganst the nal poverty rate.15.10.05.00 -.05 -.10 -.15-1 0 1 2 3 4 5 Log nal poverty rate ($2/day) Fgure 5: Rate of poverty reducton plotted aganst dstrbuton-corrected rate of growth.3.2.1.0 -.1 -.2 -.3 -.4 -.10 -.05.00.05.10 Poverty-adjusted rate of growth n survey mean 38

Table 1: Summary statstcs No. observatons Mean Standard devaton Year Earlest survey 92 1990.23 5.51 Latest survey 92 2003.34 3.10 Survey mean Earlest survey 92 126.88 98.55 ($PPP, 2005) Latest survey 92 151.00 104.84 Annualzed rate of growth n survey mean 92 1.61 4.01 (%/year) Gn ndex (%) Earlest survey 92 42.49 9.87 Latest survey 92 41.96 8.33 Poverty rate for $1.25 Earlest survey 92 31.46 24.77 a day (%) Latest survey 92 24.12 24.55 Poverty rate for $2 Earlest survey 92 46.42 33.57 a day (%) Latest survey 92 39.79 31.04 Share of developng- Earlest survey 92 48.43 29.27 world mddle class (%) Latest survey 92 52.97 25.17 Share of Western Earlest survey 92 5.15 8.20 mddle class (%) Latest survey 92 7.23 9.14 Income share of mddle Earlest survey 89 45.26 5.96 three quntles (%) Latest survey 89 45.54 4.95 Note: The sample s all Part 2 member countres of the World Bank wh adequate natonally-representatve household surveys and for whch the estmated headcount ndex for the $2 a day lne s posve n the earlest survey. 39

Table 2: Correlaton matrx Growth of poverty rate for $2/day ( g ( H ) ) Growth rate of survey mean ( g ( ) ) -0.573 Survey mean ( ln ) 0.017-0.355 Poverty rate for $2/day ( ln H ) 0.017 0.209-0.859 Gn ndex of nequaly ( ln G ) 0.176-0.048 0.010 0.253 Mddle class populaton share ( MC ) -0.122-0.244 0.880-0.815-0.199 Western mddle class share ( 1 F (13) ) 0.189-0.335 0.742-0.722 0.136 0.399 Income share of mddle three quntles ( MQ ) -0.139-0.017 0.069-0.324-0.959 0.279-0.054 Tme between survey rounds ( ) 0.108-0.107 0.070 0.083 0.190-0.046 0.134-0.146 g ( H ) g ( ) ln ln H ln G MC 1 F (13) MQ Note: Correlaton matrx for common sample of complete data for all varables (n-83); par-wse correlatons quoted n text use all avalable observatons for that par of varables and so may dffer from those above.

Table 3: Estmated convergence parameters (1) Surveys means (full sample) Uncondonal -0.013 (-3.413; n=99) Condonal -0.042 (-7.435; n=90) (2) Surveys means (consumpton surveys only) -0.010 (-1.882; n=74) -0.040 (-4.928; n=68) (3) Consumpton per capa from NAS -0.007 (-1.743; n=92) -0.026 (-4.431; n=90) (4) Headcount ndex ($2.00 a day) 0.005 (0.542; n=86) -0.015 (-1.035; n=86) (5) Headcount ndex ($1.25 a day) -0.005 (-0.393; n=79) -0.028 (-1.734; n=79) Note: The table gves ˆ n the regresson g ( ) ln X. T-ratos based on Whe standard errors (corrected for heteroskesdcy). The controls (all for earlest survey date) used n testng for condonal convergence were log mean consumpton per capa from NAS (for the survey means and poverty measures), log prmary school enrollment rate; log lfe expectancy; log relatve prce ndex of nvestment goods. Table 4: Alternatve estmates of the regresson of growth rates on nal mean and nal headcount ndex of poverty (1) (2) (3) (4) (5) (6) Sample wh two surveys Sample wh three surveys Full sample Consumpton surveys only NAS consumpton per capa Means from frst two surveys used as nal condons GMM estmator wh IVs from earlest survey rounds As for (5) but usng NAS consumpton nstead of survey means Intercept 0.234 (5.183) 0.300 (5.850) 0.151 (3.705) 0.235 (4.569) 0.175 (2.772) 0.177 (3.517) Log nal mean -0.035 (-5.131) -0.044 (-5.318) -0.020 (-3.037) -0.029 (-3.264) -0.019 (-1.469) -0.014 (-1.804) Log nal headcount ndex -0.017 (-3.626) -0.025 (-4.845) -0.011 (-2.711) -0.022 (-6.305) -0.020 (-3.090) -0.026 (-4.468) R 2 0.147 0.201 0.128 0.133 n.a. n.a. N 92 70 81 77 64 59 Notes: The dependent varable s the annualzed change n log survey mean ( g ) for (1), (2), (4) and (5) and annualzed change n log prvate consumpton ( per capa from NAS ( g ( C ) ) for (3) and (6). The nal mean corresponds to the same measure used for the growth rate n each regresson. The poverty rate s $2.00 for survey means and $1.25 for NAS consumpton (column 2). The t-ratos n parentheses are based on robust standard errors; denotes sgnfcant at the 5% level; denotes sgnfcant at the 1% level. 41

Table 5: Alternatve estmates of the elastcy of the survey mean to NAS consumpton per capa ˆ N R 2 Levels for latest ln lnc 0.747 97 0.823 survey (21.463) Levels for earlest ln lnc 0.748 92 0.728 survey (14.082) Fxed effects n g ( ) g ( C ) 0.508 92 0.208 levels Fxed effects n growth rates (4.936) g( ) g ( C) 0.094 (7.389) 65 0.069 Table 6: Encompassng regressons for consumpton growth rates (1) (2) (3) (4) Survey Means Consumpton from NAS Survey Means Consumpton from NAS Intercept 0.442 (0.795) 0.617 (1.234) 0.26 (1.279) -0.275 (-1.914) Inal mean ( ln for (1) and -0.058-0.035-0.060-0.030 (-5.961) (-3.657) (-6.912) (-3.764) (3) and ln C for (2) and (4)) Poverty rate ( ln H ) -0.027-0.017-0.027-0.014 (-5.482) (-3.033) (-5.750) (-3.024) Gn ndex ( ln G ) -0.020-0.081 0 0 (-0.400) (-1.784) Income share of mddle three -0.117-0.167-0.091 0 quntles ( ln MQ ) (-1.477) (-2.167) (-3.985) Share of populaton n Western mddle class ( 1 F (13) ) -0.102 (-2.284) -0.128 (-2.815) -0.110 (-2.432) -0.133 (-3.691) Prmary school enrolment rate 0.007 0.003 0 0 (log) (0.700) (0.271) Lfe expectancy (log) 0.117 (2.768) 0.154 (3.653) 0.129 (3.068) 0.139 (3.665) Prce of nvestment (log) -0.014 (-2.650) -0.016 (-3.140) -0.014 (-2.698) -0.017 (-3.434) N 0.434 0.470 0.430 0.453 R 2 88 84 88 87 Notes: The dependent varable s the annualzed change n log mean ( g ) for (1) and (3) and g C ) for (2) and (4)). The nal mean corresponds to the same measure used for the growth rate n each regresson. The share of the Western mddle class was not logged gven that 11 observatons are lost because of zeros. The t-ratos n parentheses are based on robust standard errors; denotes sgnfcant at the 5% level; denotes sgnfcant at the 1% level. ( (

Table 7: Regressons for proportonate change n poverty rate as a functon of the growth rate and nal poverty rate (1) (2) (3) (4) (5) (6) OLS IVE OLS IVE OLS IVE Intercept 0.002 (0.078) 0.008 (0.267) -0.012 (-1.908) -0.005 (0.607) -0.012 (-2.175) -0.008 (-1.365) Inal poverty rate ( ln H ) -0.004 0.008 0 0 0 0 (-0.792) (0.267) Growth rate (annualzed change -2.674-3.564-2.615-3.323 0 0 n log survey mean, g ( ) ) (-6.660) (-4.325) (-6.608) (-4.560) Growth rate nteracted wh nal 2.780 3.492 2.621 3.101 0 0 poverty rate ( g ( ). H ) (5.206) (3.650) (4.915) (3.746) (1-Poverty rate) tmes growth rate ( g ( ).(1 H ) ) 0 0 0 0-2.613 (-7.273) -3.294 (-4.585) N 91 86 91 86 91 86 R 2 0.537 0.439 0.535 0.458 0.535 0.466 Homogeney test 0.673-0.215 0.037-0.620 n.a. n.a. Notes: The dependent varable s the annualzed change n log poverty rate for $2 a day ( g ( H) ); t-ratos based on robust standard errors n parentheses; denotes sgnfcant at the 5% level; denotes sgnfcant at the 1% level. The homogeney test s the t-test for the sum of the coeffcents on the growth rate g ( ) and the growth rate nteracted wh nal poverty rate g ( ) H ; f the relatonshp s homogeneous then the coeffcents sum to zero and the regressor becomes g ).(1 H ). (