Why Don t We See Poverty Convergence?


 Kellie Thompson
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1 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 developngcountry, 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: 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.
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 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 wdelyused loglnear 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 subsample 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
3 dfferent specfcaton choces, ncludng treatng nal dstrbuton as endogenous by treatng lagged nal dstrbuton as excludable. The results suggest that meanconvergence 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 credmarket 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 quasconcave 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 effcencyenhancng 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
4 whout a lower poverty measure by redstrbutng ncome amongst the nonpoor, and poverty can be reduced whout lower nequaly. (Smlarly, efforts to help the mddleclass 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 credmarket 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
5 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 lowlevel nonconvexy, 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 BanerjeeDuflo model to llustrate ths hypothess, whch wll be tested later n the paper. The basc set up of the BanerjeeDuflo 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
6 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 meanpreservng spread n the wealth dstrbuton n ths economy wll reduce future wealth and by mplcaton the growth rate. However, the BanerjeeDuflo 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 rewre (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 meanpreservng 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
7 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 BanerjeeDuflo 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 SalaMartn (1992), crosscountry 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 countrylevel fxed effects n growth rates; I wll return to ths pont. 0 (5) 6 If there s (unrestrcted) frstorder domnance, whereby w ( p)/ H 0 for all p [0, 1], then t 1 / H t 0. However, frstorder 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
8 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 credmarket 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 polcaleconomy 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
9 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 BanerjeeDuflo 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 credmarket 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 nonconvexy at low levels due to lumpness n capal requrements (Mesnard and Ravallon, 2006). Smlarly, McKenze and Woodruff (2006) fnd no sgn of nonconvexes n producton at low levels amongst Mexcan mcroenterprses. However, Hoddnott (2006) and Barrett et al (2006) fnd evdence of wealthdfferentated behavors n addressng rsk n rural Zmbabwe and Kenya (respectvely) that are consstent wh the dea of poverty traps. Mcroemprcal 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 nutronrch 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
10 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). Mddleclass 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 dstrbutonneutral on average, meanng that changes n nequaly are roughly orthogonal to growth rates n the mean (Ravallon, 1995, 2001; Ferrera and Ravallon, 2009). Dstrbutonneutraly 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
11 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 dstrbutoncorrected 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 lognormally 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
12 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.) 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 threequarters 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 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 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
13 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 $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
14 (Czech Republc) to 62.9% (Serra Leone), both around 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 mddleclass 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 cutoff 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 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= for the earlest surveys and for the latest). The poverty measures are also strongly correlated wh the survey means; ln H and ln have a correlaton of (whle s for ln F (1.25) and ln ). The leastsquares elastcy of ln H wh respect to the nal survey mean (.e., the regresson coeffcent of ln H on ln ) s (t=13.340). (All tratos 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 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
15 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 ( (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 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: SubSaharan Afrca (SSA). By the $2.00 a day lne, the mean of H for SSA s 76.04% as compared to 29.51% for nonssa 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. Twothrds (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 nonssa 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 (0.018) for SSA versus (0.017) n nonssa 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 (t= ;n=92), whch s sgnfcantly dfferent from 1 (t=2.946). 15
16 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 countryspecfc effect, 1 s a countryspecfc convergence parameter and s a zeromean error term. (To smplfy notaton I assume evenly spaced data for now.) Next let the headcount ndex of poverty be a loglnear functon of the mean: ln H ln (8) where 0 and s a zeromean 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 loglnear 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 wdelyused 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 (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 (t=2.865). Clearly, the approxmaton that e 1 works well. 16
17 3.412) whout the controls and (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 nonparametrc 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 wdelyused (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 wh t=0.393; at the other extreme, for the $13 lne was (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
18 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 (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 (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 reestmated (10) usng cubc functons of control for the nal mean. Whle I found some sgn of hgherorder 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 (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 tratos a trato of 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
19 along wh a locallysmoothed (nonparametrc) 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 , 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 , wh trato of 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 (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 longrun value of the survey mean. Augmentng (10) wh ths extra control varable gves, for the full sample: g ( ) ln (3.942) ( 6.817) 0.011ln H ( 2.382) And for the sample of consumpton surveys: g ( ) ln (4.868) ( 6.507) 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 longrun 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
20 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 (datespecfc) 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 (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 (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 ( 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 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
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