On Measuring Pro-Poor Growth. 1. On Various Ways of Measuring Pro-Poor Growth: A Short Review of the Literature

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1 On Measuring Pro-Poor Growh 1. On Various Ways of Measuring Pro-Poor Growh: A Shor eview of he Lieraure During he pas en years or so here have been various suggesions concerning he way one should check wheher economic growh was in favor of he poor. The presen secion gives a quick survey of he differen proposals ha have appeared in he lieraure o measure "pro-poor growh". Before reviewing hese conribuions a disincion should be made beween an absolue and a relaive approach o his opic. Thus some sudies (see, Baulch and McCulloch, 2002, or Kakwani and Pernia, 2000) consider ha growh will be propoor if povery falls more han i would have fallen, had all incomes grown a he same rae. This is herefore a "relaive approach" in he sense ha a pro-poor growh requires ha he incomes of he poor grow a a higher rae han hose of he non-poor. I is however also possible o ake an "absolue approach" o povery. In such a case growh will be assumed o be "pro-poor" if he sandard living of he poor people has improved. Whaever approach one selecs i should be clear ha he answer o he quesion "was growh "pro-poor"?" will depend on he measure of povery ha is seleced and he povery line ha is adoped. a) The avallion and Chen (2003) definiion of "pro-poor" growh: avallion and Chen (2003) have proposed an ineresing ool o measure he impac of growh on povery. They called i he "Growh Incidence Curve" (GIC) and i is defined as follows. On he horizonal axis plo he various perceniles of he income (or consumpion) disribuion 1. As a consequence a he 50 h percenile he Growh Incidence Curve will indicae he growh rae of he median income. Clearly if he curve is above he horizonal axis a all poins up o some percenile p ~, we can conclude ha povery has fallen when i is measured via he headcoun raio and he povery line is no greaer han p ~ (see, Akinson, 1987). Noe ha he area under he growh incidence curve up o he headcoun raio will give he oal growh in incomes of he poor during he period under analysis. avallion and Chen (2003) have hus defined he "pro-poor growh rae" as he mean growh rae of he poor. There is clearly a difference beween his mean growh rae of he poor and he growh rae of he mean income (consumpion) of he poor. b) The Baulch and McCulloch (2002) Approach: "Pro-poor" growh may be also analyzed from a differen angle. Since an index of povery can usually be expressed as a funcion of he mean of he disribuion of he variable on he basis of which his index is compued and of he Lorenz curve corresponding o his disribuion, i is generally possible o decompose a change in 1 Naurally, if one works wih daa colleced a he household level, he variable should be some sandardized income or consumpion level, he normalizaion depending on he equivalence scale ha is chosen. 1

2 povery (in he povery index) ino elemens measuring respecively he impac of he growh rae of he mean income (consumpion), ha of he changes in he disribuion (variaions in he degree of inequaliy of he disribuion) and generally some ineracion effec (see, for example, Da and avallion, 1992). Then growh will be defined as "disribuion neural "(corresponding o a fla Growh Incidence Curve) if he redisribuion componen ha was jus menioned is nil whereas i will be "propoor" if his redisribuion componen is negaive. In oher words Baulch and McCulloch (2002) derive heir measure of pro-poor growh by comparing he acual disribuion of income wih he one ha would have been observed, had here been no change in he disribuion of incomes (ha is, had growh been "disribuion-neural"). Noe ha Kakwani (2000) proposed a decomposiion which does no include any ineracion effec. More precisely le be a povery measure ha is fully characerized by he povery line z, he mean income and he Lorenz curve L(p), so ha z,, L( p)) (1) The proporional change ( d / ) in povery beween imes and ' may hen be expressed as ( ' ' d / ) Ln[ ( z,, L ( p))] Ln[ ( z,, L ( p))] (2) where he subscrips refer o he ime period ( or '). I is assumed ha here is no change over ime in he povery line z. Using he concep of Shapley decomposiion 2 (see, Shorrocks, 1999, and Sasre and Trannoy, 2002, for more deails on his decomposiion) i can be shown ha he relaive change in povery ( d / ) may be expressed as he sum of wo componens, one, Gr, reflecing he impac of growh, inequaliy remaining consan, and he oher, In, measuring he effec of a change in inequaliy, he mean income saying consan, ha is ( d / ) Gr In (3) where Gr (1/ 2){[ Ln( z,, L ( p)))] Ln (( z,, L ( p)))] ' [ Ln( z,, L ' ' ( p)))] Ln( z,, L ' ( p)))]} (4) and In (1/ 2){[ Ln( z,, L [ Ln( z,, L ' ' ( p)))] Ln( z,, L ( p)))] ' ( p)))] Ln( z,, L ( p)))]} ' (5) 2 Kakwani (2000) did no use explicily he concep of Shapley decomposiion bu he decomposiion he proposed amouns in fac o using he Shapley decomposiion. 2

3 The concep of "povery bias of growh (PBG)" defined by Baulch and McCulloch (2002) may, in fac, be expressed as PBG In (6) In oher words Baulch and McCulloch (2002) derive heir measure of pro-poor growh by comparing he acual disribuion of income wih he one ha would have been observed, had here been no change in he disribuion of incomes (ha is, had growh been "disribuion-neural"). c) The Kakwani and Pernia (2000) Approach: These auhors defined firs wha hey called he oal povery elasiciy of growh, ha is, he percenage change in povery when he growh in he mean income (consumpion) is equal o 1%. They hen defined a second elasiciy which measures he percenage change in povery ha is observed when he growh in mean income (consumpion) is equal o 1% and here is no change over ime in relaive inequaliy. For Kakwani and Pernia (2000) he Pro-Poor Growh index (PPGI) is equal o he raio of hese wo elasiciies and hey concluded ha growh is pro-poor if his raio PPGI is greaer han one. Noe ha if here is negaive growh, growh will be defined as pro-poor in relaive erms if he relaive loss in income from negaive growh is smaller for he poor han for he non-poor, ha is if he raio PPGI is smaller han one. More precisely Le be he oal povery elasiciy of growh, ha is, he percenage change in povery ( d / ) when he growh in he mean income (consumpion) is equal o 1%. Similarly call he percenage change in povery (Gr ) ha is observed when he growh in mean income (consumpion) is equal o 1% and here is no change over ime in relaive inequaliy. The measure is also called he relaive growh elasiciy of povery and i is clearly always negaive. Kakwani and Pernia (2000) have hen defined he Pro-Poor Growh index (PPGI) as PPGI (7) Clearly growh is pro-poor if PPGI is greaer han one. d) The Approach of Kakwani and Son (2002): I may be observed ha he concep of PPGI ha was jus defined does no ake ino accoun he acual level of growh ha is observed. This is why Kakwani and Son (2002) have defined wha hey call he "povery equivalen growh rae" (PEG). The PEG refers o he growh rae ha would resul in he same level of povery reducion as he one acually observed, assuming here had been no change in inequaliy during he growh process. Growh will herefore be assumed o be pro-poor if he PEGis higher han he acual growh rae. If he PEG is posiive bu smaller han he acual growh rae, i implies ha growh is accompanied by an increase in inequaliy bu a reducion in povery is sill observed. In such a case Kakwani e al. (2004) alk abou a "rickle down" 3

4 process where he poor receive proporionally less benefis from growh han he nonpoor. Finally, if he PEG is negaive, we have he case where posiive economic growh leads o an increase in povery. More precisely call he acual growh rae (of he mean income) and * he growh rae ha would have been observed had here been no change in inequaliy. Under a disribuion neural growh scenario he relaive change in povery would hence been equal o *. We would like his hypoheical relaive change in povery o be equal o he one which was acually observed and is equal o. I is hen easy o conclude ha if * =, we mus have PEG * ( ) ( PPGI ) (8) Expression (8) implies ha growh is pro-poor if * is greaer han. e) The approach of Son (2004): Son (2004) defined wha she called a povery growh curve (PGC). I is defined as follows. Le g( p) refer o he growh rae of he mean income (consumpion) of he boom p percen of he populaion. By ploing g( p) on he verical axis agains p on he horizonal axis one obains wha Son (2003) called a Povery Growh Curve. I should be clear ha if g ( p) 0 ( g ( p) 0 ) for all p, povery decreased (increased) during he period under examinaion. If g( p) is greaer han he average growh rae for all p 100%, one can conclude ha growh was pro-poor. If g ( p) is posiive for all p 100% bu smaller han he average growh rae, one can hen conclude ha growh reduced povery bu during he period inequaliy increased. Such a siuaion could refer o wha has been called a "rickle down growh", a siuaion where growh reduces povery bu he benefis of growh are smaller for he poor han for he non-poor. Finally if g( p) is negaive for all p 100%, we have a siuaion where he increase in inequaliy more han "compensaes" growh so ha he ne effec of growh is o increase povery, a siuaion which corresponds o wha has been called "immiserizing growh". One may wonder wha difference here is beween a Growh Incidence Curve (GIC) and a Povery Growh Curve (PGC). As sressed by Son (2003) i can be shown ha he GIC is derived from firs-order sochasic dominance while he PGC is based on second-order sochasic dominance. Since second-order sochasic dominance is more likely o hold han firs-order, he PGC should provide more conclusive resuls (alhough, as sressed previously, i is based on sronger assumpions). Son (2004) emphasizes anoher poenial advanage of he PGC. Since he GIC is based on individual daa while he PGC implies esimaing he growh rae of he h mean income (consumpion) up o he p percenile, he laer procedure is somehow less prone o measuremen errors. 4

5 2) Mehodological Consideraions for he Empirical Implemenaion: While mos of he sudies menioned previously used formulaions based on a coninuous approach o he opic, we prefer o work in discree erms, among oher reasons because we also wan o check he exisence of pro-poor growh over periods ha are longer han a year. In wha follows we emphasize only he case of a relaive approach o pro-poor growh and we assume ha he povery line is consan in real erms over ime and is exogenous. Le { x} { x1,..., xn} and { y} { y1,..., yn} represen he vecor of incomes a imes 0 and 1 and le x) and y) refer o he povery index a imes 0 and 1. Finally le ( / x)) refer o he relaive change in he povery index beween imes 0 and 1, wih ( ) y) x). Assuming no change in he povery line z, he relaive change ( ) / in he povery index will now be expressed as ) / g((, I ) (9) where x is he mean income of he disribuion given by {x}, ( y x) is he difference beween he average income a imes 0 and 1 and I refers o some relaive measure of income inequaliy of he disribuion given by (x). Using he concep of Shapley decomposiion (see, Shorrocks, 1999, Sasre and Trannoy, 2002), ( ) / may be wrien as ( / ) C( C( I ) (10) where C( refers o he conribuion of he relaive change over ime in he average income and C( I ) o he conribuion of he change in relaive inequaliy beween ime 0 and ime 1. The conribuion C( x may iself be expressed as C( (1/ 2){[( / ) wih(( wih (( 0)] [( / ) wih(( Similarly he conribuion C( I ) may be wrien as 0) ( / ) 0) ( / ) wih (( 0)]} (11) C( I ) (1/ 2){[( / ) wih(( wih(( 0)] [( / ) wih (( Combining (11) and (12) we observe ha 0) ( / ) 0) ( / ) wih (( 0)]} (12) 5

6 C( C( I [( / ) wih (( ) 0)] [( / ) wih (( [( y}) x})] [( x}) x})] [( y}) x})] 0)] (13) Le us now define he expression ( / ) wih (( 0). I is easy o derive ha his expression may be also expressed as ( ({ x(1 k)}) x})/ x}) where k ( and x(1 k)}) refers o he povery rae which is observed in a disribuion where he incomes are equal o he original incomes muliplied by a facor k equal o he growh rae of he average income beween imes 0 and 1. I is should be clear ha if all he incomes are muliplied by he same consan k, by definiion relaive inequaliy will have remained consan. Similarly he expression ( / ) wih (( 0) may be wrien as ( ( y /(1 k))}) x})/ x}). where ( y /(1 k))}) refers o he povery rae which is observed in a disribuion where he incomes are equal o he incomes observed a ime 1 divided by one plus he growh rae of he average income beween ime 0 and ime 1. We herefore end up wih C( (1/ 2){[[( y}) x})] [( ( y /(1 k))}) x})]] [[( x(1 k)}) x})] [[ x}) x})]]} (1/ 2){[( y}) y /(1 k))})/ x})] [( x(1 k)}) x})]} (14) Similarly we can wrie ha C( I ) (1/ 2){[[( ({ y}) ({ ( x)] [( ({ x(1 k)}) ( x)]] [[( ({ y /(1 k)}) ( x)] [( ({ x}) ({ ( x)]]} (1/ 2){[( y}) ({ x(1 k)}))/ ( x)] [( ({ y /(1 k)}) ({ ( x)]} (15) Combining (14) and (15) we observe again ha, as expeced, C( x C( I ) ( y}) x})) / x) (16) 3) A simple illusraion: Le {x} and {y} refer respecively o he income disribuions a imes 0 and 1 wih { x } {1, 9, 20} and { y } {3,17, 25}. 6

7 The povery line z is assumed o be always equal o 5. I is easy o see ha he average incomes x and y are respecively 10 and 15. Le us now compue he hypoheical income disribuion ha would have been observed a ime 1 if here had been only growh and no change in (relaive) inequaliy. We would hen have: { } {1(15/10),9(15/10),20(15/10)} {1.5,13.5,30}. Similarly le us compue he hypoheical income disribuion ha would have been observed a ime 1 if here had been no growh and only a change inequaliy (he inequaliy observed being ha which exiss in {y} a ime 1). We would hen have { 3(10/15),17(10/15),25(10/15)} {(30/15),(170/15),(250/15)}. If we ake as povery measure he income gap raio IG ( z average inmcome of he poor) / z, we can wrie ha ( x) (5 1) / ( y) (5 3) / ( ) (5 1.5) / 5 (3.5/ 5) 0.7 ( ) (5 2) / We hen easily derive, using (14), ha C( (1/ 2){[( y}) y /(1 k))})/ x})] [( x(1 k)}) x})]} (1/ 2){[( { y} { })/ { x}] [( { } { x})/ { x}]} (1/ 2)[(0.4 Similarly we derive, using (15), ha C( I (1/ 2){[( ) / 0.8] [( ) / 0.8] [(0.1/ 0.8) (0.05/ 0.8)] 0.15/ 0.8) ) (1/ 2){[( ({ y}) x(1 k)}))/ ( x)] [( y /(1 k)}) ({ x)]} (1/ 2){[ { y} { })/ x)] [( { } { x})/ { x}]} 0.7) / 0.8] [( ) / 0.8] [(0.15/ 0.8) (0.1/ 0.8)] 0.25/ 0.8) We hen wrie ha C( x + C( I ) =-[(0.15/0.8)+(0.25/0.8)=-(0.4/0.8) And i is easy o check ha [( { y} { x})/ { x}] ( ) / / 0.8) So ha, as expeced, C( x + C( I ) = [( { y} { x})/ { x}] Using he noaions defined previously, we can also check ha he acual elasiciy of he povery index wih respec o growh may be wrien as [( { y} { x})/ { x}]/[( y x) / x] [(0.4/ 0.8) /(5/10)] 0.5/ 0.5) 1 On he conrary which measures he elasiciy of he povery index wih respec o growh, assuming here has been no change in inequaliy, will be expressed as 7

8 [( { } { x})/ { x}]/[( y x) / x] [( ) / 0.8) /(5/10)] 0.125/ 0.5) 0.25 The Pro-Poor Growh index PPGI is he expressed as PPGI and he Povery Equivalen Growh ae PEGis wrien as PEG ( PPGI) 4(15 10) /10) 45/10) 2 200% This implies ha, saring from he original disribuion { x } {1, 9, 20}, we would have o increase all he incomes by 200% and hen obain a hypoheical disribuion { } wih { } {3, 27, 60}. In such a case he average income would be 30 which indeed represens a 200% increase when compared wih he original average income 10. We can hen easily check ha he povery index income gap raio corresponding o he income disribuion { } is wrien as (5-3)/5=0.4 which is indeed he value of he povery index observed a ime 1 on he basis of disribuion {y}. 4) An Empirical Illusraion: elaive Pro-Poor Growh in Israel During he Period a) Wha do he Growh Incidence and Povery Growh Curves for he period show? Figures 1 and 2 give he Growh Incidence Curves for he periods and The horizonal line corresponds o he average growh rae of he sandardized ne income. Figure 1 indicaes ha hose who benefied he mos from growh during he period were he poores (hree of four poores perceniles) and he riches (las decile). The picure is however differen for he period where growh was clearly "ani-poor" and "pro-rich". I was "anipoor" because he growh rae in he sandardized ne income was below he average growh rae for he 45% poores perceniles. Growh was also "pro-rich" because he five highes perceniles had a growh rae higher han he average growh rae of he sandardized ne income. The picure is very similar when analyzing Povery Growh Curves during he same periods. Figure 3 indicaes ha during he period growh was "pro-poor" (for he 15 firs perceniles) while Figure 4 shows clearly ha growh was "pro-rich" during he period b) Looking a changes in he povery indices: We defined as consan povery line (in real erms) he povery line ha was observed a he middle of he period , ha is in 1998, assuming i was hen equal o half he median of he disribuion of sandardized ne income in

9 Table 1 gives firs he annual percenage change in he FGT index when he parameer is equal o 2 and when using sandardized ne incomes. This annual change is hen broken down, using a Shapley ype of decomposiion, ino wo componens. The firs componen shows wha he percenage change in povery would have been, had here been "pure" growh, ha is, growh wihou change in relaive inequaliy. The second componen shows wha he percenage change in povery would have been, had here been no growh bu only a change in relaive inequaliy (he one acually observed). 9

10 5 growh Figure 1: Growh Incidence Curve (GIC) in Israel for he sandardized ne income during he period Ne Income percenile 10

11 growh Figure 2: Growh Incidence Curve (GIC) in Israel for he sandardized ne income during he period Ne Income percenile 11

12 growh y1 Figure 3: Povery Growh Curve (PGC) in Israel for he sandardized ne income during he period Ne Income-P x percenile 12

13 5 growh y1 Figure 4: Povery Growh Curve (PGC) in Israel for he sandardized ne income during he period Ne Income-P x percenile 13

14 The resuls show periods where povery increased and periods where i decreased. If we concenrae our aenion on he las periods we observe ha povery increased during he periods and , wih, in paricular, an exremely srong increase in since povery increased by almos 52% in one year according o he FGT index. The FGT index shows ha in abou 40% of his increase was due o he negaive "pure growh" (assuming no change in relaive inequaliy). During he las wo periods ( and ) povery decreased by 9.7% and 8.6%, according o he FGT index and his decrease was mainly a "pure growh" effec. Table 1 gives also resuls for broader periods. We have divided he whole period ino hree sub-periods: a firs period ( ) where as a whole he growh rae of he per capia GDP (derived from naional accouns) was posiive, a second period ( ) according o which he growh rae of he per capia GDP was negaive and a hird period ( ) where his growh rae was again posiive. I appears ha povery decreased during he firs and hird period, increased during he second period and decreased over he whole period. However, whereas during he period of decrease in povery, he main effec was ha of pure growh, we should noe ha during he period when povery increased, his was raher he consequence of inequaliy change han of pure growh. Using again a relaive approach o pro-poor growh we compued in Table 2 he pro-poor growh index PPGI and he povery equivalen growh raes PEG, on he basis of he FGT index for he sandardized ne incomes. We observe ha here were nine periods during which growh was pro-poor ( PPGI greaer han one). The highes values of he PPGI were observed in ( PPGI =3.765), ( PPGI = 2.529) and ( PPGI = 2.363). Noe ha, during he las year of observaion ( ), growh was clearly pro-poor ( PPGI = 1.214). Table 2 gives also he Povery Equivalen Growh ae ( PEG) compued on an annual basis. I appears ha, a leas when povery is measured via he FGT index, here were seven periods during which he PEG was higher han he average growh rae of he sandardized ne income. These periods were , , , , , and

15 Period Table 1: The relaive approach o pro-poor growh, wih a consan povery line. Decomposiion of he acual percenage change in povery indices ino "pure growh" and "pure inequaliy change" componens he case of sandardized ne income. Acual percenage change in he FGT povery index (wih he parameer equal o 2) Hypoheical percenage change in he FGT povery index (wih he parameer equal o 2), assuming growh wihou inequaliy change Hypoheical percenage change in FGT povery index (wih he parameer equal o 2), assuming here was only a change in inequaliy and no growh Toal Gr In

16 Period Acual Povery Elasiciy of Growh (FGT index wih he parameer equal o 2) Table 2: The relaive approach o pro-poor growh, wih a consan povery line. Annual measures of pro-poor growh. The case of sandardized ne income. Hypoheical Povery Elasiciy of Growh, assuming no change in inequaliy (FGT index wih he parameer equal o 2) Pro-Poor Growh Index (FGT index wih he parameer equal o 2) Povery Equivalen Growh ae (FGT index wih he parameer equal o 2) Acual Annual Growh aes of Sandardized Ne Income PPGI PEG