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Pro-poor growth PEP and UNDP June 2010 – 1 / 43

Pro-poor growth

Abdelkrim Araar, Sami Bibi and Jean-Yves Duclos

Workshop on poverty and social impact analysisDakar, Senegal, 8-12 June 2010

Outline


Concepts

Setting

Comparing distributions

Pro-poor indices

Second-order pro-poorness

Inequality

Conclusion

Objectives


� Understand the different manners in which the pro-poornessof growthcan be analyzed;

� Distinguish between absolute and relative pro-poorness;� See how pro-poor judgments can focus on different aspects ofthe impact

of growth on the poor;� Define income growth and growth incidence curves;� Perform primal and dual tests for growth pro-poorness;� Examine popular indices of pro-poor growth;� Perform robustness tests for the pro-poorness of growth.

Concepts

Outline

Objectives

Concepts

Relative and absolute

Order of judgements

Setting

Comparingdistributions

Pro-poor indices

Second-orderpro-poorness

Inequality

Conclusion




Assessing whether distributional changes are “pro-poor” has becomeincreasingly widespread in academic and policy circles.

Broadly speaking, there are two ways of assessing the pro-poorness ofgrowth:

1. Using complete orderings (with specific pro-poor indices).2. Using partial orderings (i.e., robustness analysis, by “ranking” curves).



Assessing whether distributional changes are “pro-poor” has becomeincreasingly widespread in academic and policy circles.

There are two important issues that we must first discuss.



The first issue is whether our pro-poor standard should be absolute or relative.

� This is analogous to asking whether we should be interested in the impactof growth on absolute poverty or on relative inequality.

� It is indeed important to distinguish between expectationsthat growthshould change the incomes of the poor by the same absolute or by thesame proportional amount

� This is conceptually not the same� Empirically, the implications also vary significantly.

Order of judgements


The second issue is whether pro-poor judgements should put relatively moreemphasis on the impact of growth upon the poorer of the poor.

� This is equivalent to deciding whether our pro-poor judgements shouldobey ethical principles such as the Pigou-Dalton principle.

� We can consider two orders of pro-poor judgements:

� the first will obey the focus, the anonymity and the Pareto principles,� and the second will also obey the Pigou-Dalton principle.

Setting

Outline

Objectives

Concepts

Setting

Distribution

Quantiles

Censored quantilesand poverty gaps

FGT indices


Pro-poor indices


Inequality

Conclusion


Distribution


� Consider a vectory of individual living standards (income, for short)ranked in increasing order such thaty1 < y2 < ... < yn (adjusted fordifferences in needs and prices).

� For expositional simplicity, we assume that the relative individual weightφi =

1n∀i.

� Let pi = F (yi) be the proportion of individuals in the population whoenjoy a level of income that is less than or equal toyi:

pi =in

� F (yi) is called the cumulative distribution (cdf) function of thedistribution of income

Quantiles


� A pi-quantileQ(pi) is defined implicitly asF (Q(pi)) = pi, orQ(pi) = F (−1)(pi).

� Q(pi) is the income of that individual whose rank — orpercentile — inthe distribution ispi.

� A proportionpi of the population is poorer than he is; a proportion1− piis richer than him.

� µ = 1n

∑n

i=1Q(pi) =∑n

i=1 (pi − pi−1)Q(pi) is mean income.

Censored quantiles and poverty gaps


� Let Q(pi; z) be the the quantile censored at the poverty line:

Q(pi; z) = min(Q(pi), z) (1)

� Poverty gaps can then be defined as:

g(pi; z) = z −Q(pi; z) (2)

� When income atpi exceeds the poverty line, the poverty gap equals zero.� A shortfall g(pi; z) at rankpi is shown by the distance betweenz and

Q(pi).

FGT indices


� The FGT class of poverty indices uses an ethical parameterα ≥ 0 and isdefined as

P (z; α) =1

n

n∑

i=1

(

g(pi; z)

z

)α

(3)

� P (z; α = 0): poverty headcount ratio,� P (z; α = 1): average shortfall of income from the poverty line, or

average poverty gap

Comparing distributions

Outline

Objectives

Concepts

Setting


Distributive change

Pro-poorness

Absolutepro-poorness

Relative incomegrowth

Relative pro-poorness

Pro-poor indices


Inequality

Conclusion


Distributive change


Let a distributive change entail a movement from a distribution yt−1 to a

distributionyt.

Distributive change



distributionyt.

Growth in average income is given by

γt =µt − µt−1

µt−1(4)

Distributive change



distributionyt.

Let “income growth curves” be defined as the proportional change in incomeobserved at various percentiles (Ravallion and Chen (2003)):

γt(pi) =yt(pi)− yt−1(pi)

yt−1(pi). (4)

Distributive change


Let “income growth curves” be defined as the proportional change in incomeobserved at various percentiles (Ravallion and Chen (2003)):

γt(pi) =yt(pi)− yt−1(pi)

yt−1(pi). (4)

If the income-growth curve is positive everywhere overpi ∈ [0, 1], then thechange increases social welfare for all of the first-order social welfare indices.

We then have first-order welfare and (unrestricted) povertydominance.

Distributive change


The change decreases poverty for all of the poverty indices that obey“first-order” principles: focus, Pareto and anonymity

The result is valid for any choice of poverty lines.

Pro-poorness


� A test with a greater chance to succeed is to check whether theincome-growth curve is positive everywhere overpi ∈ [0, F t−1(z+)],wherez+ is an upper poverty line.

� If so, then the distributive change decreases poverty for all first-orderpoverty indices for which the poverty line does not exceedz+.

� In such circumstances, the change can be called “absolutelypro-poor”, inthe sense that the poor benefit in absolute terms from the distributivechange.

Absolute pro-poorness


First-order absolute pro-poor judgementsThe following statements are equivalent:

1. A movement fromyt−1 to yt is first-order absolutely pro-poor for all

choices of poverty lines between 0 andz+;2. Poverty is higher inyt−1 than inyt for all of the poverty indices that

obey the focus, the population invariance, the anonymity and the Paretoprinciples and for any poverty line between 0 andz+;

3. P t(z; α = 0)− P t−1(z; α = 0) ≤ 0 for all z between 0 andz+;4. Qt(pi)−Qt−1(pi) ≥ 0 for all pi between 0 andF t−1(z+).5. γt(pi) ≥ 0 for all pi between 0 andF t−1(z+).

Relative income growth


Income growth curves can also be used:

� to test whether a distributive change is “relatively pro-poor”,� in the sense that the change increases the incomes of the poorat a faster

rate than that of the incomes of the rest of the population.



Income growth curves can also be used:

� to test whether a distributive change is “relatively pro-poor”,� in the sense that the change increases the incomes of the poorat a faster

rate than that of the incomes of the rest of the population.

For that purpose, we only need to compare the income growth curveγ(pi) atvarious percentiles to the growth in some socially meaningful standard.

This standard is often taken as mean income.

If the income growth curve at allpi ∈ [0, F (z+)] is higher than the growth inmean income, then the change can be said to be first-order relatively pro-poor.



Also: Let normalized quantilesQ(pi) = Q(pi)/µ be incomes (at percentilepi) as a proportion of mean income.

If the normalized quantiles of the poor are increased by the change, then thechange is first-order relatively pro-poor.

Relative pro-poorness


First-order relative pro-poor judgementsThe following statements are equivalent:

1. A movement fromyt−1 to yt is first-order relatively pro-poor for all

choices of poverty lines between 0 andz+;

2. γt(pi) ≥ γt for all pi between 0 andF t−1(z+);

3. Qt(pi)Qt−1(pi)

−µt

µt−1 ≥ 0 for all pi between 0 andF t−1(z+);

4. F t(λµt/µt−1)− F t−1(λ) ≤ 0 for all λ between 0 andz+.

Pro-poor indices

Outline

Objectives

Concepts

Setting


Pro-poor indices

McCulloch andBaulch

Ravallion and Chen;Klasen

Using the Watts index

Rate of pro-poorgrowth


Inequality

Conclusion


McCulloch and Baulch


� The last relative pro-poor ordering is similar (for one poverty line and onepoverty index) to the one

� by McCulloch and Baulch (1999) using the difference betweenapost-change poverty headcount and the headcount that wouldhaveoccurred if all had gained equally,

� and given by

F t(z)− F t−1

(

µt−1

µtz

)

(4)

Ravallion and Chen; Klasen


� Ravallion and Chen (2003) and Klasen (2003) advocate comparison ofthe growth rate in average income to a “population weighted”averagegrowth rate of the initially poor percentiles of the population

� This compares growth rate in mean income (i.e.,γ) to average of growthrates of a lower-income group

� By treating income growth rates (rather than absolute increments) ofeveryone the same, it gives more weight to the absolute income growth ofthe poor than what is done by growth in average income

http://www2.vwl.wiso.uni-goettingen.de/ibero/papers/DB96.pdf



� The Watts (1968) index is defined as:

PWatts(z) =1

n

n∑

i=1

ln

(

z

Q(pi; z)

)

(5)

� Let γt(pi; z) be the growth rate per unit of timet of censored incomes atpercentilepi (i.e.,γt(pi; z) = 0 ∀ pi > F (z)) and letP t

Watts(z) be theWatts index at timet.



� The Watts (1968) index is defined as:

PWatts(z) =1

n

n∑

i=1

ln

(

z

Q(pi; z)

)

(5)

� In the case of a small (or “marginal”) change in distribution, the changein the Watts index is approximately given by

∆P tWatts(z)

∆t= −

1

n

n∑

i=1

γt(pi; z) (6)



� In the case of a small (or “marginal”) change in distribution, the changein the Watts index is approximately given by

∆P tWatts(z)

∆t= −

1

n

n∑

i=1

γt(pi; z) (5)

� This is the area underneath the income-growth curve up to theheadcountratio.

Rate of pro-poor growth


� For such marginal changes, Ravallion and Chen (2003)’s measure of therate of pro-poor growth is given by

1n

∑n

i=1 γt(pi; z)

F t−1(z)(6)

� For non-marginal changes, there are various alternative definitions of therate of pro-poor growth.



One is the growth rate in mean income,γ, times the ratio of the actual changein the Watts index to the change in the Watts index that would have beenobserved with the same growth rate but no change in inequality:

γ

(

P t−1Watts(z)− P t

Watts(z)

P t−1Watts(z)− P t−1

Watts(z)(zµt−1/µt)

)

(6)



Defining the poor by the proportion of those living initiallybelow the povertyline, another definition of Ravallion and Chen’s rate of pro-poor growth is theannualized change in the Watts index divided by the initial headcount index:

P t−1Watts(z)− P t

Watts(z)

F t−1(z)(6)



Yet another definition is the mean growth rate of those who were initiallypoor:

1n

∑n

i=1 γt(pi; z)

F t−1(z), (6)

which can be compared to the growth rate in average income

Second-order pro-poorness

Outline

Objectives

Concepts

Setting


Pro-poor indices


Distributivesensitivity

Second-orderabsolute judgements

Cumulating gaps

Changes incumulative gaps

Cumulating incomes

Generalized Lorenzchange

Second-order relativejudgements

Inequality

ConclusionPro-poor growth PEP and UNDP June 2010 – 23 / 43

Distributive sensitivity


� Testing for first-order pro-poor judgements can be demanding.� It requires all quantiles of the poor to undergo a rate of growth that is

either positive (for absolute judgements) or at least as large as the growthrate in the mean income (for relative judgements).

� We may want to relax this on the basis that a large growth rate for thepoorer may sometimes be deemed ethically sufficient to offset1. a negative growth rate for some percentiles of the not-so-poor for

absolute judgements;2. a low growth rate for some percentiles of the not-so-poor for relative

judgements.

� Implementing this is done by asking pro-poor judgements to obey thePigou-Dalton principle.

Second-order absolute judgements


Second-order absolute pro-poor judgementsThe following statements are equivalent:

1. A movement fromyt−1 to yt is second-order absolutely pro-poor for all

choices of poverty lines between 0 andz+;

2. Poverty is higher inyt−1 than inyt for all of the poverty indices thatobey the focus, the anonymity, the population invariance, the Pareto andthe Pigou-Dalton principles and for any choice of poverty line between 0andz+;

3. P t(z;α = 1)− P t−1(z;α = 1) ≤ 0 for all z between 0 andz+;

Cumulating gaps


The Cumulative Poverty Gap (CPG) curve (also sometimes referred to as theinverse Generalized Lorenz curve, the “TIP” curve, or the poverty profilecurve)

� cumulates the poverty gaps of the bottompj proportion of the population� and is defined as:

G(pj; z) =1

n

j∑

i=1

g(pi; z). (7)

Changes in cumulative gaps


An equivalent condition for second-order absolute pro-poor judgements is:

Gt(pi; z+)−Gt−1(pi; z

+) ≤ 0 for all pi ∈ [0, 1].

Cumulating incomes


The cumulative income up to rankpj is given by the Generalized Lorenzcurve,GL(pj):

GL(pj) = µ · L(pj) =1

n

j∑

i=1

Q(pi), (8)

Generalized Lorenz change


� Denote the proportional change in cumulative incomes as

γtGL(pi) =

GLt(pi)−GL

t−1(pi)

GLt−1(pi)

. (9)

� A sufficient condition for a second-order absolute pro-poorchange is thenthat the growth in cumulative incomes be positive:

γtGL(pi) ≥ 0 for all pi ∈ [0, F t−1(z+)]. (10)

Second-order relative judgements


� As for first-order pro-poor judgements, we may wish second-orderjudgements to require that the incomes of the poor at least keep up withthose of the rest of the population.

� This yields:Second-order relative pro-poor judgementsThe following statements are equivalent:

1. A movement fromyt−1 to yt is second-order relatively pro-poor for

all choices of poverty lines between 0 andz+;

2. P t(λµt/µt−1;α = 1)− P t−1(λ;α = 1) ≤ 0 for all λ between 0 andz+.

Inequality

Outline

Objectives

Concepts

Setting


Pro-poor indices


Inequality

Inequality

Cumulative incomes

Poverty equivalentgrowth rate

Other relativecomparisons

Illustrations to datafrom Uganda 92-99

Absolute and relativefirst-order pro-poorjudgments

Absolute and relativesecond-orderpro-poor judgments

ConclusionPro-poor growth PEP and UNDP June 2010 – 31 / 43

Inequality


� If the above conditions hold forz+ = ∞, then the change also reduces all“standard” inequality indices

� This is equivalent to checking whether the Lorenz curve is pushed up bythe distributive change.

� This is also what is proposed by Son (2004) for all values ofpi

� This is also analogous to Essama-Nssah (2005), who uses anethically-flexible weighted average of individual growth rates that doesnot make use of poverty lines and that resembles computing a change inan inequality index

Cumulative incomes


� A sufficient condition for second-order relative pro-poorness can also beimplemented by comparing the growth in the cumulative incomes of thepoor to the growth in average income.

Cumulative incomes


� A sufficient condition for second-order relative pro-poorness can also beimplemented by comparing the growth in the cumulative incomes of thepoor to the growth in average income.

� If, for all pi lower thanF (z+), the percentage growth in the cumulativeincomes of a bottom proportionpi of the population is larger than thepercentage growth in mean income, then the change can be saidto besecond-order relatively pro-poor:

γtGL(pi)− γt ≥ 0 for all pi ∈ [0, F t−1(z+)]. (11)

Cumulative incomes


To check whethergrowth is good for the poor, Dollar and Kraay (2002)proposed a comparison of the growth rate in average income tothe growthrate of the incomes in the lowest quintile

This is equivalent to checking whetherγtGL(0.2) ≥ γt

http://siteresources.worldbank.org/DEC/Resources/22015_Growth_is_Good_for_Poor.pdf

Cumulative incomes


Kakwani and Pernia (2000) suggest using the ratio of the actual change inpoverty over the change that would have been observed under distributionalneutrality.

This is given byP t−1(z;α)− P t(z;α)

P t−1(z;α)− P t−1(µt−1

µt z;α)(11)

Poverty equivalent growth rate


� Kakwani, Khandker, and Son (2003) define a “poverty equivalent growthrate” as the growth rate that would have resulted in the same level ofpoverty reduction as the present growth rate if inequality had not changed.

� This is given by:

γt

(

P t−1(z;α)− P t(z;α)

P t−1(z;α)− P t−1(µt−1

µt z;α)

)

(12)

� If this exceedsγt, the actual growth rate, the growth is judged pro-poor.

http://info.worldbank.org/etools/BSPAN/PresentationView.asp?EID=194&PID=383

Other relative comparisons


� Income growth curves and cumulative income growth curves may also beused to assess the impact of a distributive change onrelative poverty.

� The procedure is similar to that of checking whether the change ispro-poor

� We compare income growth for the poor to the growth of some centraltendency of the income distribution.

� One difference with the measurement of pro-poor growth is that thecentral tendency of interest may be some quantile (such as medianincome) if the relative poverty line is set as a proportion ofthat quantile.

Illustrations to data from Uganda 92-99


Table 1: Some pro-poor indices

Indices P (0; z) P (0; 1.5z) P (1; z) P (1; 1.5z)γ 48.2 48.2 48.2 48.2

Rav-Chen (2003) 30.1 32.6 30.1 32.6Rav-Chen (2003) -γ -18.1 -15.6 -18.1 -15.6Kakw-Pernia (2000) 0.95 0.83 0.77 0.64

Pov. Eqv. Growth Rate 45.8 39.9 37.3 31.1PEGR - γ -2.4 -8.3 -10.9 -17.1

Absolute and relativefirst-order pro-poor judgments


0.2

.4.6

.8

0 .16 .32 .48 .64 .8Percentiles (p)

Confidence interval (95 %) Estimated difference

(Order : s=1 | Dif. = ( Q_2(p) − Q_1(p) ) / Q_2(p) )

Absolute propoor curves

−.4

−.2

0.2

0 .16 .32 .48 .64 .8Percentiles (p)


(Order : s=1 | Dif. = Q_2(p) /Q_1(p) − mu_2/mu_1 )

Relative propoor curves

Absolute and relativesecond-order pro-poor judgments


0.2

.4.6

.8

0 .2 .4 .6 .8 1Percentiles (p)


(Order : s=2 | Dif. = (GL_2(p) − GL_1(p) ) / GL_2(p) )

Absolute propoor curves

−.4

−.2

0.2

0 .2 .4 .6 .8 1Percentiles (p)


(Order : s=2 | Dif. = GL_2(p)/GL_1(p) − mu_2/mu_1 )

Relative propoor curves

Conclusion

Outline

Objectives

Concepts

Setting


Pro-poor indices


Inequality

Conclusion

Summary

STATA and DASPcommands

Exercises with Stataand DASP

References


Summary


� Distinguishing between absolute and relative pro-poorness is analogousto distinguishing between the impact of growth on absolute poverty or onrelative inequality.

� Two types of pro-poor tests exist: those that use specific pro-poor indices,and those that use dominance curves.

� Pro-poor judgements can put more emphasis on the impact of growthupon the poorer of the poor by using for instance principles such as thePigou-Dalton transfer principle.

� Pro-poor dominance tests can use FGT-type curves or quantile-type ones,for primal and dual dominance, respectively.

Summary


� “Growth incidence curves” can be useful to examine the proportionalchange in income observed at various percentiles in a distribution.

� Absolute pro-poor indices usually consider the differencebetween thevalue of a post-change poverty index and that of a pre-changeindex.

� Relative pro-poor indices usually consider the differencebetween thevalue of a post-change poverty index and that of the same index if all hadgained equally in the growth process.

� Some pro-poor judgments allow for a large growth rate for thepoorer tobe deemed normatively sufficient to offset a negative growthrate forsome of the not-so-poor.

STATA and DASP commands


� FGT: Decomposition into growth and redistribution (dfgtgr)� Pro-poor growth indices (ipropoor)� Pro-poor growth curves with the dual approach. (cpropoord)

http://132.203.59.36/DASP/help/DASP_MANUAL_V2.1.htm#_Toc247593958



Exercises with Stata and DASP


� Part IV: Exercises 1.1� Part IV: Exercises 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7

http://dasp.ecn.ulaval.ca/exercises/exercises.htm#_Toc255461655

http://dasp.ecn.ulaval.ca/exercises/exercises.htm#_Toc255461656

References


ESSAMA-NSSAH, B. (2005): “A unified framework for pro-poor growthanalysis,”Economics Letters, 89, 216–221.

KAKWANI , N. AND E. PERNIA (2000): “What is Pro Poor Growth?”AsianDevelopment Review, 18, 1–16.

MCCULLOCH, N. AND B. BAULCH (1999): “Tracking pro-poor growth,”ID21 insights #31, Sussex, Institute of Development Studies.

RAVALLION , M. AND S. CHEN (2003): “Measuring Pro-poor Growth,”Economics Letters, 78, 93–99.

SON, H. (2004): “A note on pro-poor growth,”Economics Letters, 82,307–314.

WATTS, H. W. (1968): “An Economic Definition of Poverty,” inUnderstanding Poverty, ed. by D. Moynihan, New York: Basic Books.

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