Pro-poor growth. Abdelkrim Araar, Sami Bibi and Jean-Yves Duclos. Workshop on poverty and social impact analysis Dakar, Senegal, 8-12 June 2010

Transcription

1 Pro-poor growth Abdelkrim Araar, Sami Bibi and Jean-Yves Duclos Workshop on poverty and social impact analysis Dakar, Senegal, 8-12 June 2010 Pro-poor growth PEP and UNDP June / 43

2 Outline Concepts Setting Comparing distributions Pro-poor indices Second-order pro-poorness Inequality Conclusion Pro-poor growth PEP and UNDP June / 43

3 Objectives Understand the different manners in which the pro-poorness of growth can be analyzed; Distinguish between absolute and relative pro-poorness; See how pro-poor judgments can focus on different aspects of the 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. Pro-poor growth PEP and UNDP June / 43

4 Outline Objectives Concepts Relative and absolute Order of judgements Setting Comparing distributions Concepts Pro-poor indices Second-order pro-poorness Inequality Conclusion Pro-poor growth PEP and UNDP June / 43

5 Relative and absolute Assessing whether distributional changes are pro-poor has become increasingly widespread in academic and policy circles. Broadly speaking, there are two ways of assessing the pro-poorness of growth: 1. Using complete orderings (with specific pro-poor indices). 2. Using partial orderings (i.e., robustness analysis, by ranking curves). Pro-poor growth PEP and UNDP June / 43

6 Relative and absolute Assessing whether distributional changes are pro-poor has become increasingly widespread in academic and policy circles. There are two important issues that we must first discuss. Pro-poor growth PEP and UNDP June / 43

7 Relative and absolute 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 impact of growth on absolute poverty or on relative inequality. It is indeed important to distinguish between expectations that growth should change the incomes of the poor by the same absolute or by the same proportional amount This is conceptually not the same Empirically, the implications also vary significantly. Pro-poor growth PEP and UNDP June / 43

8 Order of judgements The second issue is whether pro-poor judgements should put relatively more emphasis on the impact of growth upon the poorer of the poor. This is equivalent to deciding whether our pro-poor judgements should obey 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. Pro-poor growth PEP and UNDP June / 43

9 Outline Objectives Concepts Setting Distribution Quantiles Censored quantiles and poverty gaps FGT indices Setting Comparing distributions Pro-poor indices Second-order pro-poorness Inequality Conclusion Pro-poor growth PEP and UNDP June / 43

10 Distribution Consider a vector y of individual living standards (income, for short) ranked in increasing order such that y 1 < y 2 <... < y n (adjusted for differences in needs and prices). For expositional simplicity, we assume that the relative individual weight φ i = 1 n i. Let p i = F(y i ) be the proportion of individuals in the population who enjoy a level of income that is less than or equal to y i : p i = i n F(y i ) is called the cumulative distribution (cdf) function of the distribution of income Pro-poor growth PEP and UNDP June / 43

11 Quantiles A p i -quantile Q(p i ) is defined implicitly as F(Q(p i )) = p i, or Q(p i ) = F ( 1) (p i ). Q(p i ) is the income of that individual whose rank or percentile in the distribution is p i. A proportionp i of the population is poorer than he is; a proportion1 p i is richer than him. µ = 1 n n i=1 Q(p i) = n i=1 (p i p i 1 )Q(p i ) is mean income. Pro-poor growth PEP and UNDP June / 43

12 Censored quantiles and poverty gaps Let Q(p i ; z) be the the quantile censored at the poverty line: Poverty gaps can then be defined as: Q(p i ; z) = min(q(p i ), z) (1) g(p i ; z) = z Q(p i ; z) (2) When income at p i exceeds the poverty line, the poverty gap equals zero. A shortfall g(p i ; z) at rank p i is shown by the distance between z and Q(p i ). Pro-poor growth PEP and UNDP June / 43

13 FGT indices The FGT class of poverty indices uses an ethical parameter α 0 and is defined as P(z; α) = 1 n n ( ) α g(pi ; z) (3) P(z; α = 0): poverty headcount ratio, P(z; α = 1): average shortfall of income from the poverty line, or average poverty gap i=1 z Pro-poor growth PEP and UNDP June / 43

14 Outline Objectives Concepts Setting Comparing distributions Distributive change Pro-poorness Absolute pro-poorness Relative income growth Relative pro-poorness Comparing distributions Pro-poor indices Second-order pro-poorness Inequality Conclusion Pro-poor growth PEP and UNDP June / 43

15 Distributive change Let a distributive change entail a movement from a distribution y t 1 to a distribution y t. Pro-poor growth PEP and UNDP June / 43

16 Distributive change Let a distributive change entail a movement from a distribution y t 1 to a distribution y t. Growth in average income is given by γ t = µt µ t 1 µ t 1 (4) Pro-poor growth PEP and UNDP June / 43

17 Distributive change Let a distributive change entail a movement from a distribution y t 1 to a distribution y t. Let income growth curves be defined as the proportional change in income observed at various percentiles (Ravallion and Chen (2003)): γ t (p i ) = yt (p i ) y t 1 (p i ). (4) y t 1 (p i ) Pro-poor growth PEP and UNDP June / 43

18 Distributive change Let income growth curves be defined as the proportional change in income observed at various percentiles (Ravallion and Chen (2003)): γ t (p i ) = yt (p i ) y t 1 (p i ). (4) y t 1 (p i ) If the income-growth curve is positive everywhere overp i [0,1], then the change increases social welfare for all of the first-order social welfare indices. We then have first-order welfare and (unrestricted) poverty dominance. Pro-poor growth PEP and UNDP June / 43

19 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-poor growth PEP and UNDP June / 43

20 Pro-poorness A test with a greater chance to succeed is to check whether the income-growth curve is positive everywhere overp i [0,F t 1 (z + )], where z + is an upper poverty line. If so, then the distributive change decreases poverty for all first-order poverty indices for which the poverty line does not exceed z +. In such circumstances, the change can be called absolutely pro-poor, in the sense that the poor benefit in absolute terms from the distributive change. Pro-poor growth PEP and UNDP June / 43

21 Absolute pro-poorness First-order absolute pro-poor judgements The following statements are equivalent: 1. A movement from y t 1 to y t is first-order absolutely pro-poor for all choices of poverty lines between 0 andz + ; 2. Poverty is higher in y t 1 than iny t for all of the poverty indices that obey the focus, the population invariance, the anonymity and the Pareto principles and for any poverty line between 0 and z + ; 3. P t (z; α = 0) P t 1 (z; α = 0) 0 for all z between 0 and z + ; 4. Q t (p i ) Q t 1 (p i ) 0 for all p i between 0 andf t 1 (z + ). 5. γ t (p i ) 0 for all p i between 0 andf t 1 (z + ). Pro-poor growth PEP and UNDP June / 43

22 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 poor at a faster rate than that of the incomes of the rest of the population. Pro-poor growth PEP and UNDP June / 43

23 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 poor at 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(p i ) at various percentiles to the growth in some socially meaningful standard. This standard is often taken as mean income. If the income growth curve at all p i [0,F(z + )] is higher than the growth in mean income, then the change can be said to be first-order relatively pro-poor. Pro-poor growth PEP and UNDP June / 43

24 Relative income growth Also: Let normalized quantiles Q(p i ) = Q(p i )/µ be incomes (at percentile p i ) as a proportion of mean income. If the normalized quantiles of the poor are increased by the change, then the change is first-order relatively pro-poor. Pro-poor growth PEP and UNDP June / 43

25 Relative pro-poorness First-order relative pro-poor judgements The following statements are equivalent: 1. A movement from y t 1 to y t is first-order relatively pro-poor for all choices of poverty lines between 0 andz + ; 2. γ t (p i ) γ t for all p i between 0 and F t 1 (z + ); 3. Q t (p i ) Q t 1 (p i ) µt µ t 1 0 for all p i between 0 and F t 1 (z + ); 4. F t (λµ t /µ t 1 ) F t 1 (λ) 0 for all λ between 0 and z +. Pro-poor growth PEP and UNDP June / 43

26 Outline Objectives Concepts Setting Comparing distributions Pro-poor indices McCulloch and Baulch Ravallion and Chen; Klasen Using the Watts index Rate of pro-poor growth Pro-poor indices Second-order pro-poorness Inequality Conclusion Pro-poor growth PEP and UNDP June / 43

27 McCulloch and Baulch The last relative pro-poor ordering is similar (for one poverty line and one poverty index) to the one by McCulloch and Baulch (1999) using the difference between a post-change poverty headcount and the headcount that would have occurred if all had gained equally, and given by ( ) µ F t (z) F t 1 t 1 z µ t (4) Pro-poor growth PEP and UNDP June / 43

28 Ravallion and Chen; Klasen Ravallion and Chen (2003) and Klasen (2003) advocate comparison of the growth rate in average income to a population weighted average growth rate of the initially poor percentiles of the population This compares growth rate in mean income (i.e., γ) to average of growth rates of a lower-income group By treating income growth rates (rather than absolute increments) of everyone the same, it gives more weight to the absolute income growth of the poor than what is done by growth in average income Pro-poor growth PEP and UNDP June / 43

29 Using the Watts index The Watts (1968) index is defined as: P Watts (z) = 1 n n ln i=1 ( z Q(p i ; z) ) (5) Let γ t (p i ; z) be the growth rate per unit of time t of censored incomes at percentile p i (i.e., γ t (p i ; z) = 0 p i > F(z)) and let PWatts t (z) be the Watts index at time t. Pro-poor growth PEP and UNDP June / 43

30 Using the Watts index The Watts (1968) index is defined as: P Watts (z) = 1 n n ln i=1 ( z Q(p i ; z) ) (5) In the case of a small (or marginal ) change in distribution, the change in the Watts index is approximately given by P t Watts (z) t = 1 n n γ t (p i ; z) (6) i=1 Pro-poor growth PEP and UNDP June / 43

31 Using the Watts index In the case of a small (or marginal ) change in distribution, the change in the Watts index is approximately given by P t Watts (z) t = 1 n n γ t (p i ; z) (5) i=1 This is the area underneath the income-growth curve up to the headcount ratio. Pro-poor growth PEP and UNDP June / 43

32 Rate of pro-poor growth For such marginal changes, Ravallion and Chen (2003) s measure of the rate of pro-poor growth is given by 1 n n i=1 γt (p i ; z) F t 1 (z) For non-marginal changes, there are various alternative definitions of the rate of pro-poor growth. (6) Pro-poor growth PEP and UNDP June / 43

33 Rate of pro-poor growth One is the growth rate in mean income, γ, times the ratio of the actual change in the Watts index to the change in the Watts index that would have been observed with the same growth rate but no change in inequality: ( P t 1 Watts γ (z) Pt Watts (z) ) P t 1 (6) Watts (z) Pt 1 Watts (z)(zµt 1 /µ t ) Pro-poor growth PEP and UNDP June / 43

34 Rate of pro-poor growth Defining the poor by the proportion of those living initially below the poverty line, another definition of Ravallion and Chen s rate of pro-poor growth is the annualized change in the Watts index divided by the initial headcount index: P t 1 Watts (z) Pt Watts (z) F t 1 (z) (6) Pro-poor growth PEP and UNDP June / 43

35 Rate of pro-poor growth Yet another definition is the mean growth rate of those who were initially poor: 1 n n i=1 γt (p i ; z), (6) F t 1 (z) which can be compared to the growth rate in average income Pro-poor growth PEP and UNDP June / 43

36 Outline Objectives Concepts Setting Comparing distributions Pro-poor indices Second-order pro-poorness Distributive sensitivity Second-order absolute judgements Cumulating gaps Changes in cumulative gaps Cumulating incomes Generalized Lorenz change Second-order relative judgements Second-order pro-poorness Inequality Conclusion Pro-poor growth PEP and UNDP June / 43

37 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 growth rate in the mean income (for relative judgements). We may want to relax this on the basis that a large growth rate for the poorer may sometimes be deemed ethically sufficient to offset 1. 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 the Pigou-Dalton principle. Pro-poor growth PEP and UNDP June / 43

38 Second-order absolute judgements Second-order absolute pro-poor judgements The following statements are equivalent: 1. A movement from y t 1 to y t is second-order absolutely pro-poor for all choices of poverty lines between 0 andz + ; 2. Poverty is higher in y t 1 than iny t for all of the poverty indices that obey the focus, the anonymity, the population invariance, the Pareto and the Pigou-Dalton principles and for any choice of poverty line between 0 andz + ; 3. P t (z;α = 1) P t 1 (z;α = 1) 0 for all z between 0 andz + ; Pro-poor growth PEP and UNDP June / 43

39 Cumulating gaps The Cumulative Poverty Gap (CPG) curve (also sometimes referred to as the inverse Generalized Lorenz curve, the TIP curve, or the poverty profile curve) cumulates the poverty gaps of the bottom p j proportion of the population and is defined as: G(p j ;z) = 1 n j g(p i ; z). (7) i=1 Pro-poor growth PEP and UNDP June / 43

40 Changes in cumulative gaps An equivalent condition for second-order absolute pro-poor judgements is: G t (p i ; z + ) G t 1 (p i ; z + ) 0 for all p i [0,1]. Pro-poor growth PEP and UNDP June / 43

41 Cumulating incomes The cumulative income up to rank p j is given by the Generalized Lorenz curve, GL(p j ): GL(p j ) = µ L(p j ) = 1 j Q(p i ), (8) n i=1 Pro-poor growth PEP and UNDP June / 43

42 Generalized Lorenz change Denote the proportional change in cumulative incomes as γgl t (p i) = GLt (p i ) GL t 1 (p i ) GL t 1. (9) (p i ) A sufficient condition for a second-order absolute pro-poor change is then that the growth in cumulative incomes be positive: γ t GL (p i) 0 for all p i [0, F t 1 (z + )]. (10) Pro-poor growth PEP and UNDP June / 43

43 Second-order relative judgements As for first-order pro-poor judgements, we may wish second-order judgements to require that the incomes of the poor at least keep up with those of the rest of the population. This yields: Second-order relative pro-poor judgements The following statements are equivalent: 1. A movement from y t 1 to y t is second-order relatively pro-poor for all choices of poverty lines between 0 and z + ; 2. P t (λµ t /µ t 1 ;α = 1) P t 1 (λ;α = 1) 0 for all λ between 0 and z +. Pro-poor growth PEP and UNDP June / 43

44 Outline Objectives Concepts Setting Comparing distributions Pro-poor indices Second-order pro-poorness Inequality Inequality Inequality Cumulative incomes Poverty equivalent growth rate Other relative comparisons Illustrations to data from Uganda Absolute and relative first-order pro-poor judgments Absolute and relative second-order pro-poor judgments Pro-poor growth PEP and UNDP June / 43

45 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 by the distributive change. This is also what is proposed by Son (2004) for all values ofp i This is also analogous to Essama-Nssah (2005), who uses an ethically-flexible weighted average of individual growth rates that does not make use of poverty lines and that resembles computing a change in an inequality index Pro-poor growth PEP and UNDP June / 43

46 Cumulative incomes A sufficient condition for second-order relative pro-poorness can also be implemented by comparing the growth in the cumulative incomes of the poor to the growth in average income. Pro-poor growth PEP and UNDP June / 43

47 Cumulative incomes A sufficient condition for second-order relative pro-poorness can also be implemented by comparing the growth in the cumulative incomes of the poor to the growth in average income. If, for all p i lower thanf(z + ), the percentage growth in the cumulative incomes of a bottom proportionp i of the population is larger than the percentage growth in mean income, then the change can be said to be second-order relatively pro-poor: γ t GL(p i ) γ t 0 for all p i [0, F t 1 (z + )]. (11) Pro-poor growth PEP and UNDP June / 43

48 Cumulative incomes To check whether growth is good for the poor, Dollar and Kraay (2002) proposed a comparison of the growth rate in average income to the growth rate of the incomes in the lowest quintile This is equivalent to checking whetherγgl t (0.2) γt Pro-poor growth PEP and UNDP June / 43

49 Cumulative incomes Kakwani and Pernia (2000) suggest using the ratio of the actual change in poverty over the change that would have been observed under distributional neutrality. This is given by P t 1 (z;α) P t (z;α) P t 1 (z;α) P t 1 ( µt 1 µ t z;α) (11) Pro-poor growth PEP and UNDP June / 43

50 Poverty equivalent growth rate Kakwani, Khandker, and Son (2003) define a poverty equivalent growth rate as the growth rate that would have resulted in the same level of poverty reduction as the present growth rate if inequality had not changed. This is given by: γ t ( P t 1 (z;α) P t (z;α) P t 1 (z;α) P t 1 ( µt 1 µ t z;α) ) (12) If this exceeds γ t, the actual growth rate, the growth is judged pro-poor. Pro-poor growth PEP and UNDP June / 43

51 Other relative comparisons Income growth curves and cumulative income growth curves may also be used to assess the impact of a distributive change on relative poverty. The procedure is similar to that of checking whether the change is pro-poor We compare income growth for the poor to the growth of some central tendency of the income distribution. One difference with the measurement of pro-poor growth is that the central tendency of interest may be some quantile (such as median income) if the relative poverty line is set as a proportion of that quantile. Pro-poor growth PEP and UNDP June / 43

52 Illustrations to data from Uganda Table 1: Some pro-poor indices Indices P(0; z) P(0; 1.5z) P(1; z) P(1; 1.5z) γ Rav-Chen (2003) Rav-Chen (2003) - γ Kakw-Pernia (2000) Pov. Eqv. Growth Rate P EGR - γ Pro-poor growth PEP and UNDP June / 43

53 Absolute and relative first-order pro-poor judgments Absolute propoor curves (Order : s=1 Dif. = ( Q_2(p) Q_1(p) ) / Q_2(p) ) Percentiles (p) Relative propoor curves (Order : s=1 Dif. = Q_2(p) /Q_1(p) mu_2/mu_1 ) Percentiles (p) Confidence interval (95 %) Estimated difference Confidence interval (95 %) Estimated difference Pro-poor growth PEP and UNDP June / 43

54 Absolute and relative second-order pro-poor judgments Absolute propoor curves (Order : s=2 Dif. = (GL_2(p) GL_1(p) ) / GL_2(p) ) Percentiles (p) Relative propoor curves (Order : s=2 Dif. = GL_2(p)/GL_1(p) mu_2/mu_1 ) Percentiles (p) Confidence interval (95 %) Estimated difference Confidence interval (95 %) Estimated difference Pro-poor growth PEP and UNDP June / 43

55 Outline Objectives Concepts Setting Comparing distributions Pro-poor indices Second-order pro-poorness Conclusion Inequality Conclusion Summary STATA and DASP commands Exercises with Stata and DASP References Pro-poor growth PEP and UNDP June / 43

56 Summary Distinguishing between absolute and relative pro-poorness is analogous to distinguishing between the impact of growth on absolute poverty or on relative 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 growth upon the poorer of the poor by using for instance principles such as the Pigou-Dalton transfer principle. Pro-poor dominance tests can use FGT-type curves or quantile-type ones, for primal and dual dominance, respectively. Pro-poor growth PEP and UNDP June / 43

57 Summary Growth incidence curves can be useful to examine the proportional change in income observed at various percentiles in a distribution. Absolute pro-poor indices usually consider the difference between the value of a post-change poverty index and that of a pre-change index. Relative pro-poor indices usually consider the difference between the value of a post-change poverty index and that of the same index if all had gained equally in the growth process. Some pro-poor judgments allow for a large growth rate for the poorer to be deemed normatively sufficient to offset a negative growth rate for some of the not-so-poor. Pro-poor growth PEP and UNDP June / 43

58 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) Pro-poor growth PEP and UNDP June / 43

59 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 Pro-poor growth PEP and UNDP June / 43

60 References ESSAMA-NSSAH, B. (2005): A unified framework for pro-poor growth analysis, Economics Letters, 89, KAKWANI, N. AND E. PERNIA (2000): What is Pro Poor Growth? Asian Development Review, 18, 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, SON, H. (2004): A note on pro-poor growth, Economics Letters, 82, WATTS, H. W. (1968): An Economic Definition of Poverty, in Understanding Poverty, ed. by D. Moynihan, New York: Basic Books. Pro-poor growth PEP and UNDP June / 43