Concepts and Operationalisation of Pro-Poor Growth: A Usable PPG Index

Concepts and Operationalisation of Pro-Poor Growth:

A Usable PPG Index

EADI Conference, Bonn 26 June 2014

Mario Negre

German Development InstituteWorld Bank Research Group

© 2012 German Development Institute / Deutsches Institut für Entwicklungspolitik (DIE)

Outline

1. Introduction2. Defining PPG3. PPG operationalisation and indices4. A usable PPG index5. PPG Performance6. Case Study7. Conclusions

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Introduction

Inequality increasingly recognised as key factor for Poverty Reduction... (and perhaps for growth?)

Ravallion (2001): i) g 7x more Pov reducing when Ineq

ii) ↑ Ineq ↓ Pov reduction rate

IMF: ↓ net Ineq robustly correlated with faster and more durable growth, for a given level of redistribution (Berg, Ostry and Zetelmeyer, 2012) – somewhat flimsy evidence (Kraay, forthcoming)

Somewhat contradictory evidence from cross-country literature (Dollar and Kraay, 2002; Kraay, 2006; Dollar, Kleineberg and Kraay, 2013)

Otherwise increasing academic evidence (political science, governance, stability, etc)

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Defining PPG

Approaches: Absolute Poverty reducing growth Relative Disproportionally benefiting the poor

Absolute approach reductio ad absurdum:

Pro-Poor = Pro-Nonpoor !

4


PPG Operationalisation

Shapley Decomposition (1953; Game Theory) Shorrocks (1999) generalisation for Poverty: It calculates the marginal impact on

poverty of “eliminating each contributing factor in sequence, and then assigns to each factor the average of its marginal constributions in all possible sequences.”

Exact Decomposition:

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∆ 𝑃 𝑖𝑗=𝐺𝑖𝑗+𝑅 𝑖𝑗

𝐺𝑖𝑗=12 [𝑃 (µ 𝑗 ,𝐿 𝑗 (𝑝 ) )−𝑃 (µ𝑖 ,𝐿 𝑗 (𝑝 ) )+𝑃 (µ 𝑗 ,𝐿𝑖 (𝑝 ) )−𝑃 (µ𝑖 ,𝐿𝑖 (𝑝 ) ) ]

𝑅𝑖𝑗=12 [𝑃 (µ𝑖 ,𝐿 𝑗 (𝑝) )− 𝑃 (µ𝑖 ,𝐿𝑖 (𝑝 ) )+𝑃 (µ 𝑗 ,𝐿 𝑗 (𝑝 ) )−𝑃 (µ 𝑗 ,𝐿𝑖 (𝑝 ) ) ]


PPG Indices

Kakwani and Pernia‘s (2000) Kakwani, Son and Khandker (2004)

+ per capita growth - per capita growth Poverty Equivalent Growth Rate (PEGR)

Limitations: Lack of comparability (+ vs. - growth)

Φ+, Φ- → ±∞ when G → 0, R → -G

Φ falls into two non-contiguous intervals for recessions (one of them not accounted for in Kakwani and Pernia (2000))

Other problems of lack of meaning and monotonicity in PEGR

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𝛷=𝐺+𝑅𝐺 𝛷=

𝐺𝐺+𝑅 𝛾∗=𝛷𝛾


Problems with the Kakwani and Pernia’s index:

For the case of anti-nonpoor per capita recession:

i)

ii)

Unaccounted for

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0<|𝑅|<|𝐺|⇒ 𝐺𝐺+𝑅→ { 1 𝑖𝑓 |𝑅|→0∞ 𝑖𝑓 |𝑅|→|𝐺|

⇒∅∈ (1 ,∞ )

0<|𝐺|<|𝑅|⇒ 𝐺𝐺+𝑅→ {−∞ 𝑖𝑓 |𝑅|→00 𝑖𝑓 |𝑅|→∞

⇒∅∈ (−∞ ,0 )

{𝐺>0𝑅<0


Problems with the PEGR:1. First, when 2. Second, in per capita recessionsi) Anti-poor recession

The correct result should be:

ii) Anti-nonpoor recession with

The correct result should be:

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∅→∞𝐺>0

𝛾∗=∅𝛾

{𝐺>0𝑅>0

⇒∅∈ (0,1 )⇒|𝛾∗|<|𝛾| h𝑤𝑖𝑡 𝛾∗ ,𝛾<0

|𝛾∗|>|𝛾|

|𝑅|<|𝐺|

{𝐺>0𝑅<0

⇒∅∈ (1 ,∞ )⇒|𝛾∗|>|𝛾| h𝑤𝑖𝑡 𝛾∗ ,𝛾<0

|𝛾∗|<|𝛾|


iii) Anti-nonpoor recession with

with increasing over the interval The correct result should be: and decreasing over this interval

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|𝑅|>|𝐺|

{𝐺>0𝑅<0

⇒∅∈ (−∞ ,0 )⇒|𝛾∗|>0

𝛾∗ 𝑅∈ (−∞ ,−𝐺 )|𝛾∗|>0


A usable PPG Index

Φ = - R general for any poverty measure or income level

(Poverty Bias of Growth)

Based on PPG relative approach

PPG should satify these porperties:i) It is + (-) when

ii) It is zero when

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𝛾𝑝𝑜𝑜𝑟>𝛾>𝛾𝑛𝑜𝑛𝑝𝑜𝑜𝑟 (𝛾𝑝𝑜𝑜𝑟<𝛾<𝛾𝑛𝑜𝑛𝑝𝑜𝑜𝑟 )𝛾𝑝𝑜𝑜𝑟=𝛾=𝛾𝑛𝑜𝑛𝑝𝑜𝑜𝑟


What about using the Headcount Index (H)?

If all the poor increase their income

without going above the poverty line and the nonpoor experience no change

it should be PPG but RH=0 because H didn‘t change

Thus, it doesn‘t satisfy desirable properties

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What about using the Poverty Gap (PG)?It satisfies properties and it can be mathematically linked to: (For the case of constant population and number of poor)

Substituting

in

it can be shown that

12

𝑅𝑃𝐺=1

2𝑧𝑁 (𝛾−𝛾𝑝𝑜𝑜𝑟 )(1+ 11+𝜇 )∑

𝑖

𝑞

𝑥1𝑖

𝛾𝑝𝑜𝑜𝑟>𝛾>𝛾𝑛𝑜𝑛𝑝𝑜𝑜𝑟

iq

i

ii

n

i

i

zxz

nzxI

zxz

nPPG

111

11

1

1

2212

2

112 ,,,,

21 xzPxzPxzPxzPR


…if you don’t believe me:

If the population and the number of poor remain unchanged, N1 = N2 = N and q1 = q2 = q and the growth in the mean of the poor can be defined as:

13

2 1 2 1

11

2

12

21

12

2

1

2

111121 q

i

q

i

q

i

q

iiiii xz

Nxz

Nxz

Nxz

NzR

2 1

11

2

12

2

1

2

12112121 q

i

q

iiiPG xz

Nxz

NzR

q

iiiPG xx

zNR 2

2

11

1

2 1121

1

1

2

q

ii

q

ii

p

x

x

11

2

q

iiiPG xx

zNR 21 1

11221

q

iipPG x

zNR 11

1121


RPG < 0 Pro-Poor Growth

RPG > 0 Pro-NonPoor Growth

If G > 0 Anti-Poor/NonPoor Recession (also cases with positive per capita growth but higher population growth)

PPG Rate:

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𝛾∗=𝛾+𝜗∅=𝛾−𝜗 𝑅𝑃𝐺


Pro-Poor Performance

Φt = Φ / t to compare pro-poorness over time Φ that would have beeen necessary to meet a given target PG reduction

(halving, eradicating)

Φ that would be necessary to achieve a target given a forecast economic growth

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Poverty Gap Target-based Pro-Poor Performance Trend


Example - Honduras

ϕPG > 0 Pro-Poor Growth

ϕPG < 0 Pro-Nonpoor Growth

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© 2012 German Development Institute / Deutsches Institut für Entwicklungspolitik (DIE) 17

Halving 1992‘s PG by 2015 with 2004-7 growth


Why using this PPG Index? Because…

It‘s based on the relative approach it works – it measures:

• if g is pro-poor• how pro-poor it is

Even politicians can understand it: “how distributional shifts affect the PG“ It focuses on what happens to the poor (or those below a chosen income) –

unlike Gini, GIC or SP It’s a monitoring and assessment tool over time It’s calculable with current datasets (expenditure/consumption)

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Thank you.

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Documents

Concepts and Operationalisation of Pro-Poor Growth: A Usable PPG Index