Robust pro-poorest poverty reduction with counting measures: the - - PDF document

Robust “pro-poorest” poverty reduction with counting measures: the anonymous case

Jos´ e Gallegos1 Gast´

• n Yalonetzky2

1Peruvian Ministry of Deveolpment and Social Inclusion 2Leeds University Business School

December 2014

Table of contents

Introduction Inequality-sensitive counting poverty measures The anonymous case Variable deprivation weights General conditions Specific conditions Statistical inference Empirical illustration Concluding remarks

Introduction

Pro-poor growth

I Ongoing interest in the concept of pro-poor growth.

Introduction

Pro-poor growth

I Ongoing interest in the concept of pro-poor growth. I Traditionally focused on continuous variables (e.g. income,

consumption).

Introduction

Pro-poor growth

I Ongoing interest in the concept of pro-poor growth. I Traditionally focused on continuous variables (e.g. income,

consumption).

I Straightforward first notion: growth pro-poor when the income of

the poor rises.

Introduction

Pro-poor growth

I Ongoing interest in the concept of pro-poor growth. I Traditionally focused on continuous variables (e.g. income,

consumption).

I Straightforward first notion: growth pro-poor when the income of

the poor rises.

I More subtle, interesting notion: growth pro-poor when income

grows monotonically faster at lower initial quantiles.

Introduction

Pro-poor growth

I Ongoing interest in the concept of pro-poor growth. I Traditionally focused on continuous variables (e.g. income,

consumption).

I Straightforward first notion: growth pro-poor when the income of

the poor rises.

I More subtle, interesting notion: growth pro-poor when income

grows monotonically faster at lower initial quantiles. Growth that reduces inequality.

Introduction

Pro-poor growth with other indicators of wellbeing

I Recent interest in connecting pro-poor growth with non-monetary

measures of wellbeing and/or multidimensional (counting) poverty indices.

Introduction

Pro-poor growth with other indicators of wellbeing

I Recent interest in connecting pro-poor growth with non-monetary

measures of wellbeing and/or multidimensional (counting) poverty indices.

I Examples: Kacem (2013) uses a non-monetary index of wellbeing of

poverty as the initial condition, and the checks whether income growth is pro-poor.

Introduction

Pro-poor growth with other indicators of wellbeing

I Recent interest in connecting pro-poor growth with non-monetary

measures of wellbeing and/or multidimensional (counting) poverty indices.

I Examples: Kacem (2013) uses a non-monetary index of wellbeing of

poverty as the initial condition, and the checks whether income growth is pro-poor.

I Examples: Boccanfuso et al. (2009) apply the continuous-variable

toolkit to deprivation scores of a non-monetary poverty index based

• n MCA.

Introduction

Pro-poor growth with other indicators of wellbeing

I Recent interest in connecting pro-poor growth with non-monetary

measures of wellbeing and/or multidimensional (counting) poverty indices.

I Examples: Kacem (2013) uses a non-monetary index of wellbeing of

poverty as the initial condition, and the checks whether income growth is pro-poor.

I Examples: Boccanfuso et al. (2009) apply the continuous-variable

toolkit to deprivation scores of a non-monetary poverty index based

• n MCA. However this technique is not suitable when the number
• f deprivation dimensions is relatively small.

Introduction

This paper’s question

I What are the conditions under which a poverty reduction

experience is robustly more “pro-poorest” than another one, in the context of counting measures of multidimensional poverty?

Introduction

This paper’s question

I What are the conditions under which a poverty reduction

experience is robustly more “pro-poorest” than another one, in the context of counting measures of multidimensional poverty?

I Under which conditions does poverty reduction not only

reduce the average poverty score further but also decrease deprivation inequality among the poor, in a robust manner?

Introduction

Our contribution: Anonymous assessment

I Comparing two cross-sectional datasets in different points in time,

there is a second-order dominance condition based on reverse generalized Lorenz curves (RGL curves) whose fulfillment ensures that poverty decreases along with a reduction in deprivation inequality for a broad family of inequality-sensitive poverty measures.

Introduction

Our contribution: Anonymous assessment

I Comparing two cross-sectional datasets in different points in time,

there is a second-order dominance condition based on reverse generalized Lorenz curves (RGL curves) whose fulfillment ensures that poverty decreases along with a reduction in deprivation inequality for a broad family of inequality-sensitive poverty

• measures. It was developed by Lasso de la Vega (2010), and by

Chakravarty and Zoli (2009,2012).

Introduction

Our contribution: Anonymous assessment

I Comparing two cross-sectional datasets in different points in time,

there is a second-order dominance condition based on reverse generalized Lorenz curves (RGL curves) whose fulfillment ensures that poverty decreases along with a reduction in deprivation inequality for a broad family of inequality-sensitive poverty

• measures. It was developed by Lasso de la Vega (2010), and by

Chakravarty and Zoli (2009,2012).

I However the condition’s fulfillment is specific only to a particular

vector of deprivation weights (and deprivation lines). If the weights change, the condition needs to be tested again, without a priori guarantee that a robust “pro-poorest” poverty reduction comparison will hold.

Introduction

Our contribution: Anonymous assessment

I Comparing two cross-sectional datasets in different points in time,

there is a second-order dominance condition based on reverse generalized Lorenz curves (RGL curves) whose fulfillment ensures that poverty decreases along with a reduction in deprivation inequality for a broad family of inequality-sensitive poverty

• measures. It was developed by Lasso de la Vega (2010), and by

Chakravarty and Zoli (2009,2012).

I However the condition’s fulfillment is specific only to a particular

vector of deprivation weights (and deprivation lines). If the weights change, the condition needs to be tested again, without a priori guarantee that a robust “pro-poorest” poverty reduction comparison will hold.

I We refine this second-order condition in order to render it robust to

a broad array of deprivation weights.

Introduction

Our contribution: Anonymous assessment

I We derive two conditions whose fulfillment is necessary, but

insufficient, to ensure second-order dominance for every conceivable weighting vector.

Introduction

Our contribution: Anonymous assessment

I We derive two conditions whose fulfillment is necessary, but

insufficient, to ensure second-order dominance for every conceivable weighting vector.

I We show how to derive sets of conditions whose fulfillment is

necessary and sufficient to ensure robust poverty comparisons with counting measures for broad families of deprivation weights.

Introduction

Empirical illustration

I We illustrate these conditions with the Peruvian ENAHO,

using both cross-section and panel datasets.

Introduction

Empirical illustration

I We illustrate these conditions with the Peruvian ENAHO,

using both cross-section and panel datasets. We find:

Introduction

Empirical illustration

I We illustrate these conditions with the Peruvian ENAHO,

using both cross-section and panel datasets. We find:

I Robust poverty reduction between 2002 and 2013 at national,

urban and rural level, also for 22 of 25 departments.

Introduction

Empirical illustration

I We illustrate these conditions with the Peruvian ENAHO,

using both cross-section and panel datasets. We find:

I Robust poverty reduction between 2002 and 2013 at national,

urban and rural level, also for 22 of 25 departments.

I Egalitarian poverty reduction not robust to different weighting

choices for the national, urban, and rural samples.

Introduction

The organization of the rest of this presentation

I Inequality-sensitive counting poverty measures.

Introduction

The organization of the rest of this presentation

I Inequality-sensitive counting poverty measures. I The anonymous case.

Introduction

The organization of the rest of this presentation

I Inequality-sensitive counting poverty measures. I The anonymous case. I Variable deprivation weights.

Introduction

The organization of the rest of this presentation

I Inequality-sensitive counting poverty measures. I The anonymous case. I Variable deprivation weights. I Empirical illustration.

Introduction

The organization of the rest of this presentation

I Inequality-sensitive counting poverty measures. I The anonymous case. I Variable deprivation weights. I Empirical illustration. I Concluding remarks.

Inequality-sensitive counting poverty measures

Basic setting and notation

We have N individuals (or households) and D indicators of

• wellbeing. If xnd < zd then n is deprived in d.

Inequality-sensitive counting poverty measures

Basic setting and notation

We have N individuals (or households) and D indicators of

• wellbeing. If xnd < zd then n is deprived in d.

We weight each indicator with wd 2 [0, 1] such that PD

d=1 wd = 1.

Inequality-sensitive counting poverty measures

Basic setting and notation

We have N individuals (or households) and D indicators of

• wellbeing. If xnd < zd then n is deprived in d.

We weight each indicator with wd 2 [0, 1] such that PD

d=1 wd = 1.

Then the deprivation score for each individual is: cn ⌘

D

X

d=1

wdI(xnd < zd) (1)

Inequality-sensitive counting poverty measures

Basic setting and notation

We have N individuals (or households) and D indicators of

• wellbeing. If xnd < zd then n is deprived in d.

We weight each indicator with wd 2 [0, 1] such that PD

d=1 wd = 1.

Then the deprivation score for each individual is: cn ⌘

D

X

d=1

wdI(xnd < zd) (1) A person is deemed poor if: cn k, where k 2 [0, 1].

Inequality-sensitive counting poverty measures

Basic setting and notation

We have N individuals (or households) and D indicators of

• wellbeing. If xnd < zd then n is deprived in d.

We weight each indicator with wd 2 [0, 1] such that PD

d=1 wd = 1.

Then the deprivation score for each individual is: cn ⌘

D

X

d=1

wdI(xnd < zd) (1) A person is deemed poor if: cn k, where k 2 [0, 1]. Very important: Note that for a given choice of Z and W there is

• nly ONE vector of possible values for cn. Its maximum number of

elements is PD

i=0

D

i

• . Then the distribution of cn is discrete.

Inequality-sensitive counting poverty measures

Inequality-sensitive poverty measures

We consider the following individual poverty functions: pn = I(cn k)g(cn) (2)

Inequality-sensitive counting poverty measures

Inequality-sensitive poverty measures

We consider the following individual poverty functions: pn = I(cn k)g(cn) (2) where g is the intensity function, and: g(0) = 0, g(1) = 1, g0, g00 > 0.

Inequality-sensitive counting poverty measures

Inequality-sensitive poverty measures

We consider the following individual poverty functions: pn = I(cn k)g(cn) (2) where g is the intensity function, and: g(0) = 0, g(1) = 1, g0, g00 > 0. Then the following social poverty indices: P = 1 N

N

X

n=1

pn (3)

Inequality-sensitive counting poverty measures

Properties

P with pn satisfies several properties including:

• 1. Focus (FOC): P should not be affected by changes in cn as

long as cn < k.

Inequality-sensitive counting poverty measures

Properties

P with pn satisfies several properties including:

• 1. Focus (FOC): P should not be affected by changes in cn as

long as cn < k.

• 2. Monotonicity (MON): P should increase whenever cn

increases, and n is poor.

Inequality-sensitive counting poverty measures

Properties

P with pn satisfies several properties including:

• 1. Focus (FOC): P should not be affected by changes in cn as

long as cn < k.

• 2. Monotonicity (MON): P should increase whenever cn

increases, and n is poor.

• 3. Progressive deprivation transfer (PROG): A rank-preserving

transfer of a deprivation from a poorer to a less poor individual (both being poor) should decrease P.

Inequality-sensitive counting poverty measures

Useful statistics

Headcount ratio: H(k) ⌘ 1 N

N

X

n=1

I(cn k) (4)

Inequality-sensitive counting poverty measures

Useful statistics

Headcount ratio: H(k) ⌘ 1 N

N

X

n=1

I(cn k) (4) Adjusted headcount ratio (Alkire and Foster, 2011): M(k) ⌘ 1 N

N

X

n=1

I(cn k)cn (5)

Inequality-sensitive counting poverty measures

Useful statistics

Censored deprivation headcount ratio (Alkire and Santos 2014): Hd(k) ⌘ 1 N

N

X

n=1

I(xnd < zd ^ cn k) (6)

Inequality-sensitive counting poverty measures

Useful statistics

Censored deprivation headcount ratio (Alkire and Santos 2014): Hd(k) ⌘ 1 N

N

X

n=1

I(xnd < zd ^ cn k) (6) Uncensored deprivation headcount ratio: Hd(0) = 1 N

N

X

n=1

I(xnd < zd ^ cn 0) = 1 N

N

X

n=1

I(xnd < zd) (7)

The anonymous case

Robust general poverty reduction in the anonymous case

Theorem 1 First-order dominance (Lasso de la Vega, 2010) PA < PB for all P satisfying FOC and MON if and only if HA(k)  HB(k) 8k 2 [0, 1] ^ 9k|HA(k) < HB(k).

The anonymous case

Robust general poverty reduction in the anonymous case

Theorem 1 First-order dominance (Lasso de la Vega, 2010) PA < PB for all P satisfying FOC and MON if and only if HA(k)  HB(k) 8k 2 [0, 1] ^ 9k|HA(k) < HB(k). Theorem 1 can also be restricted to apply to a subset of k, ruling

• ut the values below certain kmin.

The anonymous case

Robust general poverty reduction in the anonymous case

Theorem 1 First-order dominance (Lasso de la Vega, 2010) PA < PB for all P satisfying FOC and MON if and only if HA(k)  HB(k) 8k 2 [0, 1] ^ 9k|HA(k) < HB(k). Theorem 1 can also be restricted to apply to a subset of k, ruling

• ut the values below certain kmin. For this purpose, cn needs to be

censored such that cn = 0 if cn < k.

The anonymous case

Robust egalitarian poverty reduction in the anonymous case

Theorem 2 Second-order dominance (Lasso de la Vega, 2010; Chakravarty and Zoli, 2009) PA < PB for all P satisfying FOC, MON, and PROG if and only if MA(k)  MB(k) 8k 2 [0, 1] ^ 9k|MA(k) < MB(k).

The anonymous case

Robust egalitarian poverty reduction in the anonymous case

Theorem 2 Second-order dominance (Lasso de la Vega, 2010; Chakravarty and Zoli, 2009) PA < PB for all P satisfying FOC, MON, and PROG if and only if MA(k)  MB(k) 8k 2 [0, 1] ^ 9k|MA(k) < MB(k). Theorem 2 can also be restricted to apply to a subset of k, ruling

• ut the values below certain kmin.

The anonymous case

Robust egalitarian poverty reduction in the anonymous case

Theorem 2 Second-order dominance (Lasso de la Vega, 2010; Chakravarty and Zoli, 2009) PA < PB for all P satisfying FOC, MON, and PROG if and only if MA(k)  MB(k) 8k 2 [0, 1] ^ 9k|MA(k) < MB(k). Theorem 2 can also be restricted to apply to a subset of k, ruling

• ut the values below certain kmin. For this purpose, cn needs to be

censored such that cn = 0 if cn < k.

Variable deprivation weights General conditions

General necessary conditions

Proposition 1 If MA(k)  MB(k) 8k 2 [0, 1] ^ 9k|MA(k) < MB(k) for all possible weighting vectors W then: HA(1)  HB(1).

Variable deprivation weights General conditions

General necessary conditions

Proposition 1 If MA(k)  MB(k) 8k 2 [0, 1] ^ 9k|MA(k) < MB(k) for all possible weighting vectors W then: HA(1)  HB(1). Hence, if we find HA(1) > HB(1), we can conclude that we cannot find any W such that A dominates B.

Variable deprivation weights General conditions

General necessary conditions

Proposition 2 If MA(k)  MB(k) 8k 2 [0, 1] ^ 9k|MA(k) < MB(k) for all pos- sible weighting vectors W then: HA

d (0)  HB(0) 8d 2 [1, 2, ..., D].

Variable deprivation weights General conditions

General necessary conditions

Proposition 2 If MA(k)  MB(k) 8k 2 [0, 1] ^ 9k|MA(k) < MB(k) for all pos- sible weighting vectors W then: HA

d (0)  HB(0) 8d 2 [1, 2, ..., D].

Hence, if we find 9d|HA

d (0) > HB(0) then we can be sure that A

does not dominate B for every conceivable W .

Variable deprivation weights General conditions

General sufficient conditions

Proposition 3 “curve crossing” If HA(1) > HB(1) and 9d|HA

d (0)  HB d (0) then there will be at

least one vector W such that A and B cannot be ordered according to the stochastic dominance criterion of theorem 2.

Variable deprivation weights Specific conditions

Example 1: Necessary and sufficient conditions for D = 2

Theorem 3 PA < PB for all P satisfying FOC, MOC, and PROG, if and only if propositions 1 and 2 hold.

Variable deprivation weights Specific conditions

Example 2: Necessary and sufficient conditions for cases in which one deprivation is indispensable for poverty identification, and the others are equally weighted

We have: wr > PD

d6=r wd and kmin = wr, with wd = 1 1wr 8d 6= r.

Variable deprivation weights Specific conditions

Example 2: Necessary and sufficient conditions for cases in which one deprivation is indispensable for poverty identification, and the others are equally weighted

We have: wr > PD

d6=r wd and kmin = wr, with wd = 1 1wr 8d 6= r.

We define the following censored headcount: ˆ Hd,r(j) ⌘ 1 N

N

X

n=1

I(xnd < zd ^ [xnr < zr ^ ˆ cn j]) j 2 [ 1 D , 2 D , ..., 1] (8)

Variable deprivation weights Specific conditions

Example 2: Necessary and sufficient conditions for cases in which one deprivation is indispensable for poverty identification, and the others are equally weighted

We have: wr > PD

d6=r wd and kmin = wr, with wd = 1 1wr 8d 6= r.

We define the following censored headcount: ˆ Hd,r(j) ⌘ 1 N

N

X

n=1

I(xnd < zd ^ [xnr < zr ^ ˆ cn j]) j 2 [ 1 D , 2 D , ..., 1] (8) Theorem 4 PA < PB for all P satisfying FOC, MOC, and PROG, for all W such that wr > PD

d6=r wd, wd = 1 1wr 8d 6= r and kmin 2 [wr, 1], if and

• nly if 8r : ˆ

HA

d,r(j)  ˆ

HB

d,r(j) 8(d, j) 2 [1, 2, ..., D]⇥[ 1 D , 2 D , ..., 1] ^

9(d _ j)|ˆ HA

d,r(j) < ˆ

HB

d,r(j).

Statistical inference

Test of theorem 2

We test: Ho : MA(k) = MB(k) 8k 2 [0, v2, ..., 1] (9) Ha : 9k|MA(k) > MB(k), (10)

Statistical inference

Test of theorem 2

We test: Ho : MA(k) = MB(k) 8k 2 [0, v2, ..., 1] (9) Ha : 9k|MA(k) > MB(k), (10) with the following statistics: T(k) = MA(k) MB(k) q

σ2

MA(k)

NA

+

σ2

MB (k)

NB

, (11) where: σ2

MA(k) ⌘

1 NA

NA

X

n=1

[cn]2I(cn k) [MA(k)]2 (12)

Statistical inference

Test of theorem 2

Then we test Ho : T(k) = 0 against Ha : T(k) > 0 for every relevant value of k.

Statistical inference

Test of theorem 2

Then we test Ho : T(k) = 0 against Ha : T(k) > 0 for every relevant value of k. We conclude that A does not dominates B in terms of theorem 2 if 9k|T(k) > Tα, where Tα is the right-tail critical value for a one-tailed “z-test” corresponding to a level of significance α.

Statistical inference

Test of theorem 2

Then we test Ho : T(k) = 0 against Ha : T(k) > 0 for every relevant value of k. We conclude that A does not dominates B in terms of theorem 2 if 9k|T(k) > Tα, where Tα is the right-tail critical value for a one-tailed “z-test” corresponding to a level of significance α. Since we test multiple comparisons, the actual size of the whole test is not α. Under reasonable assumptions, it is β = Pl

i=1[l i + 1]αi(1)i1. We choose α = 0.01, so that

β ⇡ 0.05.

Statistical inference

Test of proposition 1

Same procedure as before but now we have only one comparison based on T(1).

Statistical inference

Test of proposition 1

Same procedure as before but now we have only one comparison based on T(1). Plus we note that in the case of k = 1: σ2

MA(1) = H(1)[1 H(1)]

(13) Then we test Ho : T(1) = 0 against Ho : T(1) > 0, using standard critical values for a one-tailed “z-test”.If we reject the null then we conclude that A does not dominate B irrespective of W .

Statistical inference

Test of proposition 2

Same testing procedure as the one used for Theorem 2 but now we construct the following statistics: Td = HA

d (0) HB d (0)

r

σ2

HA d

(0) NA

+

σ2

HB d

(0) NB

, (14) where: σ2

HA

d (0) ⌘ HA

d (0)[1 HA d (0)]

(15)

Statistical inference

Test of proposition 2

Same testing procedure as the one used for Theorem 2 but now we construct the following statistics: Td = HA

d (0) HB d (0)

r

σ2

HA d

(0) NA

+

σ2

HB d

(0) NB

, (14) where: σ2

HA

d (0) ⌘ HA

d (0)[1 HA d (0)]

(15) If we reject the null then we conclude that it is not true that A dominates B for every conceivable weighting vector W .

Empirical illustration

Background

I Peru experienced a commodity boom between 2003 and 2007,

then between 2008 and 2013 affected by world crisis.

Empirical illustration

Background

I Peru experienced a commodity boom between 2003 and 2007,

then between 2008 and 2013 affected by world crisis.

I GDP per capita increased (especially during boom) and

monetary poverty fell.

Empirical illustration

Background

I Peru experienced a commodity boom between 2003 and 2007,

then between 2008 and 2013 affected by world crisis.

I GDP per capita increased (especially during boom) and

monetary poverty fell.

I How did the population fare in terms of non-monetary poverty

measured with counting indices?

Empirical illustration

Data

I Anonymous analysis: Peruvian National Household Surveys

(ENAHO) for 2002 and 2013.

Empirical illustration

Data

I Anonymous analysis: Peruvian National Household Surveys

(ENAHO) for 2002 and 2013.

I Non-anonymous analysis: ENAHO panel datasets:

2002-2004-2006 and 2007-2008-2010.

Empirical illustration

Data

I Anonymous analysis: Peruvian National Household Surveys

(ENAHO) for 2002 and 2013.

I Non-anonymous analysis: ENAHO panel datasets:

2002-2004-2006 and 2007-2008-2010.

Empirical illustration

Poverty estimation choices

Four poverty dimensions:

• 1. Household education: Deprived if either at least one member

in school age is delayed by more than a year, or if the head or his/her partner did not complete primary education.

Empirical illustration

Poverty estimation choices

Four poverty dimensions:

• 1. Household education: Deprived if either at least one member

in school age is delayed by more than a year, or if the head or his/her partner did not complete primary education.

• 2. Physical dwelling conditions: Deprived if either more than

three people per room, or inadequate building materials, or location inadequate for human inhabitation.

Empirical illustration

Poverty estimation choices

Four poverty dimensions:

• 1. Household education: Deprived if either at least one member

in school age is delayed by more than a year, or if the head or his/her partner did not complete primary education.

• 2. Physical dwelling conditions: Deprived if either more than

three people per room, or inadequate building materials, or location inadequate for human inhabitation.

• 3. Access to services: Deprived if either lacking electricity,

lacking piped water, lacking sewage/septic tank, or lacking telephone landline.

Empirical illustration

Poverty estimation choices

Four poverty dimensions:

• 1. Household education: Deprived if either at least one member

in school age is delayed by more than a year, or if the head or his/her partner did not complete primary education.

• 2. Physical dwelling conditions: Deprived if either more than

three people per room, or inadequate building materials, or location inadequate for human inhabitation.

• 3. Access to services: Deprived if either lacking electricity,

lacking piped water, lacking sewage/septic tank, or lacking telephone landline.

• 4. Vulnerability to dependency burden: Deprived if members

below 14 or above 64 years old are at least three times as many as those between 14 and 64.

Empirical illustration

Poverty estimation choices

Four poverty dimensions:

• 1. Household education: Deprived if either at least one member

in school age is delayed by more than a year, or if the head or his/her partner did not complete primary education.

• 2. Physical dwelling conditions: Deprived if either more than

three people per room, or inadequate building materials, or location inadequate for human inhabitation.

• 3. Access to services: Deprived if either lacking electricity,

lacking piped water, lacking sewage/septic tank, or lacking telephone landline.

• 4. Vulnerability to dependency burden: Deprived if members

below 14 or above 64 years old are at least three times as many as those between 14 and 64.

Empirical illustration

Poverty estimation choices

Four poverty dimensions:

• 1. Household education: Deprived if either at least one member

in school age is delayed by more than a year, or if the head or his/her partner did not complete primary education.

• 2. Physical dwelling conditions: Deprived if either more than

three people per room, or inadequate building materials, or location inadequate for human inhabitation.

• 3. Access to services: Deprived if either lacking electricity,

lacking piped water, lacking sewage/septic tank, or lacking telephone landline.

• 4. Vulnerability to dependency burden: Deprived if members

below 14 or above 64 years old are at least three times as many as those between 14 and 64. Each dimension weighted equally, so score can take values: 0,0.25,0.5,0.75,1.

Empirical illustration

Anonymous results

RGL curves of deprivation counts. Peru, 2002-2013.

Empirical illustration

Anonymous results

RGL curves of deprivation counts. Urban and rural Peru, 2002-2013.

Empirical illustration

Anonymous results

RGL curves of deprivation counts. Peruvian rainforest, 2002-2013.

Empirical illustration

Anonymous results

RGL curves of deprivation counts. Southern Peru, 2002-2013.

Empirical illustration

Anonymous results

RGL curves of deprivation counts. South-central Peru, 2002-2013.

Empirical illustration

Anonymous results

RGL curves of deprivation counts. Central Peru, 2002-2013.

Empirical illustration

Anonymous results

RGL curves of deprivation counts. Northern Peru, 2002-2013.

Empirical illustration

Test results for Theorem 2

Ha : 9k|M2002(k) > M2013(k) k National Urban Rural 0.25 31.862 24.784 25.758 0.5 29.742 20.580 25.158 0.75 16.519 11.881 11.565 1

• 0.763
• 0.261
• 0.954

Empirical illustration

Test results for Theorem 2

Ha : 9k|M2002(k) > M2013(k) k National Urban Rural 0.25 31.862 24.784 25.758 0.5 29.742 20.580 25.158 0.75 16.519 11.881 11.565 1

• 0.763
• 0.261
• 0.954

We reject the null that poverty was robustly lower in 2002 for the three samples.

Empirical illustration

Test results for Theorem 2

Ha : 9k|M2002(k) > M2013(k) Rainforest k Amazonas Loreto Madre de Dios San Martin Ucayali 0.25 7.454 5.987 5.549 7.103 2.189 0.5 7.296 5.181 5.188 6.610 2.719 0.75 3.788 4.609 4.435 3.711 0.741 1 0.581 0.619 1.328

• 0.613
• 2.268

Empirical illustration

Test results for Theorem 2

Ha : 9k|M2002(k) > M2013(k) Rainforest k Amazonas Loreto Madre de Dios San Martin Ucayali 0.25 7.454 5.987 5.549 7.103 2.189 0.5 7.296 5.181 5.188 6.610 2.719 0.75 3.788 4.609 4.435 3.711 0.741 1 0.581 0.619 1.328

• 0.613
• 2.268

We reject the null in all cases but in the case of Ucayali there is evidence of significant curve-crossing.

Empirical illustration

Test results for Theorem 2

Ha : 9k|M2002(k) > M2013(k) South k Puno Arequipa Tacna Moquegua 0.25 3.391 2.002 2.901 8.019 0.5 2.950 1.576 1.874 6.844 0.75

• 0.678

0.658 0.045 3.137 1

• 2.456
• 1.000
• 1.735

0.724

Empirical illustration

Test results for Theorem 2

Ha : 9k|M2002(k) > M2013(k) South k Puno Arequipa Tacna Moquegua 0.25 3.391 2.002 2.901 8.019 0.5 2.950 1.576 1.874 6.844 0.75

• 0.678

0.658 0.045 3.137 1

• 2.456
• 1.000
• 1.735

0.724 We reject the null in all cases, except Arequipa, but in the case of Puno there is evidence of significant curve-crossing.

Empirical illustration

Test results for Theorem 2

Ha : 9k|M2002(k) > M2013(k) South-center k Cusco Ayacucho Apurimac Huancavelica Ica 0.25 4.498 7.220 7.008 9.864 8.307 0.5 5.096 6.885 7.098 10.742 6.446 0.75 1.906 4.742 3.742 4.565 2.683 1

• 0.664

0.700 2.245 0.853

• 1.865

Empirical illustration

Test results for Theorem 2

Ha : 9k|M2002(k) > M2013(k) South-center k Cusco Ayacucho Apurimac Huancavelica Ica 0.25 4.498 7.220 7.008 9.864 8.307 0.5 5.096 6.885 7.098 10.742 6.446 0.75 1.906 4.742 3.742 4.565 2.683 1

• 0.664

0.700 2.245 0.853

• 1.865

We reject the null in all cases.

Empirical illustration

Test results for Theorem 2

Ha : 9k|M2002(k) > M2013(k) Center k Pasco Huanuco Callao Junin Lima Ancash 0.25 5.728 9.340 2.181 7.202 7.907 10.421 0.5 4.818 9.347 2.467 6.441 6.313 11.074 0.75 3.503 5.682 2.243 4.635 4.098 6.398 1 0.543

• 0.881

0.422

• 1.018

0.610

• 0.068

Empirical illustration

Test results for Theorem 2

Ha : 9k|M2002(k) > M2013(k) Center k Pasco Huanuco Callao Junin Lima Ancash 0.25 5.728 9.340 2.181 7.202 7.907 10.421 0.5 4.818 9.347 2.467 6.441 6.313 11.074 0.75 3.503 5.682 2.243 4.635 4.098 6.398 1 0.543

• 0.881

0.422

• 1.018

0.610

• 0.068

We reject the null in all cases.

Empirical illustration

Test results for Theorem 2

Ha : 9k|M2002(k) > M2013(k) North k Tumbes La Libertad Cajamarca Piura Lambayeque 0.25 1.587 3.586 7.901 7.838 9.827 0.5 0.430 2.995 7.459 7.449 8.328 0.75

• 0.769

1.665 7.038 2.147 2.384 1

• 3.181
• 1.000

1.718

• 0.355
• 0.555

Empirical illustration

Test results for Theorem 2

Ha : 9k|M2002(k) > M2013(k) North k Tumbes La Libertad Cajamarca Piura Lambayeque 0.25 1.587 3.586 7.901 7.838 9.827 0.5 0.430 2.995 7.459 7.449 8.328 0.75

• 0.769

1.665 7.038 2.147 2.384 1

• 3.181
• 1.000

1.718

• 0.355
• 0.555

We reject the null in all cases, except in the case of Tumbes.

Empirical illustration

Test results for Proposition 1

Ha : H2002(1) > H2013(1) Department T(1) Department T(1) National

• 0.763

Junin

• 1.018

Urban

• 0.261

La Libertad

• 1.000

Rural

• 0.954

Lambayeque

• 0.555

Amazonas 0.581 Lima 0.610 Ancash

• 0.068

Loreto 0.619 Apurimac 2.245 Madre de Dios 1.328 Arequipa

• 1.000

Moquegua 0.724 Ayacucho 0.700 Pasco 0.543 Cajamarca 1.718 Piura

• 0.355

Callao 0.422 Puno

• 2.456

Cusco

• 0.664

San Martin

• 0.613

Huancavelica 0.853 Tacna

• 1.735

Huanuco

• 0.881

Tumbes 3.181 Ica

• 1.865

Ucayali

• 2.268

Empirical illustration

Test results for Proposition 2

Ha : 9d|H2002

d

> H2013

d

Hd National Urban Rural Education 22.818 20.187 11.268 Dwelling 20.701 12.661 16.193 Services 37.414 24.917 42.225 Burden

• 18.082
• 11.423
• 14.786

Empirical illustration

Test results for Proposition 2

Ha : 9d|H2002

d

> H2013

d

Hd National Urban Rural Education 22.818 20.187 11.268 Dwelling 20.701 12.661 16.193 Services 37.414 24.917 42.225 Burden

• 18.082
• 11.423
• 14.786

We reject the null for the three samples.

Concluding remarks

Concluding remarks

I When the anonymous RGL curve conditions are met, we

conclude that poverty changed consistently, in the sense that the result is robust to different choices of inequality-sensitive poverty indices and counting identification approaches.

Concluding remarks

Concluding remarks

I When the anonymous RGL curve conditions are met, we

conclude that poverty changed consistently, in the sense that the result is robust to different choices of inequality-sensitive poverty indices and counting identification approaches.

I However these conditions only work for specific choices of

deprivation lines and weight.

Concluding remarks

Concluding remarks

I When the anonymous RGL curve conditions are met, we

conclude that poverty changed consistently, in the sense that the result is robust to different choices of inequality-sensitive poverty indices and counting identification approaches.

I However these conditions only work for specific choices of

deprivation lines and weight. When the latter change, testing is required again.

Concluding remarks

Concluding remarks

I When the anonymous RGL curve conditions are met, we

conclude that poverty changed consistently, in the sense that the result is robust to different choices of inequality-sensitive poverty indices and counting identification approaches.

I However these conditions only work for specific choices of

deprivation lines and weight. When the latter change, testing is required again.

I When do the conditions work also for any choice of weight?

Concluding remarks

Concluding remarks

I When the anonymous RGL curve conditions are met, we

conclude that poverty changed consistently, in the sense that the result is robust to different choices of inequality-sensitive poverty indices and counting identification approaches.

I However these conditions only work for specific choices of

deprivation lines and weight. When the latter change, testing is required again.

I When do the conditions work also for any choice of weight?

We provided two key necessity propositions.

Concluding remarks

Concluding remarks

I When the anonymous RGL curve conditions are met, we

conclude that poverty changed consistently, in the sense that the result is robust to different choices of inequality-sensitive poverty indices and counting identification approaches.

I However these conditions only work for specific choices of

deprivation lines and weight. When the latter change, testing is required again.

I When do the conditions work also for any choice of weight?

We provided two key necessity propositions.

I We also show how to derive necessary and sufficient

robustness conditions for subsets of weights.

Concluding remarks

Concluding remarks

I In the anonymous assessment we found robust egalitarian

poverty reduction at the national, urban and rural level in Peru between 2002 and 2013 (although the point estimate H(1) was higher in 2013 in all these cases).

Concluding remarks

Concluding remarks

I In the anonymous assessment we found robust egalitarian

poverty reduction at the national, urban and rural level in Peru between 2002 and 2013 (although the point estimate H(1) was higher in 2013 in all these cases). At the Department level, we found 22 out 25 cases of robust poverty

• reduction. The other cases include curve-crossing (Puno,

Ucayali) and robust poverty increase (Tumbes, although point estimates hint at crossing).

Concluding remarks

Concluding remarks

I In the anonymous assessment we found robust egalitarian

poverty reduction at the national, urban and rural level in Peru between 2002 and 2013 (although the point estimate H(1) was higher in 2013 in all these cases). At the Department level, we found 22 out 25 cases of robust poverty

• reduction. The other cases include curve-crossing (Puno,

Ucayali) and robust poverty increase (Tumbes, although point estimates hint at crossing).

I We find that egalitarian poverty reduction is not robust to

different weighting choices for the national, urban, and rural cases.

Concluding remarks

Concluding remarks

I In the anonymous assessment we found robust egalitarian

poverty reduction at the national, urban and rural level in Peru between 2002 and 2013 (although the point estimate H(1) was higher in 2013 in all these cases). At the Department level, we found 22 out 25 cases of robust poverty

• reduction. The other cases include curve-crossing (Puno,

Ucayali) and robust poverty increase (Tumbes, although point estimates hint at crossing).

I We find that egalitarian poverty reduction is not robust to

different weighting choices for the national, urban, and rural cases.

I Worth paying attention to the intersection headcounts H(1).