This paper proposes a framework for analyzing pro-poor reductions in multidimensional poverty that considers changes in both the average poverty level and inequality among the poor. The authors define a counting measure of multidimensional poverty based on equal weights across multiple dimensions of well-being. They illustrate how to identify when one poverty reduction is more pro-poor than another using reverse generalized Lorenz curves. An empirical application to Peru between 2002-2013 finds reductions in both multidimensional poverty and inequality among the poor during this period, with larger decreases occurring in urban versus rural areas.

1. “Pro-poorest” poverty reduction
with counting measures
José V. Gallegos
(Peruvian Ministry of Development and Social Inclusion)
Gastón Yalonetzky
(University of Leeds)
Discussed by:
Olga Cantó
(Universidad de Alcalá and EQUALITAS)

2. Motivation
• Pro-poorness of GDP growth largely analysed (last two decades)
assuming that poverty can be adequately measured by a monetary
variable and just one dimension: household disposable income
(continuous variable to measure individual well-being).
• Recently, clear need to connect pro-poor growth with non-monetary
measures of well-being and multidimensional poverty indices
(Berenger and Bresson, 2012; Ben Haj Kacem, 2013; Bonccanfuso et al,
2009).
• Need a framework for poverty dominance (incidence, intensity and
inequality) for multidimensional poverty counting measures: when
poverty indicators are not continuous (no quantile link possible) and
number of values of poverty indicator small.

3. Aim
• The aim of this paper is to identify the conditions under which a
poverty reduction is more pro-poor than another one because not
only it reduces the average poverty score but also decreases
deprivation inequality among the poor. Authors consider both the
anonymous and the non-anonymous case.
• Counting measures of deprivation measure “incidence” of deprivation by a dual-cut-off
approach (first cut-off: what does it take to be deprived in a given dimension?;
second cut-off: how many dimensions must one be deprived in to be identified as
poor?). Deprivation or poverty “intensity” is then measured by the number of
dimensions the individual is deprived from, thus weighting each dimension equally.
• To what extent does multidimensional poverty reduction (incidence and intensity)
also reduce inequality within the poor?
• Authors illustrate their approach with panel data from Peru for the 2002-2013
period.
In particular consider that:

4. Methodology (anonymous case)
• Consider that our non-monetary poverty counting measure takes into
account 4 well-being dimensions (d=4) for which weights are equal
(푤푑=1/4). The deprivation score for each individual (i) would be the
following:
푐푖 =
퐷
푑=1
푤푑 퐼 푥푖푑 < 푧푑
• Deprivation scores can then take the values: 0, 0.25, 0.5, 0.75 and 1.
If we were to pose a second cut-off 푘 (Alkire and Foster, 2011) then if
푘=0.5 (2 or more dimensions) then only 3 individuals would be
identified as multimensionally poor in this society. Authors propose an
individual poverty measure that is: 푝푖 = 푐푖× 푘, a linear transformation
of 푐푖 that takes values, 0, 0.125, 0.25, 0.375, 0.5. So that 4 individuals
are deprived.
• In this setting the author’s social poverty measure would simply be
(symmetry, scale invariance, pop. replic. invariance, additively
decomposable): 푃 =
1
푁
푁 푝푖
푛=1

5. Methodology (anonymous case)
• In order to fulfill the focus, monotonicity and progressive deprivation
transfer axioms (key issue for inequality), authors narrow down the functional
form of 푝푖: 푝푖 = 푔(푐푖 )퐼 푐푖 ≥ 푘
• Where g(c) weights identification function by intensity of poverty, understood
as number of deprivations (deprivations=2, k=0.5) in the counting approach.
In the previous example if k=0.5, 3 individuals would be identified as deprived
those where 푐푖 is 0.5, 0.75 and 1.
• For an assessment of inequality-reducing poverty fall it is necessary and
sufficient to compare RGL (reverse generalized Lorenz curves): mapping the
cumulative share of the population ranked from the highest to the lowest
values of 푐푖 (1, 0.75, 0.5,0.25, 0) to (1/5, 1.75/5, 2.25/5,2.5/5,2.5/5)=(0.2,
0.35,0.45,0.5,0.5)=L(s)
• So if L(s) of a first moment is over or equal that of a second moment and
multidimensional poverty has fallen, inequality has fallen among the poor
(for any poverty index satisfying “progressive deprivation transfer” axiom, and
for every relevant value of k).
• Further, the area under RGL curve is an index of counting poverty satisfying
the focus, monotonicity and progressive transfer axioms.

6. Empirical illustration
• Peruvian National Household Surveys (ENAHO).
• For the anonymous assessment, we have all the cross-sections
between 2002 and 2013, which deliver more than 258,000 household-year
observations
• Multidimensional poverty measure relies on 4 dimensions (education,
dwelling conditions, access to services, vulnerability to dependency):
1) School delay (=1 if there is a household member in school age who is 1 year
delayed) or Incomplete adult primary, (=1 if hh. head or partner not completed
primary education)
2) Overcrowding (=1 if ratio of hh. Members to rooms in dwelling>3) or Inadequate
construction materials (=1 if walls made o straw or inferior material, stone and mud
or wood and soil floor or in an improvised location inadequate for human
inhabitation).
3) Access to services (=1 if lack of electricity, piped water, access to sewage or septic
tank, telephone landline)
4) Vulnerability (=1 if ratio of members younger than 14 or older than 64 to members
between 14 and 64 >3)
Each dimension is weighted equally so score can take only values: (0, 0.25, 0.5, 0.75, 1)

7. Results for the anonymous case
Adjusted
headcount
ratio
Multidimensional headcount
RGL for 2013 is always above that of 2002, so given the particular choice
of deprivation lines and dimensional weights, multidimensional poverty
decreased together with a reduction in deprivation inequality among the
poor. k=1 (4 dimensions), 0.75 (3 dimensions), 0.5 (2 dimensions), 0.25
(1 dimension)

8. Results for the anonymous case
Reduction in urban
areas was stronger
even if the poverty
situation in the cities
was less serious in
2002. Urban case
35% reduction of RGL
curve area A(0) while
16.6% in rural case
(here we consider
poor those that lack of
one dimension or
more).

9. Results for the anonymous case
Arequipa, Tacna and
Puno have crossings
of RGL when k=1
(most extreme
multidimensional
poverty case). When
k<1 the conclusion is
different.

10. Methodology (non-anonymous case)
• In the non-anonymous case authors track the experience of each individual
across periods and construct a transition matrix so to compute the expected
value of the deprivation score conditional on a given value of the
deprivation score in the initial year (the score times the conditional
probability).
• We can then compare different transition matrices and rank them in terms
of their capacity to reduce poverty, giving more weight to reductions of the
expected deprivation score of those who start the poorest.
• If RGL for population B is larger than for population A, then the transition
matrix of A induces a stronger reduction in poverty than B in terms of giving
more weight to the expected deprivation scores of those who start with a
higher score (the poorest)
• If matrices are monotone then we do not need to compute RGL curves, just
construct the ratio of the conditional expected scores of population A to
population B and see if all these ratios are smaller than 1 and adequately
ordered. If the denominator (expected score of B) is always larger than the
numerator and the higher the deprivation level the larger the ratio, then matrix
A induces a stronger reduction in poverty than B.

11. Results for the non-anonymous
case
The expected deprivation scores increase with value initial score (monotone matrices)
Large path-dependence or “low mobility”, Shorrocks M index: 0.41, 0.41, 0.33, 0.37. More
stability at the top of the distribution (being non deprived conditional on not being deprived in
t-1 is between 82 and 88%) than at the bottom (being deprived in every dimension
conditional on being in that situation in t-1 ranges from 42 to 70%)

12. Results for the non-anonymous
case
Expected egalitarian poverty reduction
If the initial score distributions were identical, the expected social poverty induced by matrix 1
(2002-2004) would be lower than those produced by any other matrix (same for 2 in
comparison to 3 and 4). The conditional distributions of expected deprivation scores
produced before the crisis second-order dominate those during the crisis. This means that
before the crisis (conditioned on different initial deprivation scores) the average expected
deprivation was lower and less disperse.
This happened even if deprivation was moving towards smaller values. This means that even
though the distribution of poverty scores improved with a higher proportion of lower scores,
each transition conducts somewhat less towards an egalitarian poverty reduction (a
diminishing marginal return).

13. Discussion
• There is room for motivation improvement.
• There is room for discussion of previous literature and more explicit
connection with related papers (this will probably ease the reading and put
the paper in context in the current state of the art).
• How do RGL relate to TIP curves in one-dimensional poverty
measurement (anonymous)? Authors could comment on this, it would be
really helpful for a better understanding of their proposal.
• Not everybody agrees that reducing “inequality within the poor” is so
important, in general people believe that incidence and intensity are crucial
but inequality is less relevant. Maybe authors could comment on that.
• How does the spurious “regression to the mean” affect your results for
the “non-anonymous” case? We should not view that effect as pro-poor
should we?
Minor comments:
Improving notation would be interesting (difficult to understand at some points).
More explicit explanation would be useful at some points too!