is in its early stages.2 Therefore in this paper we want to contribute to this new strand ... The Alkire-Foster family o
Measuring the dynamics of multiple deprivations among children: the cases of Andhra Pradesh, Ethiopia, Peru and Vietnam Mauricio Apablaza University of Nottingham, UK - Universidad del Desarrollo, Chile
Gaston Yalonetzky OPHI, University of Oxford, UK
Abstract This paper documents changes in the joint incidence of multiple deprivations during childhood using a novel decomposition of changes in the AlkireFoster family of multidimensional poverty measures, suitable for panel data. Changes in the adjusted headcount ratio are decomposed into changes in the multidimensional headcount and changes in the average number of deprivations among the poor. Each of the latter in turn are further decomposed into changes in relevant statistics including the transition probabilities of moving into and out of multidimensional poverty. Keywords: multidimensional poverty dynamics, child poverty, Young Lives.
1. Introduction The literature on poverty dynamics is very rich by now, and has at least three basic strands. First, literature that computes and models transition probabilities into and out of poverty (e.g. Jenkins (2000); Cappellari and Jenkins (2004); Petesch (2007)). Second, literature that provides measures of chronic versus transient poverty (e.g. Bossert et al. (2010); Foster (2009); Foster and Santos (2009); Hoy et al. (2010)). Third, literature that tests for poverty traps.1 All these strands focus on poverty dynamics over one relevant dimension of well-being (e.g. income or consumption), but research on poverty dynamics over several dimensions of well-being, considered jointly at the same time, is in its early stages.2 Therefore in this paper we want to contribute to this new strand of the literature by proposing a procedure to document multidimensional poverty dynamics using a time decomposition of the Alkire-Foster family of indices, in particular the adjusted headcount ratio. Nobody denies the multidimensionality of poverty and wellbeing, yet the idea of condensing all the information into one index has proven controversial (e.g. see Ravallion (2010b,a)), or challenging, at best (Atkinson, 2003). While looking at several dimensions one-at-a-time certainly makes sense in many situations, whenever one studies the breadth of multiple deprivations in each person, resorting to composite indices is unavoidable. Approaches like that of Alkire and Foster (2010) (or alternatively Duclos et al. (2006); Bourguignon and Chakravarty (2003)) are helpful in accounting for multiple deprivations. The Alkire-Foster family of measures, that we use in this paper, accounts for multiple deprivations using the counting approach (for a discussion see Atkinson (2003)). This approach identifies the multidimensionally poor by identifying the dimensions in which the person is deprived, constructing a weighted sum of these deprivations, and comparing it against a multidimensional poverty counting threshold. We do not use the approach to build up a measure of chronic poverty (although it is possible with further methodological work). Instead we use the Alkire-Foster measures to compute transitions into and out of multidimensional poverty and link them to changes in multi1
See Azariadis and Stachurski (2005) for a review. See Addison et al. (2009); for a good discussion. Interesting recent examples are Calvo (2008) and Roelen (2010). 2
2
dimensional poverty headcounts and changes in the breadth of deprivations. In this paper we focus on multidimensional child poverty. The measurement of child poverty has been well justified on the grounds of being intrinsically important, the relatively high degree of vulnerability to deprivations among children, and the future impact of child poverty in terms of adult poverty (White et al., 2002; Harpham, 2002). In the specific application to the Young Lives datasets we document changes in the adjusted headcount ratio of multidimensional poverty, and its components, for a cohort of children in Andhra Pradesh, Ethiopia, Peru and Vietnam, between 2002, 2006-7 and 2009. Our choice of variables is informed by the extensive literature on child poverty and by data availability.3 We consider four variables that reflect children’s own characteristics and eight variables measuring wellbeing aspects of their household environments. Three of the four chosen individual variables measure three human-capital functionings, which in turn affect future human capital, i.e. child labour, school attendance and nutrition. The fourth individual variable proxies the capability of enjoying parental affection. Seven of the eight chosen variables measuring household environment provide information on the children’s capability to live in a household with adequate electricity, cooking fuel, drinking water, toilet, space (i.e. no overcrowding), access to basic household assets (e.g. radio, fridge, phone, etc.). The other variable is a measure of child mortality in the household, proxying low outcomes in the household production function of health and wellbeing. Our estimations of levels of poverty, based on the chosen variables and the use of members of the Alkire-Foster family, show a clear ordering headed by Peru as least poor country, and followed, in increasing order of poverty, by Vietnam, Andhra Pradesh and Ethiopia. By contrast, the experiences of changes in poverty and transitions show significant variation. Even though between the initial and the final wave, the transition probabilities generate similar rankings (e.g. Peru tends to exhibit higher poverty-exit probabilities and lower poverty-entry probabilities), relative performances across countries in terms of poverty reduction, within wave intervals, vary and depend on 3
These choices are further discussed in the Data section below. For some (nonexhaustive) examples of the literature on child poverty measurement, see Gordon et al. (2005); Bastos and Machado (2009); Roche (2010); Biggeri et al. (2010); Notten and Roelen (2010); Roelen (2010); UNICEF (2011)). Also see Fernandes et al. (2011) for a review of the sister literature of multidimensional child wellbeing.
3
choices for the value of the multidimensional poverty cut-off (i.e. a key parameter of the Alkire-Foster measures). The rest of the paper is organized as follows. First, the methodological section discusses the time decomposition of the poverty measures not only for panel data but also for repeated cross sectional surveys. Then follows the empirical application to the Young Lives dataset. This part of the paper starts with a description of the data and discussion of the choice of variables, followed by the results for the estimated levels of poverty and their decompositions. 2. Decomposition of changes in the MPI from one period to another For cross-sectional datasets the information consists of matrices, X t , for different periods in time. In every period, a matrix X t has N t rows representing the sample size in period t. The number of columns is the number of dimensions, D, and it is assumed to be constant across time. A typical attainment element of the matrix in period t is: xnd (∈ R), that is, the attainment of individual n in dimension d. In the first identification stage, a person n is deemed to be poor in dimension/variable d if xnd ≤ zd , where zd is the dimension-specific poverty line. For the second identification stage the number of deprivations isPcounted weighting the dimensions with weights wd such that: wd ∈ R+ and D d wd = D. For simplicity of exposition below, we also consider the weights: θd = wDd . The weighted sum of deprivations is: cn =
D X
wd I(xtnd ≤ zd )
(1)
d=1
If cn ≥ k, where k is the multidimensional poverty cut-off, then individual n is said, and identified, to be multidimensionally poor. 4 Now the multidimensional head count in period t is defined as: N 1 X t I(cn ≥ k) H(t) ≡ t N n=1
4
(2)
I () is an indicator that takes the value of 1 if the expression in parenthesis is true. Otherwise it takes the value of 0.
4
The multidimensional headcount ratio simply measures the percentage of the population that is multidimensionally poor. Another important member of the Alkire-Foster family is the adjusted-headcount ratio, M 0 . This measure quantifies the weighted average number of deprivations (as a proportion of the maximum number of possible deprivations) across the population, but censoring the deprivations of those deemed to be non-poor multidimensionally: N
1 X t I(cn ≥ k)cn M (t) ≡ t N D n=1 0
(3)
Another important statistic is the average number of deprivations (as a proportion of the maximum number of possible deprivations) suffered by the multidimensionally poor, A(t): N
X 1 I(ctn ≥ k)cn A(t) ≡ t t N H D n=1
(4)
Notice that: M 0(t) = H(t)A(t). More generally, the Alkire-Foster family is defined by the following expression: D N X xt 1 X t wd [1 − nd ]α I(xtnd ≤ zd ) I(cn ≥ k) M (t) ≡ t N D n=1 zd d=1 α
(5)
α can take any value among the positive natural numbers and, when α = 0 the adjusted headcount ratio is obtained. In this paper we focus only on M 0 , A and H because we use consider ordinal variables and Alkire-Foster measures based on α > 0 are sensitive to positive powers of the poverty gaps. As it should be clear, the poverty gaps of ordinal variables are not meaningful. 5 2.1. General results for cross-sectional and panel data The following results apply to any dataset but the cross-sectional notation (t−a) and simplifying is used for simplicity. Denoting ∆%a Y (t) ≡ Y (t)−Y Y (t−a) notation a bit, the first straight forward result is the following: 5
The results presented in this section can be developed further for Alkire-Foster measures that are relevant to exclusively continuous variables
5
∆%a M 0 (t) = ∆%a H (t) + ∆%a A (t) + ∆%a H (t) ∆%a A (t)
(6)
In other words, a percentage change in M 0 can be decomposed into the percentage change in the number of multidimensionally poor, the percentage change in the average number of deprivation of the multidimensionally poor, and a multiplicative effect. Figure 1 illustrates this decomposition. Note that ∆%a H (t) and ∆%a A (t) are not independent, but there are circumstances in which a change in one may not necessarily produce a change in the other. For instance, in the extreme case of identifying the poor by the intersection approach ∆%a A (t) = 0 and so ∆%a M 0 (t) = ∆%a H (t). Another circumstance in which a change in one element may not necessarily produce a change in the other element, is when the proportion of the multidimensionally poor remains the same, but their number of deprivations increases. For this to happen it is necessary that k < D.
Figure 1: Decomposition of ∆%M 0 H
Ht=0
Mt=0 ∆%H
Ht=1
∆%A*∆%H Mt=1
∆%A
At=1
At=0
6
A
Result (6) can be further expanded by decomposing both ∆%a H (t) and ∆%a A (t). In the case of changes in H it may be of interest to decompose it in terms of changes in the multidimensional headcount for different groups of society. We do this by partitioning society in G non-overlapping groups recalling that: G X
H (t) =
ϕti H i (t) ,
(7)
i=1 t
N 1 X t I(cn ≥ k)I(individual n belongs to group G) H (t) ≡ t Ni n=1 i
Nit Nt
ϕti =
, where Nit is the number of individuals belonging to group i in period t. From (7) it is clear that :
∆%a H (t) =
G X
∆%a ϕti H i (t) ri (t − a)
(8)
i=1
=
G X
ri (t − a) ∆%a ϕti + ∆%a H i (t) + ∆%a ϕti ∆%a H i (t)
i=1
Result (8) indicates that the percentage change in the multidimensional headcount can be decomposed into changes in the composition of the population, changes in the percentage of the multidimensionally poor within each group and a multiplicative effect. The relative impact of such changes depends on the initial contributions of every group headcount to the total, i.e. ϕt−a H i (t−a) they depend on ri (t − a) ≡ i H(t−a) . P Similarly ∆%a A (t) can also be decomposed since A (t) = D d=1 θd Ad (t) and Ad (t) is the percentage of the multidimensionally poor deprived in dimension d. Using a similar decomposition as in (7) and (8), the following decomposition is also derived:
∆%a A (t) =
D X
∆%a [θd Ad (t)] si (t − a) =
d=1
D X d=1
7
sd (t − a) ∆%a Ad (t)
(9)
Ad (t−a) . Notice that ∆%a A (t) is only affected by where sd (t − a) = θdA(t−a) ∆%a Ad (t), by mediation of the sd (t − a), because we keep the dimensional weights constant. Otherwise (9) would look like (8).
2.2. Specific results for panel data In the case of panel data N t = N ∀t, and the same individuals are tracked along the different time periods. Therefore, for instance, ∆%a H (t) can be decomposed into the transition probabilities of moving in and out of multidimensional poverty: 1 − H(t − a) ∆%a H (t) = P ctn ≥ k | cnt−a < k ( ) − P [ctn < k | ct−a ≥ k], n H(t − a) (10) where P [ctn ≥ k | cnt−a < k] is the (transition) probability of being poor in period t conditional onP having been non-poor in period t − a, i.e. P [ctn ≥ 1 t t−a k | cnt−a < k] = 1−H(t−a) N < k). Similarly, P [ctn < k | n=1 I(cn ≥ k ∧ cn ≥ k] is the (transition) probability of leaving multidimensional poverty ct−a n in period t for people who were poor in period t − a, i.e. P [ctn < k | ct−a ≥ n PN 1−H(t−a) 1 t−a t k] = H(t−a) n=1 I(cn < k ∧ cn ≥ k). H(t−a) is the ratio of non-poor to poor in the population in period t − a. Notice that (10) can also be expressed in terms of the persistence probabilities, P [ctn < k | ct−a < k] = n t−a t t−a t ≥ k]. < k | c ≥ k] = 1 − P [c ≥ k | c < k] and P [c 1 − P [ctn ≥ k | ct−a n n n n n Similar decompositions can be performed for the multidimensional headcounts of subgroups within the population. ∆%a A (t) can also be further decomposed when panel data are available, by decomposing ∆%a Ad (X t ; Z) in terms of different kinds of poverty transition probabilities. For instance, notice that: Ad (t) =
P [xtnd ≤ zd ∧ ctn ≥ k] , H (t)
(11)
where P [xtnd ≤ zd ∧ ctn ≥ k] is the probability of being multidimensionally poor and deprived in variable d. It is a poverty headcount of d censored by multidimensional poverty status. In order to ease notation, we define CHd (t) ≡ P [xtnd ≤ zd ∧ ctn ≥ k]: From (11) it is clear that: ∆%a Ad (t) =
1 + ∆%a CHd (t) −1 1 + ∆%a H (t) 8
(12)
The denominator of (12) depends on ∆%a H (t),which was decomposed in terms of transition probabilities in (10). The numerator features ∆%a CHd (t), i.e. the percentage change in the censored headcount of d. An expression of it in terms of transition probabilities is analogous to that in (10): ∆%a CHd (t)
= −
d (t−a) t−a P xtnd ≤ zd ∧ ctn ≥ k | xt−a < k ( 1−CH nd > zd ∨ cn CHd (t−a) ) t t−a P xnd > zd ∨ ctn < k | xt−a ≥k nd ≤ zd ∧ cn
(13)
Notice that the censored headcount depends on two conditions, i.e. being multidimensionally poor and being deprived in a specific dimension. Hence the transition probabilities into and out of the specific poverty status defined by the censored headcount depend on changes in both conditions. To summarize, the change in the proportion of the poor deprived in variable d, Ad , depends on a complex interplay between the transition probabilities into and out multidimensional poverty and the transition probabilities into and out of multidimensional poverty coupled with deprivation in variable d. The analysis of changes in Ad can be done at different levels of detail in the decomposition. It may focus on (12), or on the combination of (12) with (10) and (13). Figure 2: Decomposition Alkire-Foster statistics based on transition probabilities
ALKIRE-FOSTER STATISTICS D%M0 (6)
D%H
PROBABILITIES OF TRANSITION ta
n
k c
n
k c
Pr[ c
t
Pr[ c
t
Pr[ x
t
Pr[ x
t
n
k]
(10)
D%Ad
ta
k]
n
(12)
D%A (9)
zd c
t
nd
zd c
t
nd
k x
ta
n
k x
ta
n
D%CHd
zd c
ta
nd
zd c
ta
nd
n
k]
n
k]
(13)
Thus far, the decompositions outlined in (6) and (9) through (13), are related to one another. Figure 2 expresses the logical links between them, emphasizing the pathways through which the transition probabilities ultimately impact on M 0 . 9
2.3. Alternative decompositions and a dominance result There is, first, an alternative novel procedure that decomposes ∆%a M 0 in terms of ∆%a H, without the appearance of ∆%a A. The starting point is the equation describing M 0 (j) as a linear combination of several multidimensionla headcounts, derived by Alkire and Foster (2010). Now M 0 (j) denotes the adjusted-headcount ratio as a function of the multidimensional cut-off, k = j: " # D X 1 0 jH (j) + M (j) = H (k) (14) D k=j+1 Computing the percentage change on both sides of (14) yields: D X kH (t − a; j) H (k) ∆%a H (j) + ∆%a H (k) ∆%a M (j) = 0 0 DM (t − a; j) DM (t − a; k) k=j+1 0
(15) According to (15), ∆%a M 0 (j) can be expressed as a weighted average of all the ∆%a H (k) from k = j until k = D. The weights depend on the intial values of the respective H and M 0 . With equation (15) we also derive the following dominance condition:
[∆%a H (k)]B ≤ [∆%a H (k)]C ∀k = [1, D] → B C ∆%a M 0 (k) ≤ ∆%a M 0 (k) ∀k = [1, D] (16) [∆%a H (k)]B stands for the ∆%a H (k) of country B. Condition (16) states that if country B experienced a higher reduction (or lower increase) in the multidimensional headcount than country C for all values of k, then it will also exhibit a higher reduction (or lower increase) in the adjusted headcount ratio for all values of k. Linking this result to equation (10) yields the following condition: B
[P [ctn ≥ k | cnt−a < k]] B [P [ctn < k | cnt−a ≥ k]] [∆%a H (k)]B B [∆%a M 0 (k)]
≤ ≥ ≤ ≤
C
[P [ctn ≥ k | ct−a < k]] ∧ n C t t−a [P [cn < k | cn ≥ k]] ∀k = [1, D] → [∆%a H (k)]C ∀k = [1, D] → C [∆%a M 0 (k)] ∀k = [1, D] 10
(17)
Condition (17) states that if, for all k, the entry probabilities in B are not higher than in C and the exit probabilities in B are at least as high as C’s, then B experiences higher reduction (or lower increase) than C in H, and then in M 0 , for all k. This condition is related to the more direct link between the transition probabilities and ∆%a M 0 that ensues when equation (10) is combined with (15). Figure 3 illustrates this connection. Figure 3: Changes in the adjusted multidimensional headcount based on transition probabilities of H
D%M0 (15)
D%H(j) ,…, D%H(k) (10)
Pr[ c
t n
k c
ta n
k]
Pr[ c
t n
k c
ta n
k]
There is another procedure that decomposes ∆%a M 0 , but this time only in terms of changes in each of the censored headcounts, i.e. ∆%a CHd (which in turn can be decomposed into their respective transition probabilities, as in (13)). To attain this result first notice that plugging (12) into (9) yields: P 1+ D d=1 sd (t − a) ∆%a CHd (t) ∆%a A (t) = −1 (18) 1 + ∆%a H (t) Then plugging (18) into (6) yields the decomposition of ∆%a M 0 in terms of ∆%a CHd : ∆%a M 0 (t) =
D X
sd (t − a) ∆%a CHd (t)
(19)
d=1
Equation (19) states that ∆%a M 0 is a weighted sum of the percentage changes in each of the censored headcounts, where the weights are given by: 11
CHd (t−a) sd (t − a) = θdM 0 (t−a) ; i.e. the contribution of the censored headcount to the adjusted headcount ratio in the initial period. The relationship linking the transition probabilities into and out of the censored headcounts to the adjusted headcount ratio is illustrated in Figure 4:
Figure 4: Changes in the adjusted multidimensional headcount based on transition probabilities of CHd
∆
∆
∆
Pr[ x t nd ≤ zd ∧ c t n ≥ k x t − a nd > zd ∨ c t − a n < k ]
Pr[ x t nd > zd ∨ c t n < k x t − a nd ≤ zd ∧ c t − a n ≥ k ]
3. Data We use the panel dataset collected by Young Lives, an international study of childhood poverty, in Andhra Pradesh, Ethiopia, Peru and Vietnam. The surveys collected information on children’s individual, household and communal characteristics in 2002, 2006-7 and 2009. We focus the analysis on the cohort children who were 8 years old in 2002. The final sample includes only those individuals in all waves and non-missing values for the selected indicators. Table 1 shows basic information on the four samples. Interestingly the rural composition of the sample exhibits significant changes, with the exception of Ethiopia. Table 2 shows the variables that we have chosen considering both the vast literature on multidimensional child poverty and data availability. We opted 12
Table 1: Sample Characteristics
Ethiopia
Andhra Pradesh
Peru
Vietnam
Wave 1 2 3 1 2 3 1 2 3 1 2 3
Original sample 1000 980 973 1008 994 975 714 685 678 1000 990 974
Selected Sample 868 868 868 944 944 944 660 660 660 957 957 957
Mean Age 7.88 12.05 14.56 7.98 12.32 14.72 7.93 12.31 14.44 7.97 12.25 14.73
% Females 49.1%
50.6%
47.0%
50.4%
% rural 61.2% 60.7% 59.7% 75.6% 74.8% 57.1% 26.1% 40.3% 23.6% 80.6% 69.3% n.a.
to combine variables that measure functionings or capabilities exclusively attributable to the individual, and variables that measure household environment and are not exclusively attributable to the child (e.g. his/her siblings would receive the same value). Three of the four chosen individual variables measure three human-capital functionings, which in turn affect future human capital: child labour, school attendance and nutrition. The fourth individual variable is a variable of parental attachment that proxies the capability of enjoying parental affection. Seven of the eight chosen variables measuring household environment provide information on the children’s capability to live in a household with adequate electricity, cooking fuel, drinking water, toilet, space (i.e. no overcrowding), access to basic household assets (e.g. radio, fridge, phone, etc.). The other variable is a measure of child mortality in the household, proxying low outcomes in the household production function of health and wellbeing. The literature offers many other options, which stem from different ways of understanding the nature of child poverty, and also require additional information. Some authors draw their lists from development goals agreed upon in different meetings. For instance, Gordon et al. (2005) base their choice on the World Summit on Social Development, while the choices by Roche (2010) are informed by the Millenium Development Goals and by the
13
World Summit for Children. In this paper, we do not explicitly seek to justify our choices in terms of a specific worldwide agreement, but rather on the grounds of measuring aspects of the children’s functionings and capabilities, parsimony, comparability across the four datasets, and data availability. An important distinction in the literature is the one between "conventional" and subjective measures of non-income child poverty (White et al., 2002). While some of our variables are close to the conventional indicators mentioned by White et al., we do not account for others like teen pregnancy because we want to have as much commonality in the variables across genders as possible. We have also decided not to add purely subjective measures to the set for the sake of clarity and comparability across the different cultures embedded in the countries/regions of the Young Lives study. More recent approaches to choices of dimensions, and indicators, have taken different routes. A significant consensus exists about considering dwelling conditions, like access to adequate sanitation, overcrowding, electricity, and/or roof/floor/walls quality; although actual choices of dwelling conditions vary. As is clear from Table 2, we have tried to cover a substantial range of indicators describing dwelling conditions. Child labour and school attendance have deserved universal consideration in the recent literature (including the measurement of child wellbeing, see Fernandes et al. (2011)). By contrast, children’s health has not always been considered, and when it has been considered, the range of indicators has been wide. For instance, Biggeri et al. (2010); consider access to drinking water as a measure of health, whereas, Roche (2010) accounts for measles immunization and Roelen (2010) measures health poverty considering visits to professional health facilities. Clearly, data availability explains, at least partly, such different choices. In this respect, we decided to include one indicator of child nutrition (based on the BMI) and to include some dwelling environment conditions that affect a child’s health. Several other environmental variables have been considered in the literature, but without the cross-study consistency observed for variables like school enrolment and child labour. For instance, Notten and Roelen (2010) use several measures of financial means to afford different assets and they also consider several indicators of neighborhood quality and access to public services. By contrast, Roelen (2010) accounts for whether the caregiver is disabled; Biggeri et al. (2010) have added measures of children’s autonomy; Bastos and Machado (2009) have a whole module of indicators on children’s social integration, and Gordon et al. (2005) consider measures of information deprivation. In this paper, we have focused the analysis on indicators that 14
relate to the individual child and to his/her closest environment, i.e. the dwelling and the household. Unlike other studies, we have not chosen explicitly several indicators for each dimension, in order to keep the number of variables manageable. For instance, some studies, like ours, use one indicator of education (e.g. Biggeri et al. (2010)), whereas others use several (Roelen, 2010). But the latter is partly due to the fact that studies which use several indicators of one dimension, usually measure poverty at the household level, therefore considering children from different age brackets for which different aspects of the same dimension may be relevant (e.g. school enrolment versus completion, as in the case of Roelen (2010)). By contrast, we focus on just one cohort of children6 .
6
Table 5 in the appendix gives a quick snapshot of the correlation structure across the dimensions for the four countries. Interestingly, the magnitudes and sign of the correlations vary wildly.
15
4. General Results Figure 5 shows the raw deprivations by country and wave. These raw deprivations are the percentages of children who are poor in one specific variable, regardless of whether they are deemed multidimensionally poor. In other words, these are headcounts uncensored by multidimensional poverty status (compare against Ad (t) H (t)). For instance, the raw deprivation headP t count of dimension d is: Hd (t) = N1t N n=1 I (xnd ≤ zd ). Ethiopia
Andhra Pradesh Labour 100%
Labour 100% Mortality
Mortality
Schollling
60%
60% Overcrowding
Attachment
Overcrowding
Attachment 40%
40%
20%
20% Asses
Nutrition
0%
Floor
Asses
Nutrition
0%
Floor
Electricity
Toilet
Schollling 80%
80%
1st wave
Coocking Fuel
Electricity
Toilet
Coocking Fuel
2nd wave Dr. Water
Dr. Water
3rd wave
Peru
Vietnam Labour 80%
Labour 60% Mortality
Mortality
Schollling
Schollling 60%
40% Overcrowding
Attachment
Overcrowding
40%
Attachment
20% 20%
Asses
Nutrition
0%
Floor
Electricity
Toilet
Asses
Floor
1st wave
Coocking Fuel
Electricity
Toilet
Coocking Fuel
2nd wave Dr. Water
3rd wave
Dr. Water
Figure 5: Raw Deprivation by Country and Wave
16
Nutrition
0%
The results are a good starting point to document the nature of multidimensional child poverty in the four countries studied. However, notice that they do not say much about the extent of joint multiple deprivations. For all the countries significant reductions in the raw headcounts took place between the first and the third wave, although not always monotonically; and there are a few exceptions (e.g. deprivation in cooking fuel in Andhra Pradesh). Also the figure reveals different patterns of raw deprivation across the countries. For instance, in Ethiopia overcrowding, toilet deprivation and cooking fuel deprivation remain important. By contrast, floor quality stands out in Peru, while access to water is relatively more relevant in Vietnam. Of course, there are also similarities. For instance, overcrowding is highly relevant in the four countries, and floor quality is the most relevant dimension, in terms of deprivation, both in Andhra Pradesh and Peru. Figure 6 shows the estimates of the adjusted headcount ratio, M 0 , for the four countries, three waves and all multidimensional cut-offs, k. All countries show progress in terms of poverty reduction from the first to the third wave, yet the patterns differ. For instance, the poverty profiles in Peru and Andhra Pradesh are very similar between the first and the second wave. But then clear progress occurs from the second to the third wave. Comparing across countries, Peru stands out as the least poor, followed by Vietnam and Andhra Pradesh. Then Ethiopia is the poorest of the four. This ranking remains robust across waves and multidimensional poverty cutoffs. Table 3 also documents levels, but now those of the multidimensional headcount, H, and the average (normalized) number of deprivations of the poor, A. The trends for H are similar to those for M 0 : progress from the first to the third wave but not always monotonic (e.g. Peru faced some increases in H at low levels of k from the first to the second wave). The cross-country ranking is also the same: Peru is the least poor in terms of H, followed by Vietnam, Andhra Pradesh and Ethiopia. By contrast, both the trends and the relative rankings related to A are much less consistent. In terms of trends, the four countries exhibit increases in the average number of deprivations at least for one value of k. As for rankings, in several cases, the values of A in a pairwise comparison are too close to venture any meaningful statement. The ranking found for A is much less clear than those for M 0 and H 7 .
7
Notice, for instance, some of the ties between Vietnam and Peru, Andhra Pradesh and Vietnam, and Ethiopia and Andhra Pradesh.
17
Table 2: Child Poverty Dimensions Indicator Child Related Child Labour♣ School Attendance Attachment Nutrition♦
Description (threshold)
Any "commercial" activity before 13 / Light activity from 13 (2 hours per day) No attendance to the school according to National Law Any contact with parents mum or dad Less than 2 standards deviations (BMI)
Household Related Electricity No electricity Cooking Fuel MDG definition (Branches/ Charcoal/ Coal/ Cow dung /Crop residues / Leaves/ None /Other) Drinking Water MDG definition (Unprotected/ Well/ Spring/ Pond/ River/ Stream / Canal) Toilet MDG definition (Forest/ field/ Open place / Neighbours toilet/ Communal pit latrine/ Relative’s toilet/ Simple latrine on pond/ Toilet in health post/ Other) Floor MDG definition (Earth/ Sand) Assets Less than one (Radio/ Fridge/ Table/ Bike/ Tv/ Motorbike/ Car/ Phone) Overcrowding♠ 3 or more Individuals per room Child Mortality♥ Any dead Children in the Household
Weight
1/12% 1/12% 1/12% 1/12%
1/12% 1/12%
1/12% 1/12%
1/12% 1/12% 1/12% 1/12%
♣ http://www.ilo.org/ilolex/cgi-lex/convde.pl?C138 ♦ http://www.who.int/childgrowth/software/en/ ♠ http://www.childinfo.org/mdg.html ♥ First wave includes all periods (before), for the 2nd and 3rd round only the change between interviews.
18
Ethiopia 0.50
0.50
0.45
0.45
0.45
0.45
0.40
0.40
0.40
0.40
0.35
0.35
0.35
0.35
0.30
0.30
0.30
0.30
0.25
0.25
0.25
0.25
0.20
0.20
0.20
0.20
0.15
0.15
0.15
0.15
0.10
0.10
0.10
0.10
0.05
0.05
0.05
0.05
0.00
0.00
Andhra Pradesh
0.50
0.50
0.00
0.00
1 d. 2 d. 3 d. 4 d. 5 d. 6 d. 7 d. 8 d. 9 d. 10 d. 11 d. 12 d.
1 d. 2 d. 3 d. 4 d. 5 d. 6 d. 7 d. 8 d. 9 d. 10 d. 11 d. 12 d.
M0 - 1st wave M0 - 1st wave
1 d. 2 d. 3 d. 4 d. 5 d. 6 d. 7 d. 8 d. 9 d. 10 d. 11 d. 12 d.
1 d. 2 d. 3 d. 4 d. 5 d. 6 d. 7 d. 8 d. 9 d. 10 d. 11 d. 12 d.
M0 - 2nd wave M0 - 2nd wave
M0 - 3rd wave M0 - 3rd wave
Peru
Vietnam
0.50
0.50
0.50
0.50
0.45
0.45
0.45
0.45
0.40
0.40
0.40
0.40
0.35
0.35
0.35
0.35
0.30
0.30
0.30
0.30
0.25
0.25
0.25
0.25
0.20
0.20
0.20
0.20
0.15
0.15
0.15
0.15
0.10
0.10
0.10
0.10
0.05
0.05
0.05
0.05
0.00
0.00
0.00
0.00
1 d. 2 d. 3 d. 4 d. 5 d. 6 d. 7 d. 8 d. 9 d. 10 d. 11 d. 12 d.
1 d. 2 d. 3 d. 4 d. 5 d. 6 d. 7 d. 8 d. 9 d. 10 d. 11 d. 12 d.
M0 - 1st wave M0 - 1st wave
1 d. 2 d. 3 d. 4 d. 5 d. 6 d. 7 d. 8 d. 9 d. 10 d. 11 d. 12 d.
1 d. 2 d. 3 d. 4 d. 5 d. 6 d. 7 d. 8 d. 9 d. 10 d. 11 d. 12 d.
M0 - 2nd wave M0 - 2nd wave
M0 - 3rd wave M0 - 3rd wave
Figure 6: Evolution of the Multidimensional Indicator (M0)
19
Ethiopia
Andhra P.
Peru
Vietnam
20
Cutoff (k) =⇒ H - 1st wave H - 2nd wave H - 3rd wave A - 1st wave A - 2nd wave A - 3rd wave H - 1st wave H - 2nd wave H - 3rd wave A - 1st wave A - 2nd wave A - 3rd wave H - 1st wave H - 2nd wave H - 3rd wave A - 1st wave A - 2nd wave A - 3rd wave H - 1st wave H - 2nd wave H - 3rd wave A - 1st wave A - 2nd wave A - 3rd wave 1 di. 99% 100% 98% 0.47 0.41 0.36 92% 100% 87% 0.35 0.34 0.27 77% 92% 63% 0.21 0.19 0.17 92% 96% 72% 0.27 0.22 0.21
2 di. 96% 96% 92% 0.49 0.42 0.38 82% 86% 73% 0.38 0.37 0.31 55% 58% 33% 0.26 0.26 0.24 75% 72% 49% 0.31 0.27 0.27
3 di. 90% 88% 79% 0.51 0.44 0.42 73% 76% 55% 0.41 0.40 0.36 35% 33% 16% 0.32 0.33 0.32 57% 47% 30% 0.35 0.33 0.34
4 di. 82% 76% 61% 0.53 0.47 0.47 59% 59% 35% 0.45 0.45 0.42 19% 19% 8% 0.37 0.38 0.39 37% 26% 17% 0.41 0.39 0.40
5 di. 71% 59% 44% 0.56 0.52 0.52 42% 43% 22% 0.49 0.49 0.47 7% 9% 4% 0.43 0.44 0.45 21% 12% 8% 0.47 0.46 0.48
6 di. 58% 39% 28% 0.60 0.57 0.57 24% 24% 9% 0.55 0.55 0.55 1% 2% 1% 0.51 0.51 0.53 10% 4% 4% 0.53 0.53 0.55
7 di. 40% 21% 16% 0.64 0.63 0.63 11% 10% 4% 0.61 0.61 0.61 0% 0% 0% 0.58 0.58 0.58 3% 2% 1% 0.61 0.59 0.63 1% 0% 1% 0.67 0.67 0.67
8 di. 20% 8% 7% 0.69 0.69 0.70 3% 3% 1% 0.67 0.68 0.70
9 di. 5% 2% 2% 0.77 0.76 0.78 0% 0% 0% 0.75 0.75 0.75
10 di. 1% 0% 1% 0.83 0.83 0.83
Table 3: Evolution of Headcount measure and Average level of Deprivation 11 di.
12 di.
5. Dynamic Results Table 4 and Figure 7 show the transition probabilities into and out of multidimensional poverty for the four countries, all the values of k, and for the two intermediate transitions (Table 4) and the total transition from the first to the third wave (Figure 7). Considering that the conditions for multidimensional poverty identification become more demanding as we move from a union to an intersection approach, it is not surprising that the exit probabilities tend to be higher when k increases. Likewise, it is reasonable to observe, as we do, higher entry probabilities for lower values of k. Notice though that these trends are not entirely mechanical, or trivial. For instance, between the 2nd and the 3rd way the exit probabilities in Ehtiopia are higher when k = 9 than when k = 10. Likewise, for Vietnam in the same period, the exit probability for k = 4 is very similar to that for k = 5. The crosscountry comparison reveals that no country dominates all the others in terms of the highest exit probabilities from wave 1 to 2. However Peru and Vietnam outperform Ethiopia and Andhra Pradesh. Within each of these two pairs no country dominates though. Between waves 2 and 3, the ranking situation changes: Peru exhibits the highest exit rates for all k, while Ethiopia exhibits the lowest. Between Vietnam and Andhra Pradesh the comparison depends on the choice of k. All countries, except Vietnam, exhibit consistently higher exit probabilities during the second wave interval. As for entry probabilities, again, no country dominates the others for every k and between waves 1 and 2, although Peru fares better than Ethiopia and Andhra Pradesh. Interestingly, the exit probabilities between waves 1 and 2 fall sharply when k goes from 1 to 2, with the exception of Ethiopia. For all countries there is a significant drop in entry probabilities during the second wave interval, although this is not always true in some countries for k values close to the intersection approach, which involve relatively smaller groups of people. Between waves 2 and 3 Peru again stands out as the better-off country, in this case with the lowest entry rates. Andhra Pradesh dominates Ethiopia, but then no other dominance relationship can be established between Vietnam and Andhra Pradesh, or Ethiopia. Figure 7 shows the entry and exit probabilities between wave 1 and wave 3. Like the results in Table 4, entry probabilities tend to decrease with higher values of k, while exit probabilities undergo an opposite trend. However these tendencies are not purely monotonic (e.g. the entry probabilities of Ethiopia or the exit probabilities of Vietnam). This is a hint that the behavior of the 21
transition probabilities along different values of k is not simply mechanical. Entry probabilities appear very high for low levels of k and Ethiopia shows the highest entry probabilities, followed by Andhra Pradesh. Those of Peru and Vietnam are lower and very similar to each other. As for exit probabilities, the years between waves 1 and 3 have seen complete transitions (100%) out of multidimensional poverty for high levels of k and for all countries. In the case of Peru, this is the case from k = 6 upward. All the others experience complete transitions from k = 9 upward. In other words, all countries have witnessed multidimensional child poverty disappear for the identification criteria that are closest to the pure identification approach. Peru fared the best, exhibiting the highest exit probabilities. Andhra did better than Ethiopia. The other pair-wise comparisons are inconclusive.
Entry Probabilities
Exit Probabilities
Table 4: Transition Probabilities
k 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10
Ethiopia 1-2 2-3 0.1% 2.2% 2.9% 7.0% 8.3% 15.5% 13.3% 26.4% 26.6% 36.1% 46.6% 44.0% 64.9% 55.5% 82.2% 74.0% 90.0% 50.0% 85.7% 50.0% 81.6% 61.3% 57.6% 36.6% 31.3% 20.1% 23.1% 15.6% 18.6% 10.9% 11.4% 8.0% 6.1% 5.2% 2.4% 1.8% 0.2% 0.7%
Andhra 1-2 0.2% 4.9% 6.7% 16.4% 26.2% 40.9% 62.7% 81.5%
97.2% 46.2% 27.5% 23.5% 21.2% 12.7% 6.5% 2.4% 0.4%
Pradesh 2-3 12.7% 17.9% 30.4% 44.6% 58.9% 74.4% 79.6% 96.3%
50.0% 12.4% 8.7% 6.2% 6.7% 3.8% 1.9% 0.9% 0.4%
22
Peru 1-2 2-3 5.1% 34.1% 19.2% 51.0% 34.9% 59.8% 50.4% 75.0% 59.6% 82.0% 93.3% 100.0%
Vietnam 1-2 2-3 3.5% 28.2% 15.7% 39.2% 33.3% 50.1% 46.9% 54.0% 60.3% 54.0% 69.2% 58.1% 72.4% 75.0%
84.0% 30.3% 15.9% 12.2% 6.9% 2.3% 0.2%
92.4% 33.2% 20.8% 10.6% 4.2% 1.7% 0.9% 0.1%
30.0% 10.8% 4.3% 3.8% 2.2% 1.1% 0.5%
64.9% 17.8% 11.5% 6.4% 3.2% 2.1% 1.1% 0.7%
0.329114
0.2494305
0.13617 0.398892 0.085784
Ethiopia India 1 43% 2 58% 3 32% 4 20% 5 10% 6 6% 7 entry and 5% exit Figure 7: Probabilities of 8 4% 9 2% 10 1% Entry
0.54827 0.046435 0.624294
Peru Vietnam Ethiopia India 44% 27% 33% 2% 9% 21% 13% 14% 7% 16% 13% 6% 9% 16% 30% 8% 3% 5% 30% 46% 9% 2% 2% 42% 61% 5% 1% 1% 55% 78% 3% period)0% 68% 87% (full by cut-off1% and by country 1% 0% 1% 82% 85% 0% 0% 0% 98% 100% 0% 0% 0% 100% 100% Exit
60%
100%
80%
40%
60%
40% 20%
20%
0%
0%
1
2
3
4
5
6
7
8
Ethiopia
9
1
10 India
23
2 Peru
3
4
5
6
Vietnam
7
8
9
10
6. Decomposition results Figures 8, 9, and tables 6 and 7 in the appendix, show the decompositions results based on equation (6) for different values of k. For most countries and most values of k, the main driver of changes in M 0 is the change in H. The few exceptions are provided by Ethiopia, Andhra Pradesh and Vietnam for low values of k, i.e. for identification criteria at, or close to, the union approach. Figure 10 shows the decompositions results based on equation (10). Notice that the exit probabilities are compared against an “adjusted” entry probability. The latter is simply the first element of the right-hand side ). Notice that this element also of (10), i.e. P [ctn ≥ k | cnt−a < k] ( 1−H(t−a) H(t−a) increases with k. The reason is that, even though entry probabilities do decrease as we move toward intersection approaches, the ratio(1 − H)/H also increases when going in the same direction. Moreover, this increase seems to be greater than the decrease in the entry probabilities. Hence, this "adjusted" entry probability also increases with k. As the figure 10 and tables 8 and 9 (in the appendix) show, Ethiopia and Vietnam did better than Peru and Andhra Pradesh in reducing H between wave 1 and 2. By contrast, between wave 2 and 3, Andhra Pradesh stands out as the best performer in reduction of H, while most other comparative performances depend on the value of k. In particular, Ethiopia, Peru and Vietnam exhibit some sharp percentage increases in H for high values of k. These though involve relatively small numbers of children at the base line (hence the high percentage increases). Another interesting pattern shared by Ethiopia and Vietnam is that they performed better between waves 2 and 3 for low values of k but not for high values of k. Going back to Figure 8 and 9, Ethiopia and Vietnam fare better than Peru and Andhra Pradesh in terms of reduction (or lower increases) of A, between waves 1 and 2, for all k. Between waves 2 and 3, no pair-wise comparison is robust to the value of k. Also, within countries, whether A increased or decreased depends on the choice of second-stage identification threshold. As for the adjusted headcount ratio, Tables 6 and 7 show that between wave 1 and 2, Vietnam experienced the highest reduction followed by Ethiopia. Andhra Pradesh and Peru fared the worst, but their pair-wise comparison depends on the value of k. During the last wave change (2 to 3), the only result robust to changes in k is that Andhra Pradesh did better than Ethiopia. During the same period, some countries experienced increases in 24
M 0 for intersection approaches (involving few people at the baseline). Figure 11 and Tables 10 and 11 (appendix) show the most basic decomposition of A. For these results, the deprivations of the poor have been grouped into deprivations exclusively attributable to the individual (e.g. child labour) and those related to the individual’s household environment (e.g. electricity). This is achieved by adding up the respective Ad statistics (equation 11) across the variables belonging to the same group. Figure 12 (appendix) shows the relative contributions of the children-specific deprivations to total average deprivation, A. Interestingly, for all countries and all k, these contributions increase (to the detriment of the contribution of household deprivations) from wave 1 to wave 3. For most (but not all) countries and values of k, this increase is also already patent when moving from wave 1 to 2. Then the results in Figure 11 show the decomposition of A according to equation (9). The results do not reveal clear patterns. Rather the country experiences tend to be idiosyncratic and the trends depend on the choices of k. For instance, in Ethiopia and Vietnam, changes in household deprivations among the poor seem to be the key drivers of change in A for most values of k, but several exceptions appear. Strikingly, in most cases across countries, waves and multidimensional cut-offs (k), changes in children-specific deprivations move in opposite directions to changes in household deprivations. Vietnam’s pattern is interesting because, of the four country, it is the only one in which performance in terms of change in A is consistently worse during the second time interval (waves 2 to 3), i.e. for all values of k.
25
Ethiopia 1-2 2-3
29%
25%
∆%H ∆%A
1-2 2-3
1-2 2-3
1-2 2-3
1-2 2-3
1-2 2-3
1-2 2-3
1-2 2-3
1-2 2-3
∆%H*∆%A ∆%M
1-2 2-3 83%
15% ∆%H*∆%A ∆%A
5%
∆%H
-5%
∆%M -15%
-25%
1
2
3
4
5
6
7
8
9
10
1-2 2-3
1-2 2-3
1-2 2-3
1-2 2-3
1-2 2-3
1-2 2-3
1-2 2-3
1-2 2-3
1-2 2-3
1-2 2-3
1-2
25%
Andhra Pradesh 1-2 2-3 25%
1-2 2-3
∆%H ∆%A
1-2 2-3
1-2 2-3
1-2 2-3
1-2 2-3
1-2 2-3
1-2 2-3
4
5
6
7
8
∆%H*∆%A ∆%M
15%
5% ∆%H
-5%
∆%M -15%
-25%
1
2
3
9
Figure 8: Decomposition of the adjusted headcount ratio, Ethiopia and Andhra Pradesh
26
Peru 25%
∆%H*∆%A ∆%A ∆%H*∆%A ∆%H ∆%A ∆%M ∆%H ∆%M
15% 25%
1-2 2-3
1-2 2-3
∆%H ∆%A 1-2 2-3
∆%H*∆%A ∆%M 1-2 2-3 1-2 2-3
1-2 2-3
1-2 2-3
1-2 2-3
1-2 2-3
29%
1-2 2-3
1-2 2-3
67%
1-2 2-3 29%
1-2 2-3
1-2 2-3
1-2 2-3
1-2 2-3
67%
5% 15% -5% 5% -15% -5% -25% -15%
1 1-2 2-3
25% -25%
1
Vietnam
∆%H*∆%A
1-2 2-3
15% 25%
∆%A
5% 15%
∆%H
-5% 5%
1-2 2-3
2
3
1-2 2-3
1-2 2-3
2
1-2 2-3
∆%H ∆%A
3
1-2 2-3
4 1-2 2-3
4
1-2 2-3
5 1-2 2-3
5
1-2 2-3
6 1-2 2-3
6
1-2 2-3
7 1-2 2-3
7
1-2 2-3
1-2 2-3
1-2 2-3
200%
1-2 2-3 200%
∆%H*∆%A ∆%M
∆%M -15% -5% -25% -15%
-25%
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
Figure 9: Decomposition of the adjusted headcount ratio, Peru and Vietnam
27
1-2 2-3
28
‡
†
1
2
3
4
5
6
7
8
9
10
7 5 %
1
3
4
5
Pr(Exit)
2
6
Andhra P.
7
8
10
1
2
3
4
Adjusted Pr(Entry)
9
7 5 %
Peru
5
6
7
8
10
∆%H
9
175%
7 5 %
1
2
3
4
5
Vietnam
6
7
75%
8
9
For each cuttoff, the former column represents the first wave and the latter column corresponds to the second wave. Vertical axis presents results within the range -25% and +25%. Detailed Information can be found in the appendix.
-25%
-15%
-5%
5%
15%
25%
Ethiopia
Figure 10: Decomposition of changes in the Headcount Indicator†‡
10
7 5 %
k
29
.
1
2
3
5
6
7
8
9
10
.
1
2
3
4
5
∆%Average Depriv. Household
4
7 5 %
Andhra P.
6
7
8
9
.
1
2
3
4
5
6
∆%Average Depriv. Child
7 5 %
Peru
175%
7 5 %
.
1
2
4
5
∆%A
3
Vietnam
6
75%
For each cuttoff, the former column represents the first wave and the latter column corresponds to the second wave. [ Vertical axis presents results within the range -10% and +10%. Detailed Information can be found in the appendix.
§
-10%
-5%
0%
5%
10%
Ethiopia
Figure 11: Decomposition of changes in the Average Deprivation§[
7 5 %
k
-0.01469
7. Concluding remarks This paper has sought to contribute to the analysis of multidimensional poverty dynamics firstly by providing some basic decompositions of changes in the members of the Alkire-Foster family that relate changes in their statistics (e.g. H or A) all the way back to changes in transition probabilities. An empirical illustration of these descriptive tools is provided by an analysis of multidimensional child poverty in Andhra Pradesh, Ethiopia, Peru and Vietnam using the three available waves of the Young Lives dataset. The levels estimation of H, A and M 0 reveal a clear ordering across the countries, for all k, whereby Andhra Pradesh is not poorer than Ethiopia, Vietnam is not poorer than Andhra Pradesh, and Peru is not poorer than Vietnam. However the decompositions unpack a wide variety of experiences in terms of poverty reduction, or increase. In terms of changes in H, Peru and Ethiopia turn up as the most and least successful in terms of poverty reduction. An examination of the transition probabilities underpinning the change in H reveals that these two countries also take top and bottom positions in terms of exit and entry probabilities. By contrast, the experiences of change in A are much more varied. Only Vietnam shows a consistent pattern of deterioration across all k. When dominance patterns are found for ∆%H they get reflected by those for ∆%M 0 . A case in point is the dominance of Vietnam over Peru between waves 1 and 2 (Figures 8 and 9). This empirical result is in tune with the dominance results that we derived in the paper. Interestingly, this formal result leaves the changes in A out of the picture. The examples from our empirical application illustrate this point very well by showing the coexistence of a clear ordering for H and M 0 with an unclear pattern for A. Further work on this paper should compute the decompositions linking changes in A to transition probabilities (equations 9 through 13). We also aim at providing confidence intervals for the computed statistics. In addition, we may want to test the robustness of our comparisons to changes in the values of other key parameters of the measures used, chiefly the poverty lines and weights attributed to each variable. Stochastic dominance approaches like that of Yalonetzky (2011) could also be informative.
30
8. Appendix
Figure 12: Contribution of Children Dimensions to the Total Average Deprivation
Ethiopia
Andhra P.
Peru
Vietnam
40%
1st wave 0.061522 0.056969 0.054259 0.052318 0.050934 0.059621 0.063492 0.085714 0.111111
2nd wave 0.321998 0.294638 0.276833 0.255205 30% 0.242894 0.229672 0.211604 0.237113 0.222222
3rd wave 0.215892 0.216981 0.236648 0.253855 0.297297 0.275862 0.291045 0.348837 0.296296
1st wave 0.018062 0.016917 0.014085 0.015326 0.018349 0.052632 0.142857
2nd wave 0.263543 0.182594 0.13785 0.112583 0.115942 0.139535 0.142857
3rd wave 0.149052 0.162362 0.165605 0.175824 0.254902 0.333333
1st wave 0.115439 0.118223 0.12087 0.112849 0.121646 0.114695 0.135135 0.125
3
7
2nd wave 0.360976 0.314698 0.283922 0.255941 0.226804 0.206612 0.163265
3rd wave 0.234069 0.242898 0.246032 0.243827 0.239362 0.222222 0.259259 0.360976 0.25 0.014085
20%
10%
0% 1
2
3
4
5
6
7
8
9
10
1
2
4
5
6
8
1st wave
9
10
1
2
2nd wave
31
3
4
5
6
7
8
9
3rd wave
10
1
2
3
4
5
6
7
8
9
10
Vietnam
Peru
Andhra Pradesh
Ethiopia
Table 5: Correlation (Spearman) between deprivations all years per countryz]
z ]
Child Labour Schooling Attachment Nutrition Electricity Cooking Fuel Dr. Water Toilet Floor Assets Overcrowding Mortality Child Labour Schooling Attachment Nutrition Electricity Cooking Fuel Dr. Water Toilet Floor Assets Overcrowding Mortality Child Labour Schooling Attachment Nutrition Electricity Cooking Fuel Dr. Water Toilet Floor Assets Overcrowding Mortality Child Labour Schooling Attachment Nutrition Electricity Cooking Fuel Dr. Water Toilet Floor Assets Overcrowding Mortality
CL 1
S
A
N
1 -0.04 -0.07
1 0.1
E
CF
DW
T
F
AS
O
1 0.08 0.22 0.34 0.12 0.04
1 0.04 0.21 0.17 0.14
1 0.41 0.2 0.07
1 0.25 0.14
1
1 0.35 0.39 0.2 0.09
1 0.4 0.23 0.11
1 0.26 0.17
1 0.07
1 0.36 0.2 0.12
1 0.19 0.14
1 0.08
1 0.3 0.25 0.13
1 0.2 0.17
1 0.11
1 0.05 0.08 -0.08 -0.07 -0.04 -0.09 -0.05 -0.09 1 0.17 0.08 -0.05 0.04 -0.11
-0.09 -0.09 1 0.16
-0.06 0.28 0.06 0.2 0.15 0.15 0.25 0.14 0.19 1 0.12 -0.04
0.05 -0.08 -0.05 -0.12
0.1 0.08 -0.06
1 -0.04
0.09 -0.07 0.09
1 0.08 0.08 0.06
1 0.08 0.06
0.06
1 0.08
1 0.08 0.45 0.06 0.39 0.52 0.21 0.1
1 0.2 0.14 0.19 0.38 0.33 0.16 0.11
1 0.11 0.64 0.3 0.42 0.2 0.09
1 0.1 0.14 0.18 0.11
1 1
-0.07
-0.11 -0.10 -0.12 1 0.15
-0.07
0.08
1 0.06 0.34 0.14 0.38 0.41 0.18 0.09
0.1 0.07 0.08
1 0.09 0.09 0.06
1 0.14 0.24 0.13 0.11
1 0.17 0.11 0.08
1 0.42 0.39 0.18 0.2 0.11
1 0.43 0.24 0.23 0.11
1 -0.05 0.09 -0.04 -0.04 0.13 0.07 0.04 0.09
1 0.05
1 -0.05
0.04
-0.04
1 -0.10 0.24 0.28 0.36 0.37 0.15 0.18
1 -0.07 -0.08 -0.08 -0.05
Only results significant at 5%
CL:Child Labour, S:Schooling, A:Attachment, N:Nutrition, E:Electricity, CF:Cooking Fuel, DW:Drinking Water,
T:Toilet, F:Floor, AS:Assets, O:Overcrowding
32
Figure 13: Headcount and Average deprivation per country and wave
Ethiopia
Andhra P.
Peru
Vietnam
H 100% 90% 80%
70% 60% 50%
40%
2nd Wave
2nd Wave
2nd Wave
3rd Wave
3rd Wave
3rd Wave
1st Wave
1st Wave
1st Wave
30% 20% 10%
0% 0.3
0.8
0.2
0.1
0.7
1st Wave
2nd Wave
33
0.6
0.2
3rd Wave
0.7
A
34
1 0.1% -3.3% 0.0% -3.2% 1 -0.7% -3.7% 0.1% -4.3%
1 1.9% -0.9% -0.1% 0.9% 1 -4.1% -6.2% 0.8% -9.6%
Ethiopia 1-2 ∆%H ∆%A ∆%H*∆%A ∆%M
Ethiopia 2-3 ∆%H ∆%A ∆%H*∆%A ∆%M
Andhra P. 1-2 ∆%H ∆%A ∆%H*∆%A ∆%M
Andra P. 1-2 ∆%H ∆%A ∆%H*∆%A ∆%M 2 -5.3% -5.6% 0.9% -10.1%
2 1.3% -0.5% 0.0% 0.7%
2 -1.6% -3.1% 0.1% -4.5%
2 0.2% -3.4% 0.0% -3.2%
3 -9.2% -3.8% 1.0% -11.9%
3 0.9% -0.3% 0.0% 0.5%
3 -3.6% -2.0% 0.2% -5.3%
3 -0.5% -3.0% 0.1% -3.5%
4 -13.4% -2.2% 0.9% -14.7%
4 0.0% 0.0% 0.0% 0.0%
4 -6.7% -0.5% 0.1% -7.2%
4 -1.6% -2.7% 0.2% -4.1%
5 -16.7% -1.2% 0.6% -17.3%
5 0.8% -0.2% 0.0% 0.5%
5 -8.4% 0.1% 0.0% -8.3%
5 -4.2% -2.1% 0.4% -6.0%
6 -20.9% 0.1% -0.1% -20.8%
6 -0.3% -0.1% 0.0% -0.4%
6 -8.9% 0.3% -0.1% -8.7%
6 -8.3% -1.1% 0.4% -9.0%
7 -20.8% 0.2% -0.1% -20.7%
7 -2.2% 0.2% 0.0% -2.1%
7 -8.4% 0.4% -0.1% -8.1%
7 -12.0% -0.4% 0.2% -12.2%
8 -22.2% 1.2% -0.8% -21.8%
8 0.0% 0.2% 0.0% 0.2%
8 -5.9% 0.4% -0.1% -5.6%
8 -14.5% 0.0% 0.0% -14.5%
9
9 25.0% 0.0% 0.0% 25.0%
9 -5.0% 1.1% -0.2% -4.0%
9 -13.9% -0.3% 0.2% -14.0%
10 83.3% 0.0% 0.0% 83.3%
10 -20.0% 0.0% 0.0% -20.0%
Table 6: Decomposition of changes of the Multidimensional Indicator Ethiopia and Andhra Pradesh
35
1 4.9% -1.9% -0.1% 2.6% 1 -10.5% -4.8% 1.5% -13.8%
1 1.2% -4.1% -0.2% -3.1% 1 -8.5% -2.1% 0.5% -10.1%
Peru 1-2 ∆%H ∆%A ∆%H*∆%A ∆%M Peru 2-3 ∆%H ∆%A ∆%H*∆%A ∆%M
Vietnam 1-2 ∆%H ∆%A ∆%H*∆%A ∆%M Vietnam 2-3 ∆%H ∆%A ∆%H*∆%A ∆%M 2 -10.7% -0.3% 0.1% -10.9%
2 -1.2% -2.9% 0.1% -4.0%
2 -14.4% -2.3% 1.0% -15.7%
2 1.5% -0.3% 0.0% 1.2%
3 -12.4% 0.9% -0.3% -11.8%
3 -4.5% -1.8% 0.3% -5.9%
3 -17.0% -1.0% 0.5% -17.6%
3 -1.4% 1.0% 0.0% -0.5%
4 -12.0% 1.2% -0.4% -11.3%
4 -7.2% -1.3% 0.4% -8.1%
4 -19.8% 0.5% -0.3% -19.6%
4 0.2% 1.0% 0.0% 1.2%
5 -10.0% 1.2% -0.4% -9.2%
5 -11.2% -0.4% 0.2% -11.4%
5 -20.2% 1.2% -0.8% -19.7%
5 7.4% 0.4% 0.0% 8.0%
6 -4.7% 0.9% -0.1% -3.9%
6 -13.2% 0.0% 0.0% -13.2%
6 -15.6% 1.7% -0.8% -14.7%
6 28.6% -0.3% -0.1% 27.9%
7 -4.2% 2.1% -0.3% -2.4%
7 -11.2% -0.7% 0.3% -11.6%
7 66.7% 0.0% 0.0% 66.7%
7
8 200.0% 0.0% 0.0% 200.0%
8 -21.9% 0.0% 0.0% -21.9%
8
8
Table 7: Decomposition of changes of the Multidimensional Indicator Peru and Vietnam
36
1 0.2% 0.0% 0.2% 1 0.0% -0.7% -0.7%
1 2.6% -0.1% 2.6% 1 0.1% -4.2% -4.1%
Ethiopia 1-2 Aj. Pr(Entry) Pr(Exit) ∆%H
Ethiopia 2-3 Aj. Pr(Entry) Pr(Exit) ∆%H
Andhra P. 1-2 Aj. Pr(Entry) Pr(Exit) ∆%H
Andhra P. 2-3 Aj. Pr(Entry) Pr(Exit) ∆%H 2 0.7% -6.0% -5.3%
2 3.4% -1.6% 1.7%
2 0.8% -2.3% -1.6%
2 1.2% -1.0% 0.3%
3 0.9% -10.1% -9.2%
3 3.4% -2.2% 1.2%
3 1.6% -5.2% -3.6%
3 2.1% -2.8% -0.7%
4 1.4% -14.9% -13.4%
4 5.5% -5.5% 0.0%
4 2.1% -8.8% -6.7%
4 2.4% -4.4% -2.1%
5 2.9% -19.6% -16.7%
5 9.7% -8.7% 1.0%
5 3.7% -12.0% -8.4%
5 3.2% -8.9% -5.7%
6 4.0% -24.8% -20.9%
6 13.2% -13.6% -0.4%
6 5.8% -14.7% -8.9%
6 4.5% -15.5% -11.0%
7 5.7% -26.5% -20.8%
7 18.0% -20.9% -2.9%
7 10.1% -18.5% -8.4%
7 5.6% -21.6% -16.0%
8 9.9% -32.1% -22.2%
8 27.2% -27.2% 0.0%
8 18.7% -24.7% -5.9%
8 8.0% -27.4% -19.3%
9 33.3% -33.3% 0.0%
9 66.7% -33.3% 33.3%
9 25.0% -30.0% -5.0%
9 14.8% -33.3% -18.5%
10
10
10 100.0% -16.7% 83.3%
10 6.7% -33.3% -26.7%
Table 8: Decomposition of changes of the Multidimensional Headcount Ethiopia and Andhra Pradesh
37
1 8.2% -1.7% 6.5% 1 0.8% -11.4% -10.5%
1 2.8% -1.2% 1.6% 1 0.9% -9.4% -8.5%
Peru 1-2 Aj. Pr(Entry) Pr(Exit) ∆%H Peru 2-3 Aj. Pr(Entry) Pr(Exit) ∆%H
Vietnam 1-2 Aj. Pr(Entry) Pr(Exit) ∆%H Vietnam 2-3 Aj. Pr(Entry) Pr(Exit) ∆%H 2 2.3% -13.1% -10.7%
2 3.6% -5.2% -1.6%
2 2.6% -17.0% -14.4%
2 8.4% -6.4% 2.0%
3 4.3% -16.7% -12.4%
3 5.2% -11.1% -6.0%
3 2.9% -19.9% -17.0%
3 9.8% -11.6% -1.9%
4 6.0% -18.0% -12.0%
4 6.0% -15.6% -9.6%
4 5.2% -25.0% -19.8%
4 17.1% -16.8% 0.3%
5 8.0% -18.0% -10.0%
5 5.2% -20.1% -14.9%
5 7.1% -27.3% -20.2%
5 29.8% -19.9% 9.9%
6 14.7% -19.4% -4.7%
6 5.5% -23.1% -17.6%
6 15.6% -31.1% -15.6%
6 71.4% -33.3% 38.1%
7 20.8% -25.0% -4.2%
7 9.2% -24.1% -14.9%
7 100.0% -33.3% 66.7%
7 33.3% -33.3% 0.0%
8 233.3% -33.3% 200.0%
8 4.2% -33.3% -29.2%
8
8
Table 9: Decomposition of changes of the Multidimensional Headcount Peru and Vietnam
38
1 1.5% -4.8% -3.3% 1 -1.6% -2.1% -3.7%
1 6.1% -7.1% -0.9% 1 -4.6% -1.6% -6.2%
Ethiopia 1-2 ∆%sAd. Child ∆%sAd. Household ∆%A
Ethiopia 2-3 ∆%sAd. Child ∆%sAd. Household ∆%A
Andhra P. 1-2 ∆%sAd. Child ∆%sAd. Household ∆%A
Andhra P. 2-3 ∆%sAd. Child ∆%sAd. Household ∆%A 2 -3.8% -1.9% -5.6%
2 5.8% -6.3% -0.5%
2 -1.4% -1.7% -3.1%
2 1.4% -4.8% -3.4%
3 -2.3% -1.5% -3.8%
3 5.5% -5.8% -0.3%
3 -0.8% -1.2% -2.0%
3 1.3% -4.4% -3.0%
4 -0.6% -1.5% -2.2%
4 5.0% -5.0% 0.0%
4 -0.1% -0.5% -0.5%
4 1.1% -3.8% -2.7%
5 1.1% -2.3% -1.2%
5 4.6% -4.8% -0.2%
5 0.5% -0.4% 0.1%
5 0.9% -3.0% -2.1%
6 2.0% -1.9% 0.1%
6 4.1% -4.2% -0.1%
6 0.8% -0.5% 0.3%
6 1.0% -2.1% -1.1%
7 2.8% -2.6% 0.2%
7 3.9% -3.7% 0.2%
7 1.2% -0.8% 0.4%
7 1.1% -1.6% -0.4%
8 3.3% -2.1% 1.2%
8 3.9% -3.7% 0.2%
8 1.8% -1.4% 0.4%
8 1.0% -1.1% 0.0%
9 0.9% -0.9% 0.0%
9 4.2% -4.2% 0.0%
9 3.0% -1.9% 1.1%
9 0.2% -0.5% -0.3% 10 0.0% -3.3% -3.3%
10 -1.3% 1.3% 0.0%
Table 10: Decomposition average deprivation by Child and household Related Variables Ethiopia and Andhra Pradesh
39
1 5.7% -7.7% -1.9% 1 -3.5% -1.3% -4.8%
1 4.6% -8.7% -4.1% 1 -3.0% 0.9% -2.1%
Peru 1-2 ∆%sAd. Child ∆%sAd. Household ∆%A Peru 2-3 ∆%sAd. Child ∆%sAd. Household ∆%A
Vietnam 1-2 ∆%sAd. Child ∆%sAd. Household ∆%A Vietnam 2-3 ∆%sAd. Child ∆%sAd. Household ∆%A 2 -0.9% 0.6% -0.3%
2 4.0% -6.9% -2.9%
2 0.1% -2.4% -2.3%
2 4.1% -4.4% -0.3%
3 1.1% -0.1% 0.9%
3 3.4% -5.3% -1.8%
3 2.8% -3.8% -1.0%
3 3.0% -2.0% 1.0%
4 1.4% -0.2% 1.2%
4 3.3% -4.6% -1.3%
4 4.9% -4.4% 0.5%
4 2.4% -1.5% 1.0%
5 1.9% -0.9% 0.9%
5 2.8% -2.9% -0.1%
5 6.7% -5.4% 1.2%
5 0.0% -1.7% -1.7%
6 1.8% -1.2% 0.7%
6 2.5% -2.5% 0.0%
6 7.0% -5.3% 1.7%
6 1.8% -2.1% -0.3%
7
7
7
7
0
8
0
8
9
9
9
9
10
10
10
10
Table 11: Decomposition average deprivation by Child and household Related Variables Peru and Vietnam
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