Monitoring Progress in Child Poverty Reduction: Methodological Insights and Illustration to the Case Study of Bangladesh

Abstract

Important steps have been taken at international summits to set up goals and targets to improve the wellbeing of children worldwide. Now the world also has more and better data to monitor progress. This paper presents a new approach to monitoring progress in child poverty reduction based on the Alkire and Foster adjusted headcount ratio and an array of complementary techniques. A theoretical discussion is accompanied by an assessment of child poverty reduction in Bangladesh based on four rounds of the demographic household survey (1997–2007). Emphasis is given to dimensional monotonicity and decomposability as desirable properties of multidimensional poverty measures. Complementary techniques for analysing changes over time are also illustrated, including the Shapley decomposition of changes in overall poverty, as well as a range of robustness tests and statistical significance tests. The results from Bangladesh illustrate the value added of these new tools and the information they provide for policy. The analysis reveals two paths to multidimensional poverty reduction by either decreasing the incidence of poverty or its intensity, and exposes an uneven distribution of national gains across geographical divisions. The methodology allows an integrated analysis of overall changes yet simultaneously examines progress in each region and in each dimension, retaining the positive features of dashboard approaches. The empirical evidence highlights the need to move beyond the headcount ratio towards new measures of child poverty that reflect the intensity of poverty and multiple deprivations that affect poor children at the same time.

Appendices

Appendix 1: Measures of Depth and Severity of Child Poverty

This note outlines the measures proposed by Delamonica and Minujin (2007) with similar notation as in the introduction of this special issue.

Depth of child poverty: This is the average number of deprivations suffered by children in a given population and is given by

$$ Depth = \sum\limits_{i - 1}^{n} {{{c_{i} } \mathord{\left/ {\vphantom {{c_{i} } {(n)}}} \right. \kern-0pt} {(n)}}} $$

(1)

Where c _i represents the number of weighted deprivations suffered by child i divided by the total number of children. In the original proposal Delamonica and Minujin (2007) assume equal weight across dimensions but this can be modified depending on the purpose of the measure.

Severity (Weighted–Depth) of child poverty: This is equivalent to the depth of child poverty but it adds weight (i.e. importance) to the children who suffer more deprivation and so is given by

$$ Severity\_WD = \sum\limits_{i - 1}^{n} {{{(c_{i} )^{2} } \mathord{\left/ {\vphantom {{(c_{i} )^{2} } {(n)}}} \right. \kern-0pt} {(n)}}} $$

(2)

Severity (standard deviation of Depth) of child poverty: This is based on the standard deviation given by:

$$ Severity\_SdD = \sqrt {\sum\limits_{i - 1}^{n} {{{\left( {c_{i} - \left| {c_{i} } \right|} \right)^{2} } \mathord{\left/ {\vphantom {{\left( {c_{i} - \left| {c_{i} } \right|} \right)^{2} } {(n)}}} \right. \kern-0pt} {(n)}}} } $$

(3)

Depth of child poverty as percentage of indicator: Note that Roelen et al. (2010) normalize the depth by the total number of indicators, so it is expressed as percentage of indicator. Following this, Eq. (1) would be given by:

$$ Depth\_\% = \sum\limits_{i - 1}^{n} {{{(c_{i} \times 100)} \mathord{\left/ {\vphantom {{(c_{i} \times 100)} {(d \times n)}}} \right. \kern-0pt} {(d \times n)}}} $$

(4)

where d represents the total number of dimensions. A variant in Roelen et al. (2010) is that the number of indicators varies depending on the age group of the child which is adjusted in the “normalized” depth. Also, dimensions are measured with more than one indicator following a union approach, so a child is deprived in dimension d if the child is deprived in any of the indicators within the dimension.

Appendix 2: Technical Note on Shapley Decomposition of Change in the Adjusted Headcount (M₀)

This is an extract from a forthcoming paper from Roche (2012) which is currently in a work in progress status. For further details please contact the author.

Shapley decomposition of change in poverty by subgroup: Following a similar decomposition of change in FGT income poverty measures (Ravallion and Huppi 1991) and a Shapley value decomposition approach (Shorrocks 1999), the variation in the poverty level can be broken down into: (1) changes due to intra-sectoral or within-group poverty effect and (2) changes due to demographic or inter-sectoral effect by:

$$ \underbrace {{\Updelta M_{0} = \mathop \sum \limits_{\ell = 1}^{m} \left( {\frac{{\nu_{\ell }^{{t^{'} }} + \nu_{\ell }^{t} }}{2}} \right)\left( {M_{0\ell }^{t} - M_{0\ell }^{{t^{'} }} } \right)}}_{{{\text{Within}} - {\text{grouppoverty effec}}}} + \underbrace {{\mathop \sum \limits_{\ell = 1}^{m} \left( {\frac{{M_{0\ell }^{{t^{'} }} + M_{0\ell }^{t} }}{2}} \right)\left( {\nu_{\ell }^{t} - \nu_{\ell }^{{t^{'} }} } \right)}}_{\text{Demographic or sectoral effect}} $$

(5)

where $\Updelta M_{0} = (M_{0}^{t} - M_{0}^{{t^{\prime } }} )$ denotes the total variation of the adjusted headcount ratio between time period t and time period $t^{\prime }$, $M_{0l}^{t}$ denotes the adjusted headcount ratio in subgroup l and $v_{l}^{t}$ denotes the population share of subgroup $\ell$ from a total of m subgroups $(\ell = 1, \ldots ,m)$ in two time periods respectively $(t,t^{'})$ Note that the Shapley decomposition allows obtaining the marginal contribution of the within-group effect and of the demographic effect (see applications in monetary measures with FGT in: Duclos and Araar 2006).

Shapley decomposition of change in poverty by incidence and intensity: The adjusted headcount ratio can be expressed as the product of the multidimensional incidence and intensity of poverty among the poor, $M_{0} = H*A$ Hence, the Shapley decomposition technique (Shorrocks 1999) can be applied to decompose absolute variation in the adjusted headcount ratio into an incidence effect and an intensity effect as follows:⁶

$$ \Updelta M_{0} = \underbrace {{\frac{{A^{{t^{'} }} + A^{t} }}{2}\left( {H^{t} - H^{{t^{'} }} } \right)}}_{{{\text{Incidence}}\,{\text{of}}\,{\text{poverty}}\,{\text{effect}}}} + \underbrace {{\frac{{H^{{t^{'} }} + H^{t} }}{2}\left( {A^{t} - A^{{t^{'} }} } \right)}}_{{{\text{Intensity}}\,{\text{of}}\,{\text{poverty}}\,{\text{effect}}}} $$

(6)

where $H^{t}$ and $A^{t}$ respectively denote the headcount ratio and the intensity of poverty at time t.

Decomposition of the variation in intensity of poverty by dimension: The AF intensity of poverty A, is the average deprivation share across the poor, $A = \sum\nolimits_{i = 1}^{n} {c_{i} (k)/(qd)}$ where c _i (k) is the censored number of weighted deprivations for individual i, q is the number of poor people identified using k and d is the total number of dimensions. Thus, one might want to decompose changes in intensity of poverty by changes in the deprivations experienced by the poor in each particular dimension. Following Apablaza and Yalonetzky (2011), we know that $A^{t} = \sum\nolimits_{j = 1}^{d} {\left( {w_{j} h_{j}^{t} } \right)/d}$ where W _j denotes the dimensional weight, with $\sum\nolimits_{j = 1}^{d} {w_{j} = d}$, and $h_{j}^{t}$ is the share of the poor who are deprived in dimension j at time t.

When dimensional weight is constant across the period, the absolute change in intensity can be decomposed as follows:

$$ \Updelta A = \mathop \sum \limits_{j = 1}^{d} (w_{j} /d)\left( {h_{j}^{2} - h_{j}^{1} } \right) $$

(7)

Note that $h_{j}^{t}$ can also be expressed as $h_{j}^{t} = CH_{j}^{t} /H^{t}$, where $CH_{j}^{t}$ is the censored headcount ratio of dimension j in time t as defined in the Introduction to this special issue, and $H^{t}$ represents the proportion of poor people n/q Hence Eq. (7) can conveniently be expressed as a function of the censored headcount ratio in each dimension as:

$$ \Updelta A = \mathop \sum \limits_{j = 1}^{d} (w_{j} /d)\left( {{{CH_{j}^{2} } \mathord{\left/ {\vphantom {{CH_{j}^{2} } {H^{2} }}} \right. \kern-0pt} {H^{2} }} - {{CH_{j}^{1} } \mathord{\left/ {\vphantom {{CH_{j}^{1} } {H^{1} }}} \right. \kern-0pt} {H^{1} }}} \right) $$

(8)

Integrated decompositions: It might be convenient to undertake an integrated analysis such as combining the decomposition of changes in poverty by subgroup (Eq. 5), with the decomposition by its components (Eq. 6), and decomposition by dimensions (Eq. 8) as follows:

$$ \begin{aligned} \Updelta M_{0} & = \mathop \sum \limits_{\ell = 1}^{m} \left( {\frac{{M_{0\ell }^{{t^{'} }} + M_{0\ell }^{t} }}{2}} \right)\left( {\nu_{\ell }^{t} - \nu_{\ell }^{{t^{'} }} } \right) + \mathop \sum \limits_{\ell = 1}^{m} \left( {\frac{{\nu_{\ell }^{{t^{'} }} + \nu_{\ell }^{t} }}{2}} \right)\left( {\frac{{A_{\ell }^{{t^{'} }} + A_{\ell }^{t} }}{2}} \right)\left( {H_{\ell }^{t} - H_{\ell }^{{t^{'} }} } \right) \\ \,\quad + \mathop \sum \limits_{\ell = 1}^{m} \left( {\frac{{\nu_{\ell }^{{t^{'} }} + \nu_{\ell }^{t} }}{2}} \right)\left( {\frac{{H_{\ell }^{{t^{'} }} + H_{\ell }^{t} }}{2}} \right)\mathop \sum \limits_{j = 1}^{d} (w_{j} /d)\left( {\frac{{CH_{j}^{2} }}{{H^{2} }} - \frac{{CH_{j}^{1} }}{{H^{1} }}} \right) \\ \end{aligned} $$

(9)

Fig. 3

Robustness checks of different dimensional cut-off (k) in changes in multidimensional poverty over time for provinces in Bangladesh 1997–2004

Fig. 4

Robustness checks of different dimensional cut-off (k) in ranking among provinces across time