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Social Indicators Research

Erschienen in:

26.04.2017

First Order Dominance Techniques and Multidimensional Poverty Indices: An Empirical Comparison of Different Approaches

verfasst von: Iñaki Permanyer, M. Azhar Hussain

Erschienen in: Social Indicators Research | Ausgabe 3/2018

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Abstract

In this empirically driven paper we compare the performance of two techniques in the literature of poverty measurement with ordinal data: multidimensional poverty indices and first order dominance techniques (FOD). Combining multiple scenario simulated data with observed data from 48 Demographic and Health Surveys around the developing world, our empirical findings suggest that the FOD approach can be implemented as a useful robustness check for ordinal poverty indices like the multidimensional poverty index (MPI; the United Nations Development Program’s flagship poverty indicator) to distinguish between those country comparisons that are sensitive to alternative specifications of basic measurement assumptions and those which are not. To the extent that the FOD approach is able to uncover the socio-economic gradient that exists between countries, it can be proposed as a viable complement to the MPI with the advantage of not having to rely on many of the normatively binding assumptions that underpin the construction of the index.

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As shown in Cherchye et al. (2008), Permanyer (2011, 2012) and Foster et al. (2013), certain composite indices of well-being can be highly sensitive to the choice of alternative weighting schemes.

According to the ‘union’ approach, an individual should be labeled as ‘poor’ if s/he is deprived in at least one dimension. At the other extreme, the ‘intersection’ approach states that an individual is ‘poor’ if s/he is deprived in all dimensions simultaneously. In between these extreme perspectives, Alkire and Foster (2011) proposed a counting approach based on Atkinson (2003) suggesting that an individual is ‘poor’ when s/he is deprived in an intermediate number of dimensions that has to be decided by the analyst. These well-known approaches can be seen as particular cases of the more general identification method using partially ordered sets suggested in Fattore (2016).

A partial order relation in a set X is a binary relation satisfying reflexivity (\(x \le x\) for all \(x \in X\)), antisymmetry (if \(x \le y\) and \(y \le x\), then \(x = y\) for all \(x,y \in X\)) and transitivity (if \(x \le y\) and \(y \le z\), then \(x \le z\) for all \(x,y,z \in X\)) (see Davey and Priestley 2002).

We say that \(x = \left( {x_{1} , \ldots ,x_{k} } \right)\) vector dominates \(y = \left( {y_{1} , \ldots ,y_{k} } \right)\) if \(x_{i} \ge y_{i}\) for all \(i = 1, \ldots ,k\).

The time needed to run these simulations increases rapidly with k (for the case k = 10 the computation time for anIntel^® Xeon^® E5-1650 v3 3, 5 GHz, RAM 16 GB is about 24 h). For this reason, in our simulations we have not considered more than 10 variables.

The choice of different values of α and β for the poverty index does not substantially change our findings. The results are not shown here, but are available upon request.

In this example, the number of comparable and incomparable pairs equal 17,605 and 2295 respectively (hence, the relative shares of comparable and incomparable pairs are 88.5 and 11.5%, see Fig. 2). This means that the areas under the scaled density functions \(f_{C,3}\) and \(f_{N,3}\) equal 17,605 and 2295, respectively.

In its original definition, the UNDP’s MPI does not have the sub-domains we have introduced here. We have introduced them to have a more gradual dimensional refinement that allows exploring in more detail the effects of increasing dimensionality on the occurrence of FOD relationships.

Choosing alternative values for \(\alpha ,\beta\) leads to results that are highly correlated with the ones presented here, so they will not be reported.

For the five and ten dimensional cases the corresponding tables are considerably larger, so they are not shown here (they are available from the authors upon request).

Iglesias et al. (2016) compare confirmatory factor analysis, the Alkire and Foster counting approach and the posetic approach in the context of contemporary Switzerland.

A linear extension of is a partial order that (i) is complete over (i.e. all pairs of elements are comparable), and (ii) respects the order established by vector dominance.

Yet, imposing some simplifying assumptions (e.g. the k attributes can be completely ordered in terms of relevance) the computational time can be considerably reduced (see Fattore and Arcagni 2017).

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Arcagni, A., & Fattore, M. (2014). PARSEC: An R package for poset-based evaluation of multidimensional poverty. In R. Bruggermann, L. Carlsen, & J. Wittmann (Eds.), Multi-indicator systems and modelling in partial order. Berlin: Springer.

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Arndt, C., Siersbæk, N., Østerdal, L. P. (2015). Multidimensional first-order dominance comparisons of population wellbeing. In WIDER working paper 2015/122.

Atkinson, A. (2003). Multidimensional deprivation: Contrasting social welfare and counting approaches. Journal of Economic Inequality, 1, 51–65.CrossRef

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Davey, B., & Priestley, B. (2002). Introduction to lattices and order. Cambridge: CUP.CrossRef

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Titel: First Order Dominance Techniques and Multidimensional Poverty Indices: An Empirical Comparison of Different Approaches
verfasst von: Iñaki Permanyer
M. Azhar Hussain
Publikationsdatum: 26.04.2017
Verlag: Springer Netherlands
Erschienen in: Social Indicators Research / Ausgabe 3/2018
Print ISSN: 0303-8300
Elektronische ISSN: 1573-0921
DOI: https://doi.org/10.1007/s11205-017-1637-x

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