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Graphical Representation of Multidimensional Poverty: Insights for Index Construction and Policy Making

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Abstract

By means of probabilistic graphical models, in this paper, we present a new framework for exploring relationships among indicators commonly included in the Multidimensional Poverty Index (MPI). In particular, we propose an Ising model with covariates for modeling the MPI as an undirected graph. First, we prove why Ising models are consistent with the theoretical distribution of MPI indicators. Then, a comparison between our estimates and the association measures typically used in the literature is provided. Finally, we show how undirected graphs can complement the MPI policy-relevant properties, apart from discovering further insightful patterns that can be useful for policy purposes. This novel approach is illustrated with an empirical application for the global MPI indicators of Guinea and Ecuador, taking living areas and monetary poverty as covariates, respectively.

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Data Availability

The data that support the findings of this study are available in https://www.openicpsr.org/openicpsr/project/192052/version/V1/view.

Notes

  1. This means that if we collapse over C, the conditional association between A and B does not change. Similarly, between B and C, if we collapse over A.

  2. Matlab code available in http://onlinelibrary.wiley.com/doi/10.1111/biom.12202/

  3. The codes to compute the global MPI for both countries were taken from the Stata do-files provided by OPHI corresponding to the global MPI 2021, which are available in https://cloud-ophi.qeh.ox.ac.uk/index.php/s/SgLdxLScG9Tg6gq?path=%2F2021. For more details about technical aspects of the global MPI, see Alkire et al. (2021).

  4. The data for Guinea and Ecuador that support the findings of this study are available on the DHS website (https://dhsprogram.com/methodology/survey/survey-display-539.cfm) and in the official ECV 13-14 website (https://www.ecuadorencifras.gob.ec//documentos/web-inec/ECV/ECV_2015/)

  5. Ballon (2023) uses Evans (1996)’s criterion to assess strength of association of Cramer’s V and R measures: 00\(-\)0.19 denotes very weak association; 0.20\(-\)0.39 weak association; 0.40\(-\)0.59 moderate association; 0.60\(-\)0.79 strong association; 0.80\(-\)1.0 very strong association.

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Funding

This work was supported by ANPCYT Grant PICT 2018-04377, CONICET Grant PIP 11220200101595CO and UNL Grant CAI+D 506-201901-00041LI.

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Authors and Affiliations

  1. Instituto de Economía Aplicada Litoral (FCE), Universidad Nacional del Litoral, Moreno 2557, 3000, Santa Fe, Argentina

    Rodrigo García Arancibia

  2. Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Santa Fe, Argentina

    Rodrigo García Arancibia & Ignacio Girela

  3. Facultad de Ciencias Económicas, Universidad Nacional de Córdoba, Bv. Enrique Barros, Ciudad Universitaria, Córdoba, X5000HRV, Córdoba, Argentina

    Ignacio Girela

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  1. Rodrigo García Arancibia
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Correspondence to Rodrigo García Arancibia or Ignacio Girela.

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Appendices

Appendix 1: The Global MPI

The global MPI has been published annually by OPHI and UNPD since 2010 and covers more than 100 develo** countries with the aim of complementing globally comparable monetary poverty measures such as the \(\$ 1.90\) day line. Table 5 describes all the selected dimensions, indicators, deprivation cutoffs, and weights.

Poverty cutoff k is equal to 0.33. This means that a person is identified as poor if she is deprived in a third or more of ten (weighted) indicators or, in other words, if she is deprived in one dimension.

Table 5 MPI dimensions, indicators, deprivation cutoffs, and weights
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Appendix 2: Parameters Estimates of Ising Models

See Tables 6, 7, 8 and 9.

Table 6 Coefficient estimates of Ising model for uncensored MPI indicators in Guinea
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Table 7 Coefficient estimates of Ising model for censored MPI indicators in Guinea
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Table 8 Coefficient estimates of Ising model for uncensored MPI indicators in Ecuador
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Table 9 Coefficient estimates of Ising model for censored MPI indicators in Ecuador
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Appendix 3: Redundancy Measures

Figures 8 and 9 show the estimated unconditional association measures (Cramer’s V and Redundancy R) for Guinea and Ecuador, respectively.

Fig. 8
figure 8

Heatmaps of unconditional association measures for Guinea

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Fig. 9
figure 9

Heatmaps of unconditional association measures for Ecuador

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García Arancibia, R., Girela, I. Graphical Representation of Multidimensional Poverty: Insights for Index Construction and Policy Making. Soc Indic Res 172, 595–634 (2024). https://doi.org/10.1007/s11205-024-03325-8

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