A Multidimensional Poverty Index for Gauteng Province, South Africa: Evidence from Quality of Life Survey Data


This paper estimates a Multidimensional Poverty Index for Gauteng province of South Africa. The Alkire–Forster method is applied on Quality of Life survey data for 2011 and 2013 which offer an excellent opportunity for estimating poverty at smaller geographical areas. The results suggest that the Multidimensional Poverty Index for Gauteng is low but varies markedly by municipality and by ward, as well as across income groups. Not only are low income households more likely to be multidimensionally poor, they also suffer from higher intensities of poverty. Multidimensional poverty is highest in areas of low economic activity located on the edges of the province. However, pockets of multidimensional poverty do prevail even in better performing municipalities. Government, at all spheres, needs to devise policies that channel investments into lagging areas and avoid approaches that are indifferent to the heterogeneities that exist across localised geographical extents.

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  1. 1.

    For a concise history and use of unidimensional measures see Alkire and Foster (2011).

  2. 2.

    The Premier for Gauteng province, Mr. David Makhura stressed during the State of Province Address, that the province was adopting evidence-based planning.

  3. 3.

    Social wage refers to monetary and in-kind support given to vulnerable households. Four components make up the social wage in South Africa (i) housing and community amenities, (ii) health, (iii) education, and (iv) social protection. The first three replace or subsidise day-to-day expenses for housing, education and health hence reducing the cost of living. The fourth is income paid directly to vulnerable groups.

  4. 4.

    For example, for the Housing-adjusted standard of living dimension, the weight is calculated as: \(\frac{1}{4}\times\frac{1}{6} = \frac{1}{24}\).

  5. 5.

    The uncensored headcount of an indicator refers to the proportion of total households deprived in that indicator. The censored headcount, on the other hand, refers to proportion of all household that are multidimensionally poor (i.e. households that fall within the cut-off point of k = 33 percent) and deprived in that indicator at the same time.

  6. 6.

    Table 6 in the “Appendix” presents the results for 2011.


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The authors would like to acknowledge the invaluable review comments by Prof. Ingrid Woolard. Ingrid is a Professor in the School of Economics and a Research Associate of SALDRU at the University of Cape Town (UCT). She holds a Ph.D. in economics from UCT and is currently one of the Principal Investigators of the National Income Dynamics Study. A special thanks to participants of the 2015 Oxford Poverty & Human Development Initiative (OPHI) Summer School held at Georgetown University, Washington D.C. USA, who also gave us invaluable comments and suggestions for deepening our analysis. Special thanks to Samy Katumba, a Junior Researcher at GCRO for assisting with the GIS mapping.

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Corresponding author

Correspondence to Darlington Mushongera.

Additional information

GCRO is a partnership of the University of the Witwatersrand, Johannesburg, University of Johannesburg, Gauteng Provincial Government and Organised Local Government.



See Tables 6 and 7.

Table 6 Multidimensional poverty indicators by income group, 2013
Table 7 Proportion of households that are poor at k = 33 % per indicator, per municipality, 2011

Poorest Wards

See Figs. 5, 6 and 7.

Fig. 5

Multidimensional headcount for poorest wards, 2013, Source: Authors’ calculations based on GCRO’s 2013 Quality of Life survey

Fig. 6

Multidimensional poverty intensity for poorest wards, 2013, Source: Authors’ calculations based on GCRO’s 2013 Quality of Life survey

Fig. 7

Multidimensional Poverty Index (MPI) for poorest wards, 2013, Source: Authors’ calculations based on GCRO’s 2013 Quality of Life survey

Robustness Checks

The Pearson correlation coefficient ( r) is a measure of the strength of a linear association between two variables. In this case it was used to measure the strength between the MPI with equal weights versus the MPIs using 50 % weights per successive dimension.

$$r = \frac{{n\left( {\sum\nolimits_{i = 1}^{n} {x_{i} y_{i} } } \right) - \left( {\sum\nolimits_{i = 1}^{n} {x_{i} } } \right)\left( {\sum\nolimits_{i = 1}^{n} {y_{i} } } \right)}}{{\sqrt {\left[ {n\sum\nolimits_{i = 1}^{n} {x_{i}^{2} - \left( {\sum\nolimits_{i = 1}^{n} {x_{i} } } \right)^{2} } } \right]\left[ {n\sum\nolimits_{i = 1}^{n} {y_{i}^{2} - \left( {\sum\nolimits_{i = 1}^{n} {y_{i} } } \right)^{2} } } \right]} }}$$

Spearman’s rho (ρ) measures the strength of the association between two ranked variables. In this case the ranked variables were the MPI using equal weights and the MPI using 50 % weights successively per dimension. It is estimated using

$$\rho = 1 - \frac{{6\sum\nolimits_{i = 1}^{n} {x_{i} - y_{i} } }}{{n(n^{2} - 1)}}$$

where x i is the municipal rank using equal weights, y i is the municipal rank using 50 % weight on each dimension, and n is the number of municipalities.

Kendall’s Tau (τ) measures the association between two quantities, in this case, ranks. It is based on the number of concordant and discordances in paired observations. The ranks of the two sets of MPIs are concordant if they are in the same order with respect to each variable and discordant if they are arranged such that they are in opposite directions. The value of Kendall’s τ ranges between −1 and 1. If all pairs are discordant, τ = −1, if they are all concordant, τ = 1. Kendall’s Tau (τ) is calculated as

$$\tau = \frac{{N_{c} - N_{d} }}{n(n - 1)/2}$$

Varying the weights assigned to dimensions results in a change in the MPI and therefore the ranking of municipalities. The estimated correlation coefficients, as illustrated in Table 8 show that the municipal rankings are stable with respect to all dimensions except for the dimension on economic activity.

Table 8 Correlations between MPI and adjusted MPIs having 50 % weight on each dimension in turn

Furthermore, the analysis was also done to test the sensitivity of the choice of k i.e. the number of deprivations that a household must experience in order for them to be considered multi-dimensionally poor (Table 9). The Pearson and Kendall coefficients indicate stability with respect to choice of k, even though the Spearman coefficient is weak.

Table 9 Correlations between MPI and adjusted MPI for different choices of k

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Mushongera, D., Zikhali, P. & Ngwenya, P. A Multidimensional Poverty Index for Gauteng Province, South Africa: Evidence from Quality of Life Survey Data. Soc Indic Res 130, 277–303 (2017). https://doi.org/10.1007/s11205-015-1176-2

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  • Multidimensional Poverty Index
  • Headcount
  • Intensity
  • Quality of Life survey
  • Gauteng
  • South Africa