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Considering the Extremely Poor: Multidimensional Poverty Measurement for Germany

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Abstract

This paper applies the Alkire and Foster (J Public Econ 95:476–487, 2011) index of multidimensional poverty to German data. This is done with respect to the politically most important dimensions of poverty mentioned in the German Federal Government’s report on poverty and wealth. Additionally, a modification of the identification step of the Alkire–Foster index is proposed to guarantee that individuals, who are extremely poor in only few dimensions, are not omitted by the index.

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Notes

  1. The same aggregation step is used in Bourguignon and Chakravarty (2003).

  2. In other words a composite indicator begins with a dashboard approach and adds a aggregation function for the separate (dimensional) indicators.

  3. Composite indicators and counting approaches are different in general but may coincide in their evaluations of poverty under certain (demanding) restrictions, see e.g. Dutta et al. (2003).

  4. Throughout this paper we want to use the following notation: We use the term deprivation for a lack of an individual in a single dimension and the term poor for an individual who is considered to be (multidimensional) poor.

  5. In the original formulation the term \(1_{\{y_i>0\}}\) is not included. We want to include it here because it highlights that the measure only considers individuals who are deprived in at least one dimension.

  6. We want to focus on complete orderings due to their interpretability. See e.g. Aaberge and Peluso (2012) for a definition of partial orderings for deprivation scores.

  7. For this overview we have excluded dimensional weights. See Sect. 3 for a definition of the AF index that incorporates dimensional weights.

  8. The AROPE index identifies an individual as poor if he or she meets at least one of the conditions income poverty, low work intensity or severe material deprivation. An individual is said to be severe materially deprived if he or she cannot afford at least four out of nine items. The AF identification step can map this procedure if k = 4 and the dimensional weights are w j  = 4 for income poverty and low work intensity and w j  = 1 for the nine items of severe material deprivation. See Eurostat (2012) for further information on the AROPE index.

  9. Beside the AROPE index one can easily see that for α j  = α P BC is a special case of P AF with k = 1. But for δ = 1 also counting measures like P CD are nested by P AF.

  10. For a definition of the factorizations and a discussion of the properties of the AF index see Alkire and Foster (2011) and the discussion of the properties of the modified index at the end of Sect. 4.

  11. For information on the use of the MPI in the Human Development Report see UNDP (2014a, b).

  12. In general we allow \(\beta \neq \alpha\), so strictly speaking it is not necessary the contribution to the index that is used for identification. For a short discussion about the choice of the parameter β see Sect. 5.3.

  13. k > d is not possible in the original index of Alkire and Foster (2011) since it would lead to \(P_{\alpha ,k}^{AF}({\varvec{X}},{\varvec{\pi }},{\varvec{w}})=0\) by definition. We allow for k > d because our second condition can still be fulfilled and by setting k > d we can analyse the sole influence of the new condition.

  14. For a definition and a discussion of these and the following properties see Alkire and Foster (2011).

  15. For an English summery see Federal Ministry of Labour and Social Affairs (2013). For the 1st to 3rd report see Bundesregierung (2001, 2005, 2008), respectively.

  16. Socio-economic Panel (SOEP), Data for years 1984–2011, Version 28, SOEP, 2012, doi:10.5684/soep.v28. For more information see Wagner et al. (2007, 2008).

  17. The names of the variables are those from the English version of “SOEPinfo”, http://panel.gsoep.de/soepinfo2011/.

  18. We use the modified OECD-equivalence scale, 1 to head of household, 0.3 for each child younger than approximately 14 (since only the year of birth is available), and 0.5 to all other household members.

  19. This coincides with the definition of low work intensity by the European Union which is working less than 20 % of the possible months per year, see Eurostat (2012).

  20. Self-Evaluation, measured on a scale from 0 to 10. We assume this question to be a Likert-type item, so we are able to treat it like a metric variable, see for example Traylor (1983).

  21. We construct an equivalence scale similar to Frick (1995), i.e. 1 for the first individual, \(\frac{1}{3}\) for the second and third individual and \(\frac{2}{9}\) for all other household members. This equivalence scale was constructed to reflect the guidelines for appropriate living space of the social welfare offices in Germany, which are approximately 45m 2 for one individual, 60m 2 for two individuals, 75m 2 for three individuals and 10m 2 for each additional household member.

  22. We construct a variable by adding up the frequencies of nine different activity variables, namely attend cultural events, attend cinema, pop, jazz concerts, participate in sports, artistic activities, attend social gatherings, helping relatives, friends, perform volunteer work, participate in local politics and attend church or other religious events. We set at least one time per week equal to 1, at least one time per month equal to 0.5 (since less than one time per week and at least one time per month is 1,2 or 3 times per month and the mean is approximately 2 times per month, i.e. 0.5 times per week). Similarly we set less than one time per month and more than never equal to 0.125 times per week.

  23. Often it is argued that the researcher does not want to impose a value judgement and therefore uses equal weights. But this is no proper reasoning since equal weights mean that the dimensions are of equal importance, clearly a value judgement. We would rather argue that due to data availability many of the approaches to obtain weights do not work. So we use equal weights as a arbitrary starting point which clearly reveals that setting weights is a topic that has to be analysed in more detail.

  24. See http://www.oecdbetterlifeindex.org/ for information about the OECD Better Life Index.

  25. See http://ec.europa.eu/public_opinion/index_en.htm for further information.

  26. See e.g. Cerioli and Zani (1990) or Deutsch and Silber (2005) for applications that use frequency based weights. Also note that we have used the Headcounts of 2011 since also the weights obtained from the OECD Better Life index and the Eurobarometer survey are most recent.

  27. This means that either the individual has nothing in one dimension or is on average 50 % below the poverty line in two dimensions.

  28. We chose living because for this dimension it might be plausible that individuals compare their situations among each other, like it is for income as well.

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Acknowledgments

We would like to thank two anonymous referees and Karl Mosler for their very helpful contributions.

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Authors and Affiliations

  1. Institut für Ökonometrie und Statistik, Universität zu Köln, 50923, Cologne, Germany

    Daniel Nowak & Christoph Scheicher

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  1. Daniel Nowak
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  2. Christoph Scheicher
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Correspondence to Christoph Scheicher.

Appendices

Appendix 1: Unidimensional Distributions and Descriptive Statistics

Fig. 12
figure 12

Histograms for income (left hand side) and living, year 2011

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Fig. 13
figure 13

Bar charts for education (left hand side) and health, year 2011

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Table 3 Number of observations n and, if raising factors are used, observations \(\widetilde{n}\), mean \(\widetilde{\mu }\), median \(\widetilde{m}\) and standard deviation \(\widetilde{\sigma }\)
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Table 4 Pairwise correlations for several years
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Appendix 2: Results for Six Dimensions

Fig. 14
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Unidimensional headcounts (in %)

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Fig. 15
figure 15

Unidimensional FGT indices for α = 1

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Fig. 16
figure 16

Proportion of the poor for the AF and the modified index with k = 3, α = 1 and for several m

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Fig. 17
figure 17

Values of the AF and the modified index with k = 3, α = 1 and for several m

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Nowak, D., Scheicher, C. Considering the Extremely Poor: Multidimensional Poverty Measurement for Germany. Soc Indic Res 133, 139–162 (2017). https://doi.org/10.1007/s11205-016-1365-7

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