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Original Articles

Monitoring Inequality among Social Groups: A Methodology Combining Fuzzy Set Theory and Principal Component AnalysisFootnote1

Pages 427-452 | Published online: 18 Aug 2008
 

Abstract

The present paper contributes to operationalizing the Capability Approach by proposing a methodology for the design of sets of indicators for monitoring inequality among social groups based on census and household surveys. The result is a set of indicators and synthetic indices that can be disaggregated by social groups, in a way that allows the monitoring of inequalities in the overall achievement either of fundamental rights or of specific rights. The methodology combines the heuristic power of Principal Component Analysis in offering empirical evidence for the aggregation of indicators with the operational advantage of Fuzzy Set Theory for their final design and measurement. The paper emphasizes the complementarities of these statistical techniques. The methodology is illustrated by the design of a set of indicators for monitoring housing adequacy in the Venezuelan context.

Acknowledgements

The author is grateful to Michael Dunford, Jacqueline O'Reilly and Julie Litchfield for their supervision and helpful comments, and to Alberto Gruson for his invaluable contribution. The author is also grateful, for their helpful comments on an earlier version, to Sabina Alkire, Enrica Chiappero Martinetti, Siddiqur Osmani, Ingrid Robeyns, Paola Salardi, anonymous referees and the participants of the workshop on ‘Multidimensional Comparison’ organized by Oxford Poverty and Human Development Initiative (OPHI) at the University of Oxford (June 2007), and the participants of the 7th Human Development and Capability Association conference. This research has been made possible by the financial support of the British Chevening Scheme. The usual disclaimers apply.

Notes

1. This is a revised version of the paper that won the Wiebke Kuklys Prize for 2007 as the best paper by a graduate student of those submitted for the Human Development and Capability Association annual conference.

2. This complements those systems for monitoring inequality based on aggregated data (for example, Burchardt and Vizard, Citation2007).

3. Sen (Citation1985, Citation1992) distinguishes between the space of capabilities and the space of functionings; while the former refers to potential beings and doings, the latter refers to concrete achievements. Since capabilities are not directly observable, empirical applications remain at the level of functionings (Clark Citation2006; Chiappero Martinetti and Roche, forthcoming).

4. Other aspects, such as agency, empowerment, or subjective well‐being are also relevant, but they may be better measured separately (cf. Anand and Van Hees, Citation2006; Alkire, Citation2007).

5. Despite their not being based on the CA, there is a significant convergence between these studies and the CA's empirical application at the level of achieved functionings (cf. Roche, Citation2006).

6. These decisions are less arbitrary when they are theoretically grounded, and based on a broad knowledge of the indicators and the context (this method is extensively accepted in other disciplines in social science; cf. Ragin, Citation2000).

7. These could include similar approaches to the one used by Qizilbash and Clark (Citation2005) to specify the upper and lower cut‐off levels.

8. PCA uses the total variance, while FA just the common or share variance between the indicators.

9. The variable sewage facilities also contributes to the component related to house structure due to its high correlation with the predominant materials in the house. Certainly, a house must meet certain structural requirements for improved sanitation to be viable. Similarly, the variable sewage facilities is also highly correlated to other services and it seems more appropriate and clearer for monitoring purposes to include it only in the index of housing services.

10. The predominant material in the wall is to a certain extent an indicator of space and density, since this variable contributes significantly to this component. However, it seems to be more appropriate for monitoring purposes to include it only in structure. Appendix 1 suggests some recommendations of how to measure more appropriately the materials in the walls in order to measure functionings.

11. The wall materials also contributes to this component (see note 9), but it is only measured with housing overcrowding index in order to facilitate monitoring.

12. Logarithm of the household per‐capita income adjusted by adult equivalent scale and scale economy factor, and standardized as a fuzzy set measure.

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