Andrea Brandolini Banca d’Italia, Department for Structural Economic Analysis

1. Strategies of multidimensional measurement Andrea Brandolini Banca d’Italia, Department for Structural Economic Analysis 2012 ISFOL Conference “Recognizing the Multiple Dimensions of Poverty: How Research Can Support Local Policies” Rome, 22 -23 May 2012

2. Background World Bank, World Development Report 2000/2001: Attacking Poverty “This report accepts the now traditional view of poverty … as encompassing not only material deprivation (measured by an appropriate concept of income or consumption), but also low achievements in education and health. … This report also broadens the notion of poverty to include vulnerability and exposure to risk – and voicelessness and powerlessness” (italics added)

3. Multidimensionality in poverty research Multidimensional poverty Multidimensional deprivation Source: author’s search of "exact phrase" in Google Scholar, 21 May 2012.

4. Background Alkire & Foster “Counting and multidimensional poverty measurement”, Journal of Public Economics, 2011 “Multidimensional poverty has captured the attention of researchers and policymakers alike due, in part, to the compelling conceptual writings of Amartya Sen and the unprecedented availability of relevant data.”

5. Background Europe 2020 strategy Five headline targets for member states’ policies: “Reduction of poverty by aiming to lift at least 20 million people out of the risk of poverty or social exclusion” Risk of poverty or social exclusion→ multidimensional Poor population comprises people … … either living in households with very low work intensity (where adults work less than 20% of total work potential) … or at-risk-of-poverty after social transfers (equivalised income below 60 % of national median) … or severely materially deprived (at least 4 out of 9 deprivations owing to lack of resources)

6. Outline • Multidimensionality in practice • Empirical strategies • Do we want a single number? • Weighting • Functional form • Health and income deprivation in France, Germany and Italy, 2000 • Conclusions

7. Multidimensionality in practice • Multidimensionality has intuitive appeal • Problems arise in transforming intuition into hard data • Not every indicator needs to be appropriate E.g. “proportion of persons meeting friends or relatives less than once a month or never” (Eurostat 2000; Townsend 1979) Infrequent meetings with friends may signal … weak social ties but also … preference for quietness … or passion for internet

8. Multidimensionality in practice  Multidimensional measurement without theory may be misleading • What is needed? • Identification of relevant dimensions • Construction of corresponding indicators • Understanding of indicator metrics • Empirical strategies, i.e. tools to deal with multidimensionality

9. Social welfare approach Counting approach Item-by-item analysis Supplementation strategy Vector dominance Sequential dominance Non-aggregative strategies Multivariate techniques Multidimensional poverty indices Comprehensive analysis Well-being indicator Aggregative strategies Equivalence scales Empirical Strategies for Multiple Dimensions Source: author’s elaboration based on Brandolini e D’Alessio 1998.

10. Empirical strategies • Alternative strategies differ for extent of manipulation of raw data • the heavier the structure imposed on data, the closer to complete cardinal measure • Focus on aggregate measures, i.e. multidimensional index or well-being indicator (both single number but …) • Do we want a single number? • Weighting • Functional form

11. Do we want a single number? • Pros: communicational advantage  single complete ranking more likely to capture newspaper headlines and people’s imagination than multidimensional scorecards (‘Eye-catching property’, Streeten on HDI) • Cons: 1. different metrics 2. informational loss 3. imposed trade-offs (complements/substitutes)

12. Weighting • Different weighting structures reflect different views Sen  ‘ranges’ of weights rather than single set • Alternatives: • Equal weighting. Lack of information about ‘consensus’ view. But no discrimination. • Data-based weighting. Frequency-based or multivariate techniques. Caution in entrusting a mathematical algorithm with a normative task • Market prices. Existing for some attributes only, inappropriate for well-being comparisons

13. Functional form (Old) HDI measured average achievement in human developments in a country as where: Y = GDP per capita L = life expectancy at birth A = adult literacy G = gross school enrolment Upper/lower bars = max/min Replace prefixed minima and maxima and simplify

14. 1 year = $2,658 in Japan = $166 in Kyrgyzstan Iso-HDI Contours Source: author’s elaboration on data drawn from UNDP (2005). All countries shown in the figure have similar values of the education index, comprised between 0.93 and 0.96.

15. Functional form

16. Non poor Union poor H1+H2–H1,2 Intersection poor H1,2 Union vs. intersection Atkinson’s counting index: A = 2-κ(H1+H2) + (1–21-κ)H1,2 κ = 0 union κ ↑ more weight on multiple deprivations κ → ∞ intersection

17. Iso-poverty contours for Bourguignon-Chakravarty measure If θ → ∞ substitutability tends to 0, contours = rectangular curves If θ=α=1 attributes are perfect substitutes and convex part becomes straight line The higher  relative to , the more the two attributes are substitutes

18. Health and income deprivation in France, Germany and Italy, 2000 • European Community Household Panel (ECHP) • All persons aged 16 or more • Two indicators: • Health status: measured on a scale from 5 (very good) to 1 (very bad) and based on respondent’s self-perception Health-poor = bad or very bad health • Household equivalent income Income-poor = equivalent income < median

19. Health and income deprivation (percentage values) Source: author’ elaboration on ECHP data, Wave 8.

20. Health and income deprivation in France, Germany and Italy, 2000 Bourguignon-Chakravarty index - Different parameter values Germany Italy France Source: author’ elaboration on ECHP data, Wave 8. Logarithmic scale for horizontal axes.

21. Health and income deprivation in France, Germany and Italy, 2000 Bourguignon-Chakravarty index - Different weighting Germany Italy France from health only to income only Source: author’ elaboration on ECHP data, Wave 8.

22. Bourguignon-Chakravarty index • Health-poor: score=1,2 • Consistent with cutoff at any value between 2 and 3 • cutoff = 3 (used above) possible values=1/3,2/3 • cutoff = 2+ possible values=0,1/2 Contribution of health lower with 2+ • Germany 0.0110 instead of 0.0232 • France 0.0134 instead of 0.0195 • Agreement on identification of poor health status does not lead to unambiguous definition of poverty cutoff and then consistent with different values of index  Serious shortcoming, as general problem for any indicator in discrete space

23. Health and income deprivation in France, Germany and Italy, 2000 Atkinson’s counting index A = 2-κ(H1+H2) + (1–21-κ)H1,2 κ = 0 union κ ↑ more weight on multiple deprivations κ → ∞ intersection Italy Germany France Source: author’s elaboration on ECHP data, Wave 8.

24. Conclusion • Measurement of poverty and inequality in a multidimensional space poses new problems relative to measurement in unidimensional spaces • Understanding sensitivity of results to underlying hypotheses is crucial part of analysis • But there is value added!

25. Thank you for your attention!