Measuring freedom Most frequently, when trying to measure multi-dimensional poverty or

Measuring freedom Most frequently, when trying to measure multi-dimensional poverty or

inequality from the capability approach, researchers measure functionings rather than capabilities. This might seem disappointing, given the importance the human development approach places on freedom. However, as an increasing number of researchers have become interested in the capability approach, understanding it as the appropriate space in which well-being, inequality and poverty should be assessed, more creative ways of measuring freedoms (that is, obtaining information on the capability sets) are being devised. Some methods at the research stage include the following:

• If multi-dimensional measures aggregate functionings that nearly everyone

reasonably values, and if these functionings are not coercively imposed, then multi-dimensional measures of functionings poverty might be interpreted to reflect unfreedoms directly.

• Drawing on functioning-specific data on whether a person’s actions are coerced or are motivated by their own values, a capability measure could summarize the ordered pairs representing the achieved functionings and the respective agencies of each person.

• It may be possible to map capabilities onto ‘equivalent incomes’ which would usefully connect the capability approach and other economic analyses.

• Some researchers use subjective data regarding people’s perceptions of their opportunities in different domains as direct measures of capabilities.

• It may be possible theoretically and/or empirically to estimate the size of

the capability set associated with certain discrete functioning choices. • Even if it is not possible to map the capability set directly, data on income

and time use (at least) could be used to map the binding constraints on the capability set.

In any case, as we said at the start of this chapter, quantitative measurement is only one part of the set of activities that comprise human development. Whether or not user friendly and accurate direct measures of capabilities emerge, people’s freedoms and agency can be advanced by the human develop- ment approach in other ways.

Questions

6.1 If you were responsible for the Statistical Office of your government,

how would you measure income inequality in your country?

6.2 Without doing any calculations, which of these two income distributions do you think has a higher Gini coefficient: X = (6,3,13,8) or Y = (7,3,7,13)? Why? Which one has a higher Atkinson’s measure

POVERTY AND INEQUALITY MEASUREMENT

distributions look like? Now verify your ‘informed guesses’ by doing the calculations.

6.3 If you had to advise your government on which income poverty

measure to use to guide policy, which one would you recommend? Why?

6.4 If your organization was interested in measuring multi-dimensional

poverty, which dimensions and indicators would you use – or by what process would you decide? Why?

6.4 Suppose that you have data from your country at the regional level.

Suppose that there are three regions, and that evaluation is being done in three dimensions: health, education and income. Suppose that you have the information on the achievements in these areas, already normalized, given by:

Each row of this matrix indicates the achievements of each region in the three development dimensions. According to FLS’ index of human development HDI this index for the country? What is the value for each of the regions? What are the aggregate and regional values of human development using the traditional HDI? Compare the aggregate country values as well as the regions’ ranking obtained with the two indices. Why are they different?

6.5 What happens to the value of M 0 as k increases? In terms of policy

implication, what do you think would be some of the drawbacks of using the union approach to identify the multi-dimensionally poor, and what would be the drawbacks of using the intersection approach?

6.6 Discuss the statistics and graphs available at http://www.gapminder.org/

(a non-profit venture promoting sustainable global development and achievement of the MDGs by increased use and understanding of statistics and other information about social, economic and environmental development at local, national and global levels). What strikes you?

Notes

1 Many resources for the integrated analyses of poverty can be found on the Q- squared website, http://www.q-squared.ca/ 2 In fact, there have been proposals of ways in which the most commonly used inequality indices (originated in the personal distribution approach) can be decomposed by income source, such as by Shorrocks (1999). 3 This goes beyond the usual incorporation of ‘adult equivalent scales’, which is merely based on nutritional aspects according to age and gender.

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4 For more discussion on these issues see Ravallion (1996). 5 Shorrocks and Foster (1987) provide additional conditions by which two distributions can be ranked when their Lorenz curves cross once. Still this does not eliminate all the incompleteness. 6 Three well known additional properties are transfer sensitivity (when the measure is more sensitive to transfers at the lower end of the distribution), subgroup consistency (so that whenever inequality rises in a population subgroup, overall inequality also increases) and additive decomposability (such that total inequality can be expressed as the sum of a within-group inequality and a between-group inequality). For an in-depth discussion of these additional properties, see Foster and Sen (1997). 7 ‘Bad’ measures of inequality include the range, the Kuznets ratio, the relative mean deviation and the variance of logarithms, all of which violate the transfer property, and also the variance, which violates scale invariance. For further discussion on these measures, see Sen (1973) and Foster and Sen (1997). 8 More precisely, the decomposition of the Gini coefficient into an inequality between and an inequality within groups is possible when the distributions of the groups do not overlap. When they overlap, a residual term needs to be added to the equation. For details on this, see Foster and Sen (1997, p153). 9 This draws on Prof. James E. Foster’s class notes of his course Distribution and Development at Vanderbilt University, available in the teaching section of www.ophi.org.uk. 10 Foster and Sen (1997, pp125–127) provide a useful graphical representation of the EDE income and the associated inequality measure. 11 Note that incomes need to be strictly positive, that is why we refer to A = 1 as

a limiting case. 12 This presentation of the generalized entropy measures follows Foster and Sen (1997, pp140–141).

Foster (2006a) presents a unifying framework for measures of inequality in which he highlights that virtually all relative inequality measures are a function

arithmetic mean). 14 For in-depth discussion of this property, see Foster and Sen (1997, pp149–163) as well as Shorrocks (1980). 15 This is usually done by multiplying the cost of the food basket by the inverse of the Engel Coefficient (which is the ratio between food expenditure and total expenditure) calculated for people with incomes just above the food poverty line. 16 The need of a linen shirt and leather shoes in the England of the late 17th century remarked by Adam Smith (1776) is an example of context-specific needs. 17 For example, Foster (1998) suggests a possible hybrid line given by a weighted

geometric average of a relative threshold (z r ) and an absolute threshold (z a ): z = z z 1– r a , with 0 < < 1. By selecting the value of , one can choose the weight to be attached to each component to the hybrid line (with = 0 making it all absolute, and = 1 making it all relative). Provided z r is a fraction of a living standard, is the elasticity of the poverty line to the living standard (p339). Atkinson and Bourguignon (2001) and Ravallion and Chen (2009) provide alternative approaches and further discussion on hybrid poverty lines. 18 This sort of discussion has fostered the fuzzy sets approach to poverty

POVERTY AND INEQUALITY MEASUREMENT

measurement (Cerioli and Zani, 1990; Cheli and Lemmi, 1995, among others), as well as the development of dominance analysis in poverty measurement (Atkinson 1987; Foster and Shorrocks 1988; Foster and Jin 1998, among others). It also suggests the need to do sensitivity analysis in empirical applications. 19 Foster (2006b) provides a recent and thorough review on properties of poverty measures and the different indices proposed in the literature. 20 Watts (1969) and Sen (1976) initiated the discussion on the desirable properties for a poverty measure. 21 This implies that each income in the distribution can be measured ‘in poverty line units’. Poverty measures that are scale invariant are called relative measures, as opposed to absolute poverty measures, which are invariant to translations or additions of the same absolute amount to each income and to the poverty line. For distinction between the two, see Blackorby and Donaldson (1980), and Foster and Shorrocks (1991). 22 To avoid further technicalities, we have omitted the continuity property, which is also usually required in poverty measurement, demanding the measure not to abruptly change as incomes approach (and cross) the poverty line. 23 For more discussion on the subgroup axioms, see Foster and Sen (1997), as well as Foster and Shorrocks (1991). 24 For discussion on other poverty measures, we refer the reader to Foster (2006b), Foster and Sen (1997) or Atkinson (1987).

25 The P 2 measure has a neat relation with the squared coefficient of variation ‘transfer sensitive’ stressing transfers at low income levels.

26 For each indicator, normalization is done subtracting the minimum value from the observed value and dividing it by the difference between the maximum and the minimum values. The minimum and maximum values for life expectancy at birth are 25 and 85 years correspondingly; for the adult literacy rate and for the combined enrolment ratio are 0 and 100 correspondingly, and for GDP per capita (in PPPUS$) are 100 and 40,000. Once the adult literacy rate and the gross enrolment rate have been normalized, the composite indicator is obtained as a weighted average between the two, with a weight of 2/3 for the normalized literacy rate and of 1/3 for the normalized gross enrolment rate. 27 Formally, the distribution of health, education and income across the

population is given by vectors h = (h 1 ,h 2 ,...,h n ), e = (e 1 ,e 2 ,...,e n ) and y = (y 1 ,y 2 ,...,y n ) respectively. 28 For an analysis on this issue see Seth (2008). For criticisms of the normalization process of the HDI indicators (which implicitly affects the weights of the variables), see Kelley (1991) and Srinivasan (1994). 29 In this way, the index reflects that while there is some substitutability between the dimensions of development, this is not infinite, as it is implicitly assumed

30 As noted by Tsui (2002, p72), it is worth noticing that in the unidimensional measurement of poverty the weights used are the prices, assuming implicitly that these prices are ‘right’. Clearly this position is no less value-free than using other sets of weights. 31 For more discussion on weights in multi-dimensional measures, see Decanq and Lugo (2008). 32 The reader interested in formal statements of the properties in multi- dimensional poverty measurement can find them in Tsui (2002), Bourguignon

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and Chakravarty (2003), Alkire and Foster (2007) among others. 33 Only when the intersection approach is used for identifying the multi- dimensionally poor (k = d), is the multi-dimensional headcount ratio sensitive to the number of deprivations that the poor experience. 34 If there is more than one indicator per dimension, a structure of ‘nested’ weights can be used. For further explanation of this option, see Alkire and Foster (2007).