1. Integrating Inter-Personal Inequality in Counting Poverty Indices: The Correlation Sensitive Poverty Index Nicole Rippin 24 June 2014

2. © Deutsches Institut für Entwicklungspolitik (DIE)2 Outline I.Introduction II.The identification of the poor III.The aggregation of the individual characteristics of the poor in the ordinal framework III.I The Multidimensional Poverty Index (MPI) III.II The Correlation Sensitive Poverty Index (CSPI) IV.Empirical application V.Conclusion I. Introduction II. The Identification Step III. The Aggregation Step IV. Empirical Application V. Conclusion

3. © Deutsches Institut für Entwicklungspolitik (DIE)3  Insufficient income has for a long time been considered to be a good proxy for poverty in all its various facets.  The income approach, however, relies on critical assumptions:  Over time, serious concerns have been raised regarding the appropriateness of these simplifying assumptions (e.g. Rawls, 1971; Sen 1985, 1992; Drèze and Sen, 1989; UNDP, 1997). Economic Resources Assumption: equal individual conversion factors Ignoring in particular: -Personal heterogeneities -Variations in physical environment -Differences in social climate UtilityGoods Assumption: perfect and complete markets Ignoring in particular: -The role of public goods -Limited access -Asymmetric information ChoiceConversion Introduction I. Introduction II. The Identification Step III. The Aggregation Step IV. Empirical Application V. Conclusion

4. © Deutsches Institut für Entwicklungspolitik (DIE) I. Introduction II. The Identification Step III. The Aggregation Step IV. Empirical Application V. Conclusion  It was Amartya Sen, who developed a new approach to measure poverty and welfare: the capability approach (1979, 1985, 1992, 1999, 2009).  Thus, the capability approach implies a multidimensional approach to poverty measurement. Economic Resources Assumption: equal individual conversion factors Ignoring in particular: -Personal heterogeneities -Variations in physical environment -Differences in social climate Utility Goods Assumption: perfect and complete markets Ignoring in particular: -The role of public goods -Limited access -Asymmetric information ChoiceConversion Capability Set Functioning Bundle Choice Introduction 4

5. © Deutsches Institut für Entwicklungspolitik (DIE) I. Introduction II. The Identification Step III. The Aggregation Step IV. Empirical Application V. Conclusion  Empirical evidence demonstrates that considerable population shares might be multidimensional poor but not income poor, and vice versa (e.g. Klasen, 2000).  Already a strong trend in the last decade, multidimensional poverty measurement has been given a further boost through the introduction of the first internationally comparable Multidimensional Poverty Index MPI (Alkire and Santos, 2010).  However, in the multidimensional framework inequality does not only exist within, but also across dimensions; consequently there exists a tension between the two concepts of distributive justice and efficiency that does not exist in the one-dimensional framework:  ‘[A]n attempt to achieve equality of capabilities – without taking note of aggregative considerations – can lead to severe curtailment of the capabilities that people can altogether have’ (Sen, 1992). Introduction 5

6. © Deutsches Institut für Entwicklungspolitik (DIE) I. Introduction II. The Identification Step III. The Aggregation Step IV. Empirical Application V. Conclusion  In the ordinal context, inequality across dimensions is usually considered as the spread of simultaneous deprivations across the population, thus only accounting for distributive justice.  This work suggests to define inequality across dimensions as the correlation-sensitive spread of simultaneous deprivations across the population.  This rigour definition accounts for the tension between the two concepts of distributive justice and efficiency that Sen mentioned and has strong implications on the identification of the poor and the aggregation of individual poverty characteristics. Introduction 6

7. © Deutsches Institut für Entwicklungspolitik (DIE) I. Introduction II. The Identification Step III. The Aggregation Step IV. Empirical Application V. Conclusion 7 Theoretical Background  ℕ represents a set of n persons  ℕ represents a set of k poverty attributes  ℝ K represents the respective vector of threshold levels  ℝ + K represents a vector of weights such that  ℝ K represents the achievement vector of person i  Person i is deprived with respect to attribute j if  represents the deprivation vector of person i such that if and if  For any ℕ, the deprivation matrix is denoted by ℝ + NK  A poverty index is defined by ℝ  Society A has higher poverty than society B if and only if P ( X A ) ≥ P ( X B )  is the weighted sum of deprivations of person i

8. © Deutsches Institut für Entwicklungspolitik (DIE) I. Introduction II. The Identification Step III. The Aggregation Step IV. Empirical Application V. Conclusion 8  Let ℝ ℝ be an identification function so that person i is poor if and not poor if  Three specifications for have been suggested so far:  According to the union method, deprivation in one attribute is deprivation in all attributes (perfect complements):  According to the intersection method, poverty only occurs when there is deprivation in all attributes (perfect substitutes): Union and Intersection Method

9. © Deutsches Institut für Entwicklungspolitik (DIE) I. Introduction II. The Identification Step III. The Aggregation Step IV. Empirical Application V. Conclusion 9 Intermediate Method (Dual Cut-Off)  In response to the limited practicability of union and intersection method, the idea of an intermediate approach was brought up by Mack and Lindsay (1985) and formally introduced by Foster (2007) and Alkire and Foster (2007, 2011).  According to the intermediate method, individual i is poor if the weighted sum of deprivations is higher than a predetermined minimum level:  The intermediate method provides a practicable solution, the theoretical justification is, however, questionable: up to the cut- off, attributes are considered to be perfect substitutes, from the cut-off onwards, however, the very same attributes are considered to be perfect complements.  There is another way to identify the poor that can be derived directly from the aggregation step – by fully accounting for the two concepts of distributive justice and efficiency.

10. © Deutsches Institut für Entwicklungspolitik (DIE) I. Introduction II. The Identification Step III. The Aggregation Step IV. Empirical Application V. Conclusion 10 The Equality-Promoting Change 10  For any and X, is obtained from X by an equality-promoting change, if for some individuals g and h, and A distributional change is said to be equality-promoting whenever the difference in the number of simultaneously suffered deprivations between two individuals is reduced  Based on Chakravarty and D’Ambrosio (2006), Jayaraj and Subramanian (2010) introduced the equality-promoting change in order to capture inequality across dimensions:  Jayaraj and Subramanian (2010) then formulated the axiom Nonincreasingness under Equality-Promoting Change: For any and X, if is obtained from X by an equality-promoting change, then  The axiom captures distributive justice, yet it neglects efficiency by disregarding possible correlations between attributes.

11. © Deutsches Institut für Entwicklungspolitik (DIE) I. Introduction II. The Identification Step III. The Aggregation Step IV. Empirical Application V. Conclusion 11 The Inequality Increasing Switch  Depending on the nature as well as the strength of the correlations between attributes, poverty might very well increase under an equality-promoting change.  Thus, I introduce the concept of an inequality increasing switch:  Define Then, for two individuals g and h such that, matrix X is said to be obtained from matrix by an inequality increasing switch of attribute l if and An inequality increasing switch is a switch of attributes that increases (reduces) the number of deprivations suffered by the person with higher (lower) initial deprivation  Duclos, Sahn and Younger (2006) for instance argue that complementarities exist between the two poverty dimensions education and nutrition as better nourished children learn better. If the degree of complementarity is strong enough, poverty decreases with increasing inequality.

12. © Deutsches Institut für Entwicklungspolitik (DIE) I. Introduction II. The Identification Step III. The Aggregation Step IV. Empirical Application V. Conclusion 12 A New Axiom  Based on this concept I formulate the axiom Sensitivity to Inequality Increasing Switches: For any and X, if is obtained from X by an inequality increasing switch of non-complementary attributes, then Further, if is obtained from X by an inequality increasing switch of complement attributes, then  Example: i = 2, j = 5, z = (1 1 1 1 1)

13. © Deutsches Institut für Entwicklungspolitik (DIE) I. Introduction II. The Identification Step III. The Aggregation Step IV. Empirical Application V. Conclusion 13 A New Class of Ordinal Poverty Indices  The new axiom directly implies a new multiple step identification function that is nondecreasing in the number of deprivations and has a nondecreasing (nonincreasing) marginal in case attributes are considered to be substitutes (complements).  The former accounts for distributive justice, the latter for efficiency. Property 1 A multidimensional poverty measure P satisfies AN, NM, MN, SF, PP, FD, SD and SIIS if and only if for all and X : with ℝ ℝ non-decreasing in and a nondecreasing (nonincreasing) marginal in case attributes are considered to be substitutes (complements).

14. © Deutsches Institut für Entwicklungspolitik (DIE) I. Introduction II. The Identification Step III. The Aggregation Step IV. Empirical Application V. Conclusion 14 A New Identification Function  Consider the following multiple step identification function: ρ δ 1  1  0 min IM δ 1  min IS δ 1 ˆ    δρ 1 ˆ    δρ 1  max ρ δδ ˆ min  U  The relationship between distributive justice and efficiency is determined by an indicator for inequality aversion: alpha  In case, approximates a concave shape: as already the loss in one attribute can barely be compensated, there is no need for a strong focus on inequality  In case, approximates a convex shape: the loss in one attribute can easily be compensated, there is a need for a strong focus on inequality

15. © Deutsches Institut für Entwicklungspolitik (DIE) I. Introduction II. The Identification Step III. The Aggregation Step IV. Empirical Application V. Conclusion 15 The Correlation Sensitive Poverty Index (CSPI)  For the empirical application, I introduce the Correlation Sensitive Poverty Index (CSPI), a simple form of the new class of correlation sensitive poverty measures:  Different from any other additive/counting index, the CSPI can be decomposed into a product of poverty incidence, intensity and inequality: The headcount ratio measuring poverty incidence; the aggregate deprivation count ratio measuring poverty intensity; and the Generalized Entropy inequality index of deprivation counts measuring inequality.

16. © Deutsches Institut für Entwicklungspolitik (DIE) I. Introduction II. The Identification Step III. The Aggregation Step IV. Empirical Application V. Conclusion 16 The Multidimensional Poverty Index (MPI)  The MPI extracts information on simultaneous deprivations but only to verify whether a household is poor or not, afterwards this information is disregarded.  In the following I will compare the CSPI with the Multidimensional Poverty Index (MPI): with if and otherwise  In other words, the MPI completely neglects inequality across dimensions: it assumes that poverty attributes are not correlated at all (thereby neglecting efficiency) and considers all individuals above the dual cut-off line equally poor, regardless of the number of dimensions in which they are deprived (thereby neglecting distributive justice).

17. © Deutsches Institut für Entwicklungspolitik (DIE)  Consequently, the MPI can only be decomposed in the product of (censored) poverty incidence and intensity: The censored headcount ratio measuring poverty incidence and the censored aggregate deprivation count ratio measuring poverty intensity. I. Introduction II. The Identification Step III. The Aggregation Step IV. Empirical Application V. Conclusion 17 The Multidimensional Poverty Index (MPI)

18. © Deutsches Institut für Entwicklungspolitik (DIE) I. Introduction II. The Identification Step III. The Aggregation Step IV. Empirical Application V. Conclusion 18 The Structure of MPI and CSPI  The structure of the MPI which is also used for the CSPI: DimensionMain CapabilityIndicatorThreshold (Household Level) HealthBodily Health Nutrition At least one of the following: 1. At least one woman age 15-49 with BMI < 18.5 2. At least one child with weight-for-age z-score < -2.0 Child Mortality RateAt least one child under the age of 18 died Education Senses, Imagination and Thought SchoolingNo member with at least five years of schooling EnrolmentAt least one child in school age not enrolled Living Standards Bodily Health Control over Environment Cooking Fuel Harmful material is used for cooking (straw, dung, coal etc.) Sanitation Toilet either unhygienic (no facility, open lid, etc.) or shared Water Water source is unprotected or more than 30 minutes away ElectricityNo access to electricity FloorFloor material is earth, sand or dung AssetsNot more than one small asset and no car/truck

19. © Deutsches Institut für Entwicklungspolitik (DIE) I. Introduction II. The Identification Step III. The Aggregation Step IV. Empirical Application V. Conclusion 19 An Example from India  The following example is taken from the Indian DHS 2005:  Household 3 is deprived in five indicators (electricity, water, sanitation, floor and cooking fuel) yet it is not included in the calculation of the MPI. 0.0280.000 no yesno5 0.0490.000 no yesno yesno4 0.0770.000 no yes no 3 0.1510.389 noyes noyes no yes2 0.5220.722 yesnoyesnoyes noyes 1 AssetsCookingFlooringSanitationWaterElectricityNutritionMortalityAttendanceYears CSPIMPILiving StandardHealthEducationHH A Comparison of Five Indian Households (DHS 2005) 0.0280.000 no yesno5 0.0490.000 no yesno yesno4 0.0770.000 no yes no 3 0.1510.389 noyes noyes no yes2 0.5220.722 yesnoyesnoyes noyes 1 AssetsCookingFlooringSanitationWaterElectricityNutritionMortalityAttendanceYears CSPIMPILiving StandardHealthEducationHH A Comparison of Five Indian Households (DHS 2005)  A transfer from household 1 to household 2 does not change the value of the MPI which is still 0.222; it changes, however, the value of the CSPI, from 0.135 to 0.143.

20. © Deutsches Institut für Entwicklungspolitik (DIE) I. Introduction II. The Identification Step III. The Aggregation Step IV. Empirical Application V. Conclusion 20 Indian Poverty Maps according to MPI

21. © Deutsches Institut für Entwicklungspolitik (DIE) I. Introduction II. The Identification Step III. The Aggregation Step IV. Empirical Application V. Conclusion 21 Indian Poverty Maps according to CSPI

22. © Deutsches Institut für Entwicklungspolitik (DIE) I. Introduction II. The Identification Step III. The Aggregation Step IV. Empirical Application V. Conclusion 22 Conclusion  In a multidimensional framework, two types of inequality exist: inequality within and inequality across dimensions.  This axiomatic modification implies a new method for the identification of the poor that accounts for both the distribution of attributes as well as the correlations between them.  However, in the ordinal framework, inequality across dimensions is usually equated with the spread of simultaneous deprivations across the population (distributive justice).  This work suggests an extended definition of inequality between dimensions as the correlation-sensitive spread of simultaneous deprivations across the population.  In order to operationalise this more holistic definition of inequality between dimensions, a new axiom, Sensitivity to Inequality Increasing Switches, is introduced.

23. © Deutsches Institut für Entwicklungspolitik (DIE) I. Introduction II. The Identification Step III. The Aggregation Step IV. Empirical Application V. Conclusion 23 Conclusion  It also leads to a whole new class of ordinal poverty indices that are the first additive indices able to capture correlation- sensitivity and inequality while at the same time being fully decomposable (according to dimensions and population subgroups).  The new way to measure poverty has interesting implications for policy making:  It accounts for efficiency, i.e. scarce resources are applied in a way that their impact is strongest;  It accounts for distributive justice, i.e. ensures that the neediest are not left behind;  Due to its decomposability according to population sub- groups and poverty dimensions as well as the three I’s of poverty (incidence, intensity and inequality), it provides a detailed picture of the poverty structure in a given country.

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