Analysis of Inequality across Multi- dimensionally Poor and Population Subgroups for Counting Approaches Suman Seth and Sabina Alkire Development Studies Association Annual Conference 2013 University of Birmingham November 16, 2013

Motivation Poverty measurement tools may affect policy design and policy incentive – Incidence – Intensity – Inequality Three I’s of poverty measurement (Jenkins and Lambert 1997) 2

Concerns for Inequality Inequality among the poor – Consideration of inequality in poverty measurement has been prominent since Sen (1976) Disparity across population subgroups – Horizontal Inequality (Stewart 2000) 3

Counting Approach Counting measures – Townsend (1979), Atkinson (2003) – Adjusted headcount ratio (Alkire and Foster): several national and international (MPI, WEAI) adaptations Capturing inequality is natural for cardinal dimensions – Can reflect inequality within each dimension Not so straightforward for ordinal or binary dimensions – But can be captured across deprivation counts 4

Example: Concern for Inequality Deprivation counts (0, 2, 4, 6, 8, 10) (0, 2, 2, 4, 8, 10) (0, 2, 2, 5, 8, 9) Next period I Next period II Similar reduction in incidence and intensity, but these two situations are not the same 5

One Approach: Fine tune a poverty measure to make it sensitive to inequality – Bossert, Chakravarty and D’Ambrosio 2009, Jayaraj and Subramanian (2009), Rippin (2011), Alkire and Foster (2013) Practical Limitations: – Primarily used for ranking – The final figure obtained is not intuitive – Not suitable for capturing inequality within and between groups – Dimensional breakdown or factor decomposability not possible Alkire and Foster (2013) 6 Consideration for Inequality

Other Approach: Use a separate inequality measure? An example: Use of standard deviation in child poverty – Delamonica and Minujin (2007), Roche (2013) Advantage: – Additional information besides incidence and intensity – If decomposable, can observe inequality decomposition within and between group – Can be used with intuitive poverty measure such as Adjusted Headcount Ratio 7 Consideration for Inequality

Q: Which inequality measure to use? – Eepends on which properties we want the measure to satisfy Three key properties – Absolute inequality: if every poor’s deprivation count rises or decreases by same number, inequality should not change – Additive Decomposability: within-group + between group – Within-group Mean Independence: Total within-group does not change if no change in inequality within any subgroup 8 Consideration for Inequality

The Inequality Measure? The only absolute inequality measure that satisfies these properties is a positive multiple of variance V(x) =  i (x i –  (x)) 2 /n where, V(x): positive multiple of variance of distribution x  (x): mean of distribution x n: population size of distribution x  > 0 Chakravarty (2001), Bosmans and Cowell (2011), Chakravarty and Tyagarupananda (1998) 9

Illustrations using the Global Multidimensional Poverty Index (MPI) 10

Example on India: Castes (DHS 2 & 3) Intensity (MPI) Share of Poor Inequality (Poor) casteA_castepoor_shrvar_depr_caste_p Scheduled Tribe57.0%12.6%0.110 Scheduled Caste55.0%22.1%0.107 Other Backward Classes52.1%33.3% General50.6%32.0% India52.9%100% ST56.3%12.9%0.115 SC52.6%22.9%0.098 OBC50.8%42.1% General49.7%22.0% India 51.7%100%0.097

Example on India: Castes (DHS 2 & 3) Intensity (MPI) Share of Poor Inequality (Poor) casteA_castepoor_shrvar_depr_caste_p Scheduled Tribe57.0%12.6%0.110 Scheduled Caste55.0%22.1%0.107 Other Backward Classes52.1%33.3% General50.6%32.0% India52.9%100% ST56.3%12.9%0.115 SC52.6%22.9%0.098 OBC50.8%42.1% General49.7%22.0% India 51.7%100%0.097 Inequality among the poor fell for SC and OBC, but not for ST

Indian States (DHS 2 & 3) 13

Cross Country Comparison Two countries: different MPIs but similarly unequal 14 CountryYear Headcount RatioMPI Average Deprivation Count (Poor) Inequality (Poor) Colombia % %0.041 Lesotho % %0.042 Demographic Health Surveys

Disparity in Intensity vs. Disparity in Poverty Between group inequality among poor is not sufficient for disparity in poverty between groups – Sub-national Disparity (Alkire, Roche, Seth 2011) Example: c = (0,0,0,6,6,6,6,6,7,7), c A = (0,0,6,6,7) and c B = (0,6,6,6,7) c' = (0,0,0,6,6,6,6,6,6,6), c' A = (0,0,0,6,6) and c' B = (6,6,6,6,6) Overall inequality, within group inequalities, between group inequalities among the poor – all lower in c' than in c Disparity in poverty between subgroups? 15

Cross Country Comparisons Similar inequality among the poor but very different sub-national disparity 16 CountryYearMPI Inequality (Poor) Total Within- Group Between Group Between MPI Bolivia Zimbabwe Demographic Health Surveys

Concluding Remarks We discuss how inequality can be captured among the poor in counting approach through a positive multiple of variance A separate measure can provide more information besides a poverty measure than just ranking Although debated (Kanbur, 2006), change in inequality decomposition can provide important information 17

Concluding Remarks It is also important to capture disparity between subgroup’s poverty Same result if counted in achievement or deprivation space Future research – Compute the standard error to understand statistical significance of comparisons – Deeper analysis across countries to understand inequality decompositions and causes of change in inequality 18