1. OPHI Oxford Poverty & Human Development Initiative Department of International Development Queen Elizabeth House, University of Oxford www.ophi.org.uk Open Dialogue Day 16 June 2008

2. Counting and Multidimensional Poverty Measurement by Sabina Alkire and James FosterOPHI 16 June, 2008

3. Why Multidimensional Poverty? Capability Approach Data Tools Demand

4. How to Measure? Variables Identification Aggregation

5. Our Proposal Variables – Assume given Identification – Dual cutoffs Aggregation – Adjusted FGT

6. Review: Unidimensional Poverty Variable – income Identification – poverty line Aggregation – Foster-Greer-Thorbecke ’84 Example Incomes = (7,3,4,8) poverty line z = 5 Deprivation vector g 0 = (0,1,1,0) Headcount ratio P 0 =  (g 0 ) = 2/4 Normalized gap vector g 1 = (0, 2/5, 1/5, 0) Poverty gap = P 1 =  (g 1 ) = 3/20 Squared gap vector g 2 = (0, 4/25, 1/25, 0) FGT Measure = P 2 =  (g 2 ) = 5/100

7. Multidimensional Data Matrix of well-being scores for n persons in d domains Domains Persons

8. Multidimensional Data Matrix of well-being scores for n persons in d domains Domains Persons z ( 13 12 3 1) Cutoffs

9. Multidimensional Data Matrix of well-being scores for n persons in d domains Domains Persons z ( 13 12 3 1) Cutoffs These entries fall below cutoffs

10. Deprivation Matrix Replace entries: 1 if deprived, 0 if not deprived Domains Persons

11. Deprivation Matrix Replace entries: 1 if deprived, 0 if not deprived Domains Persons

12. Normalized Gap Matrix Matrix of well-being scores for n persons in d domains Domains Persons z ( 13 12 3 1) Cutoffs These entries fall below cutoffs

13. Gaps Normalized gap = (z j - y ji )/z j if deprived, 0 if not deprived Domains Persons z ( 13 12 3 1) Cutoffs These entries fall below cutoffs

14. Normalized Gap Matrix Normalized gap = (z j - y ji )/z j if deprived, 0 if not deprived Domains Persons

15. Squared Gap Matrix Squared gap = [(z j - y ji )/z j ] 2 if deprived, 0 if not deprived Domains Persons

16. Squared Gap Matrix Squared gap = [(z j - y ji )/z j ] 2 if deprived, 0 if not deprived Domains Persons

17. Identification Domains Persons Matrix of deprivations

18. Identification – Counting Deprivations Domains c Persons

19. Identification – Counting Deprivations Q/ Who is poor? Domains c Persons

20. Identification – Union Approach Q/ Who is poor? A1/ Poor if deprived in any dimension c i ≥ 1 Domains c Persons

21. Identification – Union Approach Q/ Who is poor? A1/ Poor if deprived in any dimension c i ≥ 1 Domains c Persons Difficulties Single deprivation may be due to something other than poverty (UNICEF) Union approach often predicts very high numbers - political constraints.

22. Identification – Intersection Approach Q/ Who is poor? A2/ Poor if deprived in all dimensions c i = d Domains c Persons

23. Identification – Intersection Approach Q/ Who is poor? A2/ Poor if deprived in all dimensions c i = d Domains c Persons Difficulties Demanding requirement (especially if d large) Often identifies a very narrow slice of population

24. Identification – Dual Cutoff Approach Q/ Who is poor? A/ Fix cutoff k, identify as poor if c i > k Domains c Persons

25. Identification – Dual Cutoff Approach Q/ Who is poor? A/ Fix cutoff k, identify as poor if c i > k (Ex: k = 2) Domains c Persons

26. Identification – Dual Cutoff Approach Q/ Who is poor? A/ Fix cutoff k, identify as poor if c i > k (Ex: k = 2) Domains c Persons Note Includes both union and intersection

27. Identification – Dual Cutoff Approach Q/ Who is poor? A/ Fix cutoff k, identify as poor if c i > k (Ex: k = 2) Domains c Persons Note Includes both union and intersection Especially useful when number of dimensions is large Union becomes too large, intersection too small

28. Identification – Dual Cutoff Approach Q/ Who is poor? A/ Fix cutoff k, identify as poor if c i > k (Ex: k = 2) Domains c Persons Note Includes both union and intersection Especially useful when number of dimensions is large Union becomes too large, intersection too small Next step How to aggregate into an overall measure of poverty

29. Aggregation Domains c Persons

30. Aggregation Censor data of nonpoor Domains c Persons

31. Aggregation Censor data of nonpoor Domains c(k) Persons

32. Aggregation Censor data of nonpoor Domains c(k) Persons Similarly for g 1 (k), etc

33. Aggregation – Headcount Ratio Domains c(k) Persons

34. Aggregation – Headcount Ratio Domains c(k) Persons Two poor persons out of four: H = 1/2

35. Critique Suppose the number of deprivations rises for person 2 Domains c(k) Persons Two poor persons out of four: H = 1/2

36. Critique Suppose the number of deprivations rises for person 2 Domains c(k) Persons Two poor persons out of four: H = 1/2

37. Critique Suppose the number of deprivations rises for person 2 Domains c(k) Persons Two poor persons out of four: H = 1/2 No change!

38. Critique Suppose the number of deprivations rises for person 2 Domains c(k) Persons Two poor persons out of four: H = 1/2 No change! Violates ‘dimensional monotonicity’

39. Aggregation Return to the original matrix Domains c(k) Persons

40. Aggregation Return to the original matrix Domains c(k) Persons

41. Aggregation Need to augment information Domains c(k) Persons

42. Aggregation Need to augment information deprivation shares among poor Domains c(k) c(k)/d Persons

43. Aggregation Need to augment information deprivation shares among poor Domains c(k) c(k)/d Persons A = average deprivation share among poor = 3/4

44. Aggregation – Adjusted Headcount Ratio Adjusted Headcount Ratio = M 0 = HA Domains c(k) c(k)/d Persons A = average deprivation share among poor = 3/4

45. Aggregation – Adjusted Headcount Ratio Adjusted Headcount Ratio = M 0 = HA =  (g 0 (k)) Domains c(k) c(k)/d Persons A = average deprivation share among poor = 3/4

46. Aggregation – Adjusted Headcount Ratio Adjusted Headcount Ratio = M 0 = HA =  (g 0 (k)) = 6/16 =.375 Domains c(k) c(k)/d Persons A = average deprivation share among poor = 3/4

47. Aggregation – Adjusted Headcount Ratio Adjusted Headcount Ratio = M 0 = HA =  (g 0 (k)) = 6/16 =.375 Domains c(k) c(k)/d Persons A = average deprivation share among poor = 3/4 Note: if person 2 has an additional deprivation, M 0 rises

48. Aggregation – Adjusted Headcount Ratio Adjusted Headcount Ratio = M 0 = HA =  (g 0 (k)) = 6/16 =.375 Domains c(k) c(k)/d Persons A = average deprivation share among poor = 3/4 Note: if person 2 has an additional deprivation, M 0 rises Satisfies dimensional monotonicity

49. Aggregation – Adjusted Headcount Ratio Observations Uses ordinal data Similar to traditional gap P 1 = HI HI = per capita poverty gap = total income gap of poor/total pop HA = per capita deprivation = total deprivations of poor/total pop Decomposable across dimensions M 0 =  j H j /d Axioms Characterization via freedom Note: If cardinal variables, can go further

50. Aggregation: Adjusted Poverty Gap Can augment information of M 0 Use normalized gaps Domains Persons

51. Aggregation: Adjusted Poverty Gap Need to augment information of M 0 Use normalized gaps Domains Persons Average gap across all deprived dimensions of the poor: G 

52. Aggregation: Adjusted Poverty Gap Adjusted Poverty Gap = M 1 = M 0 G = HAG Domains Persons Average gap across all deprived dimensions of the poor: G 

53. Aggregation: Adjusted Poverty Gap Adjusted Poverty Gap = M 1 = M 0 G = HAG =  (g 1 (k)) Domains Persons Average gap across all deprived dimensions of the poor: G 

54. Aggregation: Adjusted Poverty Gap Adjusted Poverty Gap = M 1 = M 0 G = HAG =  (g 1 (k)) Domains Persons Obviously, if in a deprived dimension, a poor person becomes even more deprived, then M 1 will rise.

55. Aggregation: Adjusted Poverty Gap Adjusted Poverty Gap = M 1 = M 0 G = HAG =  (g 1 (k)) Domains Persons Obviously, if in a deprived dimension, a poor person becomes even more deprived, then M 1 will rise. Satisfies monotonicity

56. Aggregation: Adjusted FGT Consider the matrix of squared gaps Domains Persons

57. Aggregation: Adjusted FGT Consider the matrix of squared gaps Domains Persons

58. Aggregation: Adjusted FGT Adjusted FGT is M  =  (g  (k)) Domains Persons

59. Aggregation: Adjusted FGT Adjusted FGT is M  =  (g  (k)) Domains Persons Satisfies transfer axiom

60. Aggregation: Adjusted FGT Family Adjusted FGT is M  =  (g  (  )) for  > 0 Domains Persons Satisfies numerous properties including decomposability, and dimension monotonicity, monotonicity (for  > 0), transfer (for  > 1).

61. Extension Modifying for weights Weighted identification Weight on income: 50% Weight on education, health: 25% Cutoff = 0.50 Poor if income poor, or suffer two or more deprivations Cutoff = 0.60 Poor if income poor and suffer one or more other deprivations Nolan, Brian and Christopher T. Whelan, Resources, Deprivation and Poverty, 1996 Weighted aggregation

62. Next Applications Sub-Saharan Africa Latin America China India Bhutan Questions?