Poverty measures: Properties and Robustness

1. Poverty measures:Properties and Robustness ZurabSajaia DECPI The World Bank

2. A B D C F E

3. Properties and Robustness • How do we measure “welfare”? • Individual measures of well-being • When do we say someone is "poor"? • Poverty lines • How do we aggregate data on welfare into measures of “poverty”? • How robust are these measures?

4. Three components of poverty analysis Welfare Indicators Poverty Lines Poverty Analysis

5. Adding up poverty: Headcount where q - number of people deemed poor N - population size • Advantages: easily understood • Disadvantages: insensitive to distribution below the poverty line e.g., if poor person becomes poorer, nothing happens to H • Example: A: (1, 2, 3, 4) B: (2, 2, 2, 4) C: (1,1,1,4) Let z = 3.0 HA = 0.75 = HB=HC; Table 2.1(P0)

6. Adding up poverty: Sharp povertyLow Elasticity of poverty head count with respect to the changes in poverty line Income Poverty line 2 Poverty line 1 0 Ranked Households n q1 q2

7. Adding up poverty: Shallow povertyHigh Elasticity of poverty head count with respect to the changes in poverty line Income Poverty line 2 Poverty line 1 0 Ranked Households n q1 q2

8. Changes in poverty when the average consumption increases Income Poverty line 0 Ranked Households n q2 q1

9. Changes in poverty when the consumption distribution changes Income Poverty line q 0 Ranked Households n

10. Adding up poverty: Headcount Income Poverty line 0 Ranked Households n q

11. Adding up poverty: Poverty Gap Ratio • Advantages of PG: reflects depth of poverty • Disadvantages: insensitive to severity of poverty • Example: A: (1, 2, 3, 4) B: (2, 2, 2, 4) Let z = 3.0 HA = 0.75 = HB; PGA = 0.25 = PGB Table 2.1(P1)

12. Adding up poverty: Poverty Gap Income Poverty line 0 Ranked Households n q

13. Adding up poverty: Poverty Gap • The minimum cost of eliminating poverty: (Z - z)*q-- Perfect targeting • The maximum cost of eliminating poverty: (Z*n)-- No targeting • Ratio of the minimum cost of eliminating poverty to the maximum cost with no targeting: • Poverty gap - potential saving to the poverty alleviation budget from targeting

14. Adding up poverty: Squared Poverty Gap Week Transfer Principal:A transfer of income from any person below the poverty line to anyone less poor, while keeping the set of poor unchanged, must raise poverty • Advantagesof SPG: • sensitive to differences in both depth and severity of poverty • hits the point of poverty line smoothly • Disadvantages: difficult to interpret • Example: A = (1, 2, 3, 4) B = (2, 2, 2, 4) z = 3 SPGA = 0.14; SPGB = 0.08 HA=HB, PGA=PGB but SPGA>SPGB

15. Adding up poverty: FGT-measures Additivity: the aggregate poverty is equal to population- weighted sum of poverty level in the various sub-groups of society.

16. Adding up poverty: FGT-measures P0 1 P1 P2 0 Consumption or income z Derivatives

17. Adding up poverty: FGT-measures Range of FGT Measures: Rawls’s welfare function: maximize the welfare of society's worse-off member Social and economic inequalities are to be arranged ... to the greatest benefit of the least advantaged... (Theory of Justice, pages 302-302).

18. Social Welfare function • Utilitarian Social Welfare Function • Social states are ranked according to linear sum of individual utilities: • We can assign weight to each individual’s utility: • Inclusive and Exclusive Social Welfare Functions

19. Adding up poverty: Recommendations • Does it matter in poverty comparisons what measure to use? • Depends on whether the relative inequalities have changed across the situations being compared. No changes in inequality, no change in ranking. • Recommendations: • Always be wary of using only H or PG; check SPG. • A policy conclusion that is only valid for H may be quite unacceptable.

20. Adding up poverty: Example 1 Effect of a change in price of domestically produced goods on welfare Price of rice in Indonesia: • Many poor households are net rice producers • Poorest households are landless laborers and net consumers of rice • Policy A: Decrease in price of rice.Small loss to person at poverty line, but poorest gains • Policy B: Increase in price.Poorest loses, but small gain to person at poverty line • So HA > HB yet SPGA < SPGB • Which policy would you choose?

21. Adding up poverty: Example 2 • Poverty line = 6 • Initial distribution: (1,2,3,4,5,6,7,8,9,10) HC: = 0.50 Poverty gap: (5/6, 4/6, 3/6, 2/6, 1/6, 0) = 0.25 SPG: (25/36,…,0) = 0.16 • Poverty Alleviation Budget $6 • Case 1: (6,3,3,4,5,6,7,8,9,10) HC = 0.40 PG: (0,3/6,3/6,2/6,1/6,0..0) = 0.15 SPG: (0,9/36,9/36,4/36,1/36,0..0) = 0.07 • Case 2: (1,2,6,6,6,6,7,8,9,10) HC = 0.20 PG: (5/6,4/6,0,…,0) = 0.15 SPG: (25/36,16/36,0,…,0) = 0.11

22. Robustness of poverty comparisons • Why should we worry? • Errors in living standard data • Uncertainty and arbitrariness of the poverty line • Uncertainty about how precise is the poverty measure • Unknown differences in need for the households with similar consumption level • Different poverty lines that are completely reasonable and defensible • How robust are our poverty comparisons? • Would the results of poverty comparisons change if we make alternative assumptions?

23. Robustness: Poverty incidence curve • Each point represents a headcount for each possible poverty line • Each point gives the % of the population deemed poor if the point on the horizontal axis is the poverty line.

24. Robustness: Poverty depth curve Poverty depth curve = area under poverty incidence curve • Each point on this curve gives aggregate poverty gap – the poverty gap index times the poverty line z.

25. Robustness: Poverty severity curve Poverty severity curve = area under poverty depth curve • Each point gives the squared poverty gap.

26. Robustness: First Order Dominance Test If the poverty incidence curve for distribution A is above that for B for all poverty lines up to zmax then there is more poverty in A than B for all poverty measures and all poverty lines up to zmax

27. Robustness: First Order Dominance Test • What if the poverty incidence curves intersect? • Ambiguous poverty ranking • What can you do? • restrict range of poverty lines • restrict class of poverty measures

28. Robustness: Second Order Dominance Test If the poverty deficit curve for A is above that for B up to zmax then there is more poverty in A for all poverty measures which are strictly decreasing and weakly convex in consumptions of the poor (e.g. PG and SPG; not H). • Higher rice prices in Indonesia: very poor lose, those near the poverty line gain • What if poverty deficit curves intersect?

29. Robustness: Third Order Dominance Test Poverty deficit If the poverty severity curve for distribution A is above that for distribution B then there is more poverty in A, if one restricts attention to distribution sensitive (strictly convex) measures such as SPG. • Formal test for the First Order Dominance • Kolmogorov-Smirnov test

30. Robustness: Recommendations • First construct the poverty incidence curves up to highest admissible poverty line for each distribution • If they do not intersect, then your comparison is unambiguous • If they cross each other then do poverty deficit curves and restrict range of measures accordingly • If they intersect, then do poverty severity curves • If they intersect then claims about which has more poverty are contentious