Poverty measures: Properties and Robustness Zurab Sajaia DECPI The World Bank

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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?

Three components of poverty analysis Welfare Indicators Poverty Lines Poverty Analysis

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)

Adding up poverty: Sharp poverty Low 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

Adding up poverty: Shallow poverty High 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

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

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

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

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)

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

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

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 Advantages of 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

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.

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

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).

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

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.

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?

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

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?

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.

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.

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

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

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

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?

Robustness: Third Order Dominance Test 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 Poverty deficit

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