Work Migration and Poverty Reduction in Nepal

Zurab SajaiaDECPIThe World BankPoverty measures:Properties and Robustness1

ABD

EF

C2Properties and RobustnessHow 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?33Three components of poverty analysisWelfare

IndicatorsPoverty

LinesPoverty

Analysis44Adding up poverty: Headcount5where q - number of people deemed poor N - population size

Advantages: easily understoodDisadvantages: insensitive to distribution below the poverty line e.g., if poor person becomes poorer, nothing happens to HExample: 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)

5Adding up poverty: Sharp povertyLow Elasticity of poverty head count with respect to the changes in poverty linePoverty line 1q20 Ranked Households nIncomeq1Poverty line 266Poverty line 1q20 Ranked Households nIncomeq1Poverty line 27Adding up poverty: Shallow povertyHigh Elasticity of poverty head count with respect to the changes in poverty line7Changes in poverty when the average consumption increases8IncomePoverty line0 Ranked Households nq1q2Changes in poverty when the consumption distribution changes9IncomePoverty line0 Ranked Households nq

Adding up poverty: Headcount10IncomePoverty line0 Ranked Households nqAdding up poverty: Poverty Gap Ratio11Advantages of PG: reflects depth of povertyDisadvantages: insensitive to severity of povertyExample: 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 Gap12IncomePoverty line0 Ranked Households nqAdding up poverty: Poverty GapThe minimum cost of eliminating poverty: (Z - z)*q -- Perfect targetingThe maximum cost of eliminating poverty: (Z*n) -- No targetingRatio 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

1313Adding up poverty: Squared Poverty GapWeek Transfer Principal: A transfer of income from any person belowthe 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 smoothlyDisadvantages: difficult to interpretExample: A = (1, 2, 3, 4) B = (2, 2, 2, 4)z = 3 SPGA = 0.14; SPGB = 0.08HA=HB, PGA=PGB but SPGA>SPGB

1414Adding up poverty: FGT-measures

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

1515Adding up poverty: FGT-measures

Derivatives0 Consumption or income z1P0P1P21616Range of FGT Measures:

Rawlss 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).

Adding up poverty: FGT-measures

1717Social Welfare function18Utilitarian Social Welfare FunctionSocial states are ranked according to linear sum of individual utilities:

We can assign weight to each individuals utility:

Inclusive and Exclusive Social Welfare Functions

Adding up poverty: RecommendationsDoes 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. 1919Adding up poverty: Example 1 Effect of a change in price of domestically produced goods on welfarePrice 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?2020Adding up poverty: Example 2Poverty line = 6Initial 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 $6Case 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)= 0.07Case 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)= 0.112121Robustness of poverty comparisonsWhy should we worry?Errors in living standard dataUncertainty and arbitrariness of the poverty lineUncertainty about how precise is the poverty measureUnknown differences in need for the households with similar consumption levelDifferent 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?2222Robustness: Poverty incidence curveEach 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.

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Robustness: Poverty depth curvePoverty 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.2424

Robustness: Poverty severity curvePoverty severity curve = area under poverty depth curve

Each point gives the squared poverty gap.2525Robustness: First Order Dominance TestIf 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

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Robustness: First Order Dominance TestWhat if the poverty incidence curves intersect? Ambiguous poverty ranking

What can you do?restrict range of poverty lines restrict class of poverty measures2727Robustness: Second Order Dominance TestIf 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? 2828

Poverty deficitRobustness: Third Order Dominance TestIf 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 2929Robustness: RecommendationsFirst 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 3030