Poverty measurement

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Poverty measurement

• Michael Lokshin,
• DECRG-PO
• The World Bank

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Properties and Robustness

• Questions for the analyst
• 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 a
  measure of poverty?
• How robust are the answers?

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Three components of poverty analysis
Welfare Indicators
Poverty Lines
Poverty Analysis
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Adding up poverty Headcount

• q no. people deemed poor
• n population size
• Advantage 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. HA 0.75 HBHC

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Adding up poverty Headcount
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Adding up poverty Poverty Gap
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. HA 0.75 HB PGA 0.25
PGB.
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Adding up poverty Poverty Gap
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Adding up poverty Poverty Gap

• The minimum cost of eliminating poverty (Z-?z)q
  -- Perfect targeting.
• The maximum cost of eliminating poverty Zq --
  No targeting.
• Ratio of minimum cost of eliminating poverty to
  the maximum cost with no targeting
• Poverty gap -- potential saving to the poverty
  alleviation budget from targeting.

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Adding up povertySquared 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
• Advantage of SPG sensitive to differences in
• both depth and severity of poverty.
• Hits the point of poverty line smoothly.
• Disadvantage difficult to interpret
• Example A (1, 2, 3, 4) B (2, 2, 2, 4)
• z 3 SPGA 0.14 SPGB 0.08
• HAHB, PGAPGB but SPGAgtSPGB

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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. Range
Rawls welfare function maximize the welfare of
society's worse-off member.
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Adding up poverty FGT-measures
Derivatives
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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.
• If 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.

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Adding up poverty Example 1

• Example Effect of the change in price of
  domestically produced goods on welfare.
• Price of rice in Indonesia
• Many poor households are net rice producers, the
  poorest households are landless laborers and net
  consumers of rise.
• 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 gt HB yet SPGA lt SPGB
• Which policy would you choose?

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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

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Social Welfare function

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

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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 poverty comparison results change if we
  make alternative assumptions?

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Robustness Poverty incidence curve

• 1. The poverty incidence curve
• Each point represents a headcont 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 curve

• The 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.

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Robustness Poverty severity curve

• The poverty severity curve area under poverty
  depth curve
• Each point gives the squared poverty gap.

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Robustness Formulas

• Poverty incidence curve
• Poverty deficit curve
• Poverty severity curve

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Robustness First Order Dominance Test

• If the poverty incidence curve for the A
  distribution 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 Test

• What if the poverty incidence curves intersect?
  --
• Ambiguous poverty ranking.
• You can either
• i) restrict range of poverty lines ii) restrict
  class of poverty measures

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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).
• e.g., Higher rice prices in Indonesia very poor
  lose, those near the poverty line gain.
• What if poverty deficit curves intersect?

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Robustness Third Order Dominance Test

• If the poverty severity curve for 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

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Robustness Examples

• Initial state (1,2,3)
• (2,2,3) (1,2,4) unambiguously lower poverty
• (2,2,2) poverty incidence curves cross.
• compare z1.9 and z2.1
• poverty deficit curves do not cross
• Thus poverty has fallen for all distribution
  sensitive measures.
• Example 2
• Initial State A (1,2,3) Final State B
  (1.5,1.5,2)

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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

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Robustness Egypt, poverty changes between 1996
and 2000
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Poverty profiles Additivity

• How poverty varies across sub-groups of society.
  Useful to access how the sectoral or regional
  patterns of economic change are likely to affect
  aggregate poverty.
• Additive poverty measures (e.g., FGT class).
• Suppose population is divided into m mutually
  exclusive sub-groups.
• The poverty profile is the list of poverty
  measures Pj for j1,,m.
• Aggregate poverty for additive poverty measures
• Aggregate poverty is a population weighted mean
  of the sub-group poverty measures.

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Poverty profiles Example

• Urban population (2,2,3,4)
• Rural population (1,1,1.5,2,4)
• Zu3,Zr2,n9,nu4,nr5,
• Direct way n9 q7 Hq/n0.78

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Poverty profiles Two types

• Two main ways to present poverty profiles
• Type A Incidence of poverty for sub-groups
  defined by some characteristics (e.g., place of
  residence)
• Type B Incidence of characteristics defined by
  the poverty status.

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Poverty profiles

• Select the target region for poverty alleviation.
• Geographic targeting. If one chooses South more
  money will go to poor. So Type A is preferable.
  Minimizes the poverty gap.
• General rule When making the lamp-sum transfers
  with the aim to minimize the aggregate value of
  FGT type of poverty Pa the next unit of money
  should go to the sub-group with the highest value
  of Pa-1.

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Poverty profiles Egypt regions
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Poverty profiles Egypt (Type A)
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Poverty profiles Multivariate

• Univariate Simple cross-tabulation of poverty
  measures against specific variables
• Multivariate Poverty measure is modeled as a
  function of multiple variables or poverty
  regression
• Model household expenditure or income first and
  then predict poverty measures based on this
  regression. Do not run probit on poverty measure
  when expenditure data is available.
• Steps
• Estimate regression Log(Ci)??Xi?I
• Predict consumption E(Ci)Exp(?Xi?2/2)
• Calculate poverty rates based on predicted
  consumption, or
• Calculate probability of being poor, then the
  national headcount index will be equal to
  weighted average of the predicted probability,
  etc. Simulations.

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Regression of log consumption per capita on
characteristics of household and household head
for seven regions of Egypt.
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Impact of changes in household characteristics on
poverty