Poverty measures: Properties and Robustness. Michael Lokshin DECRG-PO The World Bank. 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.
The World Bank
Questions for the analyst:
q = number of people deemed poor
n = population size
Let z = 3. HA = 0.75 = HB=HC;
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.
(Z-z)*q -- Perfect targeting.
both depth and severity of poverty.
Hits the point of poverty line smoothly.
z = 3 SPGA = 0.14; SPGB = 0.08
HA=HB, PGA=PGB but SPGA>SPGB
Additivity: the aggregate poverty is equal to population- weighted sum of poverty level in the various sub-groups of society.
Rawls welfare function: maximize the welfare of society's worse-off member.
Depends on whether the relative inequalities have changed across the situations being compared.
If no changes in inequality, no change in ranking.
HC: = 0.50
Poverty gap: (5/6,4/6,3/6,2/6,1/6,0) = 0.25
SPG: (25/36,…,0) = 0.16
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
HC = 0.20
PG: (5/6,4/6,0,…,0) = 0.15
SPG: (25/36,16/36,0,…,0) = 0.11
We can assign weight to each individual’s utility:
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
Ambiguous poverty ranking.
i) restrict range of poverty lines ii) restrict class of poverty measures
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.
(2,2,2) poverty incidence curves cross.
compare z=1.9 and z=2.1
poverty deficit curves do not cross
Thus poverty has fallen for all distribution sensitive measures.
Initial State A: (1,2,3) Final State B: (1.5,1.5,2)