lecture7_Sept26_slides

lecture7_Sept26_slides - Income Distribution Among the Poor...

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Income Distribution Among the Poor September 26, 2011 1
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Income Distribution Among the Poor n Poverty Rate n In all formulas: z = poverty line yi = family income of each individual n Notice the Indicator Function = < = N i i o z y I N P 1 ) ( 1 z y z y I z y z y I i i i i = < < = < if 0 ) ( if 1 ) (
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Calculate the poverty rate 3
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Original I ncome Distribution i y i I(y i  <= z) 1 $10 1 2 $20 1 3 $30 1 4 $40 1 5 $50 0 6 $60 0 7 $70 0 8 $80 0 9 $90 0 10 $100 0 Sum 4 Poverty rate 40% Poverty gap Depth of poverty Severity of poverty Calculating the Rate, Depth, and Severity of  Poverty (assume poverty thredhold = $45)
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Income Distribution Among the Poor n Limitations of the poverty rate? YES/NO indicator only Doesn t account for income increases, unless they are  large enough to raise a household above the poverty line.
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poverty measure 6
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Income Distribution Among the Poor n Poverty gap *Poverty gap explained: Amount of income necessary to raise  the income of everybody in poverty up to the poverty line  ( 29 = < - N i i i z y I y z 1 ) (
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n Poverty gap n Depth of poverty Income Distribution Among the Poor = < - = N i i i z y I z y z N P 1 1 ) ( 1 ( 29 = < - N i i i z y I y z 1 ) (
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Original I ncome Distribution i y i I(y i  <= z) (z - y i ) (z - y i )/z 1 $10 1 $35 0.78 2 $20 1 $25 0.56 3 $30 1 $15 0.33 4 $40 1 $5 0.11 5 $50 0 6 $60 0 7 $70 0 8 $80 0 9 $90 0 10 $100 0 Sum 4 $80 1.78 Poverty rate 40% Poverty gap $80 Depth of poverty 0.178 Severity of poverty
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Calculate the severity  of poverty measure 10
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Income Distribution Among the Poor n Severity of poverty P 2 = 1 N z - y i z ÷ 2 I ( y i < z ) i = 1 N
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Original I ncome Distribution i y i I(y i  <= z) (z - y i ) (z - y i )/z ((z - yi)/z) 2 1 $10 1 $35 0.78 0.61 2 $20 1 $25 0.56 0.31 3 $30 1 $15 0.33 0.11 4 $40 1 $5 0.11 0.01 5 $50 0 6 $60 0 7 $70 0 8 $80 0 9 $90 0 10 $100 0 Sum 4 $80 1.78 1.04 Poverty rate 40% Poverty gap $80 Depth of poverty .178 Severity of poverty .104
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Income Distribution Among the Poor n FGT Poverty measures (the general equation) n Poverty rate:   = 0 α n Depth of poverty:   = 1 α n Severity of poverty:   = 2 α n Called the Foster Greer Thorbecke (FGT) poverty  measures = < - = N i i i z y I z y z N P 1 ) ( 1 α
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n A characteristic of “good” poverty measures is that a  transfer from a person not in poverty to somebody in  poverty reduces the poverty rate … n What happens using each of these three measures? n
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lecture7_Sept26_slides - Income Distribution Among the Poor...

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