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Handbook of Income Distribution by Francois Bourguignon, Anthony B. Atkinson

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6.4.4 Application: Poverty Measures

For a poverty index, we need a poverty line that may be an exogenously given constant ζ or may depend on the income distribution ζ(F). An important class of poverty indices can then be described in the following way:

PF:=py,ζFdFy

si209_e  (6.78)

where p is a poverty evaluation function that is nonincreasing in y and takes the value zero for y ≥ ζ(F). Once again we need the IF, which is given by

IFzPF=pz,ζFPF+pζyζdFyIFzζF

si210_e  (6.79)

where pζ is the differential of p with respect to its second argument (Cowell and Victoria-Feser, ...

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