Can anyone show me how the squared poverty gap index can be rewritten as H/n*[u2+(1-u2)CV2)] as in the picture. Step by step please. I have been struggling trying to figure out how to decompose it. Thank you very much.
Dear Vatana
Start with the Foster-Greer-Thorbecke poverty index (FGT).
Setting alpha =0 yields the headcount index: H/Q
Then set alpha =1 to get the Poverty gap ratio.
Then Calculate the coefficient of variations ratio.
Combine the three above to get the formula.
See the referenced article equations (1-6) on the web. https://pdfs.semanticscholar.org/bb94/670e621ac12ffcfab32b91044913cfaac87b.pdf
I attach the file:
It is easy get expressions for the relative poverty gap but you can gat expressions for inco ti self. See the PDF
The previous file has a small error, replace it with the new one attached.
Elena Bárcena-Martín but how can we get from
= 𝐻 𝜇2[1 + 𝐶𝑣2]
to [\mu^2 + (1-\mu) CV]?
Look at the final part of Leonardo Oliveira result. You must use the fact that 𝑣𝑎𝑟(𝑟)=𝑣𝑎𝑟[(𝑧−𝑦)/𝑧]=𝑣𝑎𝑟(𝑦)/z^2,
Look to the final part of the pdf:
Oliveira (2020) formula FGT(2) com desigualdade 2.pdf
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