The Yitzhaki index of relative deprivation mathematically relates to the Gini index of income inequality. If we scale the Yitzhaki score to 0-1, then the average Yitzhaki = Gini. So is it possible to estimate a “synthetic” Yitzhaki score for an individual in a survey when the only variables available are: (1) individual income, (2) average income of the individual’s neighbourhood, and (3) Gini index of the neighbourhood. I cannot calculate the Yitzhaki in the normal way because I haven’t done a census. Any help would be appreciated. thanks
I think that you can calculate a Yizhaki index of relative neighborhood deprivation by multiplying the individual income for the Gini coefficient of her or his neighborhood. You can also calculate a general index by multiplying the individual's income by the Gini coefficient of the whole population, which you can estimate, even without a census, from the sample you have, if this is not biased or drawn from a subpopulation. Of course, in both cases, the statistical precision of the estimates will depend on the characteristics of the sample.
Relative deprivation of a person depends on her reference group. By an appropriate assumption on the reference group structure, the RD can be zero. See my European Economic Review (1982) entitled "Relative deprivation and Economic Welfare".
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