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The Asymptotic Theory of the Kakwani Class of Poverty Measures

Volume 8, Number 1 (2009), 54 - 67

The Asymptotic Theory of the Kakwani Class of Poverty Measures

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Abstract

Let Y1,Y2, .... be independent observations of the income variable of some population, with underlying distribution G. Given a poverty line Z, for each n 1, Qn is the number of poor individuals in the population. The Kakwani poverty measure Pkak,n(k) = Qn nFk(Qn) Qnå j=1 (Qn− j+1)k Z−Yj,n Z , where Fk(Qn) = åj=Qn j=1 jk, and Y1,n Y2,n ... Yn,n are the ordered incomes of the individuals of the population, is one of the most important tools for monitoring poverty in Economics. Here, we complete our asymptotic normality theory for poverty measures by a special study for the Kakwani index and for the Sen measure which is Pkak,n(1). The results are positively simulated and data driven examples are also given.