Date of Award

Spring 2006

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Computational Analysis and Modeling

First Advisor

Raja Nassar

Second Advisor

Ricardas Zitikis

Abstract

In this dissertation we develop statistical inference for the Atkinson index, one of the measures of inequality used in studying economic inequality.

Specifically, we construct empirical estimators for the Atkinson index, both in the parametric and nonparametric case, and derive formulas for the asymptotic variances for the estimators. These statistics are used for testing hypothesis and constructing confidence intervals for the Atkinson index. We test the validity and the robustness of the asymptotic theory, by simulations (using R, a language and environment for statistical computing and graphics), in the case of one and two populations. In addition to proving asymptotic normality for the theory, we develop a nonparametric bootstrap theory, as an alternative to the asymptotic theory, and present some of the advantages for this method.

It is natural, when studying income inequality, to analyze the distributions of the data sets and make statistical inference about various parameters of interest, such as means, medians, variances, etc. In trying to condense the information into a few parameters, one certainly faces a problem of constructing measures or indices that would give a proper idea about what happens in the society under consideration. The mean, as a statistical measures of distribution is useful in some instances, but not particularly relevant when, for example, we have outhers and/or skewed distributions. In addition, the mean does not tell us if inequality changes by transfers of wealth from the rich to the poor or from the poor to the rich. Hence, the need for constructing measures with various properties like transfer sensitivity, scale and/or location invariance.

Indeed, some measures, like the Gini index, are not sensitive to the transfers at the lower and upper ends of the distribution, whereas other measures like the Atkinson index are more sensitive to such transfers. In this dissertation we have chosen to work with the Atkinson index because of its econometric properties described in Chapter 1 and the lack of inferential statistics results in the literature pertaining to this index.

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