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Providing reliable inference on inequality measures is an enduring challenge, mainly due to the complications arising from nonlinearities in their definitions and from the complex nature of the underlying distributions which are typically characterized by extremely heavy tails. The thesis is concerned with proposing non-standard asymptotic and simulation-based inference procedures for moment-based inequality measures (general entropy family of inequality indices) and quantile-based measures (quantile ratio index). Inference on both types of measures is prone to heavy-tailed distributions complications and to the ratio-induced identification issues. In addition to that, moment-based measures are subject to the so-called Bahadur-Savage impossibility problem while quantile-based measures are not. On the other hand, the main difficulty with inference on quantile-based measures is the dependence of the quantile variance on the underlying density function which involves kernel estimation and bandwidth selection. The first chapter of my thesis introduces a Fieller-type method for the Theil Index and assess its finite-sample properties by a Monte Carlo simulation study. The fact that almost all inequality indices can be written as a ratio of functions of moments First and foremost, I would like to thank my supervisor Lynda Khalaf for her patience, trust, motivation, immense knowledge, and invaluable support; a better supervisor and mentor for my doctoral studies would be hard to find. I have benefited tremendously from Lynda's wisdom and guidance and I consider it a privilege to have worked under her supervision. I would also like to thank Jean-Marie Dufour (McGill University) and Emmanuel Flachaire (Aix-Marseille University) for their guidance with the first two chapters. Working with them has helped me sharpen my research skills and enrich my knowledge of econometrics and income inequality.

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