Quantile Ratio Index

Abstract

This bachelor thesis is devoted to the analysis and comparison of the traditional Gini index and the modern quantile ratio index as the income inequality measures. The main objective of this thesis is to investigate the statistical properties of the quantile ratio index and the robustness of its estimator to extreme values. In the theoretical part, an asymptotic variance estimator for the quantile ratio index and its corresponding asymptotic Wald-type confidence intervals are derived. The simulation study demonstrates the stability of the quantile ratio index for heavy-tailed distri- butions, such as Pareto(1), where the Gini index often fails. The application to selected real-world wage data confirms the robustness of the quantile ratio index estimator to extreme values. The results indicate that the quantile ratio index is a reliable alternative to the traditional measures. Therefore, it serves as a valuable and stable tool in economic analysis.

Tato bakala ́r ̌ska ́ pra ́ce se ve ̌nuje analy ́ze a srovna ́nı ́ tradic ̌nı ́ho Giniho indexu a modernı ́ho indexu podı ́lu ̊ kvantilu ̊ jakoz ̌to me ̌r pr ̌ı ́jmove ́ nerovnosti. Hlavnı ́m cı ́lem pra ́ce je prozkoumat sta- tisticke ́ vlastnosti indexu podı ́lu ̊ kvantilu ̊ a robustnost jeho odhadu vu ̊c ̌i extre ́mnı ́m hodnota ́m. V teoreticke ́ c ̌a 'sti jsou odvozeny odhad asymptoticke ́ho rozptylu pro vy ́be ̌rovy ́ index podı ́lu ̊ kvantilu ̊ a pr ̌ı 'slus ̌ne ́ asymptoticke ́ Waldovy intervaly spolehlivosti. Simulac ̌nı ́ studie demonstruje stabilitu indexu podı ́lu ̊ kvantilu ̊ u rozde ̌lenı ́ s te ̌z ̌ky ́mi chvosty, jako je Pareto(1), kde Giniho index obvykle selha ́va ́. Aplikace na vybrana ́ rea ́lna ́ data mezd potvrzuje odolnost odhadu indexu podı ́lu ̊ kvantilu ̊ vu ̊c ̌i odlehly ́m hodnota ́m. Vy 'sledky naznac ̌ujı ́, z ̌e index podı ́lu ̊ kvantilu ̊ pr ̌edstavuje spolehlivou alternativu k tradic ̌nı ́m mı ́ra ́m. Proto mu ̊z ̌e slouz ̌it jako cenny ́ a stabilnı ́ na 'stroj v ekonomicke ́ analy ́ze.