The thesis presents results from five related studies concerned with the development and application of analytical techniques for the measurement of inequality. Four of the research pieces are analytical works focusing on the methodology of inequality measurement, while the fifth is an empirical study of income mobility and inequality in Australia. The most significant work of the dissertation is concerned with the derivation of a new information-theoretic index for the measurement of inequality. The proposed index is based upon the same relationship between information theory and inequality measurement used for the construction of Generalized Entropy (GE) inequality measures and is equivalent to a technique established in the field of signal processing. The measure shares the axiomatic superiority of GE measures over other measurement techniques and exhibits an additional attractive decomposition property such that the contribution of any set of individuals towards inequality is directly observable. No existing axiomatically complete measure possesses this property and thus the new measure has a degree of dominance over other techniques such as the Gini coefficient and Theil’s entropy measures. An empirical illustration of the new index using U.S. unit record income data is provided to demonstrate the alternative decomposition technique. It is shown that persons self-described as ‘White’ or ‘Japanese’ in the U.S. census drive a greater proportion of total inequality than persons from other racial groups relative to their respective population sizes. Other theoretical work in the thesis focuses on the construction and interpretation of Lorenz curves. A new parametric functional form for estimating the Lorenz curve is presented and closed form expressions for the implicit probability density function, cumulative distribution function and Gini coefficient are derived. Furthermore the proposed Lorenz curve is shown to provide a better fit to a range of real world data than other single parameter specifications such as the Pareto formulation. In a separate chapter the issue of Lorenz curve determination is addressed by determining a convex spline to interpolate Lorenz curves from grouped data. The spline is shown to provide better estimates of the Gini coefficient than other interpolation techniques and always satisfies the regularity conditions required for a Lorenz curve. Additional work on Lorenz curves examines the link between these functions and GE inequality metrics. In the thesis it is shown that these indices may be derived as direct functions of the Lorenz curve and analytical expressions for various GE measures are given in terms of Lorenz curve parameters. These results provide a basis for studying the effect of Lorenz curve construction upon the calculation of entropy based inequality measurements. The thesis concludes with an empirical study into income inequality and mobility in Australia using the HILDA unit record and household data panel. The research shows that Australian income mobility is slightly lower than in other developed countries and that much of the observed mobility occurs at the lower end of the income distribution.
| Identifer | oai:union.ndltd.org:ADTP/287481 |
| Creators | Nicholas Rohde |
| Source Sets | Australiasian Digital Theses Program |
| Detected Language | English |
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