Measurement Of The Inequality Of Incomes:Further Investigations Of Gini Coefficient

Since China’s reform and opening-up policy introduced in 1978,China’s socialist modernization has achieved great success.In order to keep steady and orderly highspeed economic and social development,the outstanding contradictions and problems accumulated for a long time need to be solved urgently,such as the large income gap between residents and income inequality.It is also of great importance to measure and analyze the inequality in the economy scientifically,to analyze the contribution of factors to the total inequality,which has become the focus of attention and research,and is the most basic and fundamental to solve the inequality phenomenon.Based on the above research background,this thesis uses a combination of literature research,comparative analysis,qualitative analysis and quantitative analysis to study economic inequality indicators systematically.Firstly,the literature is sorted out in terms of both the calculation and application of economic inequality indicators.The development,calculation,decomposition,and applicability of the Gini coefficient and other indicators are reviewed and summarized.Then the Lorenz curves are classified according to the categories of data and the expressions of each category are given.And the formulae of the Gini coefficient are divided into continuous and discrete types and discussed separately.The equivalence of the formulae in each type is also demonstrated.Then the two formulae that are confusing in the existing literatures are distinguished and the related other formulae are corrected.The subgroup decomposition of the Gini coefficient is discussed and the inexact parts of the decomposition formulae is corrected and proved.Secondly,the Gini mean difference and its bounds are studied,generalized and compared on the basis of classical formulae.Finally,based on the theoretical study in the previous parts,a new robust estimation method for location parameter based on Gini coefficient,a new bounds on entropies based on order statistics and Gini’s mean difference are proposed and the income redistribution effect of different property tax schemes are analyzed by simulation analysis and empirical analysis.The main research contents and conclusions are as follows:(1)The studies of income inequality in the economy are a topical issue both at domestic and abroad,and there are numerous researches and empirical analyses on this subject.According to the literature on the measurement of economic inequality,it’s found that the Gini coefficient has excellent economic significance and properties among many indicators due to its generality,totality,relativity and value neutrality,and has become a commonly used method for measuring income gap.This thesis elaborates on the research hotspots such as the calculation,decomposition and application of the Gini coefficient.Then,the definition,calculation and application of other inequality measures such as Lorenz curve,coefficient of variation,generalized entropy index and Atkinson index are summarized.This chapter identifies the direction and ideas for next research.(2)As the Gini coefficient has been developed for more than one century,the formulae for calculating the Gini coefficient have evolved and been given more new meanings.In order to prevent blindness in the choice and use of Gini coefficient,it is essential to summarize and generalize these formulae.To further the study,the Lorenz curves are firstly divided into two categories according to the type of income data and the formulae for each category is given.Then this thesis presents the mathematical relations of Lorenz curves and Gini coefficients and discusses the Gini coefficient formulae for continuous and discrete income distributions,respectively,and then divides the Gini coefficient formula into several equivalent classes,some of which are proposed for the first time.And based on the existing formulae,this thesis points out the defects of the current popular calculation formulae and makes comparative analysis and improvement,discusses the existing decomposition method of Gini coefficient.Some examples also illustrate the corrected formulae are accurate.Finally,the subgroup decomposition formulae of the Gini coefficient are discussed,the formulae drived by relative deprivation theory are rededuced and the equivalence of calculations in the general case is demonstrated.(3)In this chapter the lower and upper bounds for the Gini mean difference for the case of independent and identically distributed random variables based on the information about mean,variance,skewness,and kurtosis of the distribution are obtained.Some relationships between the three dispersion measures in the general case are also discussed.The established results improve some well-known bounds and inequalities.(4)Aiming at the inadequacy of sample mean and sample median,this thesis proposes a new estimation method for location parameter based on Gini coefficient.The results of numerical simulation show that the proposed method is almost unaffected by outliers,more robust than the arithmetic mean.In addition,for application,the thesis presents a new estimate of the national average per capita disposable income from 2018 to 2020,and makes a comparison with published data.(5)Based on the theoretical study of Gini mean difference and order statistics,a new lower and upper bound for cumulative residual entropy and cumulative entropy is proposed in combination with the important indicator entropy,which is to some extent an optimization of the existing bound.(6)The Gini coefficient can also measure the redistribution effect by estimating the income change before and after the property tax policy.First,this thesis analyzes foreign property tax collection,and compares the existing property tax schemes in Shanghai and Chongqing.Then using the database of China household finance survey,this thesis analyzes income redistribution effect of property tax under the different taxation schemes.In particular,the application of "single threshold circuit breaker" on the basis of the different taxation schemes has effectively narrowed the income gap,and the progressivity has become increasingly prominent,which not only expands the collection scope,but also ensures the residents’ payment capacity.According to the empirical results,this thesis puts forward some corresponding suggestions for the further property tax reform.This thesis has several possible innovative points:(1)This thesis can summarize and sort out the existing inequality measures in a comprehensive way,and elaborate on the calculation,development and empirical analysis and application of the commonly used economic inequality measures.A more comprehensive classification of the formulae of the Gini coefficient is discussed.Various proofs are proposed and the mutual deri vability of these formulas under certain conditions is demonstrated in a detailed and systematic manner.(2)This thesis clarifies,distinguishes,and corrects erroneous opinions,inadequate deductions,and formula defects in existing studies.(3)This thesis improves the traditional classical upper and lower bounds of the Gini difference and reduce the limitation of use.Examples demonstrate that the proposed bounds perform much better than the existing ones.(4)This thesis creatively proposes a new robust estimation method for location parameter based on Gini coefficient.The new method is almost unaffected by outliers by simulation analysis and empirical analysis.Moreover,the upper and lower bounds of cumulative residual entropy and cumulative entropy are optimized based on Gini mean difference and order statistics.Finally,this thesis uses Gini coefficient to empirically analyze the income redistribution effect of the different taxation schemes,and introduces the "single threshold circuit breaker",which makes income inequality sharply decline.These analyses demonstrate that Gini coefficient has of high applicability,broad application and great research value in different fields.