A Comparative Study Of A Class Of Inequality Index Measures Related To Lorenz Curve

With the rapid development of the economy,there will be associated with a series of economic problems.The phenomenon of inequality has been the focus of economists,its existence is the root cause of economic,social,and even political problems,so countries have been embarking on inequality research.Foreign research on inequality has long been a mature method theory,but our current literature on inequality index method still stays in the traditional index such as Gini coefficient and Theil index.In order to break through this obstacle,this paper introduces a sort of inequality measure indices related to the Lorenz curve and has excellent properties:Bonferroni index(referred to as B index),De Vergottini index(referred to as V index),Zenga index(referred to as Z index)and the Canberra Index(referred to as C index).Combined with the traditional Gini coefficient,this paper reveals the correlation between these indices,and explores the relationship between these indices.In order to gain a better understanding of the differences in the indices,the paper makes measures difference analysis based on the household per capita income data in the CFPS microdata.In this paper,the inequality index related to the Lorentz curve is introduced systematically for the first time.The construction theory of each index,the definition of inequality curve and some properties of the inequality index are sorted out by literature research.On the basis of this,by the method of combining the theoretical derivation and the empirical analysis,I reveal the correlation between the indexes,make a comparative analysis of the properties of each index,and explain the measure differences of these inequality indices.The innovation of this paper mainly explores the relationship between the difference of the inequality measure level,the difference of the inequality dynamic change measure and the difference of the inequality decomposition measure through the combination of theoretical analysis and empirical analysis.From the difference of the inequality measure,I find that different inequality index has different structure,thus the result of the measurement will be different.Through the constructing idea ofthe index shows that there is a quantity relationship: Gini(7)C(8)?B ?Z ?V.The Gini coefficient is more sensitive to the middle and high income groups.The B and C indices are more sensitive to the low-income groups,and the V-index is more sensitive to the high-income groups.While the Z-index is equally concerned with high-income groups and low-income groups.For the difference of inequality decomposition measure,the difference is analyzed from the difference between the thoroughness of the index decomposition and the decomposition method.From the thoroughness of the index decomposition,only the Z index has the additive decomposability,which can be decomposed thoroughly.While other indices' decomposition are not clean,which will produce unexplained residues and lead to the ambiguous policy guidance.In addition,only the Z-index has the uniqueness of joint decomposition by sources and subpopulations.From the difference of each index decomposition method,it is possible to reduce the unequal contribution between groups by only weighting the income share of each group.If we use the population weight of each group,the contribution of inequality between groups will be increased.In addition,it may be the opposite result by using the share weight and the population weight.Finally,according to the difference analysis of each index,we get some suggestions on the selection of inequality index and its methods,and analyze the shortcomings of this paper.