Adjusted Jackknife Empirical Likelihood Estimation For S-Gini Indicesy

With the rapid development of economy,the income gap between urban and rural areas in China is expanding.The degree of income inequality and polarization are becoming increasingly serious.Income inequality is also one of the root causes of other inequalities.Therefore,the research on the indicators of income inequality not only makes people better understand the situation of national income,but also helps the government to make economic policies.Gini coefficient is a commonly used measure of income inequality.As an important indicator of income distribution,it has an important guiding significance for national macro-control.Single series Gini coefficient is the extension of Gini coefficient,including all the advantages of Gini coefficient.N.Sreelaksshmi et al.(2019)used jackknife empirical likelihood method to construct confidence interval of single series Gini coefficients and make hypothesis test.Considering the complexity of jackknife's empirical likelihood method and the possibility that the solution does not exist,this paper discusses the confidence interval estimation problem of single series Gini coefficients by adjusting jackknife's empirical likelihood method.Firstly,this paper estimates the confidence interval of single series Gini coefficients by adjusting empirical likelihood and jackknife empirical likelihood respectively,and gives the statistical properties of the estimators in theory.Secondly,the performance of the method is compared by Monte Carlo simulation.Finally,the empirical analysis is carried out by adjusting jackknife's empirical likelihood method.The results show that the confidence intervals constructed by adjusting the empirical likelihood method of jackknife have similar properties in theory.The simulation results show that the confidence intervals constructed by adjusting the empirical likelihood method of jackknife have higher coverage.In addition,the calculation of adjusted jackknife empirical likelihood method is relatively simple,and the existence of the solution is guaranteed.In a small sample,the performance of adjusted jackknife empirical likelihood method is slightly better than that of adjusted empirical likelihood method.