Lorenz curve and gini coefficient relationship help

Ask Gini: How to Measure Inequality - Scientific American

lorenz curve and gini coefficient relationship help

What is the relationship between the Lorenz curve and Gini coefficient? Give some How will having a lower Gini coefficient help with a country's economy?. A higher Gini coefficient expresses higher income inequality within a village. from Comparison of income inequality (Lorenz curve and Gini coefficient) for the four Model of relevant relationships between the valley and the mountains with . crops convenient, and with the aid of the Miyun Reservoir natural conditions. The Gini Coefficient measures the area between the Lorenz curve and the line of Fiscal policy can help redistribute income and reduce inequality through.

Census Bureau usually reports Gini coefficients based on pretax numbers, whereas many calculations for foreign countries use posttax numbers, which often include redistribution of wealth from rich to poor and tend to lower the Gini coefficient. Comparing the pretax number in one country with the posttax number in another is somewhat meaningless.

To understand what the Gini coefficient can and cannot explain, and how to interpret articles about economic inequality, a deeper look at this statistic is required. The Gini coefficient compares the income or wealth distribution of a population to a perfectly equal distribution—in which every citizen of a city or country has equal wealth. To compute the Gini coefficient, economists first find the Lorenz curve for the population. The curve is a graphical representation of the distribution of income or wealth in a society.

The x-axis is the proportion of the population, from lowest to highest income, and the y-axis is the cumulative percentage of income or wealth owned. So the point 0.

lorenz curve and gini coefficient relationship help

The Gini coefficient measures how far the actual Lorenz curve for a society's income or wealth is from the line of equality.

Both the Lorenz curve and the line of equality are plotted on a graph. Then the area between the two graphs is computed. The Gini coefficient is the area between the two graphs divided by the total area under the line of inequality. In the picture at the top right of this article, it is the area of the region labeled A divided by the combined areas for A and B.

lorenz curve and gini coefficient relationship help

This yields a number between 0 and 1, sometimes reported as a percentage—for example, 0. Enter a set of incomes to find out what the Gini coefficient of the group is and what the distribution looks like. Cowell says that the Gini coefficient is useful, particularly because it allows negative values for income and wealth, unlike some other measures of inequality.

  • Ask Gini: How to Measure Inequality
  • Explain what you understand by the Lorenz Curve and Gini Coefficient.
  • Lorenz curve

If some amount of the population has negative wealth owes moneythe Lorenz curve will dip below the x-axis. But the Gini coefficient also has limitations. For one, it takes all the data from the Lorenz curve and converts it to a single number.

Two different income distributions can have the same Gini coefficient, and a lot of information is lost in the conversion to a graph. Typically, they intersect the diagonal line only at the very first and last points. Between those points, the curves are bow-shaped below the degree line. The Lorenz curve of market income falls to the right and below the curve for after-tax income, reflecting its greater inequality.

Both curves fall to the right and below the line of equality, reflecting the inequality in both market income and after-tax income.

CONVERSABLE ECONOMIST: Lorenz curves and Gini coefficients: CBO #3.

The intuition is straightforward although the mathematical formula will look a little messier. On a Lorenz curve, greater equality means that the line based on actual data is closer to the degree line that shows a perfectly equal distribution. Greater inequality means that the line based on actual data will be more "bowed" away from the degree line. The Gini coefficient is based on the area between the degree line and the actual data line.

lorenz curve and gini coefficient relationship help

First, this paper expresses the relationship among the Gini coefficient, poverty ratio, and income mobility of 5 common Distribution Functions through math deduction; this finding cannot be found in relevant literatures. Furthermore, an empirical research result proves that the income distribution of urban residents in the period from to fits Log-Logistic Distribution. On the basis of the above analysis and empirical data, the paper explores the relations of income inequality, poverty, and income mobility of urban residents and draws some useful conclusions.

Introduction With the rapid economic development in China, the degree of residential income inequality has been increasing constantly, which, as well as the consequent poverty and the sluggish income mobility, has been restricting the harmonious and steady development of Chinese society severely.

In recent years, income inequality has been a focus of the whole society, leading to narrowing the income gap, eliminating poverty, and improving income mobility as the major challenge for the future development of China.

Lorenz curve

Hence, it becomes particularly significant to reveal the relationship among income inequality, poverty, and income mobility. Although specialists and scholars at home and abroad have carried on massive analysis on residential income inequality so far, the relationship still needs to be studied due to the restriction of data sources.

Compared with other relevant data sources, samples of National Bureau of Statistics have large amount and wide coverage which can be dated back to the early phase of the reform and opening up, so it is a perfect data source for the analysis of residential income distribution.

However, the National Bureau of Statistics only provides the limited grouped data, which is the average value of a group.

Lorenz Curve and Gini Coefficient - Measures of Income Inequality

Thus, income inequality would be underestimated if we apply it for the analysis of the residential income gap in China for the inequality is neglected. And some research related to Distribution Function provides us with exactly brand new perspectives and analysis tools for discussing these issues above, making up the deficiencies of insufficient data, and facilitating the study further related to income distribution as well as other related areas. The study on the measurement of income concentration ratio conducted by Lorenz [ 1 ] was regarded as a revolution in economics and statistics, resulting in tens of thousands of papers published in magazines about statistics and econometrics and starting the research on the relationship between the Distribution Function and income inequality.


According to the literature review of this paper, the expressions of some income inequality indexes like Gini coefficient, Theil index, Pietra index, and Zenga [ 2 ] index can be deducted directly on certain Distribution Function.

To be specific, Arnold et al. The research above connects Distribution Function with income inequality in theory, providing a solid theoretical basis for the further study on income inequality. As mentioned above, there are various means to measure the income inequality. However, Lorenz Curve and the Gini coefficient are the most commonly used Sloman [ 14 ] ; the Gini coefficient is the most important index to measure or estimate the income inequality Sen [ 15 ]Champernowne and Cowell [ 16 ] Therefore, the Gini ratio is employed in this paper as the index to evaluate income inequality.

Another significant application of Distribution Function in the research of income inequality lies in fitting the residential income distribution.

Thanks to the contribution of Pareto [ 4 ] to Distribution Function, he was honored like Lorenz on the statistical study of income distribution Arnold [ 17 ], Thereafter, many scholars have made a significant contribution in this area, such as Fisk [ 18 ]Harrison [ 19 ]Arnold [ 17 ]McDonald [ 10 ]and Kleiber and Kotz [ 5 ] As for the relationship between income inequality and poverty, scholars from home and abroad have carried out some helpful exploration, most of whose research achievements were attained by empirical research.

Bourguignon [ 20 ] analyzed the internal relationship among poverty, income inequality, and economic growth systematically with the conclusion that the reduced inequality is conducive to poverty reduction. Wan and Zhang [ 21 ] analyzed empirically the impact of the change of income inequality on poverty by Shapley decomposition with the conclusion that the success of poverty reduction in rural areas was mainly attributed to the increase of income as well as the decrease of income inequality.

lorenz curve and gini coefficient relationship help

Similar results were obtained by Nong and Xubei [ 23 ] with the help of Health and Nutrition Survey data in eight Chinese provinces. In addition, a few scholars theoretically analyzed the relationship between income inequality and poverty.

For instance, Takayama [ 24 ] deducted the mathematical relationship between Gini coefficient and poverty when researching poverty, income inequality, and their measurement.

Moreover, a lot of scholars studied the relationship between income inequality and income mobility by adopting various data and methods. Xin and Jiyong [ 26 ] decomposed income mobility into three parts, namely, increase, dispersion, and exchange, by adopting Counterfactual Decomposition and then established the panel data model to examine the respective influential effect of the three parts on income inequality.