Lorenz Curve Interpolation and the Gini Coefficient

2010 ◽  
Author(s):  
Nicholas Charles Rohde
Keyword(s):  
Gini Coefficient ◽  
Lorenz Curve ◽  
Polynomial Spline ◽  
The Philippines ◽  
The Body ◽  
Grouped Data ◽  
Parametric Methods ◽  
Lorenz Curves ◽  
Curve Interpolation ◽  
Income Decile

This article presents a simple non-polynomial spline that may be used to construct Lorenz curves from grouped data. The spline is naturally convex and works by determining a series of piecewise segments that may be joined to give a smooth and continuous Lorenz curve. The method is illustrated with an empirical example using income decile data from the Philippines from 1991-2003 where the proposed technique is used alongside other parametric and non-parametric methods. We also use the spline to approximate some known Lorenz curves and assess the technique by comparing the estimated Gini coefficient to the known Gini. Our findings suggest that the method is an attractive addition to the body of techniques used for developing Lorenz curves from grouped data.

scholarly journals Group averaging and the Gini deviation

2021 ◽  
Vol 29 (3) ◽  
pp. 595-605
Author(s):  
Oleg I. Pavlov ◽  
Olga Yu. Pavlova
Keyword(s):  
Gini Coefficient ◽  
Upper Bound ◽  
Lorenz Curve ◽  
Piecewise Linear ◽  
Geometric Parameters ◽  
Natural Question ◽  
Lorenz Curves ◽  
The Gini Coefficient ◽  
The Difference ◽  
Group Averaging

It is known that partitioning a society into groups with subsequent averaging in each group decreases the Gini coefficient. The resulting Lorenz function is piecewise linear. This study deals with a natural question: by how much the Gini coefficient could decrease when passing to a piecewise linear Lorenz function? Obtained results are quite illustrative (since they are expressed in terms of the geometric parameters of the polygon Lorenz curve, such as the lengths of its segments and the angles between successive segments) upper bound estimates for the maximum possible change in the Gini coefficient with a restriction on the group shares, or on the difference between the averaged values of the attribute for consecutive groups. It is shown that there exist Lorenz curves with the Gini coefficient arbitrarily close to one, and at the same time with the Gini coefficient of the averaged society arbitrarily close to zero.

scholarly journals Estimating Gini Coefficient from Grouped Data Based on Shape-Preserving Cubic Hermite Interpolation of Lorenz Curve

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2551
Author(s):  
Songpu Shang ◽  
Songhao Shang
Keyword(s):  
Gini Coefficient ◽  
Lorenz Curve ◽  
Strain Energy ◽  
Hermite Interpolation ◽  
Interpolation Method ◽  
Grouped Data ◽  
Shape Preserving ◽  
Unequally Spaced ◽  
Interpolation Curve ◽  
The Lorenz Curve

The Lorenz curve and Gini coefficient are widely used to describe inequalities in many fields, but accurate estimation of the Gini coefficient is still difficult for grouped data with fewer groups. We proposed a shape-preserving cubic Hermite interpolation method to approximate the Lorenz curve by maximizing or minimizing the strain energy or curvature variation energy of the interpolation curve, and a method to estimate the Gini coefficient directly from the coefficients of the interpolation curve. This interpolation method can preserve the essential requirements of the Lorenz curve, i.e., non-negativity, monotonicity, and convexity, and can estimate the derivatives at intermediate points and endpoints at the same time. These methods were tested with 16 grouped quintiles or unequally spaced datasets, and the results were compared with the true Gini coefficients calculated with all census data and results estimated with other methods. Results indicate that the maximum strain energy interpolation method generally performs the best among different methods, which is applicable to both equally and unequally spaced grouped datasets with higher precision, especially for grouped data with fewer groups.

scholarly journals AN ASSESSMENT OF TEACHERS’ COPING MANAGEMENT OF PERCEIVED STRESS AND FEAR OF THE UNKNOWN

2021 ◽  
Vol 5 (2) ◽  
pp. 217
Author(s):  
Merissa Braza Ocampo
Keyword(s):  
Perceived Stress ◽  
Negative Impact ◽  
The Philippines ◽  
The Body ◽  
Educational Institutions ◽  
Body Of Knowledge ◽  
Educational Processes ◽  
Negative Impacts ◽  
Global Uncertainty

Amidst the burgeoning research currently conducted on the effects of COVID-19, this study looks particularly at teachers’ stress and anxiety during a time of heightened global uncertainty, which also strongly affects educational processes. The paper draws on data provided through online questionnaires, and follow-up interviews with teachers at a variety of educational institutions in Japan, the Philippines, and eight other countries. Findings from 100 respondents include details regarding the extent and distribution of various behaviors and emotional tendencies gained from quantitative analysis, and additional follow up questions, all conducted online. Numerous strategies for combatting the negative impact of COVID-19 are presented, and a variety of individual responses to this predicament is stressed. The study confirms that COVID-19 is having an unprecedented impact on education, affecting not only students but teachers as well. Thus, the study aims to both assist in alleviating the negative impacts on teachers’ wellbeing and to provide helpful insights that contribute to the body of knowledge on teachers’ coping management of perceived stress and anxiety.

The Interpolation of the Lorenz Curve and Gini Index from Grouped Data

Econometrica ◽  
1976 ◽  
Vol 44 (3) ◽  
pp. 479 ◽  
Author(s):  
Joseph L. Gastwirth ◽  
Marcia Glauberman
Keyword(s):  
Lorenz Curve ◽  
Gini Index ◽  
Grouped Data ◽  
The Lorenz Curve

Anything Lorenz Curves Can Do, Top Shares Can Do: Assessing the TopBot Family of Inequality Measures

2018 ◽  
Vol 49 (4) ◽  
pp. 947-981 ◽  
Author(s):  
Guillermina Jasso
Keyword(s):  
Gini Coefficient ◽  
Probability Distributions ◽  
The United States ◽  
Current Evidence ◽  
Inequality Measure ◽  
Lorenz Curves ◽  
Inequality Measures ◽  
Top Incomes ◽  
The Gini Coefficient ◽  
And Shifts

Newly precise evidence of the trajectory of top incomes in the United States and around the world relies on shares and ratios, prompting new inquiry into their properties as inequality measures. Current evidence suggests a mathematical link between top shares and the Gini coefficient and empirical links extending as well to the Atkinson measure. The work reported in this article strengthens that evidence, making several contributions: First, it formalizes the shares and ratios, showing that as monotonic transformations of each other, they are different manifestations of a single inequality measure, here called TopBot. Second, it presents two standard forms of TopBot, which satisfy the principle of normalization. Third, it presents a new link between top shares and the Gini coefficient, showing that properties and results associated with the Lorenz curve pertain as well to top shares. Fourth, it investigates TopBot in mathematically specified probability distributions, showing that TopBot is monotonically related to classical measures such as the Gini, Atkinson, and Theil measures and the coefficient of variation. Thus, TopBot appears to be a genuine inequality measure. Moreover, TopBot is further distinguished by its ease of calculation and ease of interpretation, making it an appealing People’s measure of inequality. This work also provides new insights, for example, that, given nonlinearities in the (monotonic) relations among inequality measures, Spearman correlations are more appropriate than Pearson correlations and that weakening of correlations signals differences and shifts in distributional form, themselves signals of income dynamics.

Impact of Self-Help Group (SHG) Membership on Income and Income Inequality

2019 ◽  
pp. 341-364
Author(s):  
Maniklal Adhikary ◽  
Sumanta Kumar Das
Keyword(s):  
Income Inequality ◽  
Gini Coefficient ◽  
Rural Women ◽  
Lorenz Curve ◽  
Direct Impact ◽  
Self Help ◽  
Birbhum District ◽  
Direct Outcome ◽  
The Impact ◽  
Self Help Group

The microfinance program has now been recognized as an effective tool to empower economically the rural women folk. The earning is the most important direct outcome of micro finance participation unlike acquiring empowerment. Participation in the program helps women to inculcate their saving habit. It gives access to the formal credit to them. All these have direct impact on their economic condition. This study explores the impact of microfinance program on the income of the program participants of Birbhum District in West Bengal in India. The study also focuses on how participation helps in reducing inequality in income of the participants. The major finding of the study is that women self-help group (SHG) members have the higher level of income compared to that of non-SHG members. The study also shows that SHG participation also helps them in reducing inequalities in their income. Gini coefficient and Lorenz curve technique has been used to assess the income distribution of the respondents.

Sign in / Sign up

Export Citation Format

Share Document