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The GINI Coefficient: Measuring Income Distribution

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The GINI Coefficient: Measuring Income Distribution The GINI coefficient: Measuring Income Distribution NAME : SUDEEPA HALDER MTR NU. : 3098915 FB : 09 TERM : SS 2017 COURSE : INTERNATIONAL MANAGEMENT I +II INTRODUCTION "The Gini coefficient (sometimes expressed as a Gini ratio or a normalized Gini index) is a measure of statistical dispersion intended to represent the income or wealth distribution of a nation's residents, and is the most commonly used measure of inequality of income or wealth. It was developed by the Italian statistician and sociologist Corrado Gini and published in his 1912 paper Variability and Mutability." [1] "The Gini index is the Gini coefficient expressed as a percentage, and is equal to the Gini coefficient multiplied by 100. (The Gini coefficient is equal to half of the relative mean difference.) The Gini coefficient is often used to measure income inequality. The value of Gini Coefficient ranges from 0 to 1. Here, 0 corresponds to perfect income equality (i.e. everyone has the same income) and 1 corresponds to perfect income inequality (i.e. one person has all the income, while everyone else has zero income). Normally the mean (or total) is assumed to be positive, which rules out a Gini coefficient being less than zero or negative.The Gini coefficient can also be used to measure the wealth inequality. This function requires that no one has a negative net wealth. It is also commonly used for the measurement of discriminatory power of rating systems in the credit risk management." [See also 2] Graphical Representation: "Mathematically the Gini coefficient can be usually defined based on the Lorenz curve, which plots the proportion of the total income of the population (y axis) that is cumulatively earned by the bottom x% of the population (see graph). The line at 45 degrees thus represents perfect equality of incomes and the index is 0. The horizontal axis and the right vertical axis represent perfect inequality and index is 100." [See also 1] "The graph shows that the Gini coefficient is Source: Wikipedia 2017 equal to the area marked A divided by the sum of the areas marked A and B, that is, Gini = A / (A + B). It is also equal to 2A and to 1 - 2B due to the fact that A + B = 0.5 (since the axes scale from 0 to 1)." [1] "The more nearly equal a country's income distribution, the closer is its Lorenz curve to the 45 degree line and lower is its Gini index, e.g., a Scandinavian country with an index of 25. The more unequal a country's income distribution, the farther is its Lorenz curve from the 45 degree line and higher is its Gini index, e.g., a Sub-Saharan country with an index of 50." [4] However there are some issues in interpreting a Gini coefficient. The same value may result from many different distribution curves. The demographic structure should be taken into account. Countries with an aging population, or with a baby boom, experience an increasing pre-tax Gini coefficient even if real income distribution for working adults remains constant. Scholars have devised over a dozen variants of the Gini coefficient. CALCULATION Example: Two levels of income: "The most equal society will be one in which every person receives the same income (G = 0); the most unequal society will be one in which a single person receives 100% of the total income and the remaining N − 1 people receive none (G = 1 − 1/N)." [1] "While the income distribution of any particular country need not follow simple functions, these functions give a qualitative understanding of the income distribution in a nation given the Gini coefficient. The effects of minimum income policy due to redistribution can be seen in the linear relationships." [1] "An informative simplified case just distinguishes two levels of income, low and high. If the high income group Souce: Wikipedia 2017 is u % of the population and earns a fraction f % of all income, then the Gini coefficient is f − u. An actual more graded distribution with these same values u and f will always have a higher Gini coefficient than f − u. As per the graph the richest u % of population (red) equally share f % of all income or wealth, others (green) equally share remainder: G = f − u. A smooth distribution (blue) with same u and f always has G > f − u." [1] "An alternative approach would be to consider the Gini coefficient as half of the relative mean absolute difference, which is a mathematical equivalence. The mean absolute difference is the average absolute difference of all pairs of items of the population, and the relative mean absolute difference is the mean absolute difference divided by the average, to normalize for scale. If xi is the wealth or income of person i, and there are n persons, then the Gini coefficient G is given by: When the income (or wealth) distribution is given as a continuous probability distribution function p(x), where p(x)dx is the fraction of the population with income x to x+dx, then the Gini coefficient is again half of the relative mean absolute difference: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle G = \frac{1}{2\mu}\int_{-\infty}^\infty\int_{-\infty}^\infty p(x)p(y)\,|x-y|\,dx\,dy } Where μ is the mean of the distribution And the lower limits of integration may be replaced by zero when all incomes are positive." [1] ADVANTAGES & DISADVANTAGES OF GINI COEFFICIENT Advantages: "The Gini coefficient's main advantage is that it is a measure of inequality by means of a ratio analysis, rather than a variable unrepresentative of most of the population, such as per capita income or gross domestic product." [2] It can be used to compare income distributions across different population sectors as well as countries. It is sufficiently simple that it can be compared across countries and be easily interpreted. GDP statistics are often criticised as they do not represent changes for the whole population; the Gini coefficient demonstrates how income has changed for poor and rich. "The Gini coefficient can be used to indicate how the distribution of income has changed within a country over a period of time, thus it is possible to see if inequality is increasing or decreasing" [2] "The Gini coefficient satisfies four important principles: 1. Anonymity: it does not matter who the high and low earners are. 2. Scale independence: the Gini coefficient does not consider the size of the economy, the way it is measured, or whether it is a rich or poor country on average. 3. Population independence: it does not matter how large the population of the country is. 4. Transfer principle: if income (less than the difference), is transferred from a rich person to a poor person the resulting distribution is more equal." [2] Disadvantages: "The Gini coefficient measured for a large economically diverse country will generally result in a much higher coefficient than each of its regions has individually. For this reason the scores calculated for individual countries within the EU are difficult to compare with the score of the entire US." [2] "Comparing income distributions among countries may be difficult because benefits systems may differ. For example, some countries give benefits in the form of money while others give food stamps, which may not be counted as income in the Lorenz curve and therefore not taken into account in the Gini coefficient." [2] "As for all statistics, there will be systematic and random errors in the data. The meaning of the Gini coefficient decreases as the data become less accurate. Also, countries may collect data differently, making it difficult to compare statistics between countries." [2] "Economies with similar incomes and Gini coefficients can still have very different income distributions. This is because the Lorenz curves can have different shapes and yet still yield the same Gini coefficient. As an extreme example, an economy where half the households have no income, and the other half share income equally has a Gini coefficient of ½; but an economy with complete income equality, except for one wealthy household that has half the total income, also has a Gini coefficient of ½." [2] GINI COEFFICIENTS AROUND THE WORLD "The world Gini index is estimated around 0.52 as of 2016, marking a slight decline from a peak near 0.545 in the early 2000s. The index is well above the levels displayed in the 1970s, when Gini was estimated below 0.47. Economic expansion in Latin America, Eastern Europe and the ex- Soviet countries drove much of this recent improvement. Gini coefficients and per-capita gross domestic product (GDP) exhibit negative correlation. Less developed countries tend to lack a large middle class, with limited industrialization hampering the ability of many to earn a regular wage. South Africa is a notably high Gini nation, with a 0.625 coefficient estimated in 2013. European nations such as Denmark, Slovenia, Sweden and Ukraine have the most even income distributions, with coefficients below 0.25." [9] Source: Google images "Among the BRICS countries of Brazil, Russia, India, China and South Africa, South Africa has the highest income inequality index, a Gini index of 0.63, and the highest global ranking as the fourth unequal country in the world".[3] While low numbers represent greater equality, low numbers aren’t always a perfect indicator of economic health. Source: Google images COMPARING GINI COEFFICIENT WITH OTHER METHODS OF MEASURING INCOME INEQUALITY To measure the global economic inequality there are quite a few different income inequality metrics or methods that are commonly used.
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