Gini coefficient

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is a consistent estimator of the population Gini coefficient, but is not, in general, unbiased. Like the relative mean difference, there does not exist a sample statistic that is in general an unbiased estimator of the population Gini coefficient. Confidence intervals for the population gini coefficient can be calculated using bootstrap techniques Sometimes the entire Lorenz curve is not known, and only values at certain intervals are given. In that case, the gini coefficient can be approximated by using various techniques for interpolating the missing values of the Lorenz curve. If (Xk Yk) are the known points on the Lorenz curve, with the X k indexed in increasing order(Xk-<Xk), so that Xk is the cumulated proportion of the population variable, for k=0,n, with X0=0,Xn=1. Yk is the cumulated proportion of the income variable, for k-O,,n, with Yo If the lorenz curve is approximated on each interval as a line between consecutive points, then the area b can be approximated with trapezoids and G1=1-∑(X-Xk-1)(Yk+Y-1) k=1 is the resulting approximation for G. More accurate results can be obtained using other methods to approximate the area b, such as approximating the lorenz curve with a quadratic function across pairs of intervals, or building an appropriatel smooth approximation to the underlying distribution function that matches the known data. If the population mean and boundary values for each interval are also known these can also often be used to improve the accuracy of the approximation While most developed European nations tend to have Gini coefficients between 0. 24 and 0.36, the United States Gini coefficient is above 0.4, indicating that the United States has greater inequality. Using the Gini can help quantify differences in welfare and compensation policies and philosophies however it should be borne in mind that the gini coefficient can be misleading when used to make political comparisons between large and small countries(see criticisms section) Correlation with per-capita gDP Poor countries (those with low per-capita gDP) have Gini coefficients that fall over the whole range from low(0.25)to high(0.71), whilc rich countrics have generally low Gini coefficient(under 0.40) Advantages as a measure of inequality 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 It can be used to compare income distributions across different population sectors as well as countries, for example the gini coefficient for urban areas differs from that of rural areas in many countries( though the United States urban and rural gini coefficients are nearly identical) 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. If the gini coefficient is rising as well as gDP, poverty may not be improving for the majority of the population 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 The Gini coefficient satisfies four important principles o Anonymity: it does not matter who the high and low earners are o 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 o Population independence: it does not matter how large the population of the country is o Transfer principle: if income (less than the difference), is transferred from a rich person to a poor person the resulting distribution is more equal Disadvantages as a measure of inequality 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 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 he measure will give different results when applied to individuals instead of houscholds. When different populations are not mcasured with consistent definitions, comparison is not meaningful The lorenz curve may understate the actual amount of inequality if richer households are able to use income more efficiently than lower income households. From another point of view, measured inequality may be the result of more or less efficient use of houschold incomes 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 Economies with similar incomes and gini coefficients can still have very diffcrent income distributions This is bccause 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 72; but an economy with complete income equality, except for one wealthy household that has half the total income also has a gini coefficient of 12 Too often only the gini coefficient is quoted without describing the proportions of the quantiles used for measurement. As with other inequality coefficients, the Gini coefficient is influenced by the granularity of the measurements. For example, five 20% quantiles (low granularity) will yield a lower Gini coefficient than twenty 5% quantiles(high granularity )taken from the same distribution As one result of this criticism, additionally to or in competition with the gini coefficient entropy measures are frequently used (e.g. the atkinson and Theil indices) These measures attempt to compare the distribution of resources by intelligent players in the market with a maximum entropy random distribution, which would occur if these players acted like non-intelligent particles in a closed system following the laws of statistical physics A lower Gini coefficient tends to indicate a higher level of social and economic equality Richest 10% Richest 20% Rank Country Gini index to poorest to poorest Survey 10% 20% year Azerbaijan 193.3 2.6 2002 Denmark 2478.1 43 1997 apan 24945 3.4 1993 Sweden 2562 2000 Czech repub 2545.2 3.5 1996 orway 2586.1 3.9 2000 Slovakia 25867 4 1996 8 Bosnia and Herzegovina 26.254 3.8 2001 Uzbekistan 2686.1 2000 10 Hungary 26955 3.8 2002 10 Finland 2695.6 3.8 2000 12 Ukraine 28159 41 2003 13 Albania 28259 4.1 2002 Germany 28.36.9 4.3 2000 15 Slovenia 28459 3.9 199899 16 Rwanda 28958 4 1983-85 17 Croatia 2973 4.8 2001 18 Austria 29169 4.4 2000 19 Bulgaria 2927 4.4 2003 20 Belarus 29.769 45 2002 21 Ethiopia 3066 4.3 199900 22 Kyrgyzstan 30.36.4 4.4 2003 2 Mongolia 30.3178 9.1 1998 24 Pakistan 30.665 4.3 2002 25 Netherlands 30992 5.1 1999 6 Romania 3175 49 2003 27 South Korea 31.678 4.7 1998 28 Bangladesh 31868 4.6 2000 Indi 32.57.3 49 199900 30 Tajikistan 32678 5,2 2003 30 Canada 32.69.4 5.5 2000 32 france 32.79.1 5.6 1995 33 Belgium 338.2 49 2000 34 Sri Lanka 33.28.1 5.1 199900 34 Moldova 3328.2 5.3 2003 36Yemen 3348.6 5.6 1998 37 Switzerland 33.79 55 2000 38 Armenia 3388 2003 39 Kazakhstan 33985 2003 40 Indonesia 34378 52 2002 40 Ireland 3439.4 5.6 2000 40 Greece 343102 6,2 2000 43上gypt 3448 199900 44 Poland 34588 5.6 2002 45 Tanzania 34692 5.8 200001 45 Laos 34683 5.4 2002 47 Spain 347103 2000 48 Australia 352125 7 1994 alGeria 35396 6.1 1995 50 Estonia 358108 64 2003 51 Lithuania 36104 6.3 2003 51 Ital 3611.6 6.5 2000 51 United Kingdom 36138 7.2 1999 54 New Zealand 362125 6.8 1997 55 Benin 36.594 6 2003 56 Vietnam 3794 6 2002 57 Latvia 37.7116 68 2003 8 Jamaica 37911.4 6.9 2000 Portugal 38.515 8 1997 60 ordan 38811.3 6.9 200203 61 Republic of Macedonia 39125 7.5 2003 61 Mauritania 3912 7.4 2000 6 Israel 39213.4 7.9 2001 64 Morocco 39.5117 7.2 199899 64 Burkina Faso 39.511.6 69 2003 6 Mozambique 39612.5 7.2 199697 67 Tunisia 398134 7.9 2000 68 Russia 399127 7.6 2002 69 Guinea 40.3123 7.3 1994 69 Trinidad and Tobago 40.3144 8.3 1992 Georgia 404154 8.3 2003 ambodia 40411.6 69 1997 73 Ghana 40.814.1 84 98 73United States 40.8159 8.4 2000 73Turkmenistan 40.8123 7.7 1998 76 Senegal 41.3128 7.5 1995 77 Thailand 42126 7.7 2002 78 Zambia 42.1139 200203 79 Burundi 424193 9.5 1998 sIngapore 42.517.7 9.7 1998 80 Kenya 42.513.6 8.2 1997 Uganda 43149 8.4 888 1999 Iran 4317.2 9.7 1998 Nicaragua 43115.5 88 2001 85 Hong Kong, China(SAR)43.4.8 9.7 1996 86 Turk 43616.8 9.3 2003 87 Nigeria 43.7178 9.7 2003 87 Ecuador 43.744.9 17.3 1998 89 Venezuela 44.1204 10.6 2000 90 Cote d’ Ivoire 44616.6 9.7 2002 90 Cameroon 446157 9.1 2001 People's Republic of China 44.7 18.4 10.7 2001 93 Uruguay 449179 10.2 2003 94 Philippines 46.165 9.7 2000 95 Guinea-Bissau 4719 10.3 1993 96Ne 472158 91 2003-04 97 Madagascar 475192 2001 8 Malaysia 49222.1 12.4 1997 99 Mexico 49.5246 12.8 2002 100 Costa Rica 49930 142 2001 101 Zimbabwe 50122 12 1995 102 Gambia 50.220.2 l12 1998 103 Malawi 50.3227 11.6 1997 104 Nig 50.546 20.7 1995 104 Mali 50.523.1 12.2 1994 106 Papua New guinea 509238 12.6 196 107 Dominican Republic 51730 14.4 2003 108 El Salvador 52457.5 209 2002 109 Argentina 52834.5 17.6 2003 110 Honduras 53834.2 17.2 2003 eru 54640.5 18.6 2002 112 Guatemala 55.1482 20.3 200 113 Panama 564547 23.9 2002 114 Chile 57140.6 18.7 2000 115 Paraguay 578734 278 2002 115 South Africa 57833.1 17.9 2000 117 Brazil 8578 23.7 2003 118 Colombia 586638 25.3 2003 119 Haiti 59.271.7 26.6 200l 120 Bolivia 60.11681 423 2002 121 Swaziland 60.9497 23.8 1994 122 Central African Republic 613692 32.7 1993 123 Sierra Leone 629872 57.6 1989 124 Botswana 6377.6 31.5 1993 125 sotho 632105 44.2 1995 126Namibia 74.31288 56.1 1993 United Nations 2006 Devclopment Programme Report(p. 335

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