Theil inequality coefficient stata software

The inequality measures discussed above are each appropriate in certain circumstances. The gini coefficient is based on the comparison of cumulative proportions of the population against cumulative proportions of income they receive, and it ranges between 0 in the case of perfect equality and 1. It is shown that theils initial insight leads naturally to a very general class of inequality measures. Quantile group shares, cumulative shares lorenz ordinates, generalized lorenz ordinates, and gini number of strata 1 number of obs 9772 number of psus 9772 population size 54872650. Forecast evaluation using theils inequality coefficients. Summing all contributions to inequality by m income sources gives the total theil index. Two of the inequality measures commonly used for evaluating income inequality are the gini coefficient and the theil index see, e. Stata module to compute measures of inequality, statistical software components s373301, boston college department of economics.

Use of other measures is either not possible or problematic e. The gini coefficient is commonly used as a measure of inequality of income, consumption, or wealth. Stata command for calculating the components of the decomposition. Is the gini coefficient not a sufficient measure of. The choice of the atkinson inequality measure is guided by three factors. It is a special case of the generalized entropy index. Either theils first, or t, index or theils second, or l, index decomposition can be requested.

In summary, while it is important to incorporate theil s inequality coefficient within the syllabus of forecasting modules, there are numerous complicating factors which arise as a result of the availability of alternative specifications with differing properties, the presence of alternative definitions for associated proportions which themselves have different properties, and differing and incomplete presentations of the statistics and associated literature within textbooks and software. The first term in 4 is the weighted average of the theil inequality indexes of each group tk, with weights represented by the total income share the product of 5 see easypol module 051. Calculating gini coefficient of worldincome inequality with stata replicating and extending arrighidrangel findings with stata software related issues. Calculating gini coefficient of world income inequality. Several approaches exist for obtaining a nonparametric estimate of the intercept. Gini coefficient would would work best if data about each and every citizen in the country is available. Statistical software components from boston college department of economics. A popular measure of inequality is the gini coefficient, which ranges from 0 perfect equality to 1 perfect inequality, but is typically in the range of 0. Stata module to compute measures of inequality description. The theil index is a statistic primarily used to measure economic inequality and other economic phenomena, though it has also been used to measure racial segregation.

Lorenz in 1905 for representing inequality of the wealth distribution the curve is a graph showing the proportion of overall income or wealth assumed by the bottom x% of the people, although this is not rigorously true for a finite population see below. Measurement of inequality, 2000, in a b atkinson f bourguignon eds. The socalled atkinson class of indices is decomposable but not additively. The mathematical basics of popular inequality measures. Theils 1967 elegant first presentation of this measure of inequality was based on statistical information theory. This can ensure most accurate lorenz curve and thus most accurate computation of the coefficient. I tried to decompose the income by race and strata, but it wont work. The index can be turned into a normative measure by imposing a coefficient to weight incomes. There was an attempt to apply the gini index to measure inequality in the hdi distribution hicks, 1998. It can be viewed as a measure of redundancy, lack of diversity, isolation, segregation, inequality, nonrandomness, and compressibili. Update on other measures of income inequality atkinson index, gini coefficient, relative mean deviation, theil index, 19172015. Original article evaluating distributional differences in. Theils method actually yields an estimate of the slope of the regression line.

Tryphonopoulos, have utilized this inequality coefficient, employing actual data. The basic difference with the theil index calculated on the whole income distribution is that under the contribution of the income source k, now appears instead of yi. Actual values must be provided in the input data set for these statistics to be printed. For the gini coefficient the most commonlyused summary inequality measure in official statistics my mentor used to refer to a two percentage point change as a benchmark reference point for a large change on the grounds that such a large change was rare in rich countries. Descriptive statistics simple linear regression model. Theils informationtheoretic approach to the measurement of inequality theil 1967 is set in the context of subsequent developments over recent decades. In economics, the lorenz curve is a graphical representation of the distribution of income or of wealth. All the ingredients to carry out both the static decomposition of the index shorrocks 1980, econometrica and the dynamic decomposition mookherjee and shorrocks 1982, economic journal are easily accessible among the saved results of ineqdeco. Timmermann, 2006 for evaluating whether averages of forecasts perform better than the individual forecasts. Section 4 introduces a general class of inequality indices foreshadowed by theils work and section 5 its properties. But if we insist on the percentage change approach, then we have to conclude that 0. Theils original presentation of his inequality indicator.

The theil index is a statistic primarily used to measure economic inequality and other economic phenomena, though it has also been used to measure racial segregation the theil index t t is the same as redundancy in information theory which is the maximum possible entropy of the data minus the observed entropy. You will see that the theil index corresponds to ge1 in ineqdecos parlance. Evaluating distributional differences in income inequality. In this paper, we describe a sas macro for implementing theil regression where the estimation of the intercept is based on graybill and iyer 1994. Theil, inequality and the structure of income distribution. It is a revised and upgraded version of inequal7 and inequal published by edward whitehouse in stb23. Home site map site search free online software descriptive statistics simple linear regression model performance inequality coefficienttheil home up mse 1 mse 2 mse 3 decomp.

Thanks for contributing an answer to stack overflow. The best way to become a millionaire in five years or less 02. These two indexes were initially presented by theil 1967 and have been widely applied in the social and economic sciences. A then you have to determine what fraction of the triangle is made up of area a. The atkinson index becomes more sensitive to changes at the lower end of the income distribution as approaches 1. Particularly disappointing is that under their framework, the most popular gini coefficient violates their property of uniform additions p.

Greater weight can be placed on changes in a given portion of the income distribution by choosing, the level of inequality aversion, appropriately. I am sorry that this question is irrelevant to stata. What is the difference between the gini coefficient and. It is a revised and upgraded version of inequal published by edward whitehouse in stb23. The gini coefficient requires you to construct a lorenz curve that would look like this. It is based on the lorenz curve, a cumulative frequency curve that compares the distribution of a specific variable e. The first tests for forecasting models were developed in 1939 by tinbergen, in response to.

The stats and theil options are used to select goodnessoffit statistics. The numerical result is in terms of negative entropy so that a higher number indicates more order that is further away from the ideal of maximum disorder. Theil inequality coefficient in addition, eviews can compute the combination test, or forecast encompassing test chong and hendry, 1986. Pdf individual income inequality and its drivers in. Stata program atkinson, inequal, lorenz, relsgini these four adofiles provide a variety of measures of inequality. It seems to me that the degree of inequality, as measured by theil index, changed little in both cases. Ge class, which includes the two theil indices and the coefficient of variation.

In my function, fex 19968, ginicoeff requires two variables. One could benchmark changes in a theil index in an analogous way. Quantile group shares, cumulative shares lorenz ordinates. Macrolevel gender inequality can manifest itself in several ways, one of which is a gender wage gap. The theil index measures an entropic distance the population is away from the ideal egalitarian state of everyone having the same income.

Value the value of the inequality measure references f a cowell. Hi b, thank you for your question about a point that is often misunderstood. The theil index and the other entropy class inequality indexes. Estimation of inequality indices with decomposition by subgroup. Income inequality among individuals is measured here by five indicators. The theil index of inequality has been widely applied in the social sciences.

It was developed by the italian statistician and sociologist corrado gini and published in his 1912 paper. Notation and terminology begin with some tools for the description of income distribution. Nevertheless, th e correlation between in equality and the levels of educ ation i s rather unclear in that the values of the theil. Use excel to produce the lorenz curve and calculate gini coefficient. The gini coefficient is derived from the lorenz curve, which sorts the population from poorest to richest, and shows the cumulative proportion. However, two pages later in this same book, theil states, all applications of the inequality coefficients in the following chapters will refer to predicted and actual changes in the variables 1958, p. Inequality indices which are decomposable by population subgroup are increasingly used to analyze the anatomy of income inequality and also for analysis of secular trends.