By Antonio Villar

These lectures target to aid readers comprehend the logics and nature of the most signs of inequality and poverty, with specified realization to their social welfare underpinnings. the major strategy is composed in linking inequality and poverty dimension with welfare review. As obstacle for inequality and poverty stems from moral concerns, the dimension of these features inevitably contains a few price judgments. these price judgments will be associated, without delay or ultimately, to welfare tests at the distribution of non-public and social possibilities. Inequality and poverty are hence thought of to be partial features of the welfare evaluate of the possibilities in a given society. the amount comprises purposes that illustrate how the types should be applied. They consult with inequality of chance and poverty in schooling, utilizing PISA data.

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The second term is a measure of variability between the groups, as a weighted average of the squared mean deviations, again with weights given by the population shares. We can write: (i) σ 2W ¼ G X ng g¼1 (ii) σ 2B ¼ n σ 2g ; G 2 X ng  μg À μ n g¼1 so that we have the overall variance decomposed as the sum of two terms, σ 2 ¼ σ 2W þ σ 2B , corresponding to the within and the between components. The ratios σ 2W σ 2B σ2 , σ2 provide the “percentage” of total variability explained by each of those components.

We show there that only the original indices of Theil have the property that the weights of the within components add up to 1. The parameter θ captures the sensitivity of the index with respect to transfers depending on the part of the distribution in which those transfers take place. As θ decreases, Iθ becomes more sensitive to the transfers in the lower part of the distribution in the sense that the same amount of the transfer reduces more the inequality the lower the income of the recipient.

Ii) The joint information of two independent events is the sum of the information of each separate event: ϕðw Á w0 Þ ¼ ϕðwÞ þ ϕðw0 Þ. It can be shown that, assuming that ϕ is differentiable, those properties determine completely the functional form of the information function, which is given by:   1 ϕðwÞ ¼ ÀlogðwÞ ¼ log w In a discrete scenario, with n possible events with probabilities w1, w2,. ; logn ¼ logn ¼ ϕ ¼ n n n n n i¼1 Theil (1967) proposes applying this conceptual scheme to the analysis of income distribution by introducing two variations.

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