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wow-inequalities/docs/measures.md

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Measures

TODO:: separation of shares, inequality indices and ratios

absolute shows magnitude of difference between subgroups of pop -> focus on absolute welfare

relative shows proportional difference between subgroups of pop -> focus on welfare in relation to others

Direction

Vertical

Gini coeff, Theil, entropy measure, atkinson indexes

Horizontal

mean differences between groups; ratios between better off/worse off

GGini; GTheil; GCOV

All indicators

Absolute

  • quantiles (division by 5) / deciles (division by 10) / centiles (division by 100)

  • Absolute Gini index

    • ?

  • Standard deviation

    • deviations from norm in absolute terms

  • Foster-Greer-Thorbecke (FGT) poverty headcount ratio: absolute deprivation, proportion of population that falls below defined poverty line (= absolute threshold) [@Go2010]

Relative

  1. Share:

    • A share typically refers to a unit of ownership in a company, representing a proportional claim on its assets and earnings. Shares are also known as stocks or equity.

  2. Ratio:

    • A ratio, on the other hand, is a comparison of two quantities. It expresses the relationship between two numbers and is often used to analyze financial and economic data. For example a study analyzing rural-urban income inequality using "the percentage deviation of real wages," it sounds like it might involve a ratio. The term "percentage deviation" implies a measure of how much a variable deviates from its expected or average value, expressed as a percentage. In this case, the ratio could be the percentage deviation of real wages between rural and urban areas, helping to assess the income inequality between the two.

    The income ratio can be calculated as the ratio of the real wages of urban workers to rural workers. If the real wages for rural workers are decreasing ( deviating into the negative), it means the income of rural workers is declining relative to urban workers. This would likely result in an increase in the income ratio because the numerator (urban workers' wages) is relatively higher than the denominator (rual workers' wages). In summary, if the policy leads to a negative percentage deviation of real wages for rural workers, it would likely increase the income ratio between urban and rural workers.

  • ratios of quantiles to each other (division of various quantiles)

  • Gini coefficient:

    • based Lorenz curve - population percentage versus accumulated fractions of wealth
    • is area between lorenz curve and perfect equality
    • needs: individual/household income/wealth; pop size

  • Theil index:

    • how much income distribution (person x receives y from total income) is away from perfect uniform distribution
    • log -based
    • can be disaggregated into subgroups
    • Theil L > weighting factors are population groups; Theil T > weighting factors are fraction of appropriated income

  • Atkinson measures:

    • measures cumulative deviation of each income in relation to average income value in distribution

  • Palma ratio:

    • dividing share of income/wealth held by top 10% by bottom 40%, thus high = bad

  • s80s20, s40s20 ratios:

    • ?

  • Concentration index:

    • divide whole pop by 100 to find percentiles
    • then you know how many ppl are in each group and add their total income

  • Foster-Greer-Thorbecke-class distribution (@Sotomayor2021)