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It’s redistributive if it reduces income inequality, regardless of whether that is accomplished by literally moving money from rich to poor households.

Orsetta Causa & Mikkel Hermansen 19, members of the Economics Department of the OECD, “Income Redistribution Through Taxes and Transfers across OECD Countries,” OECD, 7/22/19, Economics Department Working Papers, No. 1453, https://one.oecd.org/document/ECO/WKP(2017)85/En/pdf

35. This paper relies on the Reynolds-Smolensky (1977) approach to quantify income redistribution achieved by taxes and transfers, following common practice in the literature.27 [FOOTNOTE 27 BEGINS] 27. See e.g. Immervoll et al. (2006); Immervoll and Richardson (2011). The voluminous political science literature on redistribution does not usually rely on this approach but on aggregate social spending and welfare measures. [FOOTNOTE 27 ENDS] “Redistribution” is meant as a reduction in household income inequality, i.e. taxes and transfers are said to “redistribute” if they reduce income inequality regardless of the extent to which this is achieved by actually transferring resources from higher-income households to lower-income households. Table 1 illustrates the underlying (linear and static) accounting framework: the left column presents the household income concepts and their components applied at the household level data, while the second and third columns contain the corresponding inequality measures allowing for deriving an aggregate redistribution measure at the country level. Income inequality is quantified by the Gini coefficient, implying that the redistributive effect of taxes and transfers is defined as the difference between the Gini coefficient of household market incomes and the Gini coefficient of household disposable incomes. Unless otherwise stated in the paper, this is measured in relative terms, that is, in per cent of the market income Gini coefficient. This normalisation allows for taking into account cross-country differences in the initial level of market income inequality. The respective redistributive effect of the various instruments of the tax and transfer system, e.g. cash transfers and personal income taxes, is assessed analogously based on the same accounting framework (see Box 4).

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