- **Progressive:** a tax (transfer) whose concentration curve lies everywhere below (above) the Lorenz curve for market income is globally progressive.<sup>21</sup>

- **Absolutely progressive** : a transfer whose concentration curve lies everywhere above the diagonal (that is, the per capita transfer decreases with income) is globally progressive in absolute terms. An absolutely progressive transfer is frequently called “pro-poor.”

- **Neutral:** a tax (transfer) whose concentration curve coincides with the Lorenz curve of market income is neutral **.**

- **Regressive** : A tax (transfer) whose concentration curve lies everywhere above (below) the Lorenz curve is globally regressive.

There are several aspects that are crucial to bear in mind when analyzing the redistributive effect (that is, the change in the distribution of income) of fiscal interventions:<sup>22</sup>

- To establish progressivity as defined in the literature it is not necessary for taxes (transfers) to be progressive for every individual in the distribution.  Taxes (transfers) can be _globally_ progressive even if they are not _everywhere_ progressive.

- The redistributive impact of a tax (transfer) depends both on its progressivity _and_ level.  For example, a particular tax can be less progressive than another tax but if the level of the former is higher, its equalizing impact will be higher as well.<sup>23</sup>

- In the face of more than one fiscal intervention, the impact of a tax (transfer) on inequality depends on the interaction among interventions.  For example, a tax can be regressive with respect to market income but progressive and equalizing with respect to market income plus transfers. Depending on the characteristics of the tax and the transfer, keeping the progressive transfer only (i.e., eliminating the regressive tax) could be less equalizing than having both.<sup>24</sup>

- Given what is mentioned in the previous paragraph, in order to assess the redistributive impact of taxes and transfers combined, we need to compare the concentration curve for after taxes and transfers income (with households ranked by market income) with the Lorenz curve for market income. The tax and transfer system combined is _globally_ progressive in the income-redistribution sense if the concentration curve for after taxes and transfers income (with households ranked by market income) lies everywhere above the Lorenz curve for market income.

- If the order of individuals in the after taxes and transfers income distribution is the same as their order using market income, this condition will ensure that the tax and transfer system is equalizing.  The total redistributive effect can be measured with the Reynolds-Smolensky index, defined as the difference between the Gini coefficient for market income (Gm) and the concentration coefficient for incomes _after_ taxes and transfers (Cpost−fisc), or:

# Reynolds Smolensky Index= RS= (Gm Cpost−fisc)

In the absence of reordering of individuals, the concentration coefficient of after taxes and transfers income is identical to the Gini coefficient, or, Cpost−fisc= Gpost−fisc. The higher the RS index, the more redistributive the fiscal system.

In the real world, however, fiscal interventions are likely to change the order of individuals. In the literature, this is known as “re-ranking.” Re-ranking occurs if individual A was poorer than individual B before a fiscal intervention, (let’s say, a cash transfer), but B is poorer than A after the intervention. Re-ranking is considered to be a typical form of horizontal inequity generated by fiscal policy.<sup>25</sup> The re-ranking definition of horizontal equity postulates

> 21 This refers to progressivity in the tax (transfer) redistribution sense.

> 22 See Duclos and Araar (2006) and Lambert (2002). For a synthesis, see Lustig (forthcoming). 23 See Duclos and Tabi (1996).

> 24 See Lambert (2002), pp. 277-278.  This counter-intuitive result is illustrated in Lambert’s Table 11.1. 25 See Duclos and Araar, op. cit., Chapter 8.

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