Shorrocks, 1991). Sen (1992) questioned the desirability of subgroup consistency, which may be less compelling when relative aspects matter. However, Decerf (2021) shows that a weak version of subgroup consistency provides the foundation for additive indices as in Eq. (1). For illustrative purposes, we assume in this section that the additive measure takes the FGT form. However, many other indices have been proposed (see Zheng (1991) for a survey).

# 2.2 Absolute poverty

The key specificity of absolute measures is that they are based on a poverty line representing consumption possibilities that are fixed across space and time. Hence, the real value represented by the poverty threshold does not change with the level of the income standard m. Thus, measure P is absolute if the threshold function is independent on m, i.e. for some za>0 we have z(m)=za for all m.

The construction of an absolute threshold is a complex task that requires making a series of difficult choices. Ravallion (1998) describes a two-step procedure in order to pin down the absolute threshold. The first step specifies a reference level of welfare below which individuals would be considered poor. The second step identifies a money metric threshold corresponding to this level of welfare. This second step is typically achieved by selecting a bundle of goods whose consumption provides the desired level of welfare and computing the cost of this bundle at prevailing prices.

The dominant procedure for the selection of the bundle of goods is the cost of basic needs approach (Ravallion, 1993; Ravallion and Sen 1996; Wodon, 1997). The typical way of operationalizing the cost of basic needs approach is to select a food bundle representing the consumption habits of the poor. Then, an allowance for non-food goods such as clothes or housing is computed. One possibility is to derive this allowance from food Engel curves. For instance, if the poor spend one-half of their budget on food, then the poverty threshold is taken to be twice the cost of the food bundle.

In practice, designing an absolute measure is a highly complex task. In order to maintain the same level of welfare, the poverty threshold must be adapted when prices vary. When all prices increase in the same proportion, such adaptation is relatively straightforward. When relative prices change, substitution effects change the consumption habits of the poor. In that case, a trade-off may appear between specificity, i.e. linking the poverty threshold to the behavior of the poor in the given context, and welfare-consistency, i.e. setting a poverty threshold that leads to a constant level of welfare. The trade-off between specificity and welfare consistency follows from the fact that the consumption habits associated to the new price vector may provide the poor with a different level of welfare as the one they reached under the initial prices. When monitoring global poverty, the World Bank relies on purchasing power parity rates (PPPs) in order to compute poverty thresholds that can be compared across different countries. The question whether these PPP conversions do provide welfare-consistent poverty thresholds frequently leads to heated debate (Summers and Heston, 1991; Deaton and Heston, 2010; Ravallion, 2018), reflecting the difficulty to ensure welfare-consistency in practice. Recently, Allen (2017) and Moatsos (2016) suggest an alternative method in order to obtain comparable poverty thresholds. These authors start from fixed requirements for several basic needs (e.g. minimal number of calories and other nutrients or minimal surface of housing) and compute the minimal cost to fulfill all these requirements at prevailing prices. This method avoids the use of PPP conversion altogether, but may generate other problems. For instance, the kinds of food diets solving such linear optimization problem are typically not consistent with prevailing 4