50%).<sup>7</sup> The UN’s <u>Sustainable Development Goals</u> also include monitoring the proportion of the population living below 50% of the median. Others have argued instead for using a fixed proportion of the mean rather than the median, and this too has been applied at country level, including in the UK.<sup>8</sup> Advocates of such relative poverty lines have often argued that the absolute lines do not keep up with evolving standards for defining poverty in growing economies. For example, Fuchs (1967, p.89) argued that “.. all so-called ‘minimum’ or ‘subsistence’ budgets are based on contemporary standards which will soon be out of date.” Similar criticisms of the US official poverty lines have been made by Citro and Michael (1995) (in an expert committee report for the National Academy of Sciences) and Blank (2008), among others.

There is, however, a long-standing concern with the Fuchs proposal (and its variants as used by Eurostat and the OECD), stemming from the fact that the monetary line then has an elasticity of unity with respect to the median. This is dubbed a “strongly relative” poverty line by Ravallion and Chen (2011) who point out that (for a broad class of poverty measures) this violates an intuitively appealing axiom, namely that if all incomes increase (decrease) by the same proportion then an aggregate poverty measure must fall (rise); strongly relative measures turn out to have similar properties in practice to standard inequality measures.<sup>9</sup> This concern is probably the main reason why the Fuchs proposal has had very few followers in the developing world (or in the US). By contrast, what Ravallion and Chen call “weakly relative” lines also entail that the line rises with the mean or median, but with an elasticity less than unity.

A further issue, which has received little attention in the literature on poverty measurement, is what the comparison income should be. The literature on relative poverty has almost universally taken the comparison income to be either the (equally-weighted) mean or the median, although there has been some debate about which is better.<sup>10</sup> Accepting that relative

> 7 Examples and discussions can be found in Fuchs (1967), Smeeding et al. (1990), Blackburn (1994), Atkinson (1998), Eurostat (2005), Nolan (2007) and OECD (2008, Chapter 5). In the context of developing countries, also see Atkinson and Bourguignon (2001) and Garroway and de Laiglesia (2012).

> 8 See, for example, Drewnowski (1977), Duclos and Makdissi (2004), and de Mesnard (2007). The UK has used the mean in official poverty measures (Atkinson, 1998).

> 9 A more formal discussion and evidence can be found in Ravallion (2016a, Chapter 8).

> 10 Advocates of the median have argued that it is robust to measurement errors at the top and bottom while advocates of the mean have argued that using the same proportion of the median as the poverty line underestimates poverty (although there is no obvious reason why one would have to use the same proportion). A more sophisticated critique of the use of the median by de Mesnard (2007) points to some paradoxical theoretical results in poverty measurement that are avoided using the mean as the comparison income level.

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