# **1. Introduction**

The methods used to set poverty lines have differed radically between rich and poor countries. Poverty in the developing world is typically measured using absolute lines, which aim to have the same real value at different dates and places. Virtually all developing countries use such lines and, at the global level, the World Bank’s “$1-a-day” line is an absolute line, aiming to have the same purchasing power in different countries and at different dates.<sup>2</sup> By contrast, the more common practice in OECD countries is to use what we shall call “strongly relative poverty lines,” which are set at a constant proportion—typically 40-60%—of the (date and countryspecific) mean or median income.<sup>3</sup> This difference in how poverty lines are set matters greatly to the properties of the resulting poverty measures. The bulk of the literature has confined attention to measures that are homogeneous of degree zero between the mean and the poverty line for any given Lorenz curve.4 Using an absolute line, such a poverty measure automatically falls when all incomes grow at the same rate, while any measure based on strongly relative lines will be unchanged.<sup>5</sup> So it is hardly surprising that this choice has been found to matter greatly to assessments of how poverty is changing over time,<sup>6</sup> as well as to cross-sectional poverty comparisons.<sup>7</sup>

> 2 The original “$1-a-day” was proposed by Ravallion et al. (1991) in a background paper for World Bank (1990); the latest update is Ravallion et al. (2008). 3

Examples for OECD countries include Smeeding et al. (1990), Atkinson (1998), Saunders and Smeeding (2002), Fouarge and Layte (2005), Eurostat (2005), Nolan (2007) and OECD (2008, Chapter 5). An exception is the official poverty line for the US, which is three times the cost of a subsistence food basket, as first proposed by Orshansky (1963). However, there has been considerable dissatisfaction with this line; for a review of the debates see Blank (2008). There has been some debate about whether the poverty measure should be anchored to the mean or the median (Saunders and Smeeding, 2002; Easton, 2002; de Mesnard, 2007); poverty lines set as a constant proportion of the median can have perverse properties when the Lorenz curve shifts (as shown by de Mesnard, 2007). This is a legitimate concern but is not central to the present paper. 4 This holds for the headcount index, poverty gap index, and indeed the entire class of Foster-GreerThorbecke (1984) measures, as well as the Watts index and many other measures. Note that the two types of measures are typically calculated on the same distribution of relative incomes, i.e., the same Lorenz curve. 5 Note also that, for a given Lorenz curve, the median is directly proportional to the mean. Thus this strong relativity property also holds when the poverty line is a fixed proportion of the median. 6 For example, the UNDP (2005, Box 3) (based on Nolan et al., 2005) showed how relative poverty measures for Ireland were rising despite higher absolute living standards for the poor; thus the UNDP (p. 334) warns that: “...when economic conditions change rapidly, relative poverty measures do not always present a complete picture of the ways that economic change affects people’s lives.” In another example, Easton (2002) argued that relative measures for New Zealand were deceptive in showed falling poverty despite lower levels of living for the poor. 7 For example, OECD (2008, Chapter 5) reports the same poverty rate for the US as Mexico. In another example, the urban poverty line proposed by Osberg and Xu (2008) for China (set at half the median) is 2.4 times their rural line, or 1.7 times when deflated by the Ravallion and Chen (2007) absolute lines. The Osberg-Xu method suggests little difference in poverty incidence between urban and rural China, while the Ravallion-Chen method indicates far higher poverty measures in rural China.

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