The paper makes three main contributions. The first is to formalize the aforementioned identification problem and so derive empirical bounds on the true global poverty measures so as to span the key parameter uncertainty.<sup>12</sup> The lower bound is an absolute line, fixed in real terms, while the upper bound is a schedule of weakly relative lines that rise with the country-specific comparison income consistently with national poverty lines. The welfare-consistent global poverty measure lies between these bounds, depending on how much the latent reference welfare level for defining poverty at the national level rises with the mean.

The second contribution concerns how the comparison income should be set, as required for the upper bound. Here our main point of departure from past work is that we take account of the bearing that inequality has on relativist comparisons. We question the long-standing assumption that the comparison income level in relativist comparisons at the country level is the median or equally-weighted mean.<sup>13</sup> It is well recognized that the mean may be too heavily influenced by very high incomes, which are probably less relevant to the relativist comparisons that are likely to be made by most people, who know little about how rich the rich are. As Duesenberry (1949) recognized, it is probably not relative income that matters but relative (observable) consumption. Nor is the median a satisfactory fix. While concerns about measurement errors at the extremes are real, there is still ample information in the data, and it is far from obvious that such information should be entirely discounted.<sup>14</sup> We argue that a better approach is to postulate that, while the relativist comparison may put lower weight on richer people, it will never put zero weight on the rich, as is the case with the median.<sup>15</sup> We provide a simple theoretical formulation that encompasses both upward and downward relative comparisons. This provides a new perspective on measuring relative poverty.

The third contribution is to provide new data on national poverty lines and survey-based distributions of consumption or income to implement the above ideas empirically. Our data on national poverty lines suggest that the rank-weighted mean is the relevant comparison income,

> 12 Chen and Ravallion (2013) note in passing that one might interpret absolute and relative lines as lower and upper bounds but they do not discuss the identification problem that motivates this interpretation.

> 13 While our focus here is on global poverty, it can also be noted that studies of the effects of relative income on subjective welfare have also relied at times on equally-weighted means, as in (for example) Hagenaars and van Praag (1985) and Luttmer (2005).

> 14 The same point can be made about the use of a fixed proportion of any quantile corresponding to a fixed percentile. For example, Citro and Michael (1995) recommend using the 33<sup>rd</sup> percentile of the distribution of consumer spending on food, clothing, shelter and utilities. This idea was adopted in 2011 by the US Census Bureau’s Supplementary Poverty Measure, which we return to.

> 15 Note that the median is unresponsive to small changes in incomes sufficiently far above (or below) the median.

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