some data come in grouped form (notably China), we use ten decile groups for every countryyear.<sup>1</sup> That is, every individual is assigned the average income of her decile (in the within-country distribution). Second, because income is difficult to measure in an economy where ownconsumption is widespread, developing countries tend to use consumption expenditure instead of income (Deaton and Zaidi, 2002).<sup>2</sup> While this is a serious issue, as Anand and Segal (2015) write, “one simply has to live with the noncomparability [because] [t]here is no reliable way to infer an income distribution from an expenditure distribution”.

An important caveat, however, is that we are likely to underestimate top incomes for a number of distinct reasons. First, we use household surveys, which do a poor job at capturing the richest households (e.g. Atkinson et al., 2011; Alvaredo and Londoño Vélez, 2013). Second, even if the survey manages to interview the richest households, their income may be understated. In particular, household surveys in developing countries often fail to capture entrepreneurial and capital incomes, which remain the main sources of incomes of the rich in developing countries according to the few available data sources (Alvaredo and Gasparini, 2015). Third, consumption surveys – which are used in most developing countries outside Latin America – understate true living standards at the top because the rich save a higher proportion of their income than the poor. Actual consumption expenditures at the top may also be underestimated because expenditure surveys capture spending on durables poorly (Aguiar and Bils, 2015).

This suggests that household surveys are likely to underestimate the _level_ of inequality. However, if top incomes increase faster than the rest, the surveys would also underestimate the _trend_ in inequality. There is some suggestive evidence pointing in that direction. First, while the evidence from administrative data remains very limited, in some of the available countries top income shares are rising contrary to household-survey-based inequality measures (e.g. Colombia, Malaysia) (Alvaredo and Gasparini, 2015).<sup>3</sup> Second, much has been written about the declining labor shares in many countries around the world (Karabarbounis and Neiman, 2014). For example, in China at the same time as the labor share was falling, household savings recorded in national accounts were growing faster than GDP.<sup>4</sup> This suggests that the inequality in incomes grew faster than the inequality in consumption expenditures, which we use to estimate inequality in China. Third, a number of alternative data sources also point toward rising top incomes. In many developing regions of the world, billionaire wealth (according to the “rich list” published by Forbes magazine) increased faster than national income (Lakner and Ruggeri Laderchi, 2016). For example, between 2012 and 2015, a period of only three years, the number of billionaires in China doubled from 251

> 1 As a result, our results would tend to underestimate within-country and thus global inequality. However, Anand and Segal (2015) argue that the differences are very small. We find that moving from percentile to decile groups in a slightly different global distribution reduces the global Gini index by approximately 0.5 percentage points.

> 2 The difference between income and expenditure are net savings.

> 3 I am abstracting here from the fact that the Gini index is most sensitive to changes around the middle, so an increase in top incomes need not show up as a significant increase in the Gini index. See Alvaredo (2011) on the relationship between top income shares and the Gini index.

> 4 Household savings as a percentage of GDP increased from 17.5 in 2000 to 23.4 in 2008 (Ma and Yi, 2010).

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