from the national accounts for those dates when surveys are not available.<sup>6</sup> In this sense, national accounts are used but only for interpolation, and the main sources of growth rates remain the household survey mean.

# _Aggregation bias_

It is important to determine at what level projections should be carried out. Ravallion (2013) conducted projections of the global poverty rate at the global level, or using a global income or expenditure distribution, and noted the risk of aggregation bias. For example, he mentioned that China has been a key contributor to global poverty reduction and it is expected that growth in China will continue. However, if the high growth rate persists, China’s poverty rate will soon reach zero, after which China’s growth will cease to contribute to the pace of global poverty reduction. To minimize this aggregation bias, it is recommended that country-level poverty projections be conducted first, then aggregated into global poverty. Other major recent studies on global poverty projection have taken this approach (see Lanjouw et al. 2013, Edward and Sumner 2013, and Chandy et al. 2013).

# **III. How Optimistic Are the Poverty Projections Done by Ravallion (2013)?**

This section reviews the approach used by Ravallion (2013) and identifies assumptions considered to be optimistic. It is first important to note how global poverty is defined. Ravallion (2013) estimates the percentage of those living on less than US$1.25 per day per capita in all developing countries, as was the practice based on the 1990s definition. However, the World Bank Group goal includes developed countries in its definition of the global poverty rate. Since the poverty rate in the developed world is negligible, the poverty rate in the developing world is higher than that of the world. To clarify the distinction, we refer to poverty rates estimated in Ravallion (2013) as the poverty rate of the developing world.

Ravallion (2013) conducted two approaches to project poverty rates of the developing world in 2027, namely a linear projection approach and a distribution-neutral approach. The linear projection approach means the poverty rate of the developing world will continue to decline by the same percentage point value per year. Ravallion (2013) estimated the average percentage reduction of the poverty rate per year from the global poverty rates between 1981 and 2010 and found that the poverty rate of the developing world has been declining by one percentage point per year (or more precisely 1.04 percentage points per year). If this pace continued, the global poverty rate would be 3 percent in 2027.

The distribution-neutral approach assumes that all countries in the developing world share the same growth rates of mean household expenditure per capita and populations without changing the shape of the distribution from the reference year.<sup>7</sup> Ravallion (2013) found that if all countries grew at 4.5 percent per year, and the shape of the distribution were the same as for 2008, the poverty rate of the developing world in 2027 would be 3 percent.

# _Why were these projections considered optimistic?_

Both approaches seem to assume that the current pace of poverty reduction would continue until 2030. This assumption may sound realistic and reasonable, but the following analyses will show that it is indeed quite optimistic.

For example, maintaining the pace – one percentage point per year – becomes increasingly difficult as the poverty rate declines. To show this, we calculate the growth rates of household expenditure (or income)

> 6 See more details in Ravallion (2013), Chen and Ravallion (2010), and Chen and Ravallion (2013).

7 More precisely, mean household expenditures (or income) per capita will grow without changing a Lorenz curve of their distribution. This is because Ravallion (2013) calls this approach an “inequality-neutral” projection.

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