per capita required to reduce the global poverty rate one percentage point per year if the distribution of household expenditure does not change and population growth is uniform for all countries between 2010 and 2030, as assumed in Ravallion’s second approach (2012, 2013). The required growth rates rise rapidly once the poverty rate reaches 10 percent (see Figure 1). If the poverty rate continues to decline one percentage point per year, it will reach 8.6 percent by 2022. To reduce it further to 6.6 percent in the next two years (2022–2024), the developing world needs to increase the annual growth rate of household expenditure per capita from 4.1 percent to 5.1 percent, which is higher than the average growth rate of the developing world as a whole between 2002 and 2010. To reduce the global poverty rate further from 6.6 to 4.6 in the following two years (2024–2026), the annual growth rate needs to increase to 7.4 percent. The required growth rate will continue to increase in the next four years to 47.9 percent.

**Figure 1:  Required Growth Rates of Mean Household Expenditure/Income Per Capita (annualized, %)**

<!-- Start of picture text --> 47.9<br>50 20.0<br>18.6<br>45 18.0<br>16.6<br>40 16.0<br>14.6<br>35 14.0<br>12.6<br>30 12.0<br>10.6<br>25 10.0<br>8.6<br>20 8.0<br>6.6<br>15 6.0<br>14.0<br>7.4 4.6<br>10 2.7 2.8 3.0 3.1 3.6 4.1 5.1 2.6 4.0<br>5 2.0<br>0.6<br>0 0.0<br>2010-122012-142014-162016-182018-202020-222022-242024-262026-282028-30<br>Annual growth rates required (%) Poverty rate (%) at the end of period<br>Annual growth rates required (%) Poverty rate (%) at the end of period<br><!-- End of picture text -->

**_Source_** : Authors’ estimations using PovcalNet (October 2013) and poverty projections of Ravallion (2012). The distribution of household expenditure per capita in 2010 is used to estimate growth rates required to reduce the global rate 1 percentage point per year.

Ravallion (2013) recognizes possible nonlinearity in the pace of poverty reduction once the poverty rate reaches 10 percent. The above analysis clarifies why we tend to have such nonlinearity. Maintaining the linearity of poverty reduction requires increased growth rates. Our analysis confirms that once the global poverty rate reaches around 10 percent, a huge rate of economic growth (7 percent or higher) is required, which makes maintaining the pace of poverty reduction almost impossible.

Another way to illustrate the nonlinearity in the pace of poverty reduction is to compare the path of the distribution-neutral projection with the path of the linear projection. In both approaches, the poverty rate of 2030 is projected to be very close to 3 percent. However, the distribution-neutral projection with a constant annual growth rate of 4.5 percent shows clear nonlinearity, which means the pace of poverty reduction slows gradually but persistently (see Figure 2) if household expenditure grows at a constant rate. Indeed, it is clear that the pace of poverty reduction is much more than one percentage point per year in the beginning and slows to near zero between 2028 and 2030.

# _Assessment of the distribution-neutral approach_

The distribution-neutral approach conducted in Ravallion (2013) makes three key assumptions: (i) a uniform population growth rate across all developing countries; (ii) uniform growth rates of mean household expenditure per capita; and (iii) no change in inequality within a country. We evaluate whether these assumptions are likely to hold and if not, the implications of a violation of these assumptions of the poverty projection.

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