It is important to stress that all the gains we discussed so far are relative gains. Of course, these translate into quite different absolute gains in annual consumption expenditure depending on the money amount in the base year. Figure 6 repeats the African GIC but uses the absolute gain (per annum) in annual consumption expenditure on the �-axis instead of the relative gain. It is thus very similar to taking the difference between the Pen’s Parade (or quantile function) in 2008 and 1993.<sup>38</sup> Precisely because the absolute gains are so different, the �-axis uses an inverse hyperbolic sine transformation instead of a linear scale.<sup>39</sup> Between 1993 and 2008, the top 5% of Africans added more than $100 per annum to their consumption expenditure, compared with $1 per annum for the 40<sup>th</sup> percentile group.

Yet another way of capturing the distribution of these gains is to look at the total gain in consumption expenditure between 1993 and 2008, and ask what share of this gain is received by different quantiles of the distribution.<sup>40</sup> Figure 7 shows that 39.4% of the total gain in consumption between 1993 and 2008 went to the top 5% of the African distribution, while the bottom 40% received 8.5%, i.e. around one quarter of the gain by the richest 5%. In EAP, the growth between 1988 and 2012 was more equally. For example, the top 5% received 20.8% of the total gain, compared with 13.2% for the bottom 40%.

In addition, a simple numerical example might help to put these gains into perspective. Between 1993 and 2008, the 13<sup>th</sup> ventile (between 65<sup>th</sup> and 70<sup>th</sup> percentile) grew by around 0.42% per annum, slightly faster than the 17<sup>th</sup> ventile (between 80 to 85) (0.40% per annum) (Figure 4). However, the 13<sup>th</sup> ventile started with an annual consumption of PPP-2011 $829 in 1988 compared with PPP2011 $1,517 for the 17<sup>th</sup> ventile. At the end of this period, they ended up with PPP-2011 $883 and PPP-2011 $1,611 respectively. Therefore, although both groups experienced comparable growth in their consumption, one group gained PPP-2011 $54 while the other gained PPP-2011 $94, implying of course quite different improvements in living standards.

> 38 The Pen’s Parade has incomes on the vertical axis for a number of quantiles along the horizontal axis (Ravallion, 2014b), or in other words, it is the inverse cumulative distribution function. Our chart is defined somewhat differently: Instead of showing quantile incomes (e.g. the income of the 5th percentile), we show average incomes for a quantile _group_ (e.g. the average income of the bottom 5%).

> 39 The inverse hyperbolic sine transformation (Burbidge et al., 1988) is similar to a logarithmic scale but can also accommodate negative values which occurs for the bottom quantile groups.

> 40 Such a comparison does not account for changes in total population. For example, Figure 4 showed that the average income of the bottom 5% fell by around 0.5% per year, while Figure 7 still shows a positive gain in total income for this group. Because population grew faster (at 3.4% per year) than total consumption (at 3% per year), the consumption for the average African in the bottom 5% fell.

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