the trends in the shares of consumption of the bottom and top quintiles have continued in the same direction.

However, the narrative about inequality is more nuanced than the summary measures suggest. The summary measures of inequality analyzed above only partially capture the changes at various points of the consumption distribution. The results of a simple inter-quantile analysis can provide more detailed information on the changes occurring at all points of the distribution (see Table 2). They show that the ratio of average consumption among the top 10 of the distribution to the average consumption among the bottom 10 had risen considerably even before 1998/99, suggesting that the more well-off had benefited more than the poorest decile from the economic growth in 1991-98. Over the years, the consumption levels of the top and the bottom of the distribution continued to diverge at a steady rate so that the gap expanded by 30 % over the full period.<sup>4</sup> The divergence was widening because the bottom 10 was being left behind, rather than because the top 10 was gaining disproportionally compared with the rest of the population. The average consumption of the 90-th percentile rose little relative to the median, while the average consumption of the bottom 10 had deteriorated by nearly 20 % by 2005/06. The bottom 10 appears to be losing ground also compared with other households in the bottom 25, who are also losing ground to the median but only half as quickly.

These preliminary findings denote a clear tendency towards rising polarization in household consumption over the period. The notion of “polarization” commonly refers to the case where there is a significant number of individuals who are very poor but there exists also a non-negligible share of the population that is quite rich. Such a gap between the poor and the rich implies evidently that there is no sizeable middle class.<sup>5</sup> As we will see later when applying relative distribution methods, the distributional changes that occurred between 1991/92 and 2012/13 hollowed out the middle of the Ghanaian household consumption distribution and increased the concentration of households around the highest and lowest deciles, hence leading to an increase of polarization.

# **2.2 Relative distribution methods**

## _2.2.1 Basic concepts_

> 4 The gap between 90-th and 10-th deciles is probably a lower bound of the real one. In general, household surveys do not contain good estimates of upper percentiles of welfare (Alvaredo and Piketty, 2010). When using consumption to rank welfare, as it is normally done in low/er middle income countries, the situation is further aggravated. Consumption is very accurate in capturing the well-being of poorer people, yet it is rather imprecise in capturing that of people living in upper percentiles.

> 5 In this paper we will analyze the median-based approach to the measurement of polarization. Since it subdivides the population into two subgroups – those above the median and those below the median, respectively – we refer to this as the case of “bi-polarization”. For a detailed explanation of the main differences not only between the study of inequality and that of polarization, but also between the concept of bi-polarization and that of “multi-polar” polarization, see e.g. Chakravarty (2009, ch. 4), Deutsch et al. (2013) and Chakravarty (2015).

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