Measuring Inequality - DARP

30 CHAPTER 2. CHARTING INEQUALITYto whether people “fall in”on the right or on the left of point P when we arrangethem in the frequency distribution diagram (Figures 2.2 and 2.7). In e¤ect thehigh/low inequality index would become a slightly modi…ed poverty index.The use of any one of the measures we have discussed in this section impliescertain value judgements concerning the way we compare one person’s incomeagainst that of another. The detail of such judgements will be explained in thenext chapter, although we have already seen a glimpse of some of the issues.2.3 RankingsFinally we consider ways of looking at inequality that may lead to ambiguousresults. Let me say straight away that this sort of non-decisive approach is notnecessarily a bad thing. As we noted in Chapter 1 it may be helpful to knowthat over a particular period events have altered the income distribution in sucha way that we …nd o¤setting e¤ects on the amount of inequality. The inequalitymeasures that we have examined in the previous section act as “tie-breakers”in such an event. Each inequality measure resolves the ambiguity in its ownparticular way. Just how we should resolve these ambiguities is taken up inmore detail in Chapter 3.QuantilesSharesTYPES OF RANKINGThe two types of ranking on which we are going to focus are highlighted inthe accompanying box. To anticipate the discussion a little I should point outthat these two concepts are not really new to this chapter, because they eachhave a simple interpretation in terms of the pictures that we were looking atearlier. In fact I could have labelled the items in the box as Parade Rankingsand Lorenz Rankings.We have already encountered quantiles when we were discussing the incomesof the 3rd and 57th minute people as an alternative to the range, R (page 24).Quantiles are best interpreted using either the Parade diagram or its equivalentthe cumulative frequency distribution (Figure 2.3). Take the Parade diagramand reproduce it in Figure 2.8 (the parade of Figure 2.1 is the solid curve labelled1984/5; we will come to the other two curves in a moment). Mark the point 0:2on the horizontal axis, and read o¤ the corresponding income on the verticalaxis: this gives the 20-percent quantile (usually known as the …rst quintile justto confuse you): the income at the right-hand end of the …rst …fth (12 minutes)of the Parade of Dwarfs. Figure 2.8 also shows how we can do the same forthe 80-percent quantile (the top quintile). In general we specify a p quantile–which I will write Q p –as follows. Form the Parade of Dwarfs and take theleading proportion p of the Parade (where of course 0 p 1), then Q p is the