Measuring Inequality - DARP

32 CHAPTER 2. CHARTING INEQUALITYFigure 2.9: Quantile ratios of earnings of adult men, UK 1968-2007. Source:Annual Survey of Hours and Earningsinequality: the movement of the corresponding income shares (which we discussin a moment) could in principle be telling us a di¤erent story. 9However, we might also be interested in the simple quantile ranking of thedistributions, which focuses on the absolute values of the quantiles, rather thanquantile ratios. For example, suppose that over time all the quantiles of thedistribution increase by 30 percent as shown by the curve labelled “hypothetical”in Figure 2.8 (in the jargon we then say that according to the quantile rankingthe new distribution dominates the old one). Then we might say “there are stilllots of dwarfs about”, to which the reply might be “yes but at least everybody isa bit taller.”Even if we cannot be speci…c about whether this means that thereis more or less inequality as a result, the phenomenon of a clear quantile rankingis telling us something interesting about the income distribution which we willdiscuss more in the next chapter. On the other hand if we were to compare1981/2 and 1984/5 in Figure 2.8 we would have to admit that over the threeyear period the giants became a little taller (Q 0:8 increased slightly), but thedwarfs became even shorter (Q 0:2 decreased slightly): the 1984/5 distributiondoes not dominate that for 1981/2.9 In case this is not obvious consider a population with just 8 people in it; in year A theincome distribution is (2; 3; 3; 4; 5; 6; 6; 7), and it is fairly obvious that Q 0:25 = 3 and Q 0:75 = 6in year B the distribution becomes (0; 4; 4; 4; 5; 5; 5; 9) and we can see now that Q 0:25 = 4 andQ 0:75 = 5. Mean income and median income have remained unchanged and the quartileshave narrowed: but has inequality really gone down? The story from the shares suggestsotherwise: the share of the bottom 25% has actually fallen (from 5=36 to 4=36) and the shareof the top 25% has risen (from 13=36 to 14=36).