The Distribution of Income in Ireland (2000) - Combat Poverty Agency

10 The Distribution of Income in Irelandbottom 10 per cent, the next per cent, . . . top 10 per cent. Inlooking at the earnings distribution we follow conventionalpractice and the deciles or quartiles of the distribution as percentagesof the median — the earnings at the 10th percentilepoint, 25th percentile . . . 90th percentile point as percentagesof median earnings. In addition, various summary measures ofinequality are employed here. These are the Gini coefficient,Theil's entropy measure, the coefficient of variation, the meanlogarithmic deviation, the Atkinson inequality measure with acoefficient (i.e. inequality aversion parameter) of 0.5 and 1.0,and the ratio of the top to the bottom decile, P 90 /P 10 . Suchmeasures, designed to summarise the degree to which incomesare concentrated, are commonly used in the study of incomeinequality. Since some inequality measures put most weight onincome differences in different parts of the distribution to others,all such measures will not always display the same trends,so it is worth looking at more than one. In addition, some measuresare more suitable than others for specific types of analysis,in particular decomposition into sub-groups or income sources.We will not attempt to review here their derivation and properties,on which there is an extensive literature: a comprehensivedescription is given in e.g. Cowell (1995).Summary measures represent one approach to capturingand comparing the level of inequality in different income distributions.Lorenz curves, on the other hand, show the wholedistribution in graphical form. As illustrated in Figure 2.1, thisshows the share of total income going to the bottom x per centof the distribution, where x goes from 0 to 100 per cent. Wherethe Lorenz curve for one distribution lies above that for anotherdistribution at all points, this means that the bottom x per centof the first distribution has a higher share than in the seconddistribution no matter which value we choose for x. For distributionswith the same mean income, it has been shown that thismeans that the first distribution can be taken to have a higherlevel of what economists term "social welfare", for quite a widevariety of social welfare functions. Where the Lorenz curvesintersect, on the other hand, no such unambiguous ranking ofthe distributions is available - it will depend on the weight weassign to different parts of the distribution (see Cowell, 1995)Measuring the Distribution of Income in Ireland 11Figure 2.1: Lorenz Curve for Income"ot tnCI* 8•a > *-•«i 3O1008060402000 20 40 60 80 100Cumulative Percentage ofIndividuals or HouseholdsWhat about where the two distributions have different levels ofmean income? Generalised Lorenz curves provide a convenientway of incorporating information about average living standardsand inequality into the comparison of the level of socialwelfare yielded by different distributions. This involves plottingcumulative mean incomes (instead of cumulative income sharesin standard Lorenz curves) against cumulative populationshares (see Shorrocks, 1983; Jenkins, 1991). Once again, unambiguousrankings will only be available in certain circumstances,but the value of the approach is precisely in allowingus to identify when that occurs.2.4 CONCLUSIONS•Line of EqualityIncomeThis chapter has outlined the data and methods to be employedin measuring the distribution of income in this study. The studyrelies on data from large-scale household surveys carried outby the ESRI and the CSO. The methodological choices faced insuch a study include the choice of income recipient unit, howbest to adjust income for the size and composition of the household,and how best to present and summarise the shape of theincome distribution. We go on in the next chapter to use thesemethods to analyse the distribution of income in Ireland in the1990s.