Measuring Inequality - DARP

36 CHAPTER 2. CHARTING INEQUALITY2.4 From charts to analysisWe have seen how quite a large number of ad hoc inequality measures are associatedwith various diagrams that chart inequality, which are themselves interlinked.But however appealing each of these pictorial representations mightbe, we seem to …nd important reservations about any of the associated inequalitymeasures. Perhaps the most unsatisfactory aspect of all of these indices isthat the basis for using them is indeed ad hoc: the rationale for using themwas based on intuition and a little graphical serendipity. What we really needis proper theoretical basis for comparing income distributions and for decidingwhat constitutes a “good”inequality measure.This is where the ranking techniques that we have been considering come inparticularly useful. Although they are indecisive in themselves, they yet providea valuable introduction to the deeper analysis of inequality measurement to befound in the next chapter.2.5 Questions1. Explain how to represent median income in Pen’s Parade. How would yourepresent the upper and lower quartiles? [See footnote 8.]2. Describe how the following would look:(a) Pen’s Parade with negative incomes.(b) The Lorenz curve if there were some individuals with negative incomesbut mean income were still positive.(c) The Lorenz curve if there were so many individuals with negativeincomes that mean income itself were negative. [See the TechnicalAppendix, page 166. for more on this.]3. DeNavas-Walt et al. (2008) presents a convenient summary of UnitedStates’income distribution data based on the Annual Social and EconomicSupplement to the 2008 Current Population Survey. (a) How would theinformation in their Table A-1 need to be adapted in order to producecharts similar to Figure 2.2? (b) Use the information in Table A-3 toconstruct Pen’s Parade for 1967, 1987, 2007: how does the Parade appearto have shifted over 40 years? (c) Use the information in Table A-3 toconstruct the Lorenz curves for 1967, 1987, 2007: what has happened toinequality over the period? [Document is available on-line using the linkon the website http://darp.lse.ac.uk/MI3]4. Reconstruct the histogram for the UK 1984/5, before-tax income, usingthe …le “ET income distribution” on the website (see the Technical Appendixpage 174 for guidance on how to use the …le). Now merge adjacentpairs of intervals (so that, for example the intervals [£ 0,£ 2000] and