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Lect1 inequality-measurement



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  • Unequal access to lifetime economic resources begins from parental wealth and access to resources, so inequality and deprivation cannot be blamed on individuals’ bad decisions Growth spreading its benefits equitably or inequitably among the population People derive their satisfaction/happiness not from the absolute level of their consumption but from how their consumption compares with that of the people around them
  • Some ground clearing… inequality is multidimensional: encompasses both inequality in opportunities and inequality in outcomes Fundamental disparities are ultimately linked to differences in personal capabilities and political freedoms, but… by studying the analysis of differences across the population in access to and control over economic resources, we hope to capture the essence of inequality multidimensionality disparities in personal income and wealth stand for an important component of all differences
  • In the functional distribution view, Income inequality is determined by the market conditions in each of the factor markets as well as by the pre-existing distribution of wealth (financial and physical capital, and land or real estate property). This view is particularly relevant if we want to emphasise the analysis of the existent class structure of the society (workers, capitalists, landlords) and the degree of market power each has in the demand and supply of production factors. In relation to history and political economy causes, we have Market and Structural Inequality : the former arises from the very functioning of a market economy, i.e. rewards to risk-taking, entrepreneurship, skill acquisition and saving all affect income and wealth accumulation; the latter can be traced in discrimination due to political connections and social status due to historical factors (colonial legacy, gentry) that are at the origin of wealth disparities.
  • The 1 st set of arrows describes how income is generated from the production process The 2 nd set of arrows tells us different categories of income are funnelled to households; and the direction and magnitude of these flows depend on who owns which and how much factors of production Functional distribution is useful to understand how inequalities are created, and in turn how they are connected to growth
  • What are the desirable properties that an inequality index should satisfy? 4 principles: (i) Anonymity; (ii) Population; (iii) Relative income; (iv) Dalton principle it is difficult to reach unanimity on what a desirable index should satisfy There is inevitably a trade off: if you lay down weak criteria, then many indices can be suggested but probably giving contrasting results; if you impose strong criteria, you will reduce the number of admissible indices, but the criteria loses wide approval
  • The poorest 20% population earns 10% of overall income The slope of the curve at each point is simply the contribution of the person at that point to the cumulative share of national income 45-degree line: any cumulative fraction of the population would share exactly that very same fraction of national income The poor makes a small marginal contribution to national income – shallow Lorenz curve at low cumulative income values The rich makes a high marginal contribution to national income – steep Lorenz curve at high cumulative income values
  • It can be shown that an inequality measure is consistent with Lorenz criterion iff it is simultaneously consistent with the previous 4 criteria


  • 1. 1Economic Inequality: concept and measurement• The analysis of the distribution of income, orwealth, among different groups in society. Why?• Motivation: (i) philosophical and ethical for aversionto inequality per se; (ii) inequality in income andwealth affects the possibility of growth; (iii) DCs areprone to huge disparities in living standardsOutline• Nature of economic inequality• Measuring inequality• Complete measures
  • 2. 2Economic inequality is the fundamental disparity thatpermits one individual certain material choices, whiledenying another individual those very same choices• Disparities in wealth or incomeAspects of the distribution of income and wealth:• Over which time period we study them? Current orlifetime inequality hide considerations of social mobility• The distribution of income can also be observed withrespect to the class of recipient (i.e. population groupedby gender, ethnicity, age, marital status andgeographical area)Perspectives on economic inequality
  • 3. 3Perspectives on economic inequality 2• The distribution of income can be observed among thepopulation, called size (or personal) distribution of income,and can be expressed between some demographic unit:households, individual earners, or all individuals withrespect to the command over some definition of income(gross or net) or expenditure.• Functional distribution of income relates to disparities infactors of production rewards: income inequality dependson how labour, (physical and financial) capital and land arerewarded with wage, profit, interest and rent (the last twoare property income), respectively.• The distribution of wealth measures the value of a person’sassets at some point in time. It is related to inheritance,different propensities to save, investment talent/luck, andincome inequality. Empirically, it is very hard to measure itbecause a stock of assets is measurable only when sold.
  • 4. 4Perspectives on economic inequality 3Household2Household3Household4WagesofDifferentSkillsProfitsRentsProductionHousehold1FunctionalDistribution PersonalDistributionOwnershipof FactorsFunctional and personal distribution of income
  • 5. 5Inequality comparisons
  • 6. 6Measuring inequality: notation• Goal: we have to develop indices that permit the rankingof (lifetime) income or wealth distributions in two differentsituations• Suppose society is composed of i=1,2,…, n individuals;income distribution is a description of how much yi isreceived by each i: (y1, y2,… yn); we want to compare twodistributions• Inequality measure, I, is a rule that assigns a degree ofinequality to each possible distribution of the national cake• I=I(y1, y2,… yn), defined over all conceivable distributions(y1, y2,… yn)
  • 7. 7Inequality measures: Lorenz curve 1A diagrammatic way to depict distribution• X-axis: cumulative percentages of the populationarranged in increasing of income• Y-axis: % of national income accruing to any fraction ofthe population thus arranged• The graph connecting these points is the Lorenz curve• If everybody earned the same income, this curve wouldcoincide with the 45oline• The overall distance between the 45oline and the Lorenzcurve is indicative of the amount of inequality present inthe society
  • 8. 8Inequality measures: Lorenz curve 2Cumulative Population 100%100%CumulativeIncome20%10%A80%70%B45 0LorenzCurveThe Lorenz curve of a distribution of income
  • 9. 9Inequality measures: Lorenz curve 30L(1)L(2)450CumulativePopulation100%CumulativeIncome100%Using Lorenz curve to make judgements• L(1) lies above L(2)• Interpretation: if we choosea poorest x% of thepopulation, then L(1)always has this poorest x%earning at least as much asthey do under L(2)• It stands to reason that L(1)should be judged moreequal than L(2)• This criterion for inequality comparison is known as Lorenzcriterion
  • 10. 10Lorenz curves for selected countries 1Lorenz curves for different countries (Deininger and Squire, 1996)Brazil2717350204060801000 20 40 60 80 100Cumulative Shares of Population (%)CumulativeSharesofIncome(%)Mexico31022410204060801000 20 40 60 80 100Cumulative Shares of Population (%)CumulativeSharesofIncome(%)Egypt92137590204060801000 20 40 60 80 100Cumulative Shares of Population (%)CumulativeSharesofIncome(%)India92138590204060801000 20 40 60 80 100Cumulative Shares of Population (%)CumulativeSharesofIncome(%)Kenya31021380204060801000 20 40 60 80 100Cumulative Shares of Population (%)CumulativeSharesofIncome(%)Uganda71731520204060801000 20 40 60 80 100Cumulative Shares of Population (%)CumulativeSharesofIncome(%)
  • 11. 11Lorenz curves for selected countries 2Korea72036580204060801000 20 40 60 80 100Cumulative Shares of Population (%)CumulativeSharesofIncome(%)Taiwan72038610204060801000 20 40 60 80 100Cumulative Shares of Population (%)CumulativeSharesofIncome(%)United Kingdom82036590204060801000 20 40 60 80 100Cumulative Shares of Population (%)CumulativeSharesofIncome(%)United States51532560204060801000 20 40 60 80 100Cumulative Shares of Population (%)CumulativeSharesofIncome(%)
  • 12. 12ReferencesCore readings:• Ray D., (1998), Development Economics, Princeton University Press, Chapter: 6• McKay A., (2002), “Defining and Measuring Inequality”, ODI Inequality briefing paper NoRecommended readings:• Champernowne D.G. and Cowell F.A., (1998), Economic Inequality and Income Distribution,Cambridge University Press, Chapters: 3 – 4. This is a valid alternative to the core readings,but it is more detailed and technical.• Jenkins S., (1991), “The measurement of income inequality”, chapter 1 in Osberg L. (ed),Economic inequality and poverty, M.E. Sharpe. It is a comprehensive exposition, with afocus also on operational issues, on the measurement of inequality.• Hale T., (2003), “The theoretical basis of popular inequality measures”, University of TexasInequality Project (UTIP),• Litchfield J.A., (1999), “Inequality: Methods and Tools”, Text for the World Bank PovertyNetwebsite:, March 1999Other useful references for developing economies are on land and education inequality:• Ray D., (1998), Development Economics, Princeton University Press, Chapter: 12• Frankema E.H.P., (2006), “The Colonial Origins of Inequality: Exploring the Causes andConsequences of Land Distribution”, Groningen Growth and Development Centre, ResearchMemorandum GD-81, University of Groningen• Frankema E.H.P. and Bolt J., (2006), “Measuring and Analysing Educational Inequality: TheDistribution of Grade Enrolment Rates in Latin America and Sub-Saharan Africa”, GroningenGrowth and Development Centre, Research Memorandum GD-86