Poverty and Inequality Measurement By Dr. Dario Debowicz
Capacitybuilding in distributionalindicators and micro-simulationslinkedto CGE modelingDario Debowiczand Sherman Robinson
Schedule week by weekWeek 1. Introduction and Poverty and Inequality MeasurementWeek 2. Practice on Measurement. Linking CGE and micro-simulationsmodelWeek 3. Linking IFPRI CGE model with HIES 2010-11 to microsimulatepoverty indicators. Explanation and illustration with productivity-relatedsimulationsWeek 4. Group presentations extending previously done analysis (tax,exchange rate, energy)Week 5. First draft of appendix to previous studiesWeek 6. Feedback on studiesWeek 7. Delivery of appendix to previous studies.
Dario Debowicz20 March 2013Based on PatriciaJustino, 15 January 2009The Measurement of Poverty andInequality
Summary1. The concept of inequality2. The relationship between poverty and inequality3. Indices of inequality4. Inequality decompositions5. Multidimensional inequality6. Income mobility across quintiles and generations7. A recent study of inequality
• Economic inequality: disparities in income(consumption expenditure) or wealth betweenindividuals, households or groups of individualsor households. Unit can also be region, country,etc• Important to distinguish between short-termand long-term inequality (inequality estimatesmove very slowly)
Inequalityinworldincome…• World incomes are unequally distributed (inequalitybetween countries). In 2002:• Pc per year income of richest country (Switzerland) (US$ 37930)421 times largest than poorest country (RD Congo) (US$ 90)• PPP pc per year income of richest country (Norway) (US$ 35840)73 times largest than poorest country (Sierra Leone) (US$ 490)• Low and middle income countries produce 19.4% ofworld’s income (43.6% ppp); they have around 85% ofworld’s pop• Share of income of richest (poorest) countries more orless unchanged since 1960. However:• World distribution can be constant in relative terms but there hasbeen lots of change within the distribution.• Ups as well as downs!• Greatest mobility amongst middle-income countries
…Inequalityinworldincome• Income distribution is also highly unequal withincountries• E. g. UK (1991): poorest 10% of population (lowest decile) gets2.6% of all national income; richest 10% of population (top decile)gets 27.3% of total income• There seems to be an inverted-U pattern in both betweenand within country inequality (Kuznets):• Low inequality amongst poor countries; high inequality amongstmiddle income countries; low inequality amongst high incomecountries• For a given country: low inequality at low levels of economicdevelopment; higher inequality in transition periods, lowerinequality at higher levels of development
Inequalityof what?• Underlying notion of well-being can include manydimensions (like poverty):• Income or consumption expenditure• Education, health, nutrition and life expectancy• Wealth• Access to public services• Participation in public life
Unitofanalysis• We need to distinguish between inequalitybetween countries (weighted and unweighted)and inequality between individuals/households• Since WWII, unweighted inequality betweencountry risen, while weighted between countryinequality has fallen• Inequality between individuals is larger thaninequality between countries
Equalityofopportunitiesor equalityofoutcomes?Whatviewonsocialjustice?• Inequality of “outcomes”: refers to the distribution ofincomes (or other welfare dimension) resulting jointly fromthe efforts made by a person and the particularcircumstances under which this effort is made; it is mostlyconcerned with income inequality• Inequality of “opportunities”: refers to the heterogeneity inpersonal circumstances that lie beyond the control of theindividual, but that nevertheless affect the results of hisefforts, and possibly the levels of those efforts themselves(Roemer, 1998: John Rawls, Amartya Sen and others)• If there is equality of opportunities then resulting incomeinequality reflects the results of a fair system because itreflects differences individual talents, efforts andaccomplishments
But:• Unequal education systems• Changing demographic patterns i.e. population ageing• Unequal access to health care• Etc………• This can be counteracted by income mobility (implies lookingat inequality in long-term):→ it is often argued that the USA can sustain larger incomeinequality than other industrialized countries becausepossibilities for income mobility (across time for same individualand across generations) are higher; i.e. equality of opportunitiesis higher. More on this later………• Data typically allows us to analyse distribution of outcomes(monetary and non-monetary); difficult to capture andmeasure distribution of opportunities (see paper byBourguignon and Ferreira in reading list for discussion andexample…)
Why concernwith inequality?• Ethical and moral reasons: similar individualsshould not be treated differently• Functional reasons: inequality may affect prospectsfor economic growth and poverty reduction
2. The relationship between poverty and inequality
Inequalityvs Poverty• Inequality refers to the whole distribution, rather thanjust the part below the poverty line; it’s a morerelative concept• Is there a relationship between poverty andinequality?• Rising income inequality slows down the povertyreducing effect of growth• High initial income inequality reduces subsequentpoverty reduction; it is possible for inequality toincrease sufficiently high to result in rising poverty(Ravallion)• Inequality impacts on level of growth that is possible;therefore potential to reduce poverty will be affected
Main indicators• Share of income received by top 20% or bottom20%• Ratio of top 20% to bottom 20% income (orconsumption expenditure)• Relative mean deviation• Coefficient of variation• Gini coefficient• Generalised entropy measures
Measuringeconomicinequality• Define a vector y = y1, y2….yi….yn, with yi∈ℜ• n = number of units in the population (such as households,families, individuals or earners for example)• Let I(y) be an estimate of inequality using a hypothetical inequalitymeasure:• Anonymity: inequality measure independent of any characteristicof individuals other than their income → there is always a rankingy1 ≤ y2 ≤ ... ≤yn• Principle of Population: inequality measures invariant toreplications of the population (population size does not matter; it’sproportion of population groups that matter)for any scalar λ>0, I(y) = I(y[λ])
• Income Scale Independence (relative income principle):inequality measure invariant to uniform proportionalchanges: if each individual’s income changes by the sameproportion (as happens say when changing currency unit)then inequality should not change:for any scalar λ>0, I(y) = I(λy)• The Pigou-Dalton Transfer Principle: an income transferfrom a poorer person to a richer person should register asa rise (or at least not as a fall) in inequality and an incometransfer from a richer to a poorer person should registeras a fall (or at least not as an increase) in inequalityConsider vector y’ = transformation of the vector yobtained by a transfer δ from yj to yi , where yi>yj , andyi+δ >yj-δ,transfer principle is satisfied iff I(y’) ≥ I(y)
Relativemean deviation• M takes into account the entire distribution and notonly the extremes• M=0 if there is perfect equality; M=2(1-1/n) if allthe income is held by one individual• M is not sensitive to transfers from a poorer personto a richer person as long as both lie on the sameside of the mean income∑=−=niiyynM1_11
Coefficientof variation• Independent of mean income; concentrates on therelative variation of incomes• A transfer from a richer person to a poorer person willalways reduce the value of C (i.e., C passes the Pigou-Dalton test)• However, a transfer from a person with $500 to aperson with $400 or from a person with $100100 to aperson with $100000 causes C to fall by exactly thesame amount because C is very sensitive to transfers inthe upper tailC V y=12/_
The Ginicoefficient• Measures average difference between all possible pairs of incomesin the population expressed as a proportion of total income• 0 ≤ G ≤1; G = 0 indicates perfect equality; G = 1 means that oneindividual holds the whole income• G is sensitive to transfers from rich to poor at every level• G is closely related to the Lorenz curve of the distribution: areabetween the line of absolute equality (the diagonal) and the Lorenzcurve, when the size of each axis (those measuring acc % ofindividuals and of income) equal one.• G attaches higher weight to people in the middle of thedistribution; thus it does not fulfil the transfer sensitivity axiom.• G is a mean independent measure: if the incomes of everyone wereto double, the Gini coefficient would not be altered.Gn y ny yi jjnin=−−==∑∑12 1 11_( )
GeneralisedEntropy(GE)measures• Any measure I(y) that satisfies all of the axioms described above is a memberof the Generalised Entropy (GE) class of inequality measures:• n: number of individuals in the sample• yi: income of individual i, i ∈ (1, 2,...,n)• y bar= (1/n) ∑yi, the arithmetic mean income• Value of GE(α) ranges from 0 to ∞, with zero representing an equaldistribution (all incomes identical) and higher values representing higherlevels of inequality• α represents the weight given to distances between incomes at differentparts of the income distribution, and can take any real value:• for more negative values of α GE becomes more sensitive to gaps betweenincomes in the lower tail of the distribution• for more positive values GE becomes more sensitive to changes that affect theupper tail• the commonest values of α used are 0,1 and 2( ) ( )∑=−−=niiyyGE1221)(αααy
• When α = 0 (v close to zero) we have the mean logdeviation :• When α = 1 we have the Theil index:• With α=2 the GE measure becomes 1/2 the squaredcoefficient of variation, CV:∑==niiyynGE1log1)0(∑==niiiyyyynGE1log1)1(( )211211∑ −==nii yynyCV
Cumulative % of PopulationLine of Equality45°1000 100Cumulative %of IncomeLorenzCurveABIf two Lorenz curves cross → need partial rankings given by inequality measuresLorenz curves
Gini Coefficient =AreaBAreaAAreaA+The coefficient can vary between 0 and 1:0: no inequality – everyone receives exactly thesame amount of welfare1: perfect inequality – one person owns all thewealth (or education, or power, etc)
Foster-Greer-Thorbeque (FGT) Poverty MeasuresP0 = Poverty Headcount Ratio (HCR)P1 = Poverty Gap RatioP2 = Squared Poverty Gap Ratiowhere:z is the poverty lineyi is the income of person iN is the number of people in the populationM is the number of poor peopleαα ∑= −=MiizyzNP1)(1
Poverty and Inequality in Brazil, 1985-2001HeadcountindexPovertygapSquaredpovertygapIncomeGini1985 15.8 4.7 1.8 0.601995 14.0 3.9 1.5 0.601996 14.9 4.6 1.9 0.601999 9.9 3.2 1.3 0.612001 8.2 2.1 0.7 0.59Source: World Bank, Global Poverty Monitoring, http://www.worldbank.org/research/povmonitor/index.htmNote: The headcount index indicates the percentage of individuals below the poverty line of US$1 per day.
Often we need to distinguish between:• Inequality ‘between’ and ‘within’ countries or groups ofindividuals/households or regions that form the country(unweighted and weighted)
Year InequalitywithincountriesInequalitybetweencountriesTotalInequality1820 0.462 0.061 0.5221910 0.498 0.299 0.7971950 0.323 0.482 0.8051992 0.342 0.513 0.855Source: Bourguignon and Morrisson (2002), “Inequality Among World Citizens, 1820-1992”, American Economic Review.
Within-Group Income Inequalities in Brazil 1996Pop. % Mean income GE(0) GE(1)White 54.5 323.7 0.63 0.66Black 7.2 135.7 0.46 0.49Asian 0.5 580.6 0.54 0.49Mixed 37.7 136.5 0.55 0.59Indigenous 0.2 153.3 0.77 0.74North 4.8 180.2 0.59 0.66North East 29.1 130.2 0.71 0.85Centre West 6.8 249.3 0.63 0.73South East 43.9 309.2 0.57 0.61South 15.4 268.2 0.57 0.62Urban 79.7 277.5 0.62 0.66Rural 20.3 95.4 0.55 0.64Source: Justino, Patricia and Niimi, Yoko (2005), Multidimensional Inequality and HouseholdWelfare: An Empirical Analysis, mimeo.
Share of Between-Group Inequalities in Total Inequality inBrazil 1996Race State Region Urban/RuralGE(0) 13.2 12.0 9.3 10.9GE(1) 11.5 10.5 7.8 7.9GE(2) 4.7 4.4 3.0 2.8Source: Justino, Patricia and Niimi, Yoko (2005), Multidimensional Inequality and HouseholdWelfare: An Empirical Analysis, mimeo.
5. Multidimensional inequalityAs with poverty, inequality is a multidimensionalphenomenon………
Summary Measures of Household Income andEducation Inequality in Brazil 1996PcincomePaeincomeMaxyearsschoolingSchoolingheadSchoolingfatherSchoolingmotherMean 240.54 464.46 7.590 4.908 2.444 2.119St dev 441.45 760.05 4.124 4.350 3.400 3.098Gini 0.596 0.569 0.310 0.490 0.644 0.675GE (0) 0.677 0.601 0.730 2.441 4.190 4.705GE (1) 0.718 0.635 0.177 0.444 0.826 0.916GE (2) 1.684 1.339 0.148 0.393 0.968 1.069Note: Information on education of father and mother was collected for individuals aged 15or above.Source: Source: Justino, Patricia and Niimi, Yoko (2005), Multidimensional Inequality andHousehold Welfare: An Empirical Analysis, mimeo.
Correlation Matrix for Income and Education HouseholdInequalities in Brazil 1996Incomequintile 1Incomequintile 2Incomequintile 3Incomequintile 4Incomequintile 5Education quintile 1 58.53 36.40 25.49 13.41 5.54Education quintile 2 17.70 20.27 15.79 10.22 3.49Education quintile 3 16.50 26.72 29.51 27.24 12.63Education quintile 4 6.65 15.08 25.14 36.02 31.11Education quintile 5 0.63 1.54 4.07 13.10 47.23Total 100.0 100.0 100.0 100.0 100.0Source: Source: Justino, Patricia and Niimi, Yoko (2005), Multidimensional Inequality and HouseholdWelfare: An Empirical Analysis, mimeo.
6. Income mobility across quintiles and generations
• Income mobility refers to the amount ofmovement across income ranks experienced bypersons or families• The simplest measure of economic mobility is thepercentage of individuals who move into a newincome quintile• Income mobility is important because it offsetsinequality: increasing inequality may be moreaccepted if accompanied by increasing mobility
Income Mobility Transition Matrix for USA, 1968-91Gottschalk1968IncomeQuintile1991 Income QuintileLowest Second Middle Fourth Highest TotalLowest 46.7 24.5 17.3 8.7 2.7 100.0Second 23.6 26.2 26.4 14.3 9.6 100.0Middle 13.6 21.8 20.2 26.2 18.2 100.0Fourth 9.2 16.7 20.4 26.2 27.6 100.0Highest 6.7 10.8 16.1 24.5 42.0 100.0Total 100.0 100.0 100.0 100.0 100.0
• Dahan and Gaviria (1999): use sibling correlations inschooling to measure differences in intergenerationalmobility in Latin America• Intuition: if there is perfect social mobility, familybackground would not matter and siblings shouldbehave as two random people chosen from the totalpopulation. If, on the other hand, family backgroundmatters, then siblings would behave in a similarfashion
Sibling Correlations of Schooling Outcomes: Latin America and theUnited StatesCountry Year Mobility index Inequality of schoolingArgentina 1996 0.437 0.26Bolivia 1997 0.561 0.35Brazil 1996 0.531 0.49Chile 1996 0.435 0.25Colombia 1997 0.587 0.38Costa Rica 1995 0.340 0.36Ecuador 1995 0.577 0.35Mexico 1996 0.594 0.38Nicaragua 1993 0.576 0.66Panama 1997 0.480 0.32Peru 1997 0.385 0.27El Salvador 1995 0.599 0.55Uruguay 1995 0.418 0.25Venezuela 1995 0.438 0.32Average 0.490 0.37USA 1996 0.203 0.17
Factorsthat influenceincomemobility• Family transmission of wealth (through inheritance)• Family transmission of ability (better educated parentstend to have better educated children)• Imperfect capital markets (inability to borrow and otherconstraints)• Neighbourhood segregation effects (self-imposed andexternally imposed)• Self-fulfilling beliefs (sociology and phycology)
Milanovic,Branko,Lindert,PeterandWilliamson,Jeffrey(2007),MeasuringAncientInequality,WorldBankPolicyResearchWorkingPaperno.4412,TheWorldBank,November2007.• → Instead of actual inequality indices, authors calculate inequalitypossibility frontiers and inequality extraction ratios, i.e. they assesshow actual inequality compares with the maximum feasibleinequality that could have been extracted by the elite i.e. thatcoming from distributing income just to guarantee subsistenceminimum for its poorer classes• Main findings:• Income inequality in still-pre-industrial countries today is not verydifferent from inequality in distant pre-industrial times• Extraction ratio – how much potential inequality was convertedinto actual inequality – was larger in ancient times than now• Differences in lifetime survival rates between rich and poorcountries and between rich and poor individuals within countrieswere higher two centuries ago; there was greater lifetimeinequality in the past than now