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What is inequality and how we measure it Milanovic, Global inequality and its implications Lectures 1 & 2

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Absolute vs. relative

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Is conception of inequality based on absolute or relative income distances? Does inequality increases if all incomes go up by the same percentage? (stay the same, go up, even go down; Dalton) How about when they all go up by the same constant? Is inequality anonymous? If poor and rich swap places (note: this is pro-poor growth) will inequality be less or the same?

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Relative inequality is about ratios; absolute inequality is about differences. –State A: two incomes $1,000 and $10,000 per year –State B: these rise to $2,000 and $20,000 –Ratio is unchanged but the absolute gain to the rich is twice as large in state B 40% of participants in experiments view inequality in absolute terms (Amiel and Cowell). Relative and absolute inequality

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Absolute inequalityRelative inequality Growth and inequality The tide rises all boats by the same proportion of their initial income; no Δ in relative inequality But absolute income differences increase Source: Ravallion (2003)

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Important definitions to keep in mind Welfare aggregates: expenditures, consumption, income (net or gross) Who is the recipient: household or individual? What is the ranking criterion: income per capita, household income, or income per equivalent unit?

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Issues to keep in mind Survey issues: non-compliance (refusal to participate), underreporting, top-coding. Researchers can do nothing about these. Income: valuation of home consumption, imputed rent, self-employment income, property income; net or gross income. Researchers can do very little about that. Coverage and classification of expenditures Distinguish consumption and expenditures (use of imputation; treatment of bulky purchases like cars)

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Survey non-compliance Distinguish from income underreporting Both stronger among the rich than the poor; underestimate of inequality If survey non-compliance increases in income (as empirical studies show) => poverty HC overestimated, inequality probably underestimated (although we cannot establish Lorenz dominance) We believe that non-compliance increases in income because (mean) richer areas generally show higher % of refusal to participate US inequality may be underestimated by as much as 4 Gini points or 10% (Korinek, Mistiaen, Ravallion, 2006)

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Income vs. expenditures

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Income vs. expenditures (or consumption)? Income: gives actual economic power Expenditures or consumption: give actual standard of living Savings (as % of income) generally larger for higher income households => inequality of income greater than inequality of expenditures Income can be negative; C cannot be => inequality of income greater than inequality of expenditures So at both ends, income gives higher inequality (would also give greater poverty)

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Welfare metric: Income vs. expenditure or consumption Income and expenditure per capita by percentile (people ranked by YPC) People at the bottom (up to 30 th percentile) dissave; people at the top (richest 30 percent) save

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This despite high correlation in general between income and expenditures(so high ρ can sometimes be misleading) South African 1998 expenditure and income per capita (in logs)

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Blue line: the story as before. Red line: high C households dissave. Gini for YPC = 28.4; Gini for XPC = 26.7 Expenditure-to-income ratio across ventiles Data Poland Heide; see XYratios.xls file

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The consumption-income ratios: overall net dissaving (asset sales); or more likely, better reporting of consumption than income in HS Blue line: the same story as before; Red line: C-rich people underreport their income Source: Serbia LSMS 2002; file poorAZ.xls Overall C/Y ratio = 1.09 Overall C/Y=1.12

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Where in terms of YPC distribution, are high C people who report C/Y ratio>2? Graph shows where in YPC distribution are people from the 20 th (highest) C ventile whose reported C/Y is greater than 2. They are across all income distribution even among those who are income poor. Source: Serbia LSMS 2002;

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Actual distributions and functional forms: Actual income distribution (Malaysia 1997 YPC) and log- normal curve imposed on it

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Individuals vs. households

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What type of distribution: Recipient Ranking criterion HouseholdPerson Household income D(H|Yh)--- Household income per capita D(H|Yp)D(p|Yp)

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D(p|yp) and D(h|yh): Mexico 2002 Expressed in terms of either mean per capita or mean per HH income.

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Difference between D(p|Yp) and D(H|Yh)

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Equivalence scales (economies of size)

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Equivalence scales The basic idea: to reach the same degree of utility, people may not need the same amount of income But we know nothing about how individuals convert income into utility (no inter-personal comparisons) What we know (or suppose): (i) cost of food is less for children than for adults; (ii) people who live together share public goods (its cheaper in per capita terms for two people to live together than individually; think of heating costs)

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Equivalence scale is then needed to adjust household income for components (i) and (ii) Instead of dividing total household income (Y) by number of people (n), we have y*=Y/n Θ where y* = true welfare of each individual in household and Θ = a parameter that (broadly speaking) expresses economies of size

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The Barten model 1.WITH PUBLIC AND PRIVATE GOODS ONLY where y*=true income or consumption (welfare) per household member at the optimum, Y=total household income or consumption, n= number of household members, ρ = share of spending on food (economies of size=0). = the (reverse) of the economy of size in the consumption of housing. (Note that if housing were a pure public good, would be equal to 0, and the entire utility from the public good would be consumed by each household member). = the (reverse of) the overall level of publicness in consumption. reflects both the composition of consumption (between the public and private goods), and the economies of size in the consumption of public good. is a technological parameter, is an overall calculated elasticity.

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2. Including children too 3. Finally, s implify (so that new theta includes both public-private and child-adult components)

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Malaysia 1995: Sensitivity of inequality measures on the assumptions regarding economies of scale and size (theta)

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Combine equivalence scales and welfare concept

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Sensitivity of inequality measures to equivalence scales and income vs. expenditure welfare indicator IncomeExpenditure Source: South Africa 1994-95

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Sensitivity of inequality measures to equivalence scales and income vs. expenditure welfare indicator (cont.) IncomeExpenditure Source: Hungary 1993

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Generally, Gini (and other inequality measures) go down as equivalence scales increase (means that larger households gain some utility because of economies of size, and also probably because they have more children) But this is not always the case as illustrated on the examples of South Africa and Hungary If YPC does not fall much with HH size, then Gini might not change much as equivalence scales increase

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Measures of inequality

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Welfarist approach (Dalton) to inequality vs. measurement only (Gini) The methods of Italian writers…are not…comparable to his [Daltons] own, inasmuch as their purpose is to estimate, not the inequality of economic welfare, but the inequality of incomes and wealth, independently of all hypotheses as to the functional relations between these quantities and economic welfare or as to the additive character of the economic welfare of individuals. Corrado Gini, Measurement of Inequality of Incomes, Economic Journal, March 1921.

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Inequality measurement axioms 1. If all incomes are multiplied by a constant (Y1=Y*C), inequality does not change. 2. Increase of all incomes by a constant (Y1=Y+C), reduces inequality (follows from 1). New distribution is Lorenz-superior. 3. If number of recipients is multiplied (at each income level) by a constant, inequality does not change 4. Progressive transfer (which does not change the rankings of individuals) reduces inequality (Daltons axiom). (Dalton improvement = income of the poor by at least as much as income of the rich goes down. 5. Symmetry or anonymity: if two people swap positions, inequality does not change. 6. Inequality measure lies in [0,1] domain.

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Measures of inequality Desirable properties and how different measures satisfy them. GiniTheilMean log deviation Relative mean deviation Formula Compares persons income to: Other persons incomehis share in population mean FeaturesMean-normalized measure. Shows percentage difference between incomes of two randomly selected individuals Compares relative incomes of all individuals (either population weighted or income weighted) Mean-normalized measure Intuitive explanation Gini of 30 means that the expected difference in income btw. 2 randomly selected persons is 60 of overall mean income. Shows percentage difference between income of a randomly selected individual and overall mean income. Shows percentage of total income that should be transferred so that all incomes are the same. Income-scale independence (if all incomes increase by the same %, measure does not change) Yes

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GiniTheilMean log deviation Relative mean deviation Absolute increase of all incomes reduces inequality Yes Size independence (population size does not affect the measure) Yes Progressive transfer reduces inequality (The Pigou-Dalton transfer principle) Yes Not if both individuals have incomes greater (or lower) than the mean. Symmetrical (if two people change their places, measure is not affected) Yes Measure varies between 0 and 1 YesNot bounded from above. Yes Decomposability (between recipients and between income sources) Yes, between income sources No, between recipients Yes (both) No Sensitivity to transfers Greatest at the mode (varies as density function of the distribution) Insensitive if transfers take place between two individuals with income greater (or lower) than the mean.

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Gini decomposability By income source By recipient Where π=share (of recipients) in total income, p=share in total population, s=share (of income source) in total income, μ=mean, L=overlap term and R i =cov(x i,r(y))/cov(x i,r(x i ) source correlation coefficient with total income

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Gini calculation from grouped data Often, the true Gini is approximated by the following heuristic formula: True Gini = 1/3 Gini (min) + 2/3 Gini (max) Where fi=frequency of i-th group, q i =cumulative share of income received by the bottom i groups

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EXAMPLE. Romania 1998 (Integrated Household Survey results as reported in Statistical Yearbook 1999). Lower boundUpper boundMean incomePercentage of people in interval Width of the interval (2)-(1) 24000025879625101014.218796 25879733382432138511.575027 33382539377737867810.759952 3937784505714301131056793 4505725079014989019.657329 5079025739615567229.466059 5739626560096328889.282047 6560107695817409809.1113571 7695829866948987818.5217112 986728138672812067667.8400000 mean 100 552538 The very lowest and the very top interval (both in italics) are assumed. The results are as follows (using Kakwanis formulas). Gini minimum is 26.09, Gini maximum is 27.51 (a difference of 5.4 percent). The heuristic Gini would then be 27.04. A very simple formula (approximation; when N, it is exact; practically, good as soon as N>10 or 12):

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Lorenz- and first-and second- order dominance

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Lorenz curves: Indonesia (rural) and France compared

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Lorenz curves that intersect (with almost the same Gini) Source: thepast.xls (lorenz2)

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Generalized Lorenz curve: real ($PPP) income at the same percentile levels

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Another example of a generalized Lorenz curve: France vs. United States

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Second order dominance: real ($PPP) income at the same cumulative percentile levels

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Empirical and probability income distributions

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Several often-used functional distributions Lognormal (the most popular) Pareto (the oldest; good fit for highest incomes) Where y l =minimum possible value of y, α=Pareto constant (=1.5) Singh-Maddala

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Gini distribution Where Y t =total income, Y y =aggregate income up to income level y, γ (gamma)=parameter, C=constant.

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For each distribution, one can calculate corresponding Ginis, Lorenz curves and any measure of inequality Often used as approximations to empirical (true) distributions, or a way to estimate distribution if we have only a few data points (e.g., if only published group data are available)

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Data sources

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D-SAll countries, 60-96, ~700 observations, 122 countries Ginis, quintilesSparse data (average= 6 out of 27); quintiles often obtained from sdary sources; update forthcoming WIDERAll countries, 60-96, ~900 HS Ginis; 122 countries Ginis, quintiles, wage distributions Sparse data; broader coverage than D-S; better documentation WorldYDAll countries, 1988-1998, ~350 surveys Fractiles; on average about 13-14 (mostly deciles, ventiles) Dense data; limited coverage in time; panel: 90 countries EEurope27 countries, 1995-2002 DecilesMedium density of data

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LSMSAbout 40 surveys; 30 countries, from early 1980 to 2002; LDCs; often very poor Y.X data, but also health, education, HH characteristics Not uniform surveys, but similar; standardization proceeeing; many accesible Africa Data baseAbout 200 various surveys Y,X surveys but also nutritional, core welfare ind. local surveys, labor force etc Not uniform; quality varies (generally low); access controlled by NSOs LIS29 countries; mostly OECD Y data onlyLissified data (major advantage); all accessible HEIDE8 countries in EEurope/FSU, early 1990s X, Y dataStandardized data; all accessible

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Where to access the data D-S: http://www.worldbank.org/research/growth/dddeisqu.htm. http://www.worldbank.org/research/growth/dddeisqu.htm WorldYD: http://www.worldbank.org/research/inequality/data.htm http://www.worldbank.org/research/inequality/data.htm WIDER: http://www.wider.unu.edu/wiid/wiid.htmhttp://www.wider.unu.edu/wiid/wiid.htm Eeuropean data: http://www.worldbank.org/research/inequality/data.htm http://www.worldbank.org/research/inequality/data.htm Texas Inequality Project (sectoral distribution of wages; approximates distribution of wages) http://utip.gov.utexas.edu/. http://utip.gov.utexas.edu/

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How to access the data D-S: http://www.worldbank.org/research/growth/dddeisqu.htm. http://www.worldbank.org/research/growth/dddeisqu.htm WorldYD: http://www.worldbank.org/research/inequality/data.htm http://www.worldbank.org/research/inequality/data.htm WIDER: http://www.wider.unu.edu/wiid/wiid.htmhttp://www.wider.unu.edu/wiid/wiid.htm Eeuropean data: http://www.worldbank.org/research/inequality/data.htm http://www.worldbank.org/research/inequality/data.htm Texas Inequality Project (sectoral distribution of wages; approximates distribution of wages) http://utip.gov.utexas.edu/. http://utip.gov.utexas.edu/

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LIS: http://www.lisproject.org/http://www.lisproject.org/ LSMS: http://www.worldbank.org/lsms/http://www.worldbank.org/lsms/ Africa: http://www4.worldbank.org/afr/poverty/databank/default.c fm. http://www4.worldbank.org/afr/poverty/databank/default.c fm HEIDE: http://www.worldbank.org/research/inequality/data.htm http://www.worldbank.org/research/inequality/data.htm

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India/China India: micro data in principle available but difficult to get. Recently, work on state-level micro data (Jha), and possibility to buy micro data from NSO. China: no access to micro data granted; only fractile tabulations for country, rural/urban areas and in some cases provinces. (Many individual surveys of counties, cities even provinces, but these are not official surveys.)

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A few other surveys of interest US: Current population survey http://www.bls.census.gov/cps/cpsmain.htm (annual from 1937 or 1943; accessible)http://www.bls.census.gov/cps/cpsmain.htm UK: Family Expenditure Survey: data from 1990 accessible http://www.data- archive.ac.uk/findingData/fesAbstract.asp.http://www.data- archive.ac.uk/findingData/fesAbstract.asp Russia: Russia Living Standards Monitoring Survey: annual from 1992 http://www.cpc.unc.edu/projects/rlms/rlms_home.html (accessible) http://www.cpc.unc.edu/projects/rlms/rlms_home.html Indonesia: SUSENAS (very large survey), annual Malaysia: Household Income and LF Survey (very large; impossible to access) Thailand: Socio-economic survey Brazil, PNAD, annual survey from 1976 (huge sample) Mexico: Encuesta Nacional de Ingresos y Gastos Germany: Socio-economic Panel (SOEP) accessible http://dpls.dacc.wisc.edu/apdu/gsoep_cd_TOC.html Japan: Family Income & Expenditure Survey: impossible to access, significant coverage problems Italy: Banco dItalia Survey; data from 1977 accessible at http://www.bancaditalia.it/pubblicazioni/statistiche/ibf European Union: European Socio-economic panel (several waves). Spain: ECPF accessible at http://www.ine.es/daco/daco42/daconepf.ht.http://www.ine.es/daco/daco42/daconepf.ht

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