What is inequality and how we measure it

1
What is inequality and how we measure it

• Milanovic, Global inequality and its
  implications
• Lectures 1 2

2
Absolute vs. relative
3
Absolute vs. relative

• 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?

4
Relative and absolute inequality

• 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).

5
Growth and inequality
Absolute inequality
Relative inequality
The tide rises all boats by the same proportion
of their initial income no ? in relative
inequality
But absolute income differences increase
Source Ravallion (2003)
6
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?

7
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)

8
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) gt 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 gt inequality of income
  greater than inequality of expenditures
• Income can be negative C cannot be gt 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
consumptionIncome and expenditure per capita by
percentile (people ranked by YPC)
People at the bottom (up to 30th percentile)
dissave people at the top (richest 30 percent)
save
12
This despite high correlation in general between
income and expenditures(so high ? can sometimes
be misleading)
South African 1998 expenditure and income per
capita (in logs)
13
Expenditure-to-income ratio across ventiles
Blue line the story as before. Red line high C
households dissave. Gini for YPC 28.4 Gini for
XPC 26.7
Data Poland Heide see XYratios.xls file
14
The consumption-income ratiosoverall net
dissaving (asset sales) or more likely, better
reporting of consumption than income in HS
Overall C/Y1.12
Overall C/Y ratio 1.09
Blue line the same story as before Red line
C-rich people underreport their income
Source Serbia LSMS 2002 file poorAZ.xls
15
Where in terms of YPC distribution, are high C
people who report C/Y ratiogt2?
Graph shows where in YPC distribution are people
from the 20th (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
16
Actual distributions and functional forms
Actual income distribution (Malaysia 1997 YPC)
and log-normal curve imposed on it
17
Individuals vs. households
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What type of distribution
Recipient Ranking criterion Household Person
Household income D(HYh) ---
Household income per capita D(HYp) D(pYp)
19
D(pyp) and D(hyh)Mexico 2002
Expressed in terms of either mean per capita or
mean per HH income.
20
Difference between D(pYp) and D(HYh)
21
Equivalence scales (economies of size)
22
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 yY/nT where y
  true welfare of each individual in household
  and T a parameter that (broadly speaking)
  expresses economies of size

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The Barten model

• WITH PUBLIC AND PRIVATE GOODS ONLY
• where ytrue income or consumption (welfare)
  per household member at the optimum, Ytotal
  household income or consumption, n number of
  household members, ? share of spending on food
  (economies of size0).
• ? 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, simplify (so that new theta includes
  both public-private and child-adult components)

26
Malaysia 1995 Sensitivity of inequality measures
on the assumptions regarding economies of scale
and size (theta)
27
Combine equivalence scales and welfare concept
28
Sensitivity of inequality measures to equivalence
scales and income vs. expenditure welfare
indicator
Income
Expenditure
Source South Africa 1994-95
29
Sensitivity of inequality measures to equivalence
scales and income vs. expenditure welfare
indicator (cont.)
Income
Expenditure
Source Hungary 1993
30

• 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

31
Measures of inequality
32
Welfarist approach (Dalton) to inequality vs.
measurement only (Gini)

• The methods of Italian writersare notcomparable
  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
  (Y1YC), inequality does not change.
• 2. Increase of all incomes by a constant
  (Y1YC), 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 inequalityDesirable properties and
how different measures satisfy them.
Gini Theil Mean log deviation Relative mean deviation
Formula
Compares persons income to Other persons income his share in population mean mean
Features Mean-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 Yes Yes Yes
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Gini Theil Mean log deviation Relative mean deviation
Absolute increase of all incomes reduces inequality Yes Yes Yes Yes
Size independence (population size does not affect the measure) Yes Yes Yes Yes
Progressive transfer reduces inequality (The Pigou-Dalton transfer principle) Yes 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 Yes Yes Yes
Measure varies between 0 and 1 Yes Not bounded from above. Not bounded from above. Yes
Decomposability (between recipients and between income sources) Yes, between income sources No, between recipients Yes (both) 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.
36
Gini decomposability

• By income source
• By recipient

Where pshare (of recipients) in total income,
pshare in total population, sshare (of income
source) in total income, µmean, Loverlap term
and Ricov(xi,r(y))/cov(xi,r(xi) source
correlation coefficient with total income
37
Gini calculation from grouped data
Where fifrequency of i-th group, qicumulative
share of income received by the bottom i groups
Often, the true Gini is approximated by the
following heuristic formula True Gini 1/3 Gini
(min) 2/3 Gini (max)
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EXAMPLE. Romania 1998 (Integrated Household
Survey results as reported in Statistical
Yearbook 1999).
Lower bound Upper bound Mean income Percentage of people in interval Width of the interval (2)-(1)
240000 258796 251010 14.2 18796
258797 333824 321385 11.5 75027
333825 393777 378678 10.7 59952
393778 450571 430113 10 56793
450572 507901 498901 9.6 57329
507902 573961 556722 9.4 66059
573962 656009 632888 9.2 82047
656010 769581 740980 9.1 113571
769582 986694 898781 8.5 217112
986728 1386728 1206766 7.8 400000
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 Ngt10 or 12)
39
Lorenz- and first-and second-order dominance
40
Lorenz curves Indonesia (rural) and France
compared
41
Lorenz curves that intersect (with almost the
same Gini)
Source thepast.xls (lorenz2)
42
Generalized Lorenz curve real (PPP) income at
the same percentile levels
43
Another example of a generalized Lorenz curve
France vs. United States
44
Second order dominance real (PPP) income at the
same cumulative percentile levels
45
Empirical and probability income distributions
46
Several often-used functional distributions

• Lognormal (the most popular)
• Pareto (the oldest good fit for highest incomes)
• Where ylminimum possible value of y, aPareto
  constant (1.5)
• Singh-Maddala

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• Gini distribution
• Where Yttotal income, Yyaggregate income up to
  income level y, ? (gamma)parameter, Cconstant.

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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-S All countries, 60-96, 700 observations, 122 countries Ginis, quintiles Sparse data (average 6 out of 27) quintiles often obtained from sdary sources update forthcoming
WIDER All countries, 60-96, 900 HS Ginis 122 countries Ginis, quintiles, wage distributions Sparse data broader coverage than D-S better documentation
WorldYD All countries, 1988-1998, 350 surveys Fractiles on average about 13-14 (mostly deciles, ventiles) Dense data limited coverage in time panel 90 countries
EEurope 27 countries, 1995-2002 Deciles Medium density of data
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LSMS About 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 base About 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
LIS 29 countries mostly OECD Y data only Lissified data (major advantage) all accessible
HEIDE 8 countries in EEurope/FSU, early 1990s X, Y data Standardized data all accessible
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Where to access the data

• D-S http//www.worldbank.org/research/growth/ddde
  isqu.htm.
• WorldYD http//www.worldbank.org/research/inequal
  ity/data.htm
• WIDER http//www.wider.unu.edu/wiid/wiid.htm
• Eeuropean data http//www.worldbank.org/research/
  inequality/data.htm
• Texas Inequality Project (sectoral distribution
  of wages approximates distribution of wages)
  http//utip.gov.utexas.edu/.

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How to access the data

• D-S http//www.worldbank.org/research/growth/ddde
  isqu.htm.
• WorldYD http//www.worldbank.org/research/inequal
  ity/data.htm
• WIDER http//www.wider.unu.edu/wiid/wiid.htm
• Eeuropean data http//www.worldbank.org/research/
  inequality/data.htm
• Texas Inequality Project (sectoral distribution
  of wages approximates distribution of wages)
  http//utip.gov.utexas.edu/.

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• LIS http//www.lisproject.org/
• LSMS http//www.worldbank.org/lsms/
• Africa http//www4.worldbank.org/afr/poverty/data
  bank/default.cfm.
• HEIDE http//www.worldbank.org/research/inequalit
  y/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.censu
  s.gov/cps/cpsmain.htm (annual from 1937 or 1943
  accessible)
• UK Family Expenditure Survey data from 1990
  accessible http//www.data-archive.ac.uk/findingDa
  ta/fesAbstract.asp.
• Russia Russia Living Standards Monitoring
  Survey annual from 1992 http//www.cpc.unc.edu/pr
  ojects/rlms/rlms_home.html (accessible)
• 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/pubblica
  zioni/statistiche/ibf
• European Union European Socio-economic panel
  (several waves).
• Spain ECPF accessible at http//www.ine.es/daco/d
  aco42/daconepf.ht.