APPENDIX A
Measurement of Living Standards
and Inequality
Measurement of Living Standards
To examine poverty and inequality, we need a measure of well-being. Ideally, this measure should correspond as closely as possible to the way individuals experience their standards of living, including the effects of access
to social services; social stigma; stress; insecurity; vulnerability; and social
exclusion. Here we focus only on material well-being, which we measure
using information on household expenditure or income.
The construction of the measure of material well-being involves two
steps. First, we need to decide whether to base it on income or consumption, and which components of income or consumption to include. Second, we need to decide how to adjust the income or consumption measure
for economies of scale at the household level.
To estimate a poverty rate based on the measure of well-being, we need
to establish a poverty line. The poverty line is discussed below. More detailed information on the measurement of living standards and the calculation of poverty and inequality statistics can be found in World Bank
(1993), Ravallion (1994), and Deaton (1997). This measure of well-being
can also be used to calculate inequality statistics.
Material Well-Being as a Consumption or Income Aggregate
There are several reasons why household consumption (money expenditures plus the value of food produced on a household plot) is believed to
be more accurate than income for measuring well-being in transition econo367
append-a.p65
367
8/31/2000, 3:26 AM
368
M AKING T RANSITION WORK
FOR
EVERYONE
mies. In many CIS countries people are paid very irregularly, with several
months of wage arrears common. In this context, consumption is smoothed
while income is very erratic. Furthermore, income underreporting is
marked, because survey respondents are not willing to fully disclose illegal or semilegal income sources. Finally, produce from the household plot
has become a mainstay of food consumption and this is not a standard
component of money income.
Hence, in this book, we rely mainly on consumption-based measures
of poverty, although we use income-based ones for a few countries where
a measure of consumption information is available.1 Consumption is generally defined as the sum of expenditures on current purchases plus the
value of food produced and consumed by the household. Ideally, the usevalue rather than the purchase expenditures of consumer durables and
real estate should be included. In practice, the imputation of these usevalues is not always possible and the monetary value of home-production
is not always known. Hence, the consumption definitions used for the
countries in this study vary somewhat in their treatment of consumer
durables and the value of food produced by the household (see table C.2
for details).
This book uses both the income and consumption aggregates to calculate measures of inequality. While consumption may be a more accurate
measure of material well-being, examining income inequality offers two
benefits. First, it is easier to make international comparisons using income inequality since income inequality statistics are available for more
countries. Second, we can obtain insights into the drivers of inequality by
decomposing income inequality into the contributions of the various income sources.
Adjustment for Economies of Scale
Household income or expenditure needs to be adjusted for household
composition to be a useful measure of material well-being. Clearly, a oneperson household living on $250 per month is materially better off than a
five-person household living on $250 per month. A simple solution is to
divide by the number of household members, but most people would agree
that a five-person household with $250 per month is better off than a
single person having to live on $50 per month because of economies of
scale in consumption. Economies of scale arise in many ways—for example, by sharing certain expenditures such as expenditures on housing,
utilities, cars, or newspapers. Apart from household size, the age or gender of household members may also influence the amount of income or
append-a.p65
368
8/31/2000, 3:26 AM
APPENDIX A: MEASUREMENT
OF
L IVING STANDARDS
AND I NEQUALITY
369
consumption needed to attain a certain level of well-being. It is commonly
thought, for example, that the consumption needs of very young children
are less than working-age adults.
Economies of scale can be approximated by adjusting the household
size variable to derive a variable called equivalent household size. For
example, a household with an equivalent size of 3.5 needs to spend 3.5
times as much as a single adult in order to be equally well off as the single
adult. The equivalence scale usually takes both the age structure and the
number of individuals in a household into account. A large class of twoparameter equivalence scales can be described by the formula
Equivalent size = (adults + α * children)θ
where adults stands for the number of adults in the household, children
stands for the number of children ages 15 and below, and α and θ are
parameters between 0 and 1. A higher θ implies fewer economies of scale.
A lower value of α gives less weight to children’s consumption. A simplified one-parameter version of this scale allows only household size to vary:
Equivalent size = (household size)θ.
The special case of both α and θ = 1 yields the familiar per capita measure.
Some commonly used scales do not fall in the category of equivalence
scales described by the above formula. The OECD, for example, has used
the following equivalence scale:
Equivalent size = 0.3 + 0.7 * adults + 0.5 * children.
The OECD currently uses a revised scale with stronger scale economies:
Equivalent size = 0.5 + 0.5 * adults + 0.3 * children.
Unfortunately, there is no accepted way to estimate equivalence scales
(Deaton and Paxon 1996, Deaton 1997). A number of methods are used,
but each has major drawbacks. As a result, a wide variety of equivalence
scales is used in various countries. This makes intercountry comparisons
of poverty and inequality difficult, because measures of poverty and inequality are sensitive to the equivalence scale used. The literature suggests
that a one-parameter scale (based on household size) give fairly similar
results to two-parameter equivalence scales; results based on the OECD
scales show similar results to one-parameter equivalence scales with a
append-a.p65
369
8/31/2000, 3:26 AM
370
M AKING T RANSITION WORK
FOR
EVERYONE
value of θ around 0.5–0.6 (Figini 1998). Varying the economy of scale
parameter may change the relative poverty risks of different demographic
subgroups of the population, notably the elderly and children, as Lanjouw
and others (2000) show.
Because there is no generally accepted way to estimate equivalence
scales, in this book we calculate poverty and inequality measures using
three different values of θ = 0.5, 0.75, and 1.00 for the poverty line set at
50 percent of median expenditure (or income). In the main text we report
results based on θ = 0.75, which seems a reasonable estimate for transition
countries, in light of the fact that energy prices are subsidized and housing
costs are not included in expenditure estimates—two major sources of
economies of scale in OECD economies.
Poverty Lines
The third task is to set a poverty line. There are two types of poverty lines:
absolute and relative. Absolute lines set an absolute minimum standard of
living and are typically based on a fixed basket of food products (deemed
to represent minimum nutritional intake necessary for good health) plus
an allowance for other expenditures (such as housing and clothing). Hence
absolute lines can vary across countries, depending on the composition of
the consumption basket.
To facilitate comparisons across countries, a poverty line is fixed in
U.S. dollars and then converted into national currency units using purchasing power parity (PPP) exchange rates. PPP rates measure the relative
purchasing power of different currencies over equivalent goods and services. Market exchange rates are not appropriate for welfare comparisons
because they do not account for the sometimes substantial differences in
relative prices between economies. PPP rates also take into account differences in the structure of consumption between countries. However, they
are not without problems (see World Bank 2000).
This book uses an absolute poverty line of $2.15 per person per day to
derive cross-country estimates of absolute deprivation. This poverty line
is roughly equal to the lowest absolute poverty lines that are used by
transition countries in the Europe and Central Asia region and that are
based on a nationally determined minimum food basket plus an allowance for nonfood expenditures. Because most transition countries have
national absolute poverty lines that exceed $2.15 per day per person, we
also provide poverty estimates based on an absolute poverty line of $4.30
per day per person. The absolute poverty lines are converted into national currency using 1996 PPP exchange rates (the most recent ones avail-
append-a.p65
370
8/31/2000, 3:26 AM
APPENDIX A: MEASUREMENT
OF
L IVING STANDARDS
AND I NEQUALITY
371
able). Next, the absolute poverty line, expressed in 1996 national currency, is adjusted for inflation using the national consumer price index to
yield an absolute poverty line for the year in which the consumption or
income data were collected.
Irrespective of absolute needs, people may consider themselves poor
when their living standards are substantially below those of others in their
country. This type of poverty is captured by relative poverty lines, which
define poverty relative to national living standards. Relative poverty lines
are useful for international comparisons of the characteristics of the worst
off individuals in each country. Relative poverty lines are usually set as a
fixed percentage of median or mean equivalent household income. We
calculate poverty profiles using three common relative poverty lines. For
clarity of exposition, we use 50 percent of median income as our base
relative poverty line in the main text. However, Appendix D also reports
poverty estimates for one-third and two-thirds of median consumption.
Poverty and Inequality Statistics
Poverty Statistics
The simplest and most commonly used measure of poverty is the headcount
index, which is given by the fraction of individuals with equivalent consumption below the poverty line.2 This measure, however, does not tell us
whether the poor are only slightly below the poverty line or whether their
consumption falls substantially short of the poverty line. Moreover, the
headcount measure also does not reveal whether all the poor are about
equally poor or whether some are very poor and others just below the
poverty line.
To examine these three dimensions of poverty—headcount, shortfall,
and inequality among the poor—we use the Foster, Greer, and Thorbecke
(1984) class of poverty measures. This class is described by
P (α ) =
1
n
n
∑
i =1

 z − ci

, 0 
 max 
z



α
where α is the parameter (explained below), z is the poverty line, ci is
equivalent consumption of individual i, and n is the total number of individuals. If we set α equal to 0, we obtain P(0), or the poverty headcount
index. P(0) simply measures the fraction of individuals below the poverty
line. If we set α equal to 1, we obtain P(1), or the poverty deficit. The
append-a.p65
371
8/31/2000, 3:26 AM
372
M AKING T RANSITION WORK
FOR
EVERYONE
poverty deficit is a poverty measure that takes into account how far the
poor, on average, are below the poverty line. One can show
P(1) = P(0) * (Average Deficit)
where the average deficit is the amount, measured as a percentage of the
poverty line, by which the mean consumption of the poor on average falls
short of the poverty line. An average deficit of 20 percent means that
mean consumption of the poor falls 20 percent short of the poverty line. A
poverty deficit of 5 percent means that if a country could mobilize resources equal to 5 percent of the poverty line for every individual and
distribute these resources to the poor in the amount needed to bring each
individual up to the poverty line, then, in theory, poverty could be eliminated.
Finally, if we set α equal to 2, we obtain P(2), sometimes also called the
severity of poverty or FGT(2). This poverty measure captures difference
in the severity of poverty, since it effectively gives more weight to those
consumption of the poorest.
In our presentation of the poverty results, we rely mainly on the headcount index.
Inequality Statistics
There are many ways to measure inequality because inequality is a multidimensional concept. This book relies mostly on three types of inequality
measures: (1) quantile ratios; (2) Gini coefficients; and (3) Theil inequality measures.
Quantile ratios are straightforward indicators of inequality that are
easy to interpret. The most common quantile ratio is the 90/10 ratio, which
is the equivalent consumption at the 90th percentile of the equivalent consumption distribution divided by the equivalent income at the 10th percentile. This measure is easy to interpret. For example, if the 90/10 ratio is
equal to 4, then the poorest person of the richest 10 percent of the population consumes 4 times as much as the richest person of the poorest 10
percent. The 90/10 ratio can be decomposed; it is equal to the product of
the 90/50 ratio and the 50/10 ratio. This decomposition tells us to what
extent the 90/10 ratio is driven by inequality in the top of the distribution
versus inequality at the bottom end. Quantile ratios are insensitive to outliers either in the very top or very bottom tail of the consumption distribution. However, quantile ratios do not reflect what happens in other parts
of the distribution. For example, no change in inequality anywhere be-
append-a.p65
372
8/31/2000, 3:26 AM
APPENDIX A: MEASUREMENT
OF
L IVING STANDARDS
AND I NEQUALITY
373
tween the 11th and the 89th percentile would ever be reflected in a 90/10
ratio. To address this shortcoming, we also use Gini and Theil coefficients.
The Gini coefficient is given by:
G=
2
µ n2

n
∑  r
i
−
i =1
n + 1
c i
2 
where there are n individuals indexed by i, their equivalent consumption
is given by ci, mean equivalent consumption is denoted by µ, and where ri
is household’s i rank in the equivalent consumption ranking (that is, for
the household with the lowest equivalent consumption ri equals 1, while
for the household with the highest equivalent consumption ri equals n).
The Gini coefficient is bounded between 0 and 1, with 0 indicating absolute equality and 1 indicating absolute inequality. The Gini coefficient is
especially sensitive to changes in inequality in the middle of the equivalent
consumption distribution.
Another widely used class of inequality indicators is the generalized
entropy class developed by Theil. Within that class, we use the Theil mean
log deviation index,
E (0 ) =
1
n
n
 µ 
1
 = ln 
n
 i 
∑ ln  c
i =1
n
∑c
i
i =1
 1
−
 n
n
∑ ln( c ).
i
i =1
and the Theil entropy index,
E (1 ) =
1
n
n
∑
i =1
ci  ci
ln 
µ
 µ
.


Both measures are zero for perfect equality. For complete inequality (one
person consumes everything), E(0) goes to infinity while E(1) reaches nln(n).
The two Theil inequality measures differ in their sensitivity to inequality
in different parts of the distribution. The entropy measure, E(1), is most
sensitive to inequality in the top range in the distribution, while the mean
log deviation measure, E(0), is most sensitive to inequality in the bottom
range of the distribution.
Inequality can be decomposed along two dimensions. One can decompose total inequality in equivalent consumption into the contribution of
each component of equivalent consumption. Because equivalent consumption has relatively uninteresting components, this decomposition is usually performed for income inequality by the sources of income (labor
income, self-employment income, state transfers, and so on). This decomposition can be performed using the Gini coefficient. The second way of
append-a.p65
373
8/31/2000, 3:26 AM
374
M AKING T RANSITION WORK
FOR
EVERYONE
decomposing inequality is to decompose it into inequality within population subgroups and between subgroups. This decomposition can be performed using the Theil indices.
Inequality Decomposition by Income Source Using Gini Coefficient
Since the source decomposition is typically performed using income, we
present it for income rather than equivalent consumption. Following
Shorrocks (1982), we decompose the Gini coefficient into the contribution of income sources. The contribution of each income source is the
product of a concentration coefficient for that income source and the
fraction of that income source in total income.
More formally, G k* , the concentration coefficient for income component k, is given by
G k* =
2
µ n2

n
∑  r
i
−
i =1
n + 1
 y k ,i
2 
where yk,i is component k of the income of individual i, mean total income is denoted by µ, and ri is household’s i rank in the ranking of total
income. The Gini coefficient is a weighted sum of the concentration coefficients
G =
K
∑
k =1
µk
G k* =
µ
K
∑S
k
G k*
k =1
where Sk = µk/µ is the share of the component k in total income. The
percentage contribution of income source k to total income equality is
found to be
Pk = S k
G k*
× 100 % .
G
The expression above gives the overall contribution of income source
k to inequality. However, we may also wish to know the marginal contribution of each source to inequality. In other words, by what percentage
would inequality increase if income source k increased by x percent?
Lerman and Yitzhaki (1994) show that the elasticity of the Gini coefficient with respect to Sk is given by:
∈G , S k =
append-a.p65
374
S k (G k* − G ) .
G
8/31/2000, 3:26 AM
APPENDIX A: MEASUREMENT
OF
L IVING STANDARDS
AND I NEQUALITY
375
Hence, whenever the concentration coefficient of income source k is
greater than the overall Gini coefficient, an increase in the income source
k (holding everything else constant) will increase inequality. In particular,
if the share of income source k increases by 1 percent, overall inequality
will increase by ∈G, Sk percent.
Inequality Decomposition by Population Subgroup Using
Theil Indices
The Gini coefficient does not lend itself well to a decomposition by population groups. For that purpose, the Theil generalized entropy class of
inequality measures is used.
Decomposition by population groups allows us to look more closely at
the causes of inequality. Following Bourguignon (1979) and Shorrocks
(1980), we decompose total inequality into a component that is due to
inequality across population subgroups, and into a component that is due
to inequality within these subgroups. This decomposition can be performed
for various population groupings.
Let the population be divided into m mutually exclusive and exhaustive subgroups. Let the population share of the jth group in the population be given by wj , and the consumption share by vj.
We can now rewrite the Theil mean log deviation index as
m
m
 wj 
E(0) = ∑wj E(0) j +∑wj ln 
v 
j =1
j =1
 j
where E(0)j is the mean log deviation measure calculated for all individuals in subgroup j. The first summation is a weighted average (using population shares as weights) of the mean log deviation measures calculated
for the subgroups. Hence, this first term gives the component of overall
inequality that is due to inequality within subgroups. The second summation is the mean log deviation measure calculated on mean consumption
of each subgroup (and weighting each subgroup by its population share).
Hence, this second term gives the component of inequality that is due to
between-group differences.
The decomposition for the Theil entropy measure is similar and given
by
E (1) =
m
∑v
j =1
append-a.p65
375
j
m
 vj  vj
ln 
E (1) j + ∑ w j 

j =1
 w j  w j

,


8/31/2000, 3:26 AM
376
M AKING T RANSITION WORK
FOR
EVERYONE
where E(1)j is the Theil entropy measure calculated for all individuals in
subgroup j. The first summation is a weighted average (using consumption shares as weights) of the entropy measures calculated for the subgroups. Hence, this first term gives the component of overall inequality
that is due to inequality within subgroups. The second summation is the
entropy measure calculated on mean consumption of each subgroup (and
weighting each subgroup by its population share). Hence, this second
term gives the component of inequality that is due to between-group differences.
Notes
1. Countries where we used income-based measures include Hungary and the
Slovak Republic.
2. The exposition of the poverty and inequality measures is phrased in terms of
equivalent consumption, but the same measures could be applied to equivalent
income.
References
Bourguignon, François. 1979. “Decomposable Income Inequality Measures,”
Econometrica 47(4): 901–20.
Deaton, Angus. 1997. The Analysis of Household Surveys: A Microeconomic
Approach to Development Policy. Washington, D.C.: World Bank.
Deaton, Angus, and Christina Paxon. 1996. “Economies of Scale, Household Size,
and the Demand for Food.” Research Program in Development Studies,
Princeton University, Princeton, N.J. Processed.
Figini, Paolo. 1998. “Inequality Measures, Equivalence Scales and Adjustment
for Household Size and Composition.” LIS Working Paper No. 185 (available
on LIS web site).
Foster, James, Joel Greer, and Eric Thorbecke. 1984. “A Class of Decomposable
Poverty Measures.” Econometrica 52(3): 761–65.
Lanjouw, Peter, Branko Milanovic, and Stefano Paternostro. 1998. “Poverty and
the Economic Transition: How Do Changes in Economies of Scale Affect Poverty Rates for Different Households?” Policy Research Working Paper 2009.
World Bank: Washington, D.C.
Lerman, Robert I., and Shlomo Yitzhaki. 1994. “Effect of Marginal Changes in
Income Sources on U.S. Income Inequality.” Public Finance Quarterly 22(4):
403–17.
append-a.p65
376
8/31/2000, 3:26 AM
APPENDIX A: MEASUREMENT
OF
L IVING STANDARDS
AND I NEQUALITY
377
Ravallion, Martin. 1994. Poverty Comparisons. Chur, Switzerland: Harwood
Academic Publishers.
Shorrocks, Anthony. 1980. “The Class of Additively Decomposable Inequality
Measures.” Econometrica 48(1): 613–25.
———. 1982. “Inequality Decomposition by Factor Components.” Econometrica
50(1): 193–211.
World Bank. 1993. Poverty Reduction Handbook. Washington, D.C.: World Bank.
———. 2000. World Development Indicators. Washington, D.C.
append-a.p65
377
8/31/2000, 3:26 AM