ECONOMIC INEQUALITY: MEASUREMENT AND THE ANALYSIS

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ECONOMIC INEQUALITY: MEASUREMENT AND THE ANALYSIS

Vida Čiulevičien÷

¹

, Jonas Čiulevičius

²

Lithuanian University of Agriculture

The paper analyzes the methods and indices for evaluating population’s economic inequality. Based on the scientific literature, recommendations of international organizations and data available from the Department of Statistics at Lithuanian Republic House- hold Budget, calculations are made and actual results are discussed. Advantages and disadvantages of different methods and indices, as well as their application, are defined. Based on the official consumption expenditure data available from Lithuanian Department of Statistics an analysis of economic inequality in urban and rural areas in Lithuania was conducted. The findings revealed remarkable differences. Population in both urban and rural areas spend about 39 per cent of total consumption expenditure on food and non- alcohol beverages what is the highest indicator in the EU. Actual variation in consumption expenditures exceeds 50 per cent; consis- tently the officially shown mean of consumption expenditures is not a precise factor reflecting current situation. Actual distribution of consumption expenditures in Lithuanian cities and in the country differs greatly from the ideal one. The distributions of consumption expenditure are best described by the third power polynomial.

The findings of the study allowed for drawing a conclusion that there is no single best measure of economic inequality; each of them has its advantages and disadvantages. An exhaustive picture of the situation is only possible when different methods and indices are applied and combined.

Keywords: Economic inequality, household, consumption expenditure, statistical evaluation, methodology.

JEL Classification System: C10; D12; R20; Q15.

Introduction¹²

Recently researchers and politicians have unanimously agreed on the fact that stratification of population and inequality has increased, the social gap has become wider and the society experiences this process directly. It is well es- tablished that economic inequality is related with population’s mortality rates, their health and the quality of life in general (Bentzel, 2006; Kennedy et al., 1996; Kawachi et al., 1999 and other). In 2000 in New York at the summit of the United Nations in the presence of government delega- tions of 191 world countries, the Declaration of the Mil- lennium setting out the goals of the millennium in order to eradicate poverty and reduce inequality (Tūkstantmečio …, 2005). Being an EU member, Lithuania has set out its goals of the Millennium with a deadline of 2015 and will draw on the basis of the EU indicators system, which will be used to measure the changes of these goals.

Measuring of inequality helps to evaluate the effi- ciency of political measures for reducing it. When F.

Sakiko, the director of Humanity Development Depart- ment at the United Nations Organisation, presented her

1 Research fields: Application of statistical methods in social and economic research

Mailing address: Economics and Management faculty, Lithuanian Uni- versity of Agriculture, Department of Accounting and Finance. Address:

Universiteto g. 10, LT-53361 Akademija, Kauno r. Tel. (8 37) 752284.

E-mail address: [email protected]

2 Research fields: Development of agriculture

Mailing address: Economics and Management faculty, Lithuanian University of Agriculture, Department of Economics. Address: Univer- siteto g. 10, LT-53361 Akademija, Kauno r. Tel. (8 37) 752259 E-mail address: [email protected]

2005 report on humanity development, she raised the issue that it is important to work more intensively to measure different forms of inequality on different levels (Sakiko, 2005). The evaluation of economic inequality in Lithuania has little been analyzed. Only a few authors (Vitunskien÷, 2002; Čiulevičien÷ et al, 2006a;

Čiulevičien÷ et al, 2006b; Lazutka, 2003; Molien÷, 2000;

Molien÷, 2001; Pajuodien÷, 1997 and others) discuss some indices, usually without providing arguments for choosing some particular indices. They are mentioned only in relation with the analysis of standard of living and inequality of income and consumption expenditures. This is a knowledge gap in this area. To date, there is still no consensus between foreign scientists (Aaberge, 2007; At- kinson et al, 2002; Dagum, 1980; Sakiko, 2005; Grusky, 2001 and others) and international organisations, such as the World Bank, (Inequality …, 2003; Inequality …2005;

World …, 2005) the United Nations Organisation (An- nual …, 2006) and other on what indices need to be calculated in order to evaluate economic inequality.

The aim of this study is to investigate statistical methods of analysis of the population’s economic inequality, and to show the opportunities for the improvement of their calculation and application.

The tasks of this study: 1) to study scientific re- search papers on this issue; 2) to evaluate advantages and disadvantages of separate methods and indices; 3) to show the possibilities of improving the calculation and application of separate methods and indices.

Object of research: methods and indices of eco- nomic inequality of the population.

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The following methods of research were employed:

logical analysis and synthesis, comparative, graphical and regression analysis by STATISTICA. For practical illus- tration of separate methods and indices, data from the Department of Statistics, Household Budget is given, providing details according to the place of residence.

Income or consumption expenditure

Speaking about methods and indices for measuring inequality, it is essential to ascertain which methods are most suitable for accessible data. Inequality to use material values and services is significantly influenced by income inequality. Therefore, economic basis of residents’ differentiation is formed by the analysis of inequality and income distribution among separate groups of population. However, in order to measure precisely the amount of income and its distribution, a precise registration is essential. In Lithuania, general declaration of income has so far not existed and special research cannot always provide an exhaustive picture of population’s income. Since 1996 household budget research has taken place in Lithuania according to the re- quirements of the European Union’s association EURO- STAT (Pajamų …, 2002). However, statisticians and scientists agree on the fact that the research data on household income is not precise. Moreover, the part of residents who refuse to participate in the research is increasing every year (Vitunskien÷, 2002; Bratčikovien÷ et al, 2006; Čiulevičien÷

et al, 2006 and others). A similar situation exists in other EU countries as well. Therefore, the Committee of the European Union has ratified the list of primary objective indices, which have to be collected by national statistic services in order to implement the Regulation of the European Parliament and Board No 1177/2003 on the Association statistics of income and living conditions (Regulation …, 2003). This includes information on the income of households and residents, as well as taxes, accommodation conditions, occupation, health problems and accessibility of health care, opportunities to satisfy certain needs, etc.

Household consumption expenditure is expenditure in cash and expenditure in kind aimed at satisfying household needs, such as food, clothing, maintenance of dwelling, health care, transport, education, recreational and other needs. Average consumption expenditure is calculated per one member of the household a month (in LTL) and is an- nounced once a year. The index of consumption expenditure is important in order to evaluate the development level of the country and the level of poverty in different orders of society. This index is used when decisions on work and social security are made, as well as to prepare weights in order to calculate the index of consumption prices. In Lithuania, household consumption expenditure is classified according to Classification of Individual Consumption Purpose (COI- COP), which was first applied in 1999 and since 2003 a re- newed classification has been used. Data are collected when

households under research fill in journals and members of the households are interviewed.

Consumption expenditure and their structure provide a better view of the living standard than income because sometimes income is not regular, especially in agriculture where work is seasonal and a part of the production, mainly that of plant-growing, is received once a year.

Whereas consumption expenditure, especially for every- day goods, generally do not change significantly. From the structure of consumption expenditure we may see what peculiarities and opportunities to satisfy certain needs exist in the household. Therefore, in order to evaluate factual economic inequality we rely not on the indicators of income, but consumption expenditure.

Methodology of Evaluation of Economic Inequality and its improvement

Inequality measures the relations between the population share and expenditure, experienced by this population. Statistically it is possible to determine the limits of inequality. Maximum inequality occurs in the case when one person experiences all expenditure. Minimum inequality is when all the population shares the same amount of expenditure.

Based on the research papers and recommendations of international organisations (Aaberge, 2007; Hale, 2006;

Litchfield, 1999; Inequality ..., 2003; Inequality ..., 2006;

Grusky, 2001; Molien÷, 2000; Molien÷, 2001; Čiulevičien÷

et al, 2006a and others) we may outline methods for economic differentiation by putting them into groups: structural, graphic and special coefficients. Separate methods generally include not one but a few absolute and relative indices. Structural coefficients are most popular. Most frequently used coefficients of differentiation are as follows:

decilian, quartilian and quintilian. In order to calculate them, first absolute central and other position characteristics are identified. Since the Department of Statistics uses unequal intervals for grouping consumption expenditure in the research of household, the mode ( Mo ) is calculated according to the following formula:

































+

− + +

−

− −

−

− − +

=

1 1 1

1

1 1 min

hMo yMo hMo yMo hMo

yMo hMo yMo

hMo yMo hMo yMo hMo

xMo

Mo (1)

where

x

Momin - low line of modal interval;

y

_M_o,

o−1

y

M ,

y

_M_o₊₁ - at mode, below mode and above mode frequencies of intervals; h_M_o, h_M_o₋₁, h_M_o₊₁ - correspond- ing length of grouping interval.

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Quantiles M_e,Q₁,Q₃,q₁,q₄,D₁,D₉ are calculated on the basis of relative frequencies



f and accrued relative frequencies



f ′ up to an appropriate interval:

quantile ,

1 quantile quantile

min quantile Quantile

f f N h

x − −

+

= ⁽²⁾

Most frequently used structural coefficients of measuring inequality of consumption expenditure are calculated according to the following formulae:

Quartile Coefficient of Variation

% 100 2 :

1

" 3 ⋅



 



 −

= _e

Q Q Q M

K (3)

Quartile Coefficient of Skewness

( ) ( )

1 3

Q Q

Q M M

K_A Q ^e ^e

−

= − (4)

Quartile Coefficient of Differentiation

1 3 Q Q

KQ= ^, ⁽⁵⁾

Quintile Coefficient of Differentiation

1 4 q q

K =q ^, ⁽⁶⁾

Decile Coefficient of Differentiation:

• from grouped data

1 9 D D

KD= ^, ⁽⁷⁾

• from non-grouped data

1 10 '

D D

KD= . (8) where N – part of a quantile expressed in per cent.

Median is rarely calculated in research. It is mostly used when a mean is not a typical representative of the population under research. However, it is important to em- phasize the advantages of median in comparison with an arithmetic mean. Variables of the arithmetic mean may be influenced by casual variables of ultimate limits, whereas that does not affect the median. Since in order to calculate the median we need only numerical values of ultimate limits intervals, and the intermediate values are not used in calculations, we may state that the median is not influenced by indefinite intervals of segments. It is also expedient to calculate the median because this index is used in international comparisons in order to set poverty limits.

However, not in all cases it is possible to draw conclusions only on the basis of the above-mentioned characteristics. Absolute indices alone are not appropriate for the analysis of expenditure inequality according to the place of residence. Therefore, our suggestion is to rely on the relative indices of attribute variation. The most popular is the coefficient of variation, which shows the level of variation.

The lower the index is, the more homogeneous are expen-

ditures, and the more average expenditure is precise characteristics to define expenditure of household members.

Statistical expression of population’s economic inequality is segments of population, formed according to consumption expenditure for one member of the household on average. In order to form these segments, imitation models are used. Their essence is that an empirical line of population distribution according to the level of consumption expenditure, which is formed from the research data of household budgets, is rearranged into a theoretical line of distribution. When we have this line, mathematical function is chosen which precisely reflects the evenness of consumption expenditure. One of the time line indices of ade- quacy is Mean Absolute Percentage Error (MAPE), calculated according to the following formula:

% 100 1

% 1 100 1

1 ∑ ⋅

=

= −

∑ ⋅

= = n

t yt yt yt n n

t yt et

MAPE n ⁽⁹⁾

where:

e t

- forecast error is calculated according to the formula of remainder (difference between factual and theoretical meaning of indices

e t = y t − y t

).

In order to measure economic inequality special coefficients are frequently used, especially Gini coefficient.

Italian statistician Corrado Gini offered this measure of income (expenditures) inequality measure. The variable of this coefficient varies from 0 to 1 (0 to 100). The higher the index is the greater inequality it shows. This index is widely used in international comparisons. Gini coefficient is calculated according to Lorenz curve, which was used to measure inequality by an American economist Max Otto Lorenz. The curve illustrates which part of accumulated expenditure household, in line from the least income to the highest income, receives. If expenses are even, Lorenz curve becomes a 45-degree diagonal, i.e. the line of absolute equality. As unevenness increases, Lorenz curve moves away from this diagonal. This curve may be trans- formed into Lorenz and Gini’s coefficients (Dagum, 1980;

Grusky, 2001; Čiulevičien÷ et al, 2006b and others).

Once we have average consumption expenditure in deciles, the Gini coefficient (G) is calculated according to the following formula:

( )

xi n n

i i n xi

G 1 2

1

∑ 2

= − −

= ⁽¹⁰⁾

where: i - decile line number, n - number of deciles (n=10),

x i

- arithmetic mean of average expenditure.

For the same line the Lorenz coefficient (L) is calculated as follows:

2 10

∑1

= −

= i Fpi ti F

L ⁽¹¹⁾

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where:

pi

F - share of population, whose average expenditure is included into decile interval;

ti

F - share of population in decile, when expenditure in deciles are calculated according to the following formula:

∑=

=



 

 10

1 i xiFpi

pi iF x ti

F ^. ⁽¹²⁾

The Robin Hood index is maximum vertical distance between absolute equality and line and Lorenzo curve. It shows what part of all consumption expenditures by household economies, which have more than average ex-

penditures, should be given to members of the households whose consumption expenditures are lower than the average, in order to have evenness.

The analysis of economic inequality in Lithuania It follows from Table 1 that the characteristics of consumption expenditure in Lithuanian urban household is significantly higher than that in rural. Remarkable differences identified in the ninth decile show that consumption expenditure in urban wealthiest household economies is by even 332 LTL (According to the Bank of Lithuania the official exchange rate is 1EURO = 3.4528 LTL) higher than that in rural.

Table 1. Household consumption expenditure characteristics of location in Lithuania in 2005

LTL per capita per month Statistical characterises Indicators

Urban areas Rural areas Comparison LTL (Rural areas=base)

Mean 644.30 446.25 198.05

Weighted Mean 640.90 446.80 194.10

Measures of Central Tendency

Mode 400.00 282.20 117.80

Median 537.17 374.50 162.67

Lower Quartile 375.05 255.22 119.83

Lower Quintile 343.41 233.00 110.41

Upper Quartile 782.58 551.98 230.60

Upper Quintile 863.07 601.00 262.07

Lower Decile 268.65 177.07 91.58

Locations of other than Central

Upper Decile 1122.74 790.74 332.00

(Calculated by authors on the data of the Department of Statistics) The Department of Statistics officially shows average consumption expenditure, calculated as a simple arithmetic mean. Our calculations show that there are quite big differences between a simple arithmetic mean and a lever mean:

urban indices show even LTL 3.40 difference per one

household member a month. Thus, the lever mean illustrates average expenditure of a household more precisely.

Structural coefficients of consumption expenditure in urban household are 2.6 – 6.4 per cent lower than in rural, except for asymmetrical ones (Table 2).

Table 2. Household consumption expenditure Inequality structural coefficients in Lithuania in 2005

Indicators Urban areas Rural areas Comparison %

(Rural areas=100)

Quartile Coefficient of Variation % 37.9 39.6 95.7

Quartile Coefficient of Differentiation 2.087 2.163 96.5

Quintile Coefficient of Differentiation 2.513 2.579 97.4

Decile Coefficient of Differentiation

1) D9/D1 4.179 4.466 93.6

2) D10/D1 7.497 7.977 94.0

Quartile Coefficient of Skewness 0.2044 0.1961 104.2

Gini coefficient 0.3111 0.3175 98.0

Lorenz coefficient 0.2263 0.2309 98.0

Robin Hood index 0.2260 0.2310 97.8

(Calculated by authors on the data of the Department of Statistics) This shows that urban differences are smaller between the upper and lower values of quantiles of consumption expenditure. Quintilian variation coefficients do not exceed 50 per cent; therefore the median appropriately represents in-

termediate consumption expenditure, both urban and rural.

From Gini and Lorenz coefficients we may say that the inequality of urban household consumption expenditure is 2.0 – 6.4 per cent lower than rural. (Pajamų …, 2006) says that

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when Gini value is higher than 0.300, there exists essential unevenness of consumption expenditure differentiation. In order to reach an absolute equality of distribution of consumption expenditure, we need to redistribute 22.6 per cent of them in urban areas and 23.1 per cent in the rural areas.

The calculations show that both rural and urban variation of consumption expenditure in household exceeds 50 per cent (urban – 61.5 per cent, rural – 60.9 per cent), therefore, the mean of consumption expenditure, provided by official statistics, is not a precise representative of the situation.

When evaluating the inequality of consumption expenditure, we calculate the share of expenditure for food and non-alcohol beverages. Different level of consumption expenditure determines the level of satisfying people’s needs. More than a hundred years ago an empirical regular- ity was identified – Ernst Engel‘s Law, which shows that the higher general expenditure we have, the lower is the proportion of expenditures on food, and vice versa.

According to the data available from the Department of Statistics of Lithuania in 2005 the EU mean of expenditures for food and alcohol beverages was 13.1 per cent;

the smallest share is in Ireland, about 7 per cent, in Great Britain 9 per cent, in the Netherlands 11 per cent, in Po- land 19 per cent, in Estonia 22 per cent, whereas in Lithuania 38.8 per cent. This is the highest index among all European Union countries and 2.962 times higher than the EU average. In old EU member states the share of expenditures for hotels and restaurants makes 21.5 per cent, while in Lithuania 5.9 per cent. Evaluation of elements and structure of personal consumption expenditure is of great practical meaning in the lives of the household. It provides an opportunity to distribute expenditure ration- ally and use them better to satisfy personal needs.

Having analyzed the data according to deciles, we may see a tendency that in the 1^st decile expenditure for food makes 50-65 per cent in urban and rural households equally, while in the 10^th decile 20-35 per cent (Figure 1). We may conclude that the more expenditure households have, the smaller part of them is intended for food products.

216.7 313.2 377.0 433.4 499.2 567.5 658.4 778.1 973.4 1624.5

49.9 44.7 43.1 42.0 37.8 36.6 35.1 32.2 28.7 20.1

141.2 209.2 256.8 298.8 342.5 398.7 463.7 545.7 679.6 1126.3

65.0 65.2 62.0 59.3 59.2 55.1 52.2 49.2 46.0 35.0

Urban areas Rural areas

Fig. 1. Household food expenditure in LTL and its share in percent in total consumption expenditure Although some researchers (Lichfield, 1999; Hale,

2006; Loungani, 2003 and others) state that a logarithmic function is best in this case, our data of factual Lithuanian household budget research in 2005, did not confirm this (Figure 2).

In our case, we may see that segments of consumption expenditure in urban and in the rural areas are best described by the third power polynomial because zero hypothesis about coefficient’s equality to zero

( : 0

0 bi =

H ) were rejected with first category error possibilities lower than in practice acceptable signification level (α=0.05):

• rural areas

• yt =−63.08+226.38t−47.94t2+3.67t3⁽¹²⁾

8 . 7

; 98066 . 2 0

; 0060 . 3 0

; 01733 . 2 0

; 0193 . 1 0

=

MAPE R

p

p %);

• urban areas

453 . 2 5 26 . 71 00 . 331 14 .

81 t t t

yt =− + − + ⁽¹³⁾

9 . 7

; 98016 . 2 0

; 0052 . 3 0

; 01547 . 2 0

; 0184 . 1 0

=

MAPE R

p

p %).

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766.1

558.4 431.0

361.9 328.9 310.2

283.6 227.3 119.0

1076.0 1551.8

1098.1

796.1 613.1 516.5 473.5

451.4 417.,6 339.4

184.0 0 200 400 600 800 1000 1200 1400 1600 1800

1 2 3 4 5 6 7 8 9 10

Deciles

Consumption expenditure per capita LTL per month

Predicted rural areas

Actual rural areas

Predicted rural areas

Actual rural areas

Fig. 2. Actual and predicted consumption expenditure in Lithuania in 2005 Factual distribution of consumption expenditure in

Lithuanian urban and rural areas differs greatly from the ideal one. The biggest differences are observed in the

middle of the curve, i.e. in V, VI, VII and VIII deciles (Figure 3). Rural inequality of consumption expenditure is more significant than urban.

3.4

100.0

74.8

59.7

47.6 37.4 28.6 20.8 8.2 14.1 0

10 20 30 40 50 60 70 80 90 100

0 20 40 60 80 100

Cumulative frequencies of urban households % Cumulative frequencies of concumption expendenture of urban households %

3.2

100.0

74.8

59.5 47.3 36.9 28.0 20.3 7.8 13.6 0

10 20 30 40 50 60 70 80 90 100

0 20 40 60 80 100

Cumulative frequencies of rural households % Cumulative frequencies of concumption expendenture of rural households %

PDL Lorenz Curve

Fig. 3. Lorenz curve of Lithuanian urban and rural areas household consumption expenditure in 2005 Having recapitulated research papers (Aaberge,

2006; Amin, 2006; Atkinson et al, 2002; Bentzel, 2006;

Cowell et al, 2007; Čiulevičien÷ et al, 2006; Dagum, 1980; Grusky, 2001; Lazutka, 2003; Litchfield, 2006;

Loungani, 2003; Molien÷, 2000; Molien÷, 2001; Theil, 1989 and others) and on the basis of calculations, we may

formulate the advantages of methods and indices of inequality measurement (Table 3).

On the material of above mentioned we can empha- size: there is no one the best method or indicator – only their combination based on the available data may present the real situation of inequality.

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Table 3. Evaluation of inequality measure indicators

Indicators Advantages Disadvantages

Range Easy to understand

Easy to compute

Ignores all but two of the observations Does not weight observations Affected by inflation

Range ratios Easy to understand

Easy to compute Not affected by inflation

Ignores all but two of the observations Does not weight observations

Coefficient of Variation Fairy easy to understand Incorporate all data Not affected by inflation

If data is weighted, it is immune to outliers

Requires comprehensive individual level data No standard for an acceptable level of inequality

Gini Coefficient Widely used

Allows direct comparison between unites with different size population

Could be used on national level between different categories of population, by residence Could be used in international comparisons Attractive intuitive interpretation

Could be done dynamic analysis and evaluation about inequality changes – if inequality increase or decrease.

Requires comprehensive individual level data Requires more sophisticated computations Not always is suitable if there are consider- able regional differences

In international comparisons we can meet data comparability problem, if countries use different methodologies (one of them could count only cash money, others–including paying in kind

Lorenz Coefficient Not difficult to compute, but used as Gini thinly Cover all data

Suitable for evaluation Lorenz curve variation Robin Hood index Is additional indicator for Lorenz curve and co-

efficient

For his index graphical view we should use Lorenz curve

Conclusions and suggestions

1. Theoretical issues of measuring economic inequality have hardly been analyzed in Lithuania.

2. In order to measure economic inequality, average consumption expenditures per one member of the household a month, it is better to calculate as an arithmetic lever mean. We suggest to the Department of Statistics of Lithuania to improve calculation of this indicator, because it better shows the factual situation.

3. Factual variation of consumption expenditures exceeds 50 per cent; therefore the officially shown mean of consumption expenditures is not a precise representative of the current situation. Our proposal is to calculate consumption expenditure as mean weighted.

4. The comparative analysis shows that the level of inequality of consumption expenditures in Lithuanian rural areas is higher than in urban areas. Especially remarkable differences identified in the ninth decile shows that consumption expenditure in urban wealthiest household economies are even 332 LTL higher than rural.

5. Factual distribution of consumption expenditures in Lithuanian cities and in the country differs greatly from the ideal one. The distributions of consumption expenditure are best described by the third power polynomial.

6. The share of expenditure for food and non- alcohol drinks in Lithuania reaches about 39 per cent.

This is the highest index among all European Union countries and 2.962 times higher than the EU average.

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