Gini coefficient in relation to sectors of the Russian economy. Lorenz curve

Assess the degree of wage differentiation among workers in each sector of the Russian economy, as well as the impact of the crisis on the redistribution of income within the industry.

Materials used

Rosstat data

Brief explanations

Equal distribution of income among all residents of the country is the basis of social stability.

The Gini coefficient is a statistical indicator of the degree of stratification of society along a certain basis. This indicator is often used to determine the uneven distribution of income among the world's population.

Using the methodology for calculating the Gini coefficient (it is presented in detail in the text of the study), we examined not the entire Russian economy, but its individual sectors.

Calculation of the Gini coefficient

A few words about how this indicator is calculated.

The values that the coefficient can take range from 0 to 1. Zero means complete equality of income among all residents (in this case, workers in a particular industry), one means complete inequality (an unrealistic situation when all wages in an industry are concentrated in the hands of one person ).

If the coefficient is presented as a percentage, then it is called the Gini index.

Let's illustrate with an example.

Let's assume that all residents of the country receive the same salary, in this case the graph will look like this:

10% of the population will receive 10% of total income, 20% of residents, respectively, 20% of total income, etc. This is a completely equal distribution of income.

In the opposite case, if we assume that one person receives a salary and everyone else works for free, the Gini coefficient will be equal to one, and the income concentration graph will look like this:

In reality, the income distribution usually looks like this:

The purple curve here is a graph of the shares of income of each group of residents (in our case, workers) in total income. For example, according to this graph, the lowest 10% of employees receive only 0.8% of total industry income, 90% of employees receive 60% of total income, which means that 40% of the income is in the hands of the top 10% of employees.

The figure formed by the intersection of the red straight line and the purple curve is the inequality of income distribution. The value of the Gini coefficient is the ratio of the area of this figure to the area of the entire triangle.

An example of calculating the Gini coefficient for one of the economic sectors

Let’s use Rosstat data “Distribution of the number of employees by wages” by type of economic activity and try, based on these data, to construct a Lorenz curve and calculate the value of the Gini coefficient.

Table 1 (part 1). Distribution of the number of employees by wages and types of economic activity, in 2015 *

	Agriculture, hunting and forestry	Fishing, fish farming	Mining	Manufacturing industries	Production and distribution of electricity, gas and water	Construction
up to 5965.0	2,5	1,3	0,1	0,3	0,3	0,8
5965,1-7400,0	6,8	5,5	0,2	1,1	0,9	1,4
7400,1-10600,0	15,1	5,7	1,1	4,1	4,1	5,2
10600,1-13800,0	14,7	6,2	1,9	6,4	7,1	6,2
13800,1-17000,0	13,2	7,5	3,1	8,1	9,5	7
17000,1-21800,0	16	9,3	6,2	13,8	15,2	10,9
21800,1-25000,0	8,4	5,9	5,4	9,6	9,5	7,4
25000,1-35000,0	14,1	14,9	17	24,1	21,5	20,9
35000,1-50000,0	6,2	14,1	21,3	18,1	16,3	19,5
50000,1-75000,0	2,2	11,2	21,6	9,3	9,9	12,3
75000,1-100000,0	0,5	6	10,9	2,7	3,2	4,6
100000,1-250000,0	0,4	8,5	10,4	2,1	2,4	3,3
over 250000.0	0	4,2	0,9	0,3	0,2	0,4

Table 1 (part 2). Distribution of the number of employees by wages and types of economic activity, in 2015 *

*Data is published once every 2 years, in April.

Accrued wages	Wholesale and retail trade, repair of vehicles and motorcycles	Hotels and restaurants	Transport and communications	Financial activities	Real estate transactions, rental and provision of services	Research and Development
up to 5965.0	1	1,3	1,4	0,4	1,1	0,4
5965,1-7400,0	2,5	3,2	1,6	0,6	2,5	1,1
7400,1-10600,0	8,2	10,5	4,9	1,4	5,9	2,4
10600,1-13800,0	9	10,8	6,1	2,3	7,2	3,6
13800,1-17000,0	10	11,7	6,8	3,7	8,2	4,8
17000,1-21800,0	14,2	14	11,1	8,5	10,9	7,9
21800,1-25000,0	9	8	7,7	7,3	6,7	6,2
25000,1-35000,0	19,1	18	20,9	21,5	16,6	19,2
35000,1-50000,0	12,6	13,2	19	21,1	16,2	22,1
50000,1-75000,0	7,4	5,6	12,4	15,7	12,5	18,3
75000,1-100000,0	2,8	1,7	4,2	6,8	5,3	6,8
100000,1-250000,0	3,3	1,8	3,4	9	6,1	6,3
over 250000.0	0,7	0,3	0,5	1,7	0,8	0,7

Table 1 (part 3). Distribution of the number of employees by wages and types of economic activity, in 2015 *

*Data is published once every 2 years, in April.

Accrued wages	Public administration, compulsory social security, activities of extraterritorial organizations	Education	Health and social service provision	Providing utility, personal and social services	Of these, activities related to organizing recreation, entertainment, culture and sports
up to 5965.0	1	3,4	1,5	2,8	2,9
5965,1-7400,0	1,9	7,5	3,3	5,7	5,9
7400,1-10600,0	4	12,8	10,7	11,5	11,8
10600,1-13800,0	6	10,9	13,6	12,4	12,7
13800,1-17000,0	7	9,7	13	11,8	11,9
17000,1-21800,0	10,7	13,5	15,1	13,7	13,6
21800,1-25000,0	6,9	8	7,8	7,5	7,4
25000,1-35000,0	17,9	16,3	15	14,6	14
35000,1-50000,0	21,3	10,4	10,8	10,1	9,9
50000,1-75000,0	15,4	4,9	6,2	5,9	5,9
75000,1-100000,0	4,6	1,6	1,9	2	2,1
100000,1-250000,0	3,3	1	1,1	1,7	1,7
over 250000.0	0,2	0	0	0,4	0,4

To construct the Lorenz curve and calculate the Gini coefficient, data is needed on the share of income of each population group (in this case, industry workers) in total income. This data is in Table 1 are missing. In order to obtain such data, we will use a mathematical technique: we will multiply the average income for each interval (we define it as the middle of the interval) by the corresponding specific weights (shares) of the population, thereby obtaining the so-called percentage numbers of group incomes. Then, by calculating the shares of groups in total income and summing them up, we obtain a cumulative series of incomes, expressed as a percentage.

As an example, let’s carry out calculations for one of the industries, for example, agriculture, hunting and forestry.

Table 2. Estimated data for calculating the Gini coefficient for the industry "Agriculture, hunting and forestry"

Income	Middle of the interval	Proportion of employees receiving the appropriate level of wages	Cumulative number of employees	Group income percentages	Share in total income	Cumulative income series
up to 5965.0	4000	2,5	2,5	10000	0,51	0,02
5965,1-7400,0	6200	6,8	9,3	42160	2,15	2,66
7400,1-10600,0	9000	15,1	24,4	135900	6,94	9,60
10600,1-13800,0	11950	14,7	39,1	175665	8,97	18,57
13800,1-17000,0	15150	13,2	52,3	199980	10,21	28,78
17000,1-21800,0	18600	16	68,3	297600	15,19	43,97
21800,1-25000,0	22600	8,4	76,7	189840	9,69	53,66
25000,1-35000,0	30000	14,1	90,8	423000	21,59	75,25
35000,1-50000,0	42500	6,2	97	263500	13,45	88,71
50000,1-75000,0	62500	2,2	99,2	137500	7,02	95,72
75000,1-100000,0	87500	0,5	99,7	43750	2,23	97,96
100000,1-250000,0	100000	0,4	100	40000	2,04	100,00
over 250000.0	250000	0	100	0	0,00	100,00

Income
Middle of the interval– the average wage level in each group of workers.
Proportion of employees receiving the appropriate level of wages– Rosstat data (see Table 1).
Cumulative number of employees– accumulated frequencies. In order to calculate the value of the i-series, it is necessary to sum up the shares of workers (column 3 of Table 2) from 1 to i inclusive.
Group income percentages– calculated data used to determine the share of income of a particular group of workers in total income. They are calculated by multiplying the middle of the interval by the specific gravity (column 2 times column 3).
Share in total income– the share of income of a particular group of employees in total income. The ratio of group income (column 5) to the sum of all income (sum of income in column 5).
Cumulative income series– the sum of the shares of income to the corresponding group.

Let's build a diagram where the cumulative series of the number of employees will be plotted along the X-axis, and the cumulative series of income will be plotted along the Y-axis.

The area of the figure under the purple line can be calculated by summing up the areas of the trapezoids that make up the figure. Their total area is 3313.

The area of the figure with an absolutely uniform distribution of income is 5000 (the triangle under the straight line on Diagram 2).

Thus, the area of the figure reflecting the inequality of income distribution is 5000-3313=1687.

Therefore, the Gini coefficient for the industry agriculture, hunting and forestry equal to 1687/5000=0.337

Gini coefficient for other sectors of the economy

Using the same model, we will calculate the values of the Gini coefficient for all 17 sectors of the economy that Rosstat takes into account.

Table 3. Gini coefficient for economic sectors in 2015

Industry	Gini coefficient
Agriculture, hunting and forestry	0,337
Fishing, fish farming	0,486
Mining	0,314
Manufacturing industries	0,331
Production and distribution of electricity, gas and water	0,343
Construction	0,355
Wholesale and retail trade, repair of vehicles and motorcycles	0,395
Hotels and restaurants	0,378
Transport and communications	0,362
Financial activities	0,355
Real estate transactions, rental and provision of services	0,402
Research and Development	0,334
Public administration, compulsory social security, activities of extraterritorial organizations	0,349
Education	0,384
Health and social service provision	0,368
Providing utility, personal and social services	0,412
Activities for organizing recreation, entertainment, culture and sports	0,417

By ranking the data and presenting it in chart form, we can see that currently the greatest income equality is observed among employees in the mining sector, and the greatest inequality is in the fishing and fish farming sector.

To illustrate how different an inequality coefficient of 0.486 is from a coefficient of 0.314, here is a simple example. In fisheries and aquaculture, the top 12.4% of employees receive 40% of total income. But in the most “fair” sector from this point of view – the mining sector – a little more than 40% of the total income is already received by 22.1% of employees (see. Table 4).

Table 4

Fish farming, fish farming		Mining
		Cumulative weight in total income	Cumulative number of employees
0,11	1,3	0,01	0,1
0,83	6,8	0,03	0,3
1,91	12,5	0,22	1,4
3,46	18,7	0,65	3,3
5,85	26,2	1,53	6,4
9,49	35,5	3,71	12,6
12,29	41,4	6,01	18
21,69	56,3	15,63	35
34,29	70,4	32,70	56,3
49,01	81,6	58,16	77,9
60,05	87,6	76,14	88,8
77,92	96,1	95,76	99,2
100,00	100	100,00	100

The impact of the crisis on the differentiation of wages in economic sectors

By calculating the Gini coefficient for sectors of the economy in 2013 and comparing these values with the indicators for 2015, we will see how the crisis affected the differentiation of wages in a particular area.

Let's see if somewhere in the industry income has begun to be distributed more “fairly” among employees.

– rating of industries by growth of the Gini coefficient. The chart shows that over the past 2 years, inequality in the distribution of wages has increased significantly in the areas of fishing, fish farming (+15.3%), hotel and restaurant business (+4.82%) and construction (+3.66%).

The distribution of wages became more “fair” in healthcare and the provision of social services (-3.47%), in the field of wholesale and retail trade in motor vehicles (-2.27%), in the field of scientific research and development (-2.16% ).

In the fisheries and aquaculture sector in 2013, 8.2% of the highest paid employees had 23.56% of total income. In 2015, 22.08% of total income belonged to 3.9% of the highest paid employees. That is, in 2013, the top 1% of employees accounted for 2.87% of total industry income, and in 2015, each percent of these employees already accounted for 5.66% of total industry income.

Table 5

Fishing, fish farming
2013		2015
Cumulative weight in total income	Cumulative number of employees	Cumulative weight in total income	Cumulative number of employees
0,03	0,3	0,11	1,3
1,25	7,1	0,83	6,8
3,21	14,7	1,91	12,5
6,40	24	3,46	18,7
10,93	34,4	5,85	26,2
15,10	42,2	9,49	35,5
20,88	51,1	12,29	41,4
33,64	65,9	21,69	56,3
47,92	77,6	34,29	70,4
65,88	87,6	49,01	81,6
76,44	91,8	60,05	87,6
100	100	77,92	96,1
		100,00	100,00

conclusions

The greatest income inequality among workers in sectors of the Russian economy is observed in the sphere fisheries and fish farming. The Gini coefficient for this industry is 0,486 .
In the field fishing and fish farming 12.4% the highest paid employees receive 40% total income.
Among the top three in terms of greatest income differentiation are: activities for organizing recreation, entertainment, culture and sports(Gini coefficient 0,417 ) And utility services activities (0,412 ).
The most “fair” distribution of income is in the sphere mining. There the income differentiation coefficient is equal to 0,314 , and a little more 40% total income already received 22,1% employees.
Over the past two years (from 2013 to 2015), the degree of income stratification has changed in many areas of the economy.
Inequality in wage distribution (as measured by the Gini coefficient) has increased significantly in the areas fishing, fish farming (+15,3% ), hotel and restaurant business (+4,82% ) And construction (+3,66% ).
The distribution of wages has become more “fair” in healthcare and social services (-3,47% ), in the field wholesale and retail trade in motor vehicles (-2,27% ), in the field research and development (-2,16% ).
The differentiation of employees by wages in such areas as manufacturing industries, mining, provision of utilities, education, activities for organizing recreation, entertainment, etc..

Gini coefficient, Lorentz coefficient

Introduction. 3

Lorentz curve (Lorentz coefficient) 5

Gini coefficient. 9

Conclusion. 14

References.. 15

INTRODUCTION

With the transition to a market economy, the process of stratification of society by income level sharply intensified, and this necessitated the introduction into statistical practice of indicators for analyzing the socio-economic differentiation of the population. These indicators include:

Modal income;

Median income;

Decile coefficient of differentiation of income of the population;

Lorentz and Gini concentration coefficients.

The purpose of this work is to study such indicators of socio-economic differentiation of the population as the Lorenz and Gini coefficients.

DIFFERENTIATION OF POPULATION INCOME

Differentiation of income of the population is objectively developing differences in the level of income of individuals and social groups, caused by differences in wages and social benefits, abilities and entrepreneurship, and property status.

Cash income of the population includes wages, social transfers, business income, interest, dividends and other income from property, as well as the total cost of production - personal subsidiary plots, consumed in the family and sold. Incomes of the population are distributed unevenly among population groups.

There are a number of indicators for assessing the differentiation of income of the population that allow you to see how intensively this process is proceeding. Among them:

ü distribution of the population by level of per capita income (modal and median income) is an indicator of the share or percentage of the population in certain given intervals of average per capita monetary income.

ü distribution of the total volume of monetary income among various groups of the population - an indicator in percentage of the share of the total volume of monetary income that each of the population groups has - the curve of the actual distribution of income (Lorenz curve)

ü income concentration ratio (Gini index)

ü decile coefficient of income differentiation - the ratio of the average per capita monetary income of the last and first groups of the population. It shows how many times the income of the n% of the richest population exceeds the income of the n% of the least affluent population.

LORENTZ CURVE (LOrentz coefficient)

The Lorenz curve is a graphical representation of the concentration of individual elements of a population by group: population concentration by groups of families with different levels of per capita income; concentration of workers in groups with different wage levels.

The Lorenz curve reflects the cumulative (accumulated) shares of the population's income. The Lorenz curve is a graphical representation of a distribution function. It was proposed by American economist Max Otto Lorenz in 1905 as a measure of income inequality. In this representation, it is an image of the distribution function, which accumulates the shares of the population and income. In a rectangular coordinate system, the Lorentz curve is convex downward and passes under the diagonal of the unit square located in the I coordinate quadrant.

Each point on the Lorenz curve corresponds to a statement like “The bottom 20 percent of the population receives just 7% of income.” In the case of equal distribution, each population group has an income proportional to its size. This case is described by a line of perfect equality, which is a straight line connecting the origin and the point (1;1). In the case of complete inequality (when only one member of society has income), the curve (line of perfect inequality) first “sticks” to the x-axis, and then from the point (1;0) “soars” to the point (1;1).

If the distribution is uniform, the pairwise shares of the abscissa and ordinate axes must coincide (the abscissa axis is 0, 20, 40, 60, 80, 100, the ordinate axis, respectively, is 2, 20, 40, 60, 80, 100) and is located along the diagonal of the square, which means a complete lack of concentration of the volume of the feature.

With absolute inequality, the y-axis should be 0, 0, 0, 0, 0, 100. This means, for example, in the case of concentration of family income: the entire population except one family has no income, and this one family receives all the income. Absolute inequality is that hypothetical case when the entire population, with the exception of one person (one family), has no income, and this one (one family) receives all the income. This is almost a hypothetical case that can hardly be expected.

The Lorenz curve lies between the equality and inequality curves. Obviously, in specific cases one cannot expect either absolute equality or absolute inequality in the distribution of income among the population.

Lorenz curves are used to distribute not only income, but also household property, market shares for firms in an industry, and natural resources by state. You can meet the Lorenz curve outside of economics.

Let's consider the Lorenz curve using the example of its construction. It is most convenient to consider the construction of the Lorenz curve using the following example:

Let's imagine an economy consisting of 3 agents: A, B, C. Agent A's income is 200 units, agent B's income is 300 units, agent C's income is 500 units.

To construct the Lorenz curve, we find the shares of individuals in total income. The total income is 1000. Then person A's share is 20%, B's share is 30%, C's share is 50%.

Individual A's share of the population is 33%. His income share is 20%. Then we include in the analysis a richer individual - individual B. The combined share of A + B in the population is 67%. The joint share of A+B in income is 50% (20%+30%). Next, we will include in the analysis an even richer individual C. The combined share of A+B+C in the population is 100%. The joint share of A+B+C in income is 100% (20%+30%+50%).

Let us note the results obtained on the graph:

The line connecting the lower left point and the upper right point of the graph is called the line of uniform distribution of income. This is a hypothetical line that shows what would happen if income in the economy was distributed evenly. With an uneven distribution of income, the Lorenz curve lies to the left of this line, and the greater the degree of inequality, the stronger the bend in the Lorenz curve. And the lower the degree of inequality, the closer it is to the line of absolute equality.

In our case, the Lorenz curve looks like a piecewise linear graph. This happened because in our analysis we identified only three population groups..png" alt="/text/77/387/images/image002_67.gif" width="340" height="65"> где уi - доля доходов, сосредоточенная у i-й социальной группы населения; хi - доля населения, принадлежащая к i-й социальной группе в общей численности населения; n - число социальных групп .!}

Extreme values of the Lorentz coefficient: L = 0 in the case of complete equality in income distribution; L = 1 - with complete inequality. To quantify the degree of income inequality along the Lorenz curve, there is a special coefficient - the Gini coefficient.

GINI COEFFICIENT

The Gini coefficient, like the Lorenz coefficient, is used to characterize income concentration. The Gini coefficient is a statistical indicator of the degree of stratification of society in a given country or region in relation to any characteristic being studied. Most often in modern economic calculations, the level of annual income is taken as the characteristic being studied.

The Gini coefficient can be defined as a macroeconomic indicator that characterizes the differentiation of monetary incomes of the population in the form of the degree of deviation of the actual distribution of income from their absolutely equal distribution among the inhabitants of the country.

Sometimes a percentage representation of this coefficient is used, called the Gini index.

Sometimes the Gini coefficient (like the Lorenz curve) is also used to identify the level of inequality in accumulated wealth, but in this case the non-negativity of the household’s net assets becomes a necessary condition.

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The area of the inner figure D can most quickly be calculated by subtracting the areas of figures A, B and C from the area of the large triangle.

In this case, the Gini coefficient will be equal to:

As you know, any statistical indicator has pros and cons. The advantages of the Gini coefficient are as follows:

Allows you to compare the distribution of a characteristic in populations with different numbers of units (for example, regions with different populations).

Complements data on GDP and per capita income. Serves as a kind of correction for these indicators.

Can be used to compare the distribution of a trait (income) between different populations (for example, different countries). At the same time, there is no dependence on the scale of the economy of the countries being compared.

Can be used to compare the distribution of a trait (income) across different population groups (for example, the Gini coefficient for the rural population and the Gini coefficient for the urban population).

Allows you to track the dynamics of uneven distribution of a characteristic (income) in the aggregate at different stages.

Anonymity is one of the main advantages of the Gini coefficient. There is no need to know who has what income personally.

In addition to its advantages, any statistical indicator has its flaws. Just as the GDP indicator cannot judge the level of well-being of the economy, the Gini coefficient (and other indicators of the degree of inequality) cannot give a fully objective picture of the degree of income inequality in the economy.

This happens for several reasons:

First, individuals' income levels are not constant and can change dramatically over time. The income of young people who have just graduated from university is usually minimal, and then begins to increase as the person gains experience and builds up human capital. People's income typically peaks between the ages of 40 and 50, and then declines sharply as the person retires. This phenomenon is called the life cycle in economics.

But a person has the opportunity to compensate for differences in income at different stages of the life cycle with the help of the financial market - by taking out loans or making savings. Thus, young people at the very beginning of their life cycle willingly take out education loans or mortgage loans. People who are closer to the end of the economic life cycle are active savers.

The Lorenz curve and Gini coefficient do not take into account the life cycle, so this measure of the degree of income inequality in a society is not an accurate estimate of the degree of income inequality.

Second, individuals' incomes are affected by economic mobility. In particular, the US economy is an example of an economy of opportunity, where an individual from the bottom can, through a combination of diligence, talent and luck, become a very successful person, and history knows many similar examples. But there are also cases of loss of large fortunes or even complete bankruptcies of quite wealthy entrepreneurs. Typically, in economies such as the United States, an individual household will move through several income distribution categories over the course of its lifetime. And this is due to high economic mobility. So, for example, a household may be included in the lowest income group one year, and in the middle income group the next year. The Lorenz curve and the Gini coefficient also do not take this effect into account.

Third, individuals may receive transfers in kind, which are not reflected in the Lorenz curve, although they affect the distribution of individuals' income. Transfers in kind can be implemented in the form of assistance to the poorest segments of the population with food and clothing, but usually they are provided in the form of numerous benefits (free travel on public transport, free trips to sanatoriums, and so on). Taking into account such transfers, the economic situation of the poorest segments of the population improves, but the Lorenz curve and the Gini coefficient do not take this into account. Not so long ago in Russia, many benefits were monetized, and the objective income of the poorest segments of the population became easier to calculate. Consequently, the Lorenz curve began to better reflect the real distribution of income in society.

Thus, the Lorenz curve and the Gini coefficient are used to assess the degree of income inequality, and fall within the realm of positive economic analysis. Let us recall that positive analysis differs from normative analysis in that positive analysis analyzes the economy objectively, as it is, and normative analysis is an attempt to improve the world, to make it “as it should be.” If the assessment of the degree of inequality is a positive economic analysis, then attempts to reduce inequality in the distribution of income belong to the field of normative economic analysis.

Normative economic analysis is known for the fact that different economists can offer different, often diametrically opposed, recommendations for solving the same problem. This does not mean who is more competent and who is less competent. This only means that economists start from different philosophical views on the concept of justice, and there is no unity on this issue.

CONCLUSION

There are a number of indicators for assessing the differentiation of income of the population, in particular the Lorenz and Gini coefficients.

The Lorenz coefficient as a relative characteristic of inequality in income distribution. The Lorentz coefficient is the fraction of the area of deviation from the uniform distribution of the diagonal of a square in half the area of this square, or it is the ratio of the actual sum.

The Gini coefficient is a statistical indicator of the degree of stratification of society in a given country or region in relation to any characteristic being studied.

The Gini coefficient is equal to the ratio of the area of the figure bounded by the straight line of absolute equality and the Lorenz curve to the area of the entire triangle under the Lorenz curve.

Thus, the Lorenz curve and the Gini coefficient are used to assess the degree of income inequality and fall within the realm of positive economic analysis.

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11. Economic statistics: Textbook / ed. . - M.: INFRA-M, 2009.

GINI COEFFICIENT, an indicator used in statistics to assess the degree of concentration of the characteristic being studied or the unevenness of its distribution among units or groups of units of the statistical population. The concentration of the relative volumes of a characteristic in individual units accordingly leads to a proportional decrease in the relative volumes in the units of the remaining part of the population, which causes uneven distribution. Such unevenness may occur in the distribution of income among population groups, labor resources among regions of the country, assets among credit institutions, etc. Along with the term “concentration”, other terms are used in specific subject areas, for example, “localization” or “differentiation”.

The calculation of the Gini coefficient is based on the use of a concentration curve (Lorentz curve). To construct it, it is necessary to have a frequency distribution of units of the population under study and an interconnected frequency distribution of the characteristic being studied. At the same time, for the convenience of calculations and to increase the analyticality of the data, the population units, if possible, are divided into equal groups: 10 groups - 10% of units each or 5 groups - 20% of units each. So, for example, in the practice of statistics, when studying the differentiation of the population by income, 5 groups are distinguished according to the degree of their increase: the first - with the lowest incomes, the fifth - with the highest.

The Lorenz curve is plotted in a rectangular coordinate system. The accumulated frequencies of the volume of the population are plotted on the abscissa axis, and the accumulated frequencies of the volume of the attribute are plotted on the ordinate axis. The resulting curve will characterize the degree of concentration.

General view of the Lorenz curve.

If the distribution is strictly uniform, then the first 20% of units of the ranked population (population) have 20% of the volume of the attribute (total income), the first 40% of units have, respectively, 40% of the volume of the attribute, etc. This distribution is displayed by a straight line passing from the lower left corner of the graph to the upper right corner and is a line of uniform distribution. The stronger the concentration of the characteristic being studied, the more noticeably the Lorenz curve deviates downward from the line of uniform distribution, and vice versa, the weaker the concentration, the closer the curve will be to a straight line.

The degree of concentration (figure) is determined by the area of figure A, limited by the line of uniform distribution and the Lorenz curve. The larger the area A and the correspondingly smaller the area B, the higher the degree of concentration. By comparing area A with the area of a triangle located below the line of uniform distribution, the Gini coefficient is based, the calculation formula of which is:

where d xi is the share of the i-th group in the total volume of the population; d yi - the share of the i-th group in the total volume of the attribute; d H yi is the accumulated share of the i-th group in the total volume of the attribute.

The range of values accepted by the Gini coefficient is from 0 to 1. According to the Federal State Statistics Service, the Gini coefficient, which characterizes the differentiation of the Russian population by income, was 0.387 in 1995, and 0.407 in 2004. In the Russian Federation, the Gini coefficient began to be used only in the 1990s, and both during the economic crisis of the 1990s and during the period of economic growth of the 2000s, it showed the low egalitarianism (from the French égalité - equality) of Russian society.

The Gini coefficient is an indicator of the uniformity of distribution of consumption and income in society, and is a number from 0 to 1, where 0 is complete equality, 1 is complete inequality. This material is about how to calculate the Gini coefficient.

To calculate the Gini coefficient it is convenient to construct Lorenz curve.

A simple example of how to calculate the Gini coefficient

In a country, 40% of the income comes from 60% of the people, and 60% of all income comes from the remaining 40%. The Lorenz curve for such a society is line ADB. Straight segment AB is the Lorenz curve for a society where income is distributed equally among everyone. The Gini coefficient is the quotient of the area of the red figure divided by the sum of the areas of the red and yellow ones. That is, the larger the red triangle, the more unevenly income is distributed in society.

A more complex example from real World Bank data

Available World Bank estimates of consumption and income distribution. For example, take data from Albania. For clarity, we construct an approximate Lorentz curve point by point.

We will calculate the area of the yellow figure as the sum of the areas of trapezoids (the area of a trapezoid is equal to half the sum of its bases).

Gini coefficient

Gini coefficient- a statistical indicator of the degree of stratification of society in a given country or region in relation to any characteristic being studied.

Most often in modern economic calculations, the level of annual income is taken as the characteristic being studied. The Gini coefficient can be defined as a macroeconomic indicator that characterizes the differentiation of monetary incomes of the population in the form of the degree of deviation of the actual distribution of income from their absolutely equal distribution among the inhabitants of the country.

Sometimes a percentage representation of this coefficient is used, called Gini index.

Background

This statistical model was proposed and developed by the Italian statistician and demographer Corrado Gini (1884-1965) and published in 1912 in his work “Variability and Variability of a Character” (“Variability and Inconstancy”).

Calculation

The coefficient can be calculated as the ratio of the area of the figure formed by the Lorenz curve and the equality curve to the area of the triangle formed by the equality and inequality curves. In other words, you should find the area of the first figure and divide it by the area of the second. In case of complete equality, the coefficient will be equal to 0; in case of complete inequality it will be equal to 1.

Sometimes the Gini index is used - a percentage representation of the Gini coefficient.

or according to the Gini formula:

where is the Gini coefficient, is the cumulative share of the population (the population is pre-ranked by increasing income), is the share of income that the total receives, is the number of households, is the share of household income in total income, is the arithmetic mean of the shares of household income.

Benefits of the Gini Coefficient

Allows you to compare the distribution of a characteristic in populations with different numbers of units (for example, regions with different populations).

Complements data on GDP and per capita income. Serves as a kind of correction for these indicators.

Can be used to compare the distribution of a trait (income) between different populations (for example, different countries). At the same time, there is no dependence on the scale of the economy of the countries being compared.

Can be used to compare the distribution of a trait (income) across different population groups (for example, the Gini coefficient for the rural population and the Gini coefficient for the urban population).

Allows you to track the dynamics of uneven distribution of a characteristic (income) in the aggregate at different stages.

Anonymity is one of the main advantages of the Gini coefficient. There is no need to know who has what income personally.

Disadvantages of the Gini coefficient

Quite often, the Gini coefficient is given without describing the grouping of the population, that is, there is often no information about exactly which quantiles the population is divided into. Thus, the more groups the same population is divided into (more quantiles), the higher the Gini coefficient value for it.

The Gini coefficient does not take into account the source of income, that is, for a certain location (country, region, etc.) the Gini coefficient can be quite low, but at the same time some part of the population provides their income through backbreaking labor, and the other through property. For example, in Sweden the Gini coefficient is quite low, but only 5% of households own 77% of the shares of the total number of shares owned by all households. This provides these 5% with the income that the rest of the population receives through labor.

The method of the Lorenz curve and the Gini coefficient in studying the uneven distribution of income among the population deals only with cash income, while some workers are paid wages in the form of food, etc.; The practice of issuing wages to employees in the form of options to purchase shares of the employer company is also becoming widespread (the last consideration is unimportant, the option itself is not income, it is only an opportunity to receive income by selling, for example, shares, and when the shares are sold and the seller receives money, this income is already taken into account when calculating the Gini coefficient).

Differences in methods for collecting statistical data to calculate the Gini coefficient lead to difficulties (or even impossibility) in comparing the obtained coefficients.

Example of calculating the Gini coefficient

The preliminary coefficient in 2010 was 42% (0.420) The Gini coefficient in Russia in 2009 was 42.2% (0.422), in 2001 39.9% (0.399) In 2012, according to the Global Wealth Report, Russia is ahead of all major countries and has coefficient 0.84

Notes

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See what the “Gini Coefficient” is in other dictionaries:

- (Gini coefficient) Statistical indicator of inequality. For example, if yi is the income of the i th person, the Gini coefficient is equal to half the expected absolute difference between the incomes of two randomly selected people, i and j, divided by the average income. On the… … Economic dictionary

- (Gini coefficient) See: Lorenz curve. Business. Dictionary. M.: INFRA M, Ves Mir Publishing House. Graham Betts, Barry Brindley, S. Williams and others. General editor: Ph.D. Osadchaya I.M.. 1998 ... Dictionary of business terms

A coefficient characterizing the differentiation of monetary incomes of the population in the form of the degree of deviation of the actual distribution of income from their absolutely equal distribution among all residents of the country. See t.zh. INCOME CONCENTRATION INDEX… Encyclopedic Dictionary of Economics and Law

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Gini coefficient- a macroeconomic indicator characterizing the differentiation of monetary incomes of the population in the form of the degree of deviation of the actual distribution of income from their absolutely equal distribution among the inhabitants of the country... Dictionary of economic terms

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