Ginny coefficient example solution. Gini coefficient, Lorentz coefficient

06.05.2020

Gini coefficient. Income inequality

Gini coefficient (zhini Index) - The statistical indicator, indicative of the degree of bundle of the Company of this country or region in relation to any studied attribute (for example, in terms of the level of annual income is the most frequent application, especially under modern economic calculations). The Gini coefficient can be used to identify the level of inequality in accumulated wealth.

This statistical model has been proposed and developed by Italian statistical and demographer Korrado Gini (1884-1965) and published in 1912 in its famous work "Variability and variability of a sign" ("variability and inconstancy"). So it is macroeconomic indicatorcharacterizing the differentiation of monetary incomes of the population in the form of a degree of deviation of the actual distribution of income from absolutely equal distribution between the inhabitants of the country.

Gini coefficientdetermines the degree of distribution deviationincomes for population groups from uniform. What is he closer to zero, especially uniform distribution of income; the closer the Gini coefficient to one, the more revenues are concentrated by the richest group of citizens. For example, the value of the Gini coefficient in the United States is 0.408, in the UK - 0.361, in Sweden - 0.250, in Japan - 0.249, in Zimbabwe - 0.568, in Mexico - 0.537, in Chile - 0.565. European Block countries, such as the Czech Republic, Sweden, Norway, Denmark, Slovenia, have more low coefficient Gini, in the range of 0.2 to 0.3.

According to some estimates, one sixth part of the population of Russia focused 57% of all cash income and 92% of property income. The model of social stratification in Russia today characterizes the highest degree of differentiated society.

There is a concept decyl coefficient of differentiation of incomeWhich shows how many times the minimum income of 10% of the most secured population exceeds the maximum income among 10% of the least secured population. In 1991, the decile coefficient was 4.5 times; in 1992 - 8.0 times; In 1994, his record magnitude was observed over the time of the reforms - 15 times, in recent years - on average 14 times. The Gini coefficient in Russia in 1991 was 26%, in 1992 - 28.9%, in 1994 - 40.9%, in 1998 - 37.9%, in recent years its value is an average of 39% (2008 data).

World practice confirms that the danger of social conflicts is minimized if the gap between the revenues of the rich and the poor does not exceed 10 times.

Upper layer russian society heterogeneous, it includes members of the government engaged in the economy; Ministers and their deputies; leaders of the largest state and semi-state companies; leaders of new commercial structures; Economic consultants public organizations; leading scientists and economists; Persons cooperating or belonging to the Crime Mire, highly qualified specialists. Among the rich people, more than half are the leaders of the first level. In the pre-reform period, a high official position provided the ability to control the property and the right to privilege, and today - the assignment of property and income.

Elite from French Elite - "Best, Selected Part". In the theory of elites allocate the economic, political and spiritual elite. Under the economic elite, people receiving high and ultra-high incomes and controlling the main financial and economic structures of the country are understood, regardless of the forms of ownership. Almost all elite theories are associated with the system of power relations in society and noted inequality between the elite and all other members of society. In other words, the elite is leading representatives of the Company, determining the priorities of the development of society and affecting the bulk of the population. The economic elite includes persons who occupy the leading position in economic, political and social structures, having and aware of common interests and mutually acting. P . According to the majority of specialists, the economic elite of Russian society should include gas, oil and aerospace groups. Coal, gold, banking groups are called protoelitis, noting their powerful potential in the absence of constant intragroup interaction and contacts.

The overwhelming majority of citizens of the country appearance and constant increase in the number of dollar billionaires against the background of poverty a significant part of the population are perceived as a blatant anomaly. At the level of GDP per capita - 17 thousand dollars per poverty line in Russia live about 13 percent of the person, which, according to specialists, is almost nonsense. Especially if you consider that the share of the shadow economy in our country remains high enough - 25-30 percent. This money is not taken into account in GDP, it means that its real level is higher than the official one. At the same time, most of the income from the shadow sector gets people in non-heedy, and, it means that the real bundle of society is higher.

One way to eradicate income inequality involves support from the state of health systems, social security and education. In this case, people with smaller income can get a satisfactory physical condition, confidence in tomorrow and education. This approach provides the necessary conditions for life to everyone. Another way to combat inequality involves changes to tax system and, in particular, the system of progressive income tax. In this regard, there is a significant difference in the applicable norms of different countries, the range of interest rates in different countries is different. In the United States, interest rates of income tax are established by the government in the range of 10% - 35%, in Japan - 5% - 50%, in Canada - 15% - 29%. Only in Russia interest rate The income tax for all is the same - 13%, which leads to the fact that there are no distinction frames in the income of different layers of the population, and the rich becomes richer, and the poor are even poorer.

The number of Russian millionaires whose condition exceeds $ 100 million, by 2017 will grow by 76 percent. Such a forecast is published in the report of the Consulting company Knight Frank and Citi Private Bank.

Now in our country 2.1 thousand such Centa millionaires. And around the world - 63 thousand people. Their general condition is estimated at 39.9 trillion dollars.

Assess the degree of differentiation of wages among employees of each of the sectors 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

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

Gini coefficient is a statistical indicator of the degree of separation of society on a specific basis. This indicator is often used to determine the uneven income distribution among the population of the countries of the world.

Using the method of calculating the Gini coefficient (in the text of the study, it is detailed), we considered not the entire economy of Russia, and its individual industries.

Calculation of the coefficient of Gini.

A few words about how this indicator is calculated.

The values \u200b\u200bthat the coefficient can take are in the range from 0 to 1. Zero means full equality of income among all residents (in this case Employees of a particular industry), a unit - complete inequality (an unreal situation, when the entire wage of the industry is concentrated in the hands of one person).

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

We illustrate on the example.

Suppose that all residents of the country receive the same salary, in this case the chart will look like this:

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

In the opposite case, if we assume that one person receives a salary, and all the others work for free, the Gini coefficient will be equal to one, and the income concentration schedule will look like this:

In reality, income distribution is usually as follows:

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

The figure formed by the intersection of a red straight line and a purple curve is the inequality of income distribution. The value of the Gini coefficient is the ratio of the area of \u200b\u200bthis figure to the area of \u200b\u200bthe entire triangle.

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

We use the data of Rosstat "Distribution of the number of employees in terms of salary size" by type economic activity And try on the basis of these data to construct the Lorentz curve and calculate the value of the Gini coefficient.

Table 1 (part 1). Distribution of the number of employees in terms of salary size »These types of economic activity, in 2015 *

	Agriculture, Hunting and Forestry	Fishing, fish farming	Mining	Processing production	Production and distribution of electricity, gas and water	Building
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 in terms of salary size »These types of economic activity, in 2015 *

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

Accrued salary	Wholesale and retail, repair of motor vehicles and motorcycles	Hotels and restaurants	Transport and communication	Financial activities	Operations S. real estate, Rent and provision of services	Scientific 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 in terms of salary size »These types of economic activity, in 2015 *

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

Accrued salary	Public administration, Mandatory social Security, activity of extraterritorial organizations	Education	Health and provision of social services	Providing utility, personal and social services	Of these, activities on the organization of 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 build the Lorentz curve and calculating the Gini coefficient, data on the share of income of each population group (in this case of industry workers) in aggregate income are necessary. This data B. Table 1. No missing. In order to receive such data, we use the mathematical reception: intelligent income for each interval (we define them as a middle of the interval) to the corresponding specific weights (share) of the population, thereby having so-called percentage income. Then, having calculated the specific gravity of groups in general income and having aroused them, we obtain a cumulative revenue series, expressed as a percentage.

For example, we will carry out calculations for one of the industries, for example, agriculture, hunting and forestry.

Table 2. Estimated data for calculating the Gini coefficient by industry "Agriculture, Hunting and Forestry"

Income	Middle interval	The proportion of workers receiving the appropriate wage level	Cumulative number of employees	Group revenues, percentages	Share in total income	Cumulative revenue
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 interval – average level wages in each group of workers.
The proportion of workers receiving the appropriate level of salary - Rosstat data (see Table 1).
Cumulative number of employees - accumulated frequencies. In order to calculate the value of the i-row, it is necessary to sum up the specific weights of the workers (column 3 of table 2) from 1 to i inclusive.
Group revenues, percentages - calculated data used to determine swelling The income of a group of workers in general income. Calculate multiplication of the middle of the interval on the proportion (column 2 multiplied to column 3).
Share in total income - The proportion of revenues of a group of employees in general income. The ratio of group income (column 5) to the sum of all income (the amount of income on the column 5).
Cumulative revenue - The sum of the specific income weights to the relevant group.

We construct a diagram where the cumulative number of employees will be postponed along the axis X, and on the Y axis - a cumulative number of income.

The figure of the figure under the purple line can be treated, having aroused the area of \u200b\u200bthe trapezoids, of which the figure consists. Their total area is 3313.

The figure of the figure at an absolutely uniform distribution of income is 5000 (the triangle is direct on Diagram 2.).

Thus, the area of \u200b\u200bthe figure reflecting the inequality of income distribution is 5000-3313 \u003d 1687.

Consequently, the Gini coefficient for the industry agriculture, hunting and forestry equal to 1687/5000 \u003d 0.337

Gini coefficient for other sectors of the economy

By the same sample, we calculate the values \u200b\u200bof the Gini coefficient for all 17 sectors of the economy, which takes into account Rosstat.

Table 3. Gini coefficient for sectors of the economy in 2015

Industry	Gini coefficient
Agriculture, Hunting and Forestry	0,337
Fishing, fish farming	0,486
Mining	0,314
Processing production	0,331
Production and distribution of electricity, gas and water	0,343
Building	0,355
Wholesale and retail, repair of motor vehicles and motorcycles	0,395
Hotels and restaurants	0,378
Transport and communication	0,362
Financial activities	0,355
Real estate operations, Rent and provision of services	0,402
Scientific research and development	0,334
Public Administration, Mandatory Social Security, EXTERRIORIAL ORGANIZATIONS	0,349
Education	0,384
Health and provision of social services	0,368
Providing utility, personal and social services	0,412
Activities for the organization of recreation, entertainment, culture and sports	0,417

By exposing the data and presenting it in the form of a chart, we will see that at the moment the greatest equality of income is observed among employees in the field of mineral mining, and the greatest inequality is in the field of fishing and fish farming.

In order to illustrate how much the inequality coefficient of 0.486 differs from the coefficient of 0.314, we give a simple example. In the field of fishing and fish farming, 12.4% of the highest paid employees receive 40% of cumulative income. But in the most "fair" from this point of view, the sphere of mining of minerals - a little more than 40% of the cumulative income is already obtained 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 salary sizes in the sectors of the economy

Having calculated the Gini coefficient for sectors of the economy in 2013 and comparing these values \u200b\u200bwith the figures of 2015, we will see how the crisis has influenced the differentiation of wages in a particular sphere.

Let's see if somewhere income in the industry is distributed among the employees "Fair".

- Rating industries for the growth of the Gini coefficient. The diagram shows that over the past 2 years, inequality in the distribution of wages has significantly increased in the spheres of fisheries, fish farming (+ 15.3%), hotel and restaurant business (+ 4.82%) and construction (+ 3.66%).

More "fair" wage distribution has become in health care and the provision of social services (-3.47%), in the field of wholesale and retail motor vehicles (-2.27%), in the field scientific research and developments (-2.16%).

In the field of fishing and fish farming in 2013, 8.2% of the highest paid employees had 23.56% of cumulative income. In 2015, 22.08% of cumulative income had already belonged to 3.9% of the highest paid employees. That is, in 2013, 1% of the highest paid employees accounted for 2.87% of the total income of the industry, and in 2015, for each percentage of such employees there were 5.66% of the total income of the industry.

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 inequality of income among employees of the sectors of the Russian economy is observed in the field fisheries and fish farming. Gini coefficient for this industry is equal 0,486 .
In sphere fisheries and fish farming 12.4% the most highly paid employees get 40% Cumulative income.
In the top three leaders in the greatest differentiation of income - activities for the organization of recreation, entertainment, culture and sports (Gini coefficient 0,417 ) I. activities for the provision communal services (0,412 ).
The most "fair" income distributed mining mining. There is the coefficient of differentiation of income equal 0,314 , and a little more 40% aggregate income get already 22,1% employees.
For two recent years (From 2013 to 2015) the degree of income separation has changed in many areas of the economy.
Inequality in the distribution of wages (according to the Gini coefficient) significantly increased in spheres fisheries, fish farming (+15,3% ), hotel and restaurant business (+4,82% ) I. construction (+3,66% ).
More "fair" wage distribution has become in health and Social Services (-3,47% ) in the sphere motor vehicles wholesale and retail trade (-2,27% ) in the sphere scientific research and development (-2,16% ).
Practically did not change the differentiation of wage officers in such spheres as processing production, mining, providing utilities, education, activities for the organization of recreation, entertainment, etc..

Gini coefficient, Lorentz coefficient

Introduction 3.

Lorentz curve (Lorentz coefficient) 5

Gini coefficient. nine

Conclusion. fourteen

References .. 15

Introduction

With the transition to K. market economy The process of income separation of society in income was sharply aggravated, and this led to the need to introduce indicators to the statistical practice 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;

The concentration coefficients of Lorentz and Gini.

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

Differentiation of income of the population

Differentiation of income of the population is objectively folding differences in the level of income of individuals and social groupsdue to differences in wages and social payments, abilities and enterprise, property situation.

Money incomes of the public include salary, social transfers, entrepreneurial revenues, interest, dividends and other revenues from the property, as well as total value Products are a personal subsidiary farm consumed in the family and sold. The incomes of the population are divided into groups unevenly.

There are a number of indicators of assessing the differentiation of income of the population, which allow you to see how intensively flows this process. Among them:

ü The distribution of the population in terms of average per capita income (modal and median income) is an indicator of the specific weight or percentage of the population in certain intended intervals of secondary money incomes.

ü Distribution of the total amount of money incomes in various groups of the population - an indicator in percentage of the share of the total amount of money income, which has each of the groups of the population - the actual income distribution curve (Lorentz curve)

ü Revenue concentration coefficient (Gini Index)

ü Decyl coefficient of income differentiation is the ratio of average per capita money incomes of the last and first population groups. It shows how many times the income N% of the most secured population exceeds the income of the N% of the least secured population.

Lorentz curve (Lorentz coefficient)

The Lorentz curve is a graphic image of the concentration of individual elements of a set of groups: the concentration of population in families with different levels of shower income; Concentration of groups working with different levels of remuneration.

Lorentz's curve reflects the cumulative (accumulated) interest in the income of the population. Lorentz curve is a graphic image of the distribution function. She was proposed american economist Max Otto Lorenz in 1905 as an indicator of inequality in the income of the population. In such a representation, it is an image of the distribution function, which accumulates the shares of the number and income of the population. In the rectangular coordinate system, the Lorentz curve is convex down and passes under the diagonal of a single square located in the I coordinate quarter.

Each point on the Lorentz curve corresponds to the statement like "20 poorest percentages of the population receive only 7% income." In the case of equal distribution, each population group has income, proportional to its number. Such a case is described by the equality curve (Line of Perfect Equality), which is a direct connecting origin and point (1; 1). In the event of a complete inequality (when only one member of society has an income), the curve (Line of Perfect Inequality) first "sticks" to the abscissa axis, and then from the point (1; 0), "sweels" to the point (1; 1).

If the distribution is uniform, pairwise fractions of the abscissa axes and the ordinates should coincide (the axis of the abscissa - 0, 20, 40, 60, 80, 100, the axis of the ordinate, respectively - 2, 20, 40, 60, 80, 100) and is located diagonally, Which means the complete absence of the concentration of the scope.

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

Lorentz curve is concluded between the curves of equality and inequality. Obviously, in specific cases, neither absolute equality or absolute inequality in the distribution of income among the population cannot be expected.

The Lorentz curves are used for distributions not only income, but also the property of households, market share for firms in the industry, natural resources for states. You can meet the curve Lorentz and outside economic Science.

Consider the Lorentz curve on the example of its construction. Building the Lorentz curve is the most convenient to consider the following example:

Imagine an economy consisting of 3 agents: A, B, C. The income of agent A is 200 units, the income of agent B is 300 units, the income of the agent C is 500 units.

To build a Lorentz curve we find the share of individuals in general income. The total income is 1000. Then the share of Individual A is 20%, the share of 30%, the share of 50%.

The share in the population of Individual A is 33%. The share of its income is 20%. Then we turn on the analysis of a richer individual - the Individual V. The joint share of A + in the population is 67%. The joint share of A + in income is 50% (20% + 30%). Next, we turn on the analysis of an even more rich Individual S. The joint share of A + B + C in the population is 100%. The joint share of A + B + C in income is 100% (20% + 30% + 50%).

Note the results obtained on the schedule:

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

In our case, the Lorentz curve looks like a piecewise linear graph. It happened so because in our analysis we allocated only three groups of the population ..png "alt \u003d" (! Lang: /text/77/387/images/image002_67.gif" width="340" height="65"> где уi - доля доходов, сосредоточенная у !} i-th social population groups; xi - the proportion of the population belonging to the I-th social group in the total population; N is the number of social groups.

Extreme values \u200b\u200bof the Lorentz coefficient: L \u003d 0 in case of complete equality in the distribution of income; L \u003d 1 - with full inequality. For quantitative measurement of the degree of income inequality on the Lorentz curve exists special coefficient - Gini coefficient.

Gini coefficient

The Gini coefficient, as well as the Lorentz coefficient, is used to characterize the concentration of income. Gini coefficient is a statistical indicator of the degree of bundle of society of a given country or region in relation to any studied attribute. Most often in modern economic calculations, the level of annual income is taken as a studied attribute.

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

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

Sometimes the Gini coefficient (like the Lorentz curve) is also used to identify the level of inequality in accumulated wealth, but in this case prerequisite Standing of net household assets becomes.

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The area of \u200b\u200bthe inner figure D is faster than just possible by subtracting from the area of \u200b\u200bthe large triangle of the Square of Figures A, B and C.

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, the following:

It makes it possible to compare the distribution of the feature in aggregates with different numbers of units (for example, regions with different population).

Completes data on GDP and average per capita income. Serves a kind of correction of these indicators.

Can be used to compare the distribution of the feature (income) between different collaps (for example, different countries). There is no dependence on the scale of the economy of the compared countries.

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

Allows you to track the dynamics of uneven distribution of the feature (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 the pros, any statistical indicator has its flaws. Just like gDP indicator It is impossible to judge the level of welfare of the economy, and the Gini coefficient (and other indicators of the degree of inequality) cannot be fully an objective picture of the degree of income inequality in the economy.

This happens for several reasons:

First, the level of income of individuals is not constant and can change sharply over time. The incomes of young people who have just finished the university are usually minimal, and then begin to grow as a person is gaining experience and increases human capital. Revenues of people tend to reach a peak between 40 and 50 years, and then sharply decrease when a person retires. Eh, the phenomenon is called in the economy of the life cycle.

But person has the ability to compensate the difference in income at different stages of the life cycle using financial market - Taking loans or making savings. So, young people who are at the very beginning of the life cycle, willingly take loans for education or mortgage loans. People who are closer to the end of the economic life cycle are actively making savings.

Lorenz's curve and the Gini coefficient do not take into account life cycleTherefore, this indicator of the degree of income inequality in society is not an accurate assessment of the degree of income inequality.

Secondly, economic mobility affects incomes. In particular, the US economy is an example of an economy of opportunity when an individual from the bottom can thanks to a combination of diligence, talent and good luck, to become a very successful person, and the story knows many similar examples. But there are also cases of loss of major states or even complete bankruptcies of quite wealthy entrepreneurs. As a rule, in such economies, as the US economy, a separate household has time to visit several categories of income distribution. And it is connected with high economic mobility. For example, some household can in one year enters the group with the lowest income, and next year already in a group with an average level of income. The Lorentz curve and the Gini coefficient also do not take into account this effect.

Thirdly, individuals can receive transfers in natural uniform, which are not reflected in the Lorentz curve, although it affects the distribution of income of individuals. In general form transfers can be implemented in the form of helping the poorest population of food, clothing, but usually they are provided in the form of numerous benefits (free travel in public transport, free trips to the sanatorium and so on). Taking into account such transfers economic situation The poorest segments of the population is improved, but the Lorentz curve and the Gini coefficient do not take this. Not so long ago, many benefits were moneticed in Russia, and the objective income of the poorest segments began to be easier. Consequently, the Lorentz curve began to better reflect the real distribution of income in society.

Thus, the Lorentz curve and the Gini coefficient are used to evaluate the degree of income inequality, and are included in the area of \u200b\u200bpositive economic analysis. Recall that positive analysis differs from the regulatory analysis by the fact that a positive analysis analyzes the economy objectively as it is, and the regulatory analysis is an attempt to improve the world, to make "how it should be." If an 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 regulatory economic analysis.

Normative economic analysis It is known for the fact that different economists can offer different, often diametrical opposite recommendations for solving the same problem. This does not mean that someone is more competent, but who is less competent. It only means that economists are repelled from various philosophical views on the concept of justice, and there is no unity in this matter.

Conclusion

Differentiation of income of the population is objectively emerging differences in the level of income of individuals and social groups due to differences in wages and social benefits, abilities and enterprise, property situation.

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

Lorentz coefficient as a relative characteristics of inequality in the distribution of income. The Lorentz coefficient is the share of the area of \u200b\u200bdeviation from the uniform distribution of the diagonal of the square in the middle of the area of \u200b\u200bthis square or this is the ratio of the actual amount.

Gini coefficient is a statistical indicator of the degree of bundle of society of a given country or region in relation to any studied attribute.

The Gini coefficient is equal to the attitude of the figure of the figure, limited direct absolute equality and the Lorentz curve, to the area of \u200b\u200bthe entire triangle under the Lorentz curve.

Thus, the Lorentz curve and the Gini coefficient are used to evaluate the degree of income inequality, and are included in the area of \u200b\u200bpositive economic analysis.

BIBLIOGRAPHY

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2., Gavrilov. - SPb.: Peter, 2007.

3., Shpakovskaya-Economic statistics: Tutorial. - M.: Lawyer, 2009.

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Rosstat's data released on Monday confirmed the assumptions that the peculiarity of the current crisis is income growing inequality. Gini coefficient in Russia increased in the first half of the year for the first time since 2012

In Russia, for the first time during the current economic recession, the growth of inequalities in the income of the population was recorded. As reported today, Rosstat's data, the Gini coefficient is the most common property stratification indicator in the world - in the first half of 2016 increased to 0.399 compared with 0.396 in the first half of 2015. Before that, since the first half of 2013, this indicator decreased for three years. According to the results of the first quarter of 2016, the Gini coefficient was equal to 0.392, reported earlier Rosstat.

The share of income of 20% of the poorest population in Russia has decreased in the first half of the year by 0.1 pp. (up to 5.6%, compared with 5.7% a year earlier), and the share of incomes of 20% of the most secured citizens increased by 0.2 percentage points. (from 45.7 to 45.9%), follows from Rosstat data.

The growth of inequality is the trend of the current crisis, says RBC director of the Institute of Labor and Insurance of Ranjigs Alexander Safonov. If in 2008, the Government decided to increase wages of state employees by 30% in the midst of the crisis, now real income The population is reduced due to lack of funds in the budget for social assistance, explains Safonov. The state froze the growth of wages in the public sector, adds the chief economist of Alpha Bank Natalia Orlova. Nominal wages, according to Rosstat, grew in the first half of 2016 by 7.8% (year by year), but public sector They grow less than an average of the country - only 5-6% year by year, says Orlova.

The Gini coefficient varies from 0 to 1, the closer the value to zero, the equally distributed population income. At the same time, indicators of income inequality are susceptible to seasonal fluctuations, so the most representative data on the total year, when all quarterly and annual awards, seasonal fluctuations in labor pay, dividends, etc. are taken into account.

In 2015, Gini's coefficient in Russia amounted to 0.412, declared regarding 2014 (0.416). The indicator decreases since 2012, and he reached its maximum in Russian history in 2007.

"Unfortunately, the economy is arranged in such a way that the part of the population, which has previously received high income or is related to state orders (In particular, it concerns the military-industrial complex), or these are contractual organizations that are engaged in construction. They have a volume or fall in revenue not so significant as in commercial organizations. It turns out that part of people incomes loses, part - saves. Naturally, the Gini coefficient begins to increase, "safon argues. In addition, the most secured people part of the income has always been nominated in dollars, and in connection with the fall of the ruble, their incomes only increased.

In parallel, the number of people living beyond the poverty line (those who have income below subsistence minimum). If there were 13.4% of the total population (or 19 million people in the past crisis in 2008), now the indicator is already 15.7% (they live below the poverty line). It is the growing gap between rich and poor who can serve as an explanation of the paradoxical at first glance: retail sales in the country continue to fall, despite the growth of real salaries. Although salaries, taking into account inflation, grew over four out of five past months, the fall in retail trade remained about 5% since the beginning of 2016, wrote last week Bloomberg. Salary can grow in those people who are so consumed enough, on the other hand, people who could consume more, salaries do not grow, argues Orlov.

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

To calculate the Gini coefficient, it is convenient to build curve Lorentz.

Simple example how to calculate the Gini coefficient

In the country, 40% of income is obtained by 60% of people, and 60% of all income falls for the remaining 40 percent. The Lorentz curve for such a society is the ADB line. The straight line AB is a Lorentz curve for society, where income is distributed among all equally. Gini's coefficient is a private from dividing the square of the Red Figure on the amount of red and yellow areas. That is, the greater the red triangle, the more unevenly distributed income in society.

A more complex example from the real data of the World Bank

Available estimated data World Bank on the distribution of consumption and income. For example, we take these Albania. For clarity, at points we build an approximate curve Lorentz.

The area of \u200b\u200bthe yellow figure will be considered as the sum of the scenery of the trapezium (the area of \u200b\u200bthe trapezium is equal to half a base).