The gini coefficient has gone up means that. Lorentz curve

What is inequality, how is it measured, what methodologies are used. Gini coefficient by country and other inequality coefficients.

Different coefficients of inequality

• Quintile coefficient: the ratio of the average income of the richest 20% of the population to the average income of the poorest 20% of the population.
• Palm attitude: share of the richest 10% of the population in gross national income (GNI) divided by the poorest 40%. Based on the work of José Gabriel Palma (Palma, 2011), who found that middle-class incomes almost always account for about half of GNI, while the other half is split between the richest 10% and the poorest 40%, but the shares of the two groups vary widely across countries ...
• Gini coefficient: an indicator characterizing the deviation of the actual distribution of income individuals or households in a particular country from absolute equality. Index value 0 corresponds to absolute equality, 1 - to absolute inequality. (How to calculate)

The Gini and Palms are percentages, multiplied by 100%.

Human Development Report 2016 calculations are based on World Bank data. Detailed data on the dynamics of changes in the Gini Index by years for individual countries can be found at.

To assess the degree of differentiation of wages among workers in 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 even 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 population of countries around the world.

Using the methodology for calculating the Gini coefficient (in the text of the study, it is given in detail), we did not consider the entire economy of Russia, but its individual industries.

Gini coefficient calculation

A few words about how this indicator is calculated.

The values ​​that the coefficient can take are in the 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 the wages of the 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 us illustrate with an example.

Let's say 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 the total income, 20% of the residents, respectively, 20% of the total income, etc. This is a completely even 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 distribution of income usually looks like this:

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

The pattern formed by the intersection of the red straight line and the purple curve is inequality in the distribution of income. 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 sectors of the economy

We will use the data of Rosstat “Distribution of the number of employees by size wages»By type of economic activity and try to construct the Lorenz curve based on these data and calculate the value of the Gini coefficient.

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

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

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

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

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

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

For example, let's make calculations for one of the industries, for example, for agriculture, hunting and forestry.

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

• Income
• Middle of interval- the average level of wages in each group of workers.
• The proportion of workers 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 specific weights 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. 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 the total income. The ratio of group incomes (column 5) to the sum of all incomes (sum of incomes in column 5).
• Cumulative income series- sum specific weights income to the corresponding group.

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

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

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

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

Therefore, the Gini coefficient for the industry Agriculture, hunting and forestry equals 1687/5000 = 0.337

Gini coefficient for other sectors of the economy

Using the same model, we calculate the values ​​of the Gini coefficient for all 17 sectors of the economy, which are taken into account by Rosstat.

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

Ranking the data and plotting it, we can see that so far the greatest income equality is found among employees in the mining industry, and the greatest inequality is in fisheries and fish farming.

To illustrate how the coefficient of inequality of 0.486 differs from the coefficient of 0.314, here is a simple example. In fisheries and aquaculture, the top 12.4% of employees earn 40% of total income. But in the most "fair" area from this point of view - the field of mining - a little more than 40% of total income is received by 22.1% of employees (see. Table 4).

Table 4

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

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

Let's see if, somewhere, the income in the industry has become “fairer” among employees.

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

More "fair" distribution of wages has become in health care and social services (-3.47%), in the sphere of wholesale and retail by motor vehicles(-2.27%), in the field of research and development (-2.16%).

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

Table 5

conclusions

1. The greatest income inequality among workers in the sectors of the Russian economy is observed in the sphere of fishing and fish farming... The Gini coefficient for this industry is 0,486 .
2. In the sphere fishing and fish farming 12.4% the highest paid employees receive 40% total income.
3. In the top three in terms of the highest income differentiation - activities for the organization of recreation, entertainment, culture and sports(Gini coefficient 0,417 ) and activities to provide utilities (0,412 ).
4. The most "fair" distribution of income in the field mining... There, the income differentiation coefficient is 0,314 , and a little more 40% total income already received 22,1% employees.
5. For two last years(from 2013 to 2015) the degree of income stratification has changed in many areas of the economy.
6. Inequality in the distribution of wages (according to the Gini coefficient) has grown significantly in the spheres fishing, fish farming (+15,3% ), hotel and restaurant business (+4,82% ) and construction (+3,66% ).
7. More "fair" distribution of wages has become in healthcare and social services (-3,47% ), in the sphere wholesale and retail trade in vehicles (-2,27% ), in the sphere research and development (-2,16% ).
8. The differentiation of employees by salary in such areas as manufacturing industries, mining, provision of utilities, education, activities for the organization of recreation, entertainment, etc..

Rosstat data released on Monday confirmed speculation that growing income inequality is a feature of the current crisis. 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 downturn, an increase in income inequality has been recorded. As shown by Rosstat data published today, the Gini coefficient - the most widespread indicator of property stratification in the world - increased to 0.399 in the first half of 2016 compared to 0.396 in the first half of 2015. Prior to that, starting from the first half of 2013, this indicator had been decreasing for three years. At the end of the first quarter of 2016, the Gini coefficient was 0.392, Rosstat reported earlier.

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

The growth of inequality is a trend of the current crisis, says Alexander Safonov, director of the Institute of Labor and Insurance of the RANEPA, to RBC. If in 2008, at the height of the crisis, the government made a decision to raise public sector wages by 30%, now the real incomes of the population are decreasing due to the lack of funds in the budget for social assistance, explains Safonov. The state has frozen the growth of wages in the public sector, adds Natalia Orlova, chief economist at Alfa-Bank. Nominal salaries, according to Rosstat, grew in the first half of 2016 by 7.8% (year-on-year), but in public sector they are growing less than the national average - only 5-6% year-on-year, Orlova says.

The Gini coefficient changes from 0 to 1, the closer the value is to zero, the more evenly the population's income is distributed. At the same time, indicators of income inequality are subject to seasonal fluctuations, so the most representative data are based on the results of a full year, when all quarterly and annual bonuses, seasonal fluctuations in wages, dividends, etc. are taken into account.

In 2015, the Gini coefficient in Russia was 0.412, decreasing compared to 2014 (0.416). The indicator has been decreasing since 2012, and its maximum in Russian history it reached in 2007.

“Unfortunately, the economy is arranged in such a way that the part of the population that previously received high incomes is either connected with government orders (in particular, this concerns the military-industrial complex), or these are contractors that are engaged in construction. Their volume or drop in income is not as significant as in commercial organizations... It turns out that some people lose income, and some keep them. Naturally, the Gini coefficient starts to increase, ”says Safonov. In addition, the richest people have always had part of their incomes denominated in dollars, and due to the fall of the ruble, their incomes only increased.

At the same time, the number of people living below the poverty line is growing (those with incomes below living wage). If in the last crisis in 2008 there were 13.4% of the total population (or 19 million people), now the figure is already 15.7% (they live below the poverty line). It is the growing gap between rich and poor that can serve as an explanation for the seemingly paradoxical fact: retail sales in the country continue to fall, despite the rise in real wages. While inflation-adjusted wages have risen for four of the past five months, the retail decline has remained around 5% since the beginning of 2016, Bloomberg wrote last week. Salaries can rise for those people who already consume enough, on the other hand, for people who could consume more, salaries do not grow, Orlova argues.

I. Symbols

2.Q - quantity

3. D - demand

4.S - sentence

5.Q D - the amount of demand

6.Q S - supply value

7.Q def - deficit (deficit volume)

8.Q sales - sales volume

9.Q ISB - the amount of surplus (surplus)

10.E DP - coefficient of price elasticity of demand

11. E SP - coefficient of price elasticity of supply

12. I - income

13.E DI - coefficient of income elasticity of demand

14. E DC - coefficient of cross elasticity of demand

15. TR - total income (seller's revenue)

16. TC - total costs

17.P r - profit

18. P D - ask price

19. P S - offer price

20. P E - equilibrium price

II. Formulas:

1. y = k * x + b- the equation describing the demand function

2. Q D = k * P + b- demand function

3. E DP = Δ Q D (%) / ΔP (%)- coefficient of price elasticity of demand

4. E DP = (Q 2 –Q 1): (Q 2 + Q 1) / (P 2 –P 1): (P 2 + P 1)- the midpoint formula, where P 1 is the price of the product before the change, P 2 is the price of the product after the change, Q 1 is the amount of demand before the change in price, Q 2 is the amount of demand after the change in price;

5. E DI = (Q 2 –Q 1): (Q 2 + Q 1) / (I 2 –I 1): (I 2 + I 1)- the formula for the coefficient of elasticity of demand, where I 1 is the amount of income before the change, I 2 is the amount of income after the change, Q 1 is the amount of demand before the change in income, Q 2 is the amount of demand after the change in income;

6. E DC = (Q 2 –Q 1): (Q 2 + Q 1) / (P 2 –P 1): (P 2 + P 1)- the midpoint formula, where P 1 is the price of the second product before the change, P 2 is the price of the second product after the change, Q 1 is the amount of demand for the first product before the price change, Q 2 is the amount of demand for the first product after the change in price;

7. TR = P * Q- the formula for calculating the seller's revenue

8. P r = TR - TC- profit calculation formula;

9. Q D = k * P + b- offer function;

10. E SP = (Q S2 –Q S1): (Q S2 + Q S1) / (P 2 –P 1): (P 2 + P 1)- the formula for the supply coefficient, where P 1 is the price of the product before the change, P 2 is the price of the product after the change, Q S1 is the amount of the offer before the price change, Q S2 is the amount of the offer after the change in price;

11. Q def = Q D - Q S- the formula for determining the volume of the deficit;

12. Q def = Q S - Q D- the formula for determining the amount of excess

The formula for calculating the amount of money required for circulation:
1)

KD - a lot of money;
ET - the sum of the prices of goods;
K - goods sold on credit;
SP - urgent payments;
VP - reciprocal payments (barter transactions);
CO - turnover rate monetary unit(in year).
2)


Q is the quantity of products produced at constant prices.

Exchange equation:

M - money supply in circulation;
V is the velocity of money circulation;
Р - average prices for goods and services;
Q is the quantity of products produced at constant prices.
This equation shows that the total cost in monetary terms
are equal to the value of all goods and services produced by the economy.

Formula for finding real income:

CPI - consumer price index.

The formula for finding the purchasing power of money:

Iпсд - purchasing power of money;
Ic - price index.

The formula for finding the consumer price index:

Formula for calculating the cost consumer basket:

P 1 - the price of the first product;
Р 2 - the price of the second item;
Р n - the price of the n-th product;
Q 1 - the quantity of the first item;
Q 2 - the quantity of the second item;
Q n is the quantity of the n-th product.

Formula for calculating the inflation rate:

Depending on the rate of inflation, there are several types of it:
1. Soft (creeping), when prices rise within 1-3% per year.
2. Moderate - when prices rise up to 10% per year.
3.Galloping - when prices rise from 20 to 200% per year.
4. Hyperinflation, when prices rise catastrophically - more than 200% per year.

Formula for calculating simple interest:

S is the loan amount;
n is the number of days;
i - annual percentage in shares.

Formula for calculating compound interest:

P is the amount of debt with interest;
S is the loan amount;
n is the number of days;
N - how many times it is charged per year.

Formula for calculating compound interest calculated over several years:

P is the amount of debt with interest;
S is the loan amount;
t is the number of years;
i - annual percentage in shares.

The formula for calculating the mixed percentage for a fractional number of years:

P is the amount of debt with interest;
S is the loan amount;
t is the number of years;
i - annual percentage in shares;
n is the number of days.

Formula for calculation bank reserves:

S is the rate of required reserves in percent;
R - total amount reserves;
D - the amount of deposits on the KB account.

The formula for calculating the unemployment rate:

The formula for calculating the level of employment:

Formula for calculating cross-price elasticity:

Formula for calculating the elasticity concept:

Depreciation calculation formula:
1)

2)

Formula for calculating personal income of households:

The formula for calculating GNP by income:

The formula for calculating GNP by expenditure:

The formula for calculating the NNP:

Formula for calculating average total costs:
1)

2)

Formula for calculating total costs:

Formula for calculating average fixed costs:

Formula for calculating average variable costs:

Revenue calculation formula:
1)

2)

Formula for calculating accounting profit:

Formula for calculating economic profit:
1)

2)

The formula for calculating the profitability of products:

The formula for calculating the profitability of production:

Formula for calculating entrepreneurial income:

The formula for calculating capital productivity:

The formula for calculating the magnitude of cyclical unemployment:

The formula for calculating the amount of natural unemployment:

Formula for calculating labor productivity:

The formula for calculating the arc income elasticity:

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Gini coefficient

The most short definition Gini coefficient - coefficient concentration of wealth... The higher it is, the higher the inequality. A more complete definition- a measure of inequality in income distribution. An even more complete definition is the coefficient of deviation of the economy from absolute equality in the distribution of income.

Coefficient output from the Lorentz curve and is the ratio of the area between this curve and the line of absolute equality to total area under the line of absolute equality. The line of absolute equality is the bisector between the "household share" and "income share" axes. Coefficient can be calculated and according to the exact formula.

Maximum value coefficient is equal to one and this is - absolute inequality... The minimum is zero and this is absolute equality

Due to the socio-political significance of the estimates obtained on the basis of the coefficient, it is actively calculated, discussed and used for different levels conclusions. One of the most active areas of use is cross-country and temporal comparative analysis. For example, the coefficient Gini for Russia in 1991 it was 0.24, in 2008 it was 0.42. In the so-called "model" European and especially Nordic countries, it is in the range from 0.2 to 0.3.

But direct conclusions from the comparison of the coefficient across countries and over time are hardly appropriate. He has limitations turning into disadvantages, which is explained by two circumstances. First, the relative nature of this indicator. Secondly, its range skewness: one distribution can be more equal than another in one range, and less equal in the other with the same coefficient value for both distributions. Therefore, direct conclusions from the comparison of the coefficient in different countries and over time may lead to erroneous estimates.

Coefficient named after its author- Italian Corrado Gini, lecturer in statistics, sociology and demography at the University of Rome. The coefficient was proposed by him in 1912 year, therefore, the coefficient has a significant date - 100 years practical use

Let's calculate the share of income of poor families.
Income of all families: 1.1 million * (0.15 * 200 thousand + 0.35 * 30 thousand + 0.5 * 10 thousand) = 1.1 million * (45.5 thousand).
This means that the share of incomes of poor families = (1.1 million * (0.5 * 10 thousand) / (1.1 million * (45.5 thousand) = 0.11.
In the same way, we find the share of income of the middle class in total income(equal to 0.23).
This means that the share of incomes of the poor and middle class in total income = 0.34.
I calculated the Gini index as the ratio of the area of ​​the figure (S), enclosed between the curve of absolute equality and the Lorentz curve, to the area of ​​the figure, enclosed between the curve of absolute equality and the curve of absolute inequality (San = 0.5)
S = 0.5-S 1 -S 2 -S 3 -S 4 -S 5
S 1, S 2, S 3, S 4, S 5 can be easily found from the available data, which means that the Gini index can also be found.

How to find the data S1, S2, S3, S4, S5, what are they equal to, and what to do next, how to find exactly the Gini coefficient?

S1, S3, S5 are right-angled triangles, their area is as half the product of legs
S2, S4 are rectangles, their area is the product of the sides

· Answer:

Four-dimensional cocktail

The Economics Bar's signature cocktail requires 1 unit of A, 2 of B, 3 of C, and 4 of D (ingredient names are trade secrets and are not disclosed) to make one serving of Fine Equilibrium, the Bar's signature cocktail. However, the owner of the bar, famed bartender and economist Sam Poluelson, has only limited resources to procure the expensive ingredients. So, on the available cash he can buy either 100 units of ingredient A, 200 units of ingredient B, 300 units of ingredient C, or 400 units of ingredient D per day.
What is the maximum number of servings of the signature cocktail that Sam can make in a day?

I was the first to think of a completely different solution-logical
Note the fact that to buy any ingredient (A, B, C, D) for 1 cocktail, we need to spend 1/100 of all money, that is, for 1 cocktail we spend 1/25 of all money, so we can make 25 in total cocktails

Gini coefficient(Gini coefficient) is a quantitative indicator showing the degree of inequality of different income distribution options, developed by the Italian economist, statistician and demographer Corrado Gini (1884-1965).

The Gini coefficient is a coefficient characterizing the differentiation of the population's monetary income in the form of the degree of deviation of the actual distribution of income from their absolute equal distribution among all residents of the country. Most often in modern economic calculations, the level annual income... A percentage representation of this coefficient, called the Gini index, is sometimes used.

The Gini coefficient is calculated using the so-called. If all citizens have the same income, then the Gini coefficient is zero, but if we assume the hypothesis that all income is concentrated in one person, the coefficient will be equal to one. Thus, the Gini coefficient in a particular country is between zero and one.

Benefits of the Gini coefficient:

• allows you to compare the distribution of a trait in populations with a different number of units (for example, regions with different population sizes);
• complements data on and per capita income... Serves as a kind of amendment to 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 compared countries;
• can be used to compare the distribution of a trait (income) across different population groups (for example, the Gini coefficient for rural population and Gini coefficient for urban population);
• allows you to track the dynamics of the uneven distribution of the attribute (income) in the aggregate at different stages;
• anonymity is one of the main advantages of the Gini coefficient (identification of the subjects of assessment is not required).

Disadvantages of the Gini coefficient:

• quite often the Gini coefficient is given without a description of the grouping of the population, that is, there is often no information about which quantiles the population is divided into. So, the more groups the same population is divided into (more quantiles), the higher the value of the Gini coefficient for it;
• the Gini coefficient does not take into account the source of income, that is, for a certain geographic unit (country, region, etc.) the Gini coefficient can be quite low, but at the same time, some part of the population provides its income through overwork, and the other for property account. For example, in Sweden, the Gini coefficient is quite low, but only 5% of households own 77% of the total number of shares owned by all households. This provides 5% of the income that the rest of the population receives from labor;
• the method of the Lorenz curve and the Gini coefficient in the study of the uneven distribution of income among the population deals only with cash income, while some workers may be rewarded for their work in the form of food and other material wealth; the practice of issuing wages to employees in the form of buying shares of the employing company is also widespread (the latter consideration is immaterial, an option in 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 received money , this income is already taken into account when calculating the Gini coefficient);
• differences in the methods of collecting statistical data for calculating the Gini coefficient lead to difficulties (or even impossibility) in comparing the obtained coefficients.