The relationship of econometrics with economic theory, statistics and economic and mathematical methods. Statistical Grouping and Summary

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A study was made of the possibilities of mathematical and statistical tools of econometrics, thanks to which the assessment and analysis of the overall performance of a company employee was carried out. As an indicator of the employee's work efficiency, the company's profit indicator created by the employee was chosen. The main indicators of the dynamics of work efficiency are determined, a graphic illustration of the calculation results is given. The key factors influencing the efficiency of the work of a company employee were identified, for this, the possibilities of correlation and regression analysis were used using a matrix of pair correlations. The analysis of the seasonal component of the employee's performance indicator was carried out. The calculation and analysis of elasticity coefficients characterizing the influence of factor characteristics on the effective indicator of work efficiency is carried out. A trend analysis of key factors was carried out. The construction of the equations of pair and multiple regressions has been completed. The quality of the constructed regression equations was assessed using Fisher's criteria, Student's t-Statistics and the coefficient of determination. The calculation of point and interval forecasts of the efficiency of the company's employee for the prospective periods is carried out. Proposals have been made to improve the efficiency of the company's employees.

employee performance

correlation-regression analysis

regression quality assessment

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In order to improve the efficiency of the company as a whole and each division separately, as well as to prepare an analytical report to determine the strategic line of development, a study was made of the effectiveness of the company's employee. In the course of the study, using mathematical and statistical methods using the possibilities of correlation and regression analysis, the effectiveness of the activity of an employee of the company "Avtokholod" LLC was assessed. The following indicators were selected as indicators to be studied: the average profit of a company created by an individual employee (Y), net profit (X1), the volume of sales of services for legal entities (X2), the volume of sales of services for individuals (X3), additional profit due to expansion range of services (X4).

Identification of the dynamics of the studied indicators was carried out using the following formulas (Table 1). An illustration of the calculation results is shown in fig. 1-2.

Table 1

Indicators of the dynamics of signs

	Absolute growth	Growth rate	Rate of increase
Basic

According to the results of graphical interpretation of the calculation results, it can be argued that there is a seasonal factor in the sale of the company's products. We also see an increase in the profit of the enterprise brought by the employee due to the expansion of the range of services provided.

Rice. 1. Absolute chain increase in performance efficiency

Rice. 2. Absolute basic increase in employee performance

The choice of factor features for building regression models was carried out using mathematical and statistical tools, using the capabilities of correlation and regression analysis, using a matrix of pair correlation coefficients (Fig. 3).

Rice. 3. Matrix of pair correlations

The analysis of the matrix of pair correlations made it possible to identify the leading factor X2 (the volume of sales of services for legal entities) . In order to eliminate multicollinearity, we exclude the X3 factor (volume of services for individuals) from consideration. The X4 factor (additional profit due to the expansion of the range of services) is also expedient to be excluded from consideration due to the low correlation with the effective feature Y . The results of building multiple regression are shown in fig. 4.

Rice. 4. Results of the regression analysis

Based on the calculations performed, the multiple regression equation has the form:

Y=0.871179777.X1+ +0.919808093.X2+152.4197205.

Let's evaluate the quality of the resulting multiple regression equation: the value of the coefficient of determination equal to R = 0.964 is quite close to 1, therefore, the quality of the resulting regression equation can be considered high; the value of the Fisher criterion F=229.8248 exceeds the tabular value equal to 3.591, therefore, the regression equation can be considered statistically significant and can be used to assess the performance of a company employee. To assess the statistical significance of factor signs, Student's t-test is used. Using the function \u003d STUDENT.OBR.2X (0.05; 17), the tabular value t table \u003d 2.109815578 is determined. Comparing the calculated values ​​of t-statistics, taken modulo, with the tabular value of this criterion, we can conclude that the factors X1 and X2 are statistically significant.

Let's estimate the degree of influence of factors on the resultant sign, using the coefficients of elasticity, b - and D - coefficients (Fig. 5).

Rice. 5. Calculation of additional coefficients of the relationship of signs

The partial elasticity coefficient shows the change in the average value of the effective indicator when the average value of the factor sign changes by 1%, i.e., with an increase in net profit (X1) by 1%, the company's profit will increase by 0.287% (E1 = 0.287), with an increase by 1% 1% of the volume of sales of services for legal entities (X2) the volume of profit will increase by 0.535% (E2 \u003d 0.535) .

The β-coefficient shows the magnitude of the change in the standard deviation of the resulting attribute when the RMS of the factor attribute changes by 1 unit, i.e. with an increase by 1 unit of the RMS of net profit (X1), the RMS of the profit volume will increase by 0.304 (=0.304); with an increase by 1 unit of the standard deviation of the volume of sales of services for legal entities, the standard deviation of the organization's profit will increase by 0.727 units (= 0.727) .

Δ - coefficient shows what is the specific influence of a single factor attribute on the effective attribute when fixing the influence of all other factors at a certain level, i.e. the specific weight of the influence of the volume of sales of services for legal entities (X2) on the volume of profit (effective sign) is 72.6% (Δ2 = 0.726369), and the specific impact of net profit (X1) on profit is 27.3% (Δ1 = 0.273631) .

Using the multiple regression equation with statistically significant factors, we calculate the profit forecast that characterizes the company's performance using the capabilities of trend analysis (see Table 2) .

table 2

Results of trend analysis of factor signs

Based on the data obtained, we calculate the point forecast Y.

X1 = 1.3737t - 20.029t + 294.38, X2 = =2.099t - 16.372t + 368.2.

To determine the forecast of factor signs, we obtain:

Х1progn \u003d 1.3737.21.21-20.029.21 + 294.38 \u003d 479.5727 (thousand rubles);

Х2 progn = 2.099.21.21- -16.372.21+368.2=950.047 (thousand rubles).

To determine the forecast of employee performance:

Yprogn = 0.871179777.Х1progn + +0.919808093.Х2progn+152.4197205 = =1444.07468 (thousand rubles)

To determine the interval forecast of the effective efficiency of the employee's activity (Y), we calculate the width of the confidence interval according to the formula:

Let's carry out substitution of intermediate results of calculations, we will receive:

U(k)=80.509.2.1098*ROOT(1+0.05+((1444-855)*(1444-855))/3089500)==183.1231 (thousand rubles).

Thus, the forecast value of the company's profit Yprogn = 1444.07468 will be between

Upper bound equal to 1444.07468 + 183.1231= 1627.2 and

The lower limit is equal to 1444.07468 - 183.1231=1261 (thousand rubles).

Based on the results of the study, the following conclusions can be drawn:

An assessment was made of the performance of an individual employee of Avtoholod LLC, whose main activity is the sale and installation of additional equipment for commercial vehicles;

A multiple regression equation was constructed, which characterizes the dependence of the employee's performance on a number of factors;

The forecast value of the company's profit, calculated by the multiple regression equation, will be in the range from 1261 thousand rubles. up to 1627 thousand rubles;

This regression equation was recognized as statistically significant according to the Fisher criterion and has a sufficiently high quality, therefore, the calculation results can be considered reliable and reliable.

To improve the efficiency of both the company and its employees, it is necessary to implement a balanced and balanced policy for promoting the company's goods and services in the regional market, expand marketing research to promote services, introduce innovative business methods using modern information technologies and modeling methods and business analytics company activities.

Bibliographic link

Tsarkov A.O., Gusarova O.M. USE OF MATHEMATICAL AND STATISTICAL TOOLS OF ECONOMETRIC IN ASSESSING THE EFFICIENCY OF AN EMPLOYEE // International Student Scientific Bulletin. - 2018. - No. 4-6 .;
URL: http://eduherald.ru/ru/article/view?id=19011 (date of access: 11/25/2019). We bring to your attention the journals published by the publishing house "Academy of Natural History"

Econometrics - measurements in the economy. The word "econometrics" was introduced in 1926 by the Norwegian economist and statistician, Nobel laureate Ragnar Frisch. Modern economic education in the West rests on three pillars: macroeconomics, microeconomics and econometrics. In a centrally planned economy, econometrics was not needed, since all plans descended from above, there was no need to predict possible models of economic behavior in a given situation, for example. In addition, econometric methods were able to identify certain trends in economic development that were undesirable for the authorities. At present, our universities have begun to restructure in this direction. Why is econometrics so important? It is difficult to answer this question, and I hope that by the end of our course you will have answered this question a little. The more an economist becomes a professional, the more he understands that in economics everything depends on everything. In order to understand exactly how this dependence is expressed, econometric methods serve.

What is the science of econometrics? It is quite difficult to give a definition of a living, developing science, to describe its subject and method. "Econometrics" is the science of economic measurements, but that's the same as saying that mathematics is the science of numbers. The concept of econometrics has a somewhat narrower content and purpose than is expressed in literal translation and, at the same time, is wider than just a set of statistical tools. The modern view of econometrics is reflected in the following definition:

Econometrics - a scientific discipline that combines a set of theoretical results, techniques, methods and models designed to, on the basis of

economic theory;

economic statistics;

mathematical and statistical tools

give a specific quantitative expression to the general (qualitative) regularities determined by economic theory. (S. A. Ayvazyan, V. S. Mkhitaryan. Applied statistics and foundations of econometrics.)

In other words, econometrics allows, on the basis of the provisions of economic theory and the initial data of economic statistics, using the necessary mathematical and statistical tools, to give a specific quantitative expression to general (qualitative) patterns.

Other views:

A method of economic analysis that combines economic theory with statistical and mathematical methods of analysis. It is an attempt to improve economic forecasts and make successful policy planning possible. In econometrics, economic theories are expressed as mathematical ratios and then tested empirically by statistical methods. This system is used to create models of the national economy in order to predict such important indicators as the gross national product, unemployment rate, inflation rate and the federal budget deficit. Econometrics is being used more and more widely, despite the fact that the forecasts obtained with the help of it were not always sufficiently accurate.

The Concise Columbia Electronic Encyclopedia, Third Edition. http://www.encyclopedia.com/

“Like mathematical economics, econometrics is something that economists do rather than a specific subject area. Econometrics is concerned with the study of empirical data by statistical methods; the purpose of this is to test hypotheses and evaluate the relationships proposed by economic theory. While mathematical economics is concerned with the purely theoretical aspects of economic analysis, econometrics attempts to test theories that are already presented in explicit mathematical form. However, these two areas of economics often overlap.

from an article by Mark Blaug for the Encyclopædia Britannica

“The problems in econometrics are many and varied. The economy is a complex, dynamic, multidimensional and evolving object, so it is difficult to study it. Both society and the social system change over time, laws change, technological innovations occur, so it is not easy to find invariants in this system. Time series are short, highly aggregated, heterogeneous, non-stationary, depend on time and on each other, so we have little empirical information to study. Economic quantities are imprecisely measured, subject to significant later corrections, and important variables are often unmeasured or unobservable, so all our conclusions are imprecise and unreliable. Economic theories change over time, competing explanations coexist with each other, and therefore there is no reliable theoretical basis for models. And among econometricians themselves there seems to be no agreement on how their subject should be dealt with.

from D. F. Hendry, Dynamic Econometrics, Oxford University Press, 1995, p.5.

"There are two things you don't want to see in the manufacturing process: sausages and econometric estimates." E. Leamer E. E. Leamer, "Lets' Take the Con out of Econometrics," American Economic Review, 73 (1983), 31-43.

In an editorial opening the first issue of Econometrica (the oldest econometric journal), Nobel laureate R. Frisch wrote:

“... The main purpose [of the Econometric Society] will be to stimulate research that aims to combine the quantitative-theoretical and empirical-quantitative approaches to economic problems, and which is imbued with constructive and rigorous reasoning of the kind that prevails in the natural sciences.

But the quantitative approach to economics has several aspects, and by itself none of these aspects should be confused with econometrics. Thus, econometrics is by no means the same as economic statistics. It also does not coincide with what we call general economic theory, although a significant part of this theory, of course, is of a quantitative nature. Econometrics should also not be seen as synonymous with the application of mathematics to economic theory. Experience has shown that each of these points of view, i.e. statistics, economic theory and mathematics, is a necessary, but individually not sufficient, condition for a real understanding of the quantitative relations of modern economic life. The power lies in the combination of these three elements. And it is this combination that constitutes econometrics.”

Frisch, R. "Editorial," Econometrica, 1 (1933), 1-4.

According to our definition, econometrics is a synthesis of economic statistics, economic theory and mathematics, a science associated with the empirical derivation of economic laws, a synthesis of economic statistics, economic theory and mathematics. That is, we use data or observations in order to obtain quantitative relationships for economic laws. Note that it already follows from here that in order to use econometric methods, we need data or observations of the state or behavior of some economic entity. These data, as a rule, are not experimental, in contrast to other sciences, where math methods are used. statistics - physics, biology, etc. In economics, we cannot conduct multiple experiments in order to verify the correctness of our conclusions and this is the specificity of economic data.

Applied goals of econometrics.

derivation of economic laws;

formulation of economic models based on economic theory and empirical data;

estimation of unknown quantities (parameters) in these models;

forecasting and estimation of forecast accuracy;

How does an economist achieve his goals. In the course of an econometric study, an economist consistently goes through several stages. Stages of econometric modeling:

A person who begins to study economics, first of all, comes to the idea that in economics some variables are interconnected. The emerging demand for a product in the market is considered as a function of its price, the costs associated with the manufacture of a certain product are assumed to be dependent on the volume of production, consumer spending is associated with income, etc. - examples of relationships between two variables, with one of the variables acting as an explanatory variable, the other as explanatory. For greater realism, it is necessary to introduce other explanatory variables and a random factor into the ratio. Demand for a product - price, consumer income, prices for competing, complementary and substituting goods, etc. (write on the designation board). A variable, the process of forming the values ​​of which, for some reason, interests us, will be denoted Y and call it dependent or explainable. Variables that we expect to have an effect on the variable Y, we will denote X j and called independent or explanatory. The values ​​of these variables are external to it, nothing about how these values ​​are formed

At this stage, the process of forming the values ​​of the explained variable can be represented as the following scheme:

X 1 ,…X k- selected variables (the most significantly influencing or of particular interest to us).

Grouping individual relationships into a model - formulating some hypotheses about how the variables should be related. These hypotheses arise on the basis of theoretical economic premises, intuition, experience of the researcher, his common sense. The question immediately arises, how to check the correctness of the model? In physics, biology, everything is simple - we conduct an experiment and see if its results confirm our hypotheses. Everything is more complicated in the economy. How to conduct experiments in economics? We can only observe reality.

Thus, at this stage, the econometrician is engaged in modeling the behavior of economic objects. Modeling is a simplification of the reality of an object. The task, the art of modeling, is to as concisely and adequately as possible precisely those aspects of reality that interest the researcher.

Mathematical model of the circuit:

If , then equation (1) is called regression equationYon theX 1 ,…X k. Function f – regression function, the line that this function describes in space - regression line.

An example with wages and age - wages increase with age.

The first task is to translate these assumptions into mathematical language. Unfortunately, there is no single way to do this. What does increasing function mean. There are many functions that are increasing functions of their arguments. Linear, non-linear, different.

The way out is to initially formulate the simplest model. Let us introduce the following notation for the observed economic parameters:

W– Salary of a person;

BUT- the age of the person;

The simplest model (linear):

The equation of behavior here is in the form of exact functional dependencies. However, as we shall see later, this is unrealistic and one cannot proceed with econometric development without some additional stochastic specifications. We add a stochastic term to the behavioral equations. Because for any real economic data it is impossible to ensure the constant observance of simple ratios. In addition, of all possible explanatory variables, only a small subset of them is included in the specification, i.e., we can only talk about the model approximating some, apparently quite complex, but unknown to us relationships. To ensure equality between the right and left sides, a random error has to be introduced into each ratio.

In our model, dependencies between some variables are considered. Variables whose values ​​are explained within our model are called endogenous. Variables, the values ​​of which are not explained by our model, are external to it, we do not know anything about how these values ​​are formed, are called exogenous. Another variable is the lagged value of the endogenous variable. It is also external to our model. Exogenous variables and lag values ​​of endogenous variables are predefined variables.

In the course of our course with you, we will come across several types of econometric models that are used for analysis and forecasting:

a) time series models. Such models explain the behavior of a variable that changes over time based only on its previous values. This class includes models of trend, seasonality, trend and seasonality (additive and multiplicative forms), etc.

b) regression models with one equation. In such models, the dependent (explained) variable is represented as a function of independent (explanatory) variables and parameters. Depending on the type of function, models are either linear or non-linear. Let's study them.

c) Systems of simultaneous equations. The situation is economic, the behavior of an economic object is described by a system of equations (our example). Systems consist of equations and identities, which may contain explainable variables from other equations (therefore, the concepts of exogenous and endogenous variables are introduced).

Item 2 is called the model specification. Necessary:

a) define the goals of modeling;

b) determining the list of exogenous and endogenous variables;

c) determination of forms of dependencies between variables;

d) formulation of a priori constraints on the random term, which is important for the properties of estimates and the choice of estimation method, and some coefficients

Now we need to check the model. How to do this if we are not physicists and not biologists? The methods of econometrics, which allow empirical verification of theoretical statements and models, are a powerful tool for the development of economic theory itself. With their help, theoretical concepts are rejected and new, more useful hypotheses are accepted. A theoretician who does not use empirical material to test his hypotheses and does not use econometric methods for this runs the risk of ending up in the world of his fantasies. Gathering data is essential statistical material. Here the methods of economic statistics and statistics in general come to our aid. Conversation on this topic.

The types of data that an econometrician has to deal with when modeling economic processes are:

a) cross-sectional data - spatial data - a set of information on different economic objects at the same time;

b) time-series data - time series - observation of one economic parameter in different periods or points in time. This data is naturally ordered in time. Inflation, money supply (annual), US dollar exchange rate (daily);

c) panel data - panel data - a set of information on various economic objects for several periods of time (population census data).

model identification - statistical analysis of the model and, above all, statistical estimation of parameters. The choice of evaluation method is also included here. Depends on the features of the model.

model verification - comparison of real and model data, verification of the estimated model in order to conclude that the picture of the object obtained with its help is sufficiently realistic, or to recognize the need to evaluate a different model specification.

So, econometric methods are developed mainly for estimating the parameters of economic models. Each model contains, as a rule, several equations, and the equation includes several variables. Let's start with the simplest - a paired linear regression model.

Connection of econometrics with other disciplines. What is the specificity of the synthesis of economic theory and econometrics? Econometrics, based on the objectively existing economic laws, which are defined in economic theory qualitatively, at the conceptual level, forms approaches to their formalization, quantitative expression of relationships between economic indicators.

Economic statistics gives econometrics methods for generating the necessary economic indicators, methods for their selection, measurement, etc.

The mathematical and statistical tools developed in econometrics use and develop such sections of mathematical statistics as linear regression models, time series analysis, and the construction of systems of simultaneous equations.

It is the landing of economic theory on the basis of specific economic statistics and the extraction from this landing with the help of a suitable mathematical apparatus of quite definite quantitative relationships that are the key points in understanding the essence of econometrics, distinguishing it from mathematical economics, descriptive statistics and mathematical statistics. So mathematical economics is a mathematically formulated economic theory that studies the relationship between economic variables at a general (non-quantitative) level. It becomes econometrics when the coefficients symbolically represented in these relationships are replaced by specific numerical estimates derived from specific economic data.

Stages of building an econometric model. The main goal of econometrics is a model description of specific quantitative relationships that exist between the analyzed indicators in the studied socio-economic phenomenon.

Among applied purposes three can be distinguished:

- forecast economic and socio-economic indicators (variables) characterizing the state and development of the analyzed system;

- imitation various possible scenarios for the socio-economic development of the analyzed system, when statistically identified relationships between the characteristics of production, consumption, social and financial policies, etc. are used to track how planned (possible) changes in certain manageable parameters of production or distribution will affect the values ​​of the “output” characteristics of interest to us;

- analysis the mechanism of formation and the state of the analyzed socio-economic phenomenon. How does the mechanism of household income generation work, is there a real wage discrimination between men and women and how big is it? Knowing the real quantitative ratios in the phenomenon under study will help to better understand the consequences of the decisions made, the ongoing economic reforms, and correct them in time.

By level hierarchy of the analyzed economic system are distinguished macro level(i.e. countries as a whole), mesolevel(regions, industries, corporations), micro level(families, businesses, firms).

Profile econometric research defines the problems on which it is concentrated: investment, financial, social policy, distribution relations, pricing, etc. The more specifically the profile of the study is defined, the more adequate the chosen method and the more effective the result, as a rule.

One of the fundamental concepts of economics is the connection between economic phenomena and, accordingly, the features (variables) that characterize them. The demand for some commodity in the market is a function of price; family consumer spending is a function of its income, etc., the cost of production depends on labor productivity. In all these examples, one of the variables (factors) plays the role of the explained (resulting), and the other - explanatory (factorial).

The econometric modeling process can be broken down into six main steps.

1. Staged. At this stage, the purpose of the study is formulated, the set of economic variables participating in the model is determined. The goals of econometric research can be:

· analysis of the studied economic object;

forecast of its economic indicators;

· analysis of the possible development of the process for different values ​​of independent variables, etc.

2. A priori. It is a pre-model analysis of the economic essence of the phenomenon under study, the formation and formalization of a priori information, in particular, related to the nature and genesis of the initial statistical data and random residual components.

3. Parameterization. The simulation itself is carried out, i.e. choice of the general view of the model, including the composition and form of its constituent links.

4. Informational. The necessary statistical information is being collected, i.e. registration of values ​​of factors and indicators participating in the model.

5. Model identification. The statistical analysis of the model is carried out and, first of all, the statistical estimation of the unknown parameters of the model.

6. Model verification. The adequacy of the model is checked; it turns out how successfully the problems of specification, identification and identifiability of the model are solved; real and model data are compared, and the accuracy of model data is assessed.

The last three stages (4th, 5th, 6th) are accompanied by an extremely time-consuming model calibration procedure, which consists in sorting through a large number of calculation options in order to obtain a joint, consistent and identifiable model.

The actual mathematical model of the phenomenon under study can be formulated at a general level, without tuning to specific statistical data, i.e. it may make sense without the 4th and 5th stages. However, in this case it is not econometric. The essence of the econometric model is that, being presented as a set of mathematical relationships, it describes the functioning of a specific economic system, and not a system in general. Therefore, it "tunes" to work with specific statistical data and, therefore, provides for the implementation of the 4th and 5th stages of modeling.

4. Statistical base of econometric models. One of the most important stages in the construction of econometric models is the collection, aggregation and classification of statistical data.

The main base for econometric research is official statistics or accounting data, which are the starting point of any econometric research.

When modeling economic processes, three types of data are used:

1) spatial (structural) data, which is a set of indicators of economic variables obtained at a particular point in time (spatial slice). These include data on the volume of production, the number of employees, the income of different firms at the same time;

2) temporal data characterizing the same object of study at different points in time (time slice), for example, quarterly data on inflation, average wages, etc.;

3) panel (spatio-temporal) data, occupying an intermediate position and reflecting observations on a large number of objects, indicators at different points in time. These include: financial performance of several large mutual funds for several months; the amount of taxes paid by oil companies over the past few years, etc.

The collected data can be presented in the form of tables, graphs and charts.

5. Main types of econometric models. Econometrics distinguishes the following three classes of models depending on the data available and the objectives of modeling.

Regression models with one equation. Regression it is customary to call the dependence of the average value of a quantity (y) on some other quantity or on several quantities (x i).

In such models, the dependent (explained) variable is represented as a function , where are independent (explanatory) variables, and are parameters. Depending on the number of factors included in the regression equation, it is customary to distinguish between simple (paired) and multiple regressions.

Simple (paired) regression is a model where the mean value of the dependent (explained) variable y is considered as a function of one independent (explanatory) variable x. Implicitly, pairwise regression is a model of the form:

Explicitly:

where a and b are estimates of the regression coefficients.

Multiple Regression is a model where the average value of the dependent (explained) variable y is considered as a function of several independent (explanatory) variables x 1 , x 2 , … x n . Implicitly, pairwise regression is a model of the form:

Explicitly:

where a and b 1 , b 2 , b n are estimates of the regression coefficients.

An example of such a model is the dependence of an employee's salary on his age, education, qualifications, length of service, industry, etc.

Regarding the form of dependence, there are:

linear regression;

· non-linear regression, which assumes the existence of non-linear relationships between factors, expressed by the corresponding non-linear function. Often, models that are non-linear in appearance can be reduced to a linear form, which allows them to be classified as linear.

For example, you can explore wages as a function of the socio-demographic, qualification characteristics of an employee.

Concept of econometrics

Definition 1

Econometrics is the science of economic measurement.

In the modern sense, econometrics is a scientific discipline that combines a system of theoretical results (techniques, methods and models) in the following areas:

• economic theory;
• economic statistics;
• mathematical and statistical tools, etc.

Remark 1

Thus, econometrics, based on the provisions of economic theory and the basic provisions of economic statistics, makes it possible, using the necessary mathematical and statistical tools, to give a certain (quantitative) expression to qualitative (general) patterns.

In practice, econometric methods are used for the following purposes:

1. Deduce economic laws,
2. Formulate economic models based on knowledge of economic theory and empirical data,
3. Estimate unknown quantities (parameters) of the considered models,
4. Plan and evaluate the accuracy of forecasts,
5. Develop recommendations in the field of economic policy.

Basic methods of econometrics

There are several main methods of econometrics:

• Summary and grouping of information;
• Analysis, which can be variational and dispersion;
• Application of regression and correlation analysis;
• Dependency equations;
• statistics indexes.

Statistical Grouping and Summary

A statistical summary is a scientifically organized processing of observation materials, which consists of the following elements:

• systematization,
• data grouping,
• tabulation,
• calculation of results
• calculation of derived indicators (average and relative values).

Statistical grouping includes the process of forming homogeneous groups by the following methods:

• division of statistical aggregates into parts,
• association of the studied units into private aggregates according to the relevant characteristics.

Dispersion and variation

The variance of a trait is the average square of the deviations of options from their average value. There are several types of dispersion used in econometrics:

• General variance, which characterizes the variation of signs in the statistical population in the process of exposure to all factors;
• Intergroup dispersion, showing the size of the deviations of the average group values ​​from the total average value, while characterizing the influence of the factor that underlies this grouping;
• Intragroup variance (residual), characterizing the variation of a trait in the middle of each group.

Remark 2

One of the methods of econometrics is the use of the standard deviation, which is a generalized characteristic of the size of the variation of a feature in the aggregate.

The standard deviation is equal to the square root of the variance. At the same time, to compare changes in the same trait in several populations, a relative indicator of variation is used, which is called the coefficient of variation.

Other methods of econometrics

Consider a few more methods of econometrics:

1. The least squares method determines the exact theoretical values ​​of univariate regression models, including its graphical display;
2. Statistical indices used as a measure of quantity change, regardless of the change in qualitative characteristics (price, cost, labor productivity, etc.). Also, these indices are used in the process of characterizing a qualitative feature, regardless of changes in quantity (the volume of goods in physical terms, the number of employees, etc.).

UDC: 336 LBC: 65.05

APPLICATION OF ECONOMETRIC TOOLS TO FORM A MULTI-FACTORY CRITERIA FOR ASSESSING THE RESULTS OF AN ORGANIZATION

Suvorova L.V., Suvorova T.E., Kuklina M.V.

USING THE TOOLS OF ECONOMETRICS FOR FORMATION OF

MULTIFACTOR EVALUATION CRITERIA OF ORGANIZATION VIABILITY

Key words: company, probability, bankruptcy, bankruptcy probability, econometrics, solvency assessment, integral assessment criterion, model, assessment, criterion, predictive probability.

Keywords: company, probability, failure, the probability of failure, econometrics, viability assessment, integral evaluation criterion, model, evaluation, criterion, the forecast probability.

Abstract: the article discusses the possibility of using econometric tools for the formation of a multifactorial criterion for assessing the viability of an organization. The valuation model formed using the hierarchy analysis method is tested on the data of one hundred Russian non-financial companies, the results obtained are compared with the initial parameters of the model, after which a conclusion is made about its practical applicability.

Abstract: the article discusses the possibility of using econometric tools for the formation of multifactor criteria for evaluating the organization viability. Assessment model, formed by the analytic hierarchy process is tested on data of hundred Russian non-financial companies; these results are compared with the initial parameters of the model, and then conclude its practical applicability.

With the deteriorating economic situation both inside and outside the country, many companies are facing financial difficulties. The insolvency of an organization as a subject of economic relations may become the subject of judicial proceedings. Thus, modern financial managers are faced with the task of not only preventing crisis phenomena and ensuring the stable financial position of their enterprise, but also proving its viability to third parties.

Currently, there are quite a lot of multifactorial criteria for assessing the solvency of companies proposed by various authors, both domestic and foreign (E. Altman, R. Taffler and G. Tishaw, R. Lis, R.S. Saifulin and G.G. Kadykov , scientists of the Irkutsk State Academy of Economics, O.P. Zaitseva, W. Beaver, J. Con-

nan and M. Golder, D. Fulmer, G. Springgate). It should be noted that foreign models are not always acceptable for Russian organizations, since they use constant coefficients calculated in accordance with other economic conditions, lending and taxation features.

Diagnostics of the factors leading organizations to bankruptcy can be carried out by various methods, including analytical, expert, linear and dynamic programming methods, as well as using simulation models.

The purpose of the work is to test a new model for assessing the solvency of companies using econometric tools.

Based on the method of analysis of hierarchies, we have developed a new model for assessing the viability of an organization and determining

the threshold value of the integral indicator1:

X = 0.194*P(12) + 0.186*P(15) + 0.19*P(27) + 0.232*P(30) + 0.197*P(33),

P(12) - the degree of solvency of the organization;

P(15) - current liquidity ratio;

P(27) - return on working capital;

P(30) - capital productivity;

P(33) - return on sales

Hierarchy analysis method is a multi-criteria assessment technique, with the help of which factors-indicators are selected, and a multi-factor model is also formed. In order to find priority indicators-factors, the scale of relative importance of T. Saaty and K. Kearns was used.2 With its help, a matrix of pairwise comparisons of indicators-factors was built and a choice of local priorities was made.

The most priority among the considered factors were recognized: the degree of solvency, current liquidity ratio, return on working capital, return on assets and profitability of sales.

For further research, the priority values ​​of the selected factors were corrected by dividing their initial values ​​by the sum of the last ones, and thus a normalized priority vector was obtained for a truncated set of criteria.

The threshold value was found using empirical analysis on real data. A sample of 100 non-financial Russian companies was formed

Suvorova L.V., Suvorova T.E., Kuklina M.V.

using the database, the sample included 50 companies that are wealthy, and 50 companies that are declared bankrupt by the court. For each organization, an integral indicator was calculated and a graph of the dependence of the integral indicator on the state of the companies was plotted.

Within the framework of the model developed by us, the companies whose integral indicator does not exceed 15 turned out to be insolvent.

To assess the relationship between the probability of bankruptcy of organizations and the value of the integral criterion, we used econometric tools. For this, the same sample of 100 non-financial Russian companies was used.

Binary choice models were tested: Probk-model4 (cumulative function of the standard normal distribution) and Logit-model (integral probability function of the logistic distribution). Binary models make it possible to determine the dependence of the company's bankruptcy probability and the value of the integral criterion.

According to models of this type, the dependent variable takes two values: 0 and 1. We chose the state of the company as the dependent variable. The value "0" is assigned to a solvent organization, and the value "1" is assigned to an insolvent company. In the formed sample, the number of wealthy and insolvent companies is the same and equals 50.

All calculated coefficients, including the integral indicator for the selected companies, are presented in Table 1.

1 Suvorova, L.V., Suvorova, T.E. Assessment of the insolvency of the organization using the method of analysis of hierarchies // Proceedings of the VIII International Scientific and Practical Conference "Infrastructural Sectors of the Economy: Problems and Prospects of Development". - Novosibirsk: NSTU, 2015.

2 Makarov, A.S. On the problem of choosing criteria for the analysis of the solvency of organizations // Economic analysis: theory and practice. 2008. No. 3.

3 FIRA PRO - Information and analytical system, the first independent rating agency [Electronic resource]. - URL: http://www.fira.ru/. -Title from the screen

4 Sandor, Zolt. Econometric educational program: limited dependent variables. Multinomial Models of Discrete Choice // Quantile. - 2009. -№7. - S. 9-20.

Company Indicator-factor Integral criterion Y: 1- bankrupt company 0- bankrupt company

Return on assets, shares Current liquidity ratio, shares Degree of solvency on current liabilities, shares Return on working capital, % Return on sales, %

1 10,82 1,97 3,28 47,66 40 20,48 0

2 1,68 1,17 14,69 65,88 50 25,88 0

3 7,4 3,24 4,64 79,75 100 38,15 0

4 18,08 3,8 4,2 8,37 100 27,05 0

5 6,01 1,08 4,24 23,77 100 26,69 0

50 1,11 20,76 0,62 96,63 100 42,40 0

51 3,52 5,32 0,45 0,43 8,7 3,69 1

52 1,85 0,1 66,96 0,78 2,2 14,03 1

59 1,65 0,91 74,25 115 3,3 37,52 1

66 0,1 1 77,45 1 10 17,41 1

99 3,38 0,024 38,03 -1,47 -2,4 7,41 1

100 0,38 0,05 2,25 1,42 9,6 2,70 1

Two regression models were tested. The results of testing the models were presented using the Eviews program. Relays in Table 2.

Table 2 - Model testing

Parameters Model

Number of observations 100 100

Integrated indicator -0.149***(0.043) -0.338**(0.138)

Constant 2.391***(0.569) 5.155***(1.858)

Prob(LR statistic) 0.000 0.000

McFadden R-squared 0.769 0.804

Note. Standard errors are indicated in parentheses, significance levels are indicated by asterisks: *p<0,1; **p <0,05; ***p <0,01.

Based on the results obtained, it was concluded that both regressions are generally significant at the 1% level. The coefficient estimates are also significant at the 1% level for the Probit model and to us at 5% for the Logit model. Evaluation of the coefficient in front of the variable responsible for the value of the integral indicator,

negative. This suggests that the higher the value of the integral indicator, the lower the probability of bankruptcy.

The results of the regression evaluation can be presented in the following form:

Rg \u003d 2.391 - 0.149 * x ()

Pi \u003d L (5.155 - 0.338 * xt)

The dependence of the value of the integral indicator on the predictive probability determined using the Logit and Probit models is shown in Figure 1.

Although both models give almost the same results, no significant differences are observed. However, there is one deviation from the general dynamics.

1-1-1-1-0 -,-■

♦ Logit model ■ Probit model

The value of the integral indicator

Figure 1 - Graphical representation of the ratio of the value of the integral criterion

and estimates of the probability of bankruptcy

To determine the threshold value, predictive probabilities of bankruptcy were built for all companies from the sample for both binary models. Figures 2 and 3 show the dependence of the predictive probability on the observation number. The first 50 companies in the sample are wealthy, and the last 50 companies are declared bankrupt by the court.

These graphs also show that there is one deviation. The company corresponding to number 59 is in fact bankrupt, but the integral criterion showed the opposite conclusion. A very low forecast probability of bankruptcy was predicted for this company.

Figure 2 - Graphical representation of the ratio of predicted bankruptcy probability and company numbers for the Logit model

Thus, it was concluded that the firm, and if the predicted probability if the predicted probability of bankruptcy is more than 50% - the company is insolvent. less than 50%, then the company is

10 20 30 40 50 60 70 80 90 100

Figure 3 - Graphical representation of the ratio of the forecast probability of bankruptcy and the number of companies for the Pmbk model

As noted earlier, when calculating the multifactorial criterion using the AHP, two inaccuracies were made, namely, 2 companies with a solvency forecast are actually insolvent. This corresponds to a type I error. A similar inaccuracy occurred when predicting the probability of bankruptcy using econometric tools, but a type I error in this case

tea was 1% (only one insolvent company was predicted to have a low probability of bankruptcy). Type II error was not observed in both cases. The explanatory power of the model is found as 100% minus type I and type II errors. Both formed models, both with the help of the AHP and with the help of econometric tools, have a high explanatory power (Table 3).

Table 3 - Comparative characteristics of the AHP and econometrics tools

AHP Criterion Econometric Toolkit

Threshold X<15 - компания несостоятельна, Х>15 - the company is wealthy R<50% - компания состоятельна, Р >50% - the company is insolvent

Type I error (a company with a solvency forecast is insolvent) 2% 1%

Type II error (the company with a forecast of insolvency is solvent) 0% 0%

Model explanatory power 98% 99%

Based on the results obtained using the analysis method, we can conclude that the new model, hierarchies and verified using

toolkit of econometrics, is the key to the bankruptcy of Russian companies. optimal and applicable for diagnostic

REFERENCES

1. Makarov, A.S. On the problem of choosing criteria for the analysis of the solvency of organizations // Economic analysis: theory and practice. - 2008. - No. 3.

2. Suvorova, L.V., Suvorova, T.E. Assessment of the insolvency of an organization using the method of analysis of hierarchies // Proceedings of the 8th International Scientific and Practical Conference "Infrastructural Sectors of the Economy: Problems and Prospects for Development", NSTU, Novosibirsk, 2015.

3. Sandor, Zolt. Econometric educational program: limited dependent variables. Multinomial Models of Discrete Choice // Quantile. - 2009. - No. 7. - S. 9-20.

4. Altman, E. & Haldeman, R. (1977) ZETA Analysis: A new model to indentify bankruptcy risk of corporations. Journal of Banking and Finance, 1, 29-35.

5. Beaver, W. (1966) Financial Ratios as Predictors of Failure. Journal of Accounting Research, 4.71-111.

6. Conan, J. & Holder, M. (1979) Explicative variables of performance and management control, Doctoral Thesis, CERG, Universite Paris Dauphine.

7. FIRA PRO - Information and analytical system, the first independent rating agency [Electronic resource]. - URL: http://www.fira.ru/. - Zagl. from the screen

8. Fulmer, J. & Moon, J. (1984) A Bankruptcy Classification Model for Small Firms. Journal of Commercial Bank Lending, 25-37.

9. Springate, G. (1978) Predicting the Possibilty of Falture in a Canadian Firm. Unpublished M.B.A. Research Project, Simon Fraser University