REGIONAL AND MUNICIPAL ECONOMY

COMPARATIVE ANALYSIS OF METHODS FOR FORECASTING SOCIO-ECONOMIC DEVELOPMENT OF THE REGION [using the example of the Belgorod region)

The article discusses economic and mathematical methods, econometric models and their application in practice. Based on the comparative analysis of econometric methods, an algorithm for developing forecasts for the development of the Belgorod region was proposed, and recommendations for improving the methodological support for socio-economic forecasting were substantiated. The article reveals the features modern methods forecasting, the necessity and feasibility of their use is substantiated.

To analyze and predict phenomena and processes affecting economic development region, regression mathematical models are an effective tool. The advantage of regression models is not only the ability to determine a quantitative measure of dependence, but also to study the influence of various factors.

Key words: forecasting, forecast, economic development of the region, regression models, economic and mathematical methods, econometric models, economic modeling.

Analysis and forecasting of socio-economic development is the starting point of work when solving problems of managing the sustainable development of the region. The relevance of the mentioned task is due to the study of the development of forecasts for the development of the Belgorod region, the construction of an econometric model, the use of which will create the basis for forecasting the gross regional product. Based on a reasonable forecast, the goals of the socio-economic development of the region are determined, program activities and priorities in the development of the regional economic complex are clarified.

Forecasting the socio-economic development of a region is a prediction of the future state of the economy and social sphere, an integral part of state regulation of the economy, designed to determine the directions of development of the regional complex and its structural components. The results of forecast calculations are used government agencies to substantiate the goals and objectives of development, develop and justify the government’s socio-economic policy, and ways to rationalize the use of limited production resources.

E.S. PRIDVOROVA

Belgorod State National Research University

Pridvorova @bsu.edu.ru

The forecast for the socio-economic development of the region includes a set of specific forecasts that reflect the future of individual aspects of society, and a comprehensive economic forecast that reflects in a generalized form the development of the economy and social sphere of the region. The forecasting process itself contributes to the organization of constructive interaction between science, business, public organizations and regional government bodies, the formation of coordinated views on the problems and prospects for the development of the region. Forecasting is also of great importance in the theoretical aspect, as it is a kind of catalyst for conducting numerous studies and improving their methodology.

In the theory and practice of planning activities, a significant set of different methods for developing forecasts has been accumulated. The famous scientist Erich Jantsch counts more than a hundred of them; in practice, only 15-20 methods are used as the main ones (Fig. 1).

Essentially, methods for modeling the socio-economic development of a region can be summarized into four main groups: expert assessment; modeling; normative method; extrapolation. The development of computer science and computer technology creates the opportunity to expand the range of forecasting and planning methods used. Economic and mathematical models based on combinations of methods are returning to the fore.

System of forecasting and planning methods

"Interview" method:"

Analytical and

Method of collective idea generation “Brainstorming”

Delphi method

Commission method

Method and spelling are logical

SKOGS ЇNELSHE.

Scripting method

Foresight method

Average estimation method

Method "363"

Heuristic MET0D

List method

Median method

Method of analysis and assessment of risks

Summary method

Matrix model

Imitation

Optimal planning models

Network model

Zkeeeemshnzak

ITSCHZh models

Model of interaction between pole and environment

Model of diffusion

Model of sustainable development

The tree model sang to her

Model of innovative sustainable development

Expert Modeling Normative Extrapolation

rating |- |- yes

economic

Balance

Normative

Programming method

St atypical

?.IETOD______

Budget

Forecast cash flows

1T N TP-GTG yagtitltti forecast

Economic-mathematical epic model

To orrvyayanionno-regression ptgrd I am a model

Integer program

Inter-industry balance model

Historical methods. analogies and forecasting based on the model

Feature selection method

Method of how angry _______average________

Exponential smoothing method

Adaptive smoothing method

Construction 1) ENDE

Lead method

Envelope method

Dynamic series method

Method of NS pickles and business activity

Group argument method

Factorial analysis method

Least square method

Linegaoie program worlds

Dei graphic ______model_______

Rice. 1. Classification of forecasting and planning methods

Series History. Political science. Economy. Computer science. 2013. No. 1 (144). Issue 25/1

Drawing up forecast values ​​of criterion indicators and indicators entails uncertainty in assessments. There are many ways to reduce risks from uncertainty in estimates when making decisions and to verify forecast data. First of all, it is recommended to use the following complementary steps: justify the size of the investment; present possible results indicating the main assumptions of their achievement or likelihood (risk assessment); take into account the ideas and preferences of regional and municipal socio-economic development on the principles of sustainability; develop appropriate decision-making rules and strategies for investing in modernization and innovative transformations.

Forecasting methods are continuously enriched and improved. The choice of forecasting method depends on the period for which it is necessary to make a forecast, the ability to obtain appropriate initial data, requirements for forecast accuracy, and the amount of information. The economic literature presents a wide variety of forecasting methods. Thus, researchers say that the whole variety of forecasting methods is based on two approaches - heuristic and mathematical.

Heuristic methods are based on the use of phenomena or processes that cannot be formalized.

Mathematical forecasting methods are characterized by the selection and justification of a mathematical model of the process under study, as well as methods for determining its unknown parameters. The forecasting problem is reduced to solving equations that describe a given model for a given point in time.

Among mathematical forecasting methods, extrapolation methods stand out in a special group, which are simple, clear and easy to implement.

Currently, the most common and widely used in economics are methods of expert assessments. “Expert assessment is a formalized qualitative or quantitative assessment by experts of the characteristics of objects using the method of expert assessments, with possible subsequent comparison of the objects under study according to the corresponding characteristics.” In almost all regions Russian Federation In the course of forming forecasts for the socio-economic development of the region in the medium term, these approaches are used to predict the main parameters.

Modeling methods include a forecast based on the study of the internal logic of logical models of the development of the phenomenon under study, on the analysis of the historical continuity of the development of science and technology and future scenarios (logical analysis of the hierarchy of goals, description of real options for achieving them and assessment of resources).

Normative methods are planning methods based on the use of norms and standards to substantiate planning, program and forecast documents.

When making forecasts using extrapolation, they usually proceed from statistically emerging trends in changes in certain quantitative characteristics of an object. Estimated functional system and structural characteristics are extrapolated. Extrapolation methods are one of the most common and most developed among the entire set of forecasting methods.

Using these methods, quantitative parameters of large systems, quantitative characteristics of economic, scientific, production potential, data on the effectiveness of scientific and technological progress, characteristics of the relationship between individual subsystems, blocks, elements in the system of indicators are extrapolated complex systems and etc.

Extrapolation methods are the most common in forecasting. They are simple, clear and easy to implement on a computer. A detailed description of the extrapolation forecasting method is given in the works of scientists.

The basis of extrapolation forecasting methods is the study of time series.

Analytical methods for extrapolating trends are based on applying the least squares method to a time series and representing the pattern of development of a phenomenon over time in the form of a trend equation.

Currently one of promising directions forecasting methods are considered adaptive. Adaptive methods are used in conditions of strong fluctuations in the equations of the time series and allow, when studying trends, to take into account the influence of previous equations on subsequent values ​​of the time series. These methods are considered in most detail by scientists.

In regional studies, the prospects for the development of a particular territory are necessarily studied. The development trajectory or future state of the region as a whole and individual economic objects, in particular, is determined using the following methods: extrapolation, expert assessments, analogies, regression and correlation analyses.

The most important advantage of adaptive methods is the construction of self-correcting models that can take into account the result of the forecast made at the previous step. Let the model be in a certain state for which the current values ​​of its coefficients are determined. Based on this model, a forecast is made. When the actual value arrives, the error of the predicted value is evaluated. The prediction error enters the model through feedback and participates in it in accordance with the accepted procedure for transition from one state to another. As a result, compensating changes are developed, consisting of adjusting parameters in order to better harmonize the behavior of the model with the dynamics of the series. Then the forecast estimate for next moment time, and the whole process is repeated again.

Thus, adaptation is carried out iteratively, obtaining each new actual point of the series. The model constantly “absorbs” new information, adapts to it and therefore reflects the development trend existing in this moment. In Fig. Figure 2 shows the general scheme for constructing adaptive forecasting models.

Rice. 2. Scheme for constructing an adaptive forecasting model: y(1:) - actual levels of the time series;)’g(/) (1) - forecast made

at moment I, G units of time (steps) forward; e(+1 - forecast error, obtained as the difference between the actual and predicted value of the point indicator (1+1)

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The speed of the model’s response to changes in the dynamics of the process is characterized by the so-called adaptation parameter. The adaptation parameter must be chosen in such a way as to provide an adequate representation of the trend while filtering out random deviations. The value of the adaptation parameter can be determined on the basis of empirical data, derived analytically, or obtained based on a trial method.

As an optimality criterion when choosing an adaptation parameter, the criterion of the minimum mean square of prediction errors is usually taken.

Based on the considered features, we will define a group of forecasting methods, united under the general name adaptive.

Adaptive forecasting methods are those that allow the construction of self-correcting (self-tuning) economic and mathematical models that are able to quickly respond to changing conditions by taking into account the result of the forecast made at the previous step and taking into account the different information value of the levels of the series. Thanks to the noted properties, adaptive methods are especially successfully used in operational, short-term forecasting. This definition reflects the main character traits inherent in the approach under consideration. At the same time, the division into adaptive and non-adaptive models is often conditional.

The origins of adaptive methods lie in the exponential smoothing model. Let's assume that the time series model has the form:

y(=ax+e(, (1)

where ax = con81:;

E(- random non-autocorrelated deviations with zero mathematical expectation and dispersion.

For exponential smoothing of a series, the recurrent formula is used:

^ = ау(+, (2)

where is the value of the exponential average at time 1:; a - smoothing parameter a=sop81:, 0<а<1;

If we consistently use relation (1), then the exponential average can be expressed through the previous values ​​of the time series levels:

^ = ay, + = ay, + p(ay(_x +) =

Ау, + aru,_х + /?2^_2 = ... = ау,+ ару,_х + ар2у,_2 +... + аДу„ +... + /Г£0 ’

Thus,

^ = I]?+/??О, (3)

where n is the length of the row.

When n -> °°Р” -> 0, therefore,

Thus, the value $ turns out to be a weighted sum of all terms of the series.

Moreover, the weights of individual levels of the series decrease as they move into the past according to an exponential function (depending on the “age” of observations). That is why the value I is called the exponential average.

To eliminate excess weight imparted by E0, R. Wade proposed modifying the procedure.

Let E"0 = aE0, then EH = ay! + (1 - a) E"0 = ay! + (1 - a) aE0.

Since the weighting coefficients in the sum no longer add up to one, an additional multiplier is introduced equal to the reciprocal of the sum of the coefficients:

‘V, = s;---\-r [осуi + (l - a)aS0 ].

Then at the first iteration at a = 0.1 the weight of the current level y is determined by the expression

by -------= 0.526, and the weight of S0 is already equal to the smaller value ------= 0.474.

In short-term forecasting, it is necessary to reflect changes in the series and at the same time clean it up by filtering out random fluctuations. To do this, the value of a should be assigned one of the intermediate values ​​in the range from o to 1. If, as a result of experimental calculations, the best value of a, close to 1, is obtained, then it is advisable to check the validity of choosing a model of this type.

Sometimes searching for this parameter value is done by searching through the grid of values. In this case, the value of a at which the smallest error variance is obtained is chosen as the optimal value. In most econometric packages, for example, Mesosaurus, SPSS, STATISTIKA and others, when building these models, the menu provides an “optimization” branch that searches for values ​​using this scheme.

The study included a forecast of further changes in the industrial production index. This indicator characterizes the change in the scale of production in the periods being compared and is one of the main indicators of industrial production in the Belgorod region.

To make a forecast, we use the extrapolation method based on the construction of trend models.

Data for constructing a trend model of industrial production in the Belgorod region for 1992-2011. are presented in table. 1 .

Table 1

Initial data for constructing a trend model of industrial production in the Belgorod region for 1992-2011.

Year Industrial production index of the Russian Federation Industrial production index of the Belgorod region

1997 101,0 106,0

1999 108.9 I5.3

2000 108,7 109,1

2001 102,9 110,1

2002 103,1 116,0

2003 108.9 10b.2

2004 yu8,o yu6,z

2006 u6.z 112.8

2008 100,6 111,6

2010 108,2 110,0

2011 Yu4.7 Yu6.9

Based on the presented initial data (Table 1), four trend models were built, presented in Fig. 3-6.

Belgorod region -=-RF ------Polynomial (Belgorod region)

Rice. 3. Polynomial trend of the industrial production index

Belgorod region

If formula 5, based on an exponential smoothing model, is used to forecast a time series that has a pronounced linear trend, then the model, as a rule, will give biased forecasts, i.e. systematic error. For such time series, it is advisable to use linear growth models that also apply an exponential smoothing procedure. The forecast model is defined by the equality

YAI = a^, (5)

where is the forecast made at the moment? g units of time (steps) forward;

al,1 - rating ah,.

In these models, the forecast can be obtained using the following expression:

Zh0 = "u+" C6)

where al, s/-, are the current estimates of the coefficients; t - forecast period.

Belgorod region -■- Russian Federation Logarithmic (Belgorod region)

Rice. 4. Logarithmic trend of the industrial production index

Belgorod region

# & £ & & £ & & # / # $ & $ & / # $ / /

F- Belgorod region -■- RF -■ Power (Belgorod region)

Rice. 5. Power trend of the industrial production index of the Belgorod region

-♦- Belgorod region -■- Russian Federation Exponential (Belgorod region)

Rice. 6. Exponential trend of industrial production index

Belgorod region

In table 2 we present the equation of polynomial, logarithmic, power, exponential models of the industrial production index of the Belgorod region.

table 2

Trend models of the industrial production index of the Belgorod region

Model type Building a trend model

Polynomial model V = -0.1448 X2 +4.0849*+ 82.994

Logarithmic model y = 8.6212 1n(x) +86.856

Power model y = 87.24 x0’0862

Exponential model V = 93.819

For adequate models, the accuracy was assessed. The accuracy of the model is characterized by the difference between the value of the actual level and the value according to the constructed trend model.

To assess the quality of a one-factor model in econometrics, the coefficient of determination and the average error of approximation are used.

The average approximation error is defined as the average deviation of the obtained values ​​from the actual values ​​according to formula (7)

The permissible approximation error should not exceed 10%. The results of checking the accuracy of the model are given in table. 3.

Table 3

Average relative errors of approximation of adequate models, %

Model type Error value Exact error value Accuracy level

Logarithmic 0.22 0.228 -

Power 0.22 0.220 Exact

Polynomial 0.22 0.220 Exact

Exponential 0.22 0.229 -

So, the most accurate is the power and polynomial trend model. Let's consider the forecast of the industrial production index of the Belgorod region for 2012-2013. in table 4.

Table 4

Forecast of the industrial production index of the Belgorod region

for the period 2012-2013.

Forecast Industrial Production Index

Logarithmic trend model Power trend model Polynomial trend model Exponential trend model

2012 113.10 P3.42 104.92 116.96

2013 113,50 113,88 102,77 118,19

The index of industrial production of the Belgorod region under these conditions according to the power trend model in 2012 is projected at the level of 116.96%, and in 2013 - at the level of 118.19%., according to the polynomial trend model, the industrial production index will be 104.92 in 2012 %, and in 2013 - 102.77%.

Regression analysis methods are of great practical importance in forecasting the gross regional product for the Belgorod region. It was revealed that the advantage of the regression method should be considered its universality, a wide selection of functional dependencies, and the possibility of including the time factor in the statistical model as an independent variable.

The best results are obtained from the multiple regression model:

G=a+bl+b2x2+b3x3+....+b„xn, (8)

where Y is the dependent variable (gross regional product for the Belgorod region), x, - are independent variables (factors), b, - are regression coefficients.

Regression correlation coefficients are presented in table. 5.

The main criteria for selecting factors are accuracy, reliability, efficiency of obtaining information, as well as the ability to predict them. Based on these requirements, the following factors were selected to build the model:

Population, thousand people (x1);

Mining extraction billion rubles (x2);

Consumer Price Index (x3);

Producer price index for industrial goods (xD

Table 5

Regression coefficients and correlation coefficients

Independent variables Regression coefficients Correlation coefficients

Xi Population, thousand people 1.24 0.95

x2 Mineral extraction, billion rubles. 12.57 0.94

Source data for the period 1995-2011 was used. After determining the regression coefficients, the regression equation takes the following form:

Y=-18684.2-+1.24^ + 12.57X2-1.83X3-1.2bx^. (9)

The correlation coefficient takes values ​​in the range from -1 to +1. If the coefficient is greater than 0.7, the relationship is strong or close. The strongest relationship is with the population factor. The coefficient of determination for the model is R2=0.95.

The calculated correlation coefficient indicates a very close dependence of changes in gross output on changes in its factors. The coefficient of determination, which characterizes the quality of the selection of a straight-line regression line for the forecast, is 0.95. This suggests that the regression equation explains 95% of the variance of the effective attribute, and other factors account for only 5% of the variance, i.e. residual variance.

Thus, we can conclude that the study made a forecast of further changes in the industrial production index. To carry out the forecast, the extrapolation method was used based on the construction of trend models. For adequate (real) models, the accuracy was assessed. It was revealed that the most accurate are the power and polynomial trend models.

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PREDICTION SOCIO-ECONOMIC DEVELOPMENT OF THE REGION)