MATRIX REPRESENTATION OF THE KALININGRAD REGIONAL ACCOUNTS SYSTEM : EXPERIMENTAL DEVELOPMENT AND MODELLING

96 This article addresses the task of creating a regional Social Accounting Matrix (SAM) in the Kaliningrad region. Analyzing the behavior of economic systems of national and sub-national levels in the changing environment is one of the main objectives of macroeconomic research. Matrices are used in examining the flow of financial resources, which makes it possible to conduct a comprehensive analysis of commodity and cash flows at the regional level. The study identifies key data sources for matrix development and presents its main results: the data sources for the accounts development and filling the social accounting matrix are identified, regional accounts consolidated, the structure of regional matrix devised, and the multiplier of the regional social accounting matrix calculated. An important aspect of this approach is the set target, which determines the composition of matrix accounts representing different aspects of regional performance. The calculated multiplier suggests the possibility of modelling of a socioeconomic system for the region using a social accounting matrix. The regional modelling approach ensures the matrix compliance with the methodological requirements of the national system.

This article addresses the task of creating a regional Social Accounting Matrix (SAM) in the Kaliningrad region.Analyzing the behavior of economic systems of national and sub-national levels in the changing environment is one of the main objectives of macroeconomic research.Matrices are used in examining the flow of financial resources, which makes it possible to conduct a comprehensive analysis of commodity and cash flows at the regional level.The study identifies key data sources for matrix development and presents its main results: the data sources for the accounts development and filling the social accounting matrix are identified, regional accounts consolidated, the structure of regional matrix devised, and the multiplier of the regional social accounting matrix calculated.An important aspect of this approach is the set target, which determines the composition of matrix accounts representing different aspects of regional performance.The calculated multiplier suggests the possibility of modelling of a socioeconomic system for the region using a social accounting matrix.The regional modelling approach ensures the matrix compliance with the methodological requirements of the national system.Key words: Social Accounting Matrix, region, multiplier, modeling A full adaptation of the national accounting methodology to the regional level opens up new research opportunities for modelling and solving analytical and prognostic problems.A regional account system (RAS) is emerging.Among all the regional economic accounts, only goods and services production accounts are almost fully developed.Researchers are working towards an experimental assessment of a wider range of RAS indicators in view of available statistics and indirect and expert evaluations [5; 12; 13].

N. Ogneva
To eliminate data deficit when developing a RAS and ensure data reliability, researchers use the techniques of matrix representations of economic flows [5; 6; 11].A matrix structure makes it possible to balance resources and their uses for all accounts and gives an opportunity to rely on sparse data arrays.Matrix forms also increase the analytical value of regional account indicators, which create prerequisites for identifying the multiplication effect in the regional reproduction process.
A Social Accounting Matrix (SAM) is one of the promising tools to describe, analyse, and model income and expenditure flows of regional economic agents by reproduction, industrial, sectoral, and institutional parameters [4; 6; 11].The SAM structure facilitates the revision and systematisation of data contained in numerous official and unofficial autonomous sources.Moreover, the need to balance income and expenditure flows encourages researchers to compensate for absent statistically identified indicators through calculations and indirect and expert evaluations.SAM developers do not innovate the methods and procedures of data collection.Their mission is to obtain maximum significant information from the available data array.The authors of this article when developing a SAM for the Kaliningrad region pursed this objective.
The research novelty of the study is accounted for by the selected method of presenting and interpreting indicators for analysing the income and expenditure of regional economic agents.Table 1 gives a general idea about the sources of these indicators.As a follow-up to the regional balance model calculations performed at IKBFU in 2013 [2; 3], one of the model's authors created a number of experimental consolidated accounts of the Kaliningrad region (table 2).These accounts' indicators served as a reference point for the SAM.
However, the first step to a SAM is developing its structure comprised of economic agents' accounts.On the one hand, each account is represented by both a row and a column.Matrix rows correspond to the economic agents' receipts and columns to expenditure.In line with the economic approach to completing SAMs, accounts are organised into groups corresponding to the stages of reproduction process.The first group of accounts -'Goods' and 'Production' -is consistent with the process of creation of goods and resources for commodities and services.They are followed by factor accounts -labour and capital accounts corresponding to the generation of primary (factor) incomes.The third group brings together accounts representing the generation and use of disposable incomes of economic agents.The capital account is identified separately.The capital account row shows the savings of economic agents and the column investment.The last group is comprised of accounts of the rest of the world demonstrating the flows that are external to the region.
However, there is no detailed universal standard in SAM development.General economic requirements are specified in methodologies adapted to particular conditions and research problems.As a result, SAMs developed for individual Russian regions are very heterogeneous [4; 6; 10; 13].
The openness of the Kaliningrad economy, particularities of research problems, and available information resources encouraged the authors of the article to devise a technique for developing a regional SAM that would meet the above conditions.For more detail, see [7].One of the key aspects of this technique is balancing the rows and columns with the same numbers, which, ideally, should be identical.General balance correlations serving as the basis for SAM development are described in [1; 5; 6; 11].However, in practice, it is not easy to obtain a fully balanced SAM.Firstly, as an open system, a region is characterised by inconsistences in indicators related to external ties, as well as imbalances between savings and investment.At the same time, if a total of savings, entry, and imports equals a total of investment, exits, and exports, the balance is not distorted.Secondly, the imperfection of accumulation, processing, and interpretation of data and their incompleteness often result in a lack of correspondence between the other matrix accounts.This requires checking and correcting errors in the SAM for the Kaliningrad region.
The devised methodology suggests completing a 1313 matrix table bringing together the indicators of income accounts (rows) and expenditure accounts (columns) of key regional economic agents (table 3).

Expenditure of other countries
An important aspect of the SAM development technique is identifying the source of data and the means to calculate indicators for each matriх entry.Its key features employed in completing the SAM for the Kaliningrad region are shown in table 4. In the conditions of incomplete information, SAM development is not a routine task with a ready-made algorithm.

Table 4
Means to identify regional SAM paramters

Entry
Assessment method 1:2; 1:5; 1:7; 1:10; 1:12; 2:1; 3:2; 4:2; 5:3; 5:4; 8:9; 9:2; 10:6; 12:1; Statistics: the 2012 data Indirect assessments using proportional parameters (for instance, the contribution of Kaliningrad regional GRP to the national parameter value) Comment: The first number in the matrix entry label stands for the row and the second for the column (row : column) The development of balanced matrices is the first step in modelling a regional economic system.Modelling includes the following stages: a) formulating and proving the hypothesis about a set of exogenous factors; b) dividing SAM accounts into exogenous (corresponding to impact factors) and endogenous ones; c) aggregating exogenous accounts -SAM is reduced through a decrease in the number of accounts; d) calculating the Leontief multiplier to reduce the SAM; e) performing analytical and prognostic calculations using the SAM multiplier.
The openness of the Kaliningrad regional economy encouraged the authors to put forward a hypothesis that the identification of external demand and financial flows as exogenous regional factors demonstrates an important cause-effect relation describing the emergence of multiplier effects throughout the regional reproduction chain.
Based on the proposed set of exogenous factors, the 8 th , 11 th , and 12 th accounts were aggregated in the regional SAM.Table 5 presents the 2012 Kaliningrad regional SAM developed by the authors as a research experiment.Here, a total of the 8 th , 11 th , and 12 th accounts is presented in the consolidated account No. 10 'The rest of the world, including the federal government'.Other accounts are presented in the order given in table 3 and are numbered 1-9.The last row and column contain total values.After the standardisation of expenditure indicators in endogenous accounts (the Leontief model's coefficients of direct material input are calculated in a similar way), a matrix of average propensity to spend was developed.The matrix of average propensity to spend can be considered an analogue for the Leontief matrix of direct material input.In our case, it is a 99 matrix.It helps to calculate the SAM multiplier (table 6) reflecting the direct and indirect effect of a single change in exogenous accounts on the final receipt values for regional economic agents.By analogy, it was called the Leontief multiplier.With predictive estimates of exogenous parameters at hand, a researcher can use the multiplier to model future states of a regional socioeconomic system through calculating predictive SAMs.The advantages of this approach to regional modelling include balancedness ensured through meeting the requirements of the national accounting system and reinforced through using the matrix principle included in the model's structure.