SOCIAL ACCOUNTING MATRIX AS A TOOL OF EQUILIBRIUM ANALYSIS JAROSLAV HUSÁR EU BRATISLAVA, SLOVAKIA

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1 SOCIAL ACCOUNTING MATRIX AS A TOOL OF EQUILIBRIUM ANALYSIS JAROSLAV HUSÁR EU BRATISLAVA, SLOVAKIA 1. Introduction It is clear that a method of obtaining an overall picture of economic activity in an economy is an essential. This is the function of national income accounts. They are based on theory of an economic behaviour of economic agents. Within this theoretical superstructure we can analyze the functioning of a system. In last decades a new method of obtaining a picture on an economy was developed. It is a theory of social accounting matrix. 1 We present a completly new structure of social accounting matrix based on macroeconomic theory. 2. Social accounting matrix of Slovakia Since each transaction between the sectors of the economy appears twice in each sector account in the system of national accounts, the form of the matrix is a convenient way to present an overall picture of the economy. Table 1 presents a general structure of social accounting matrix based on the macroeconomic variables listed later under the Table 1. Table 1: Theoretical social accounting matrix Firms Households Govern ment Nett foreign paymen ts Net saving National income Indirect busines s taxes Depreci ation Total Firms R p T b S b NI T i D GDP Households C T p S p Government G T r T f S g Net export X-M Net investm. I r Net nat. produ. Y n Ind. bus. taxes Deprecation D Total GDP T i I f Table 1 represents a payment, the left side of the sector account, while each column shows the corresponding receipts entered on the right side of another sector account. For example, 1 This paper is the essence of my inaguration lecture in

2 consumption 251,89 is shown, reading across the Table 2 recording real Slovak data, as an expense of the household sector and also, reading down the table, as a business receipt. Data are always incomplete and rarely consistent; different bodies of statistics are often collected by a variety of agencies which do not all make use of an agreed set of definitions and classifications; different methods of collecting give rise to sampling and other errors of many kinds. So the strategy is required in order to extract the best possible quantitative description of the economy from the statistical data available. We will have shown how to cope with this problem using the logic of our matrix. The following notation is used to ease of presentation: Gross domestic product Y Net national product Y n National income NI Disposable income Y d Consumption expenditure C Government expenditure G Net export NX Net foreign investment - I f Net domestic investment - I d Household receipts - R p Transfer payments (domestic) - T d Transfers to foreigners - T f Personal saving - S p Government saving - S g Business saving - S b Direct taxes (persons)- T p Direct taxes (business) T b Indirect taxes - T i Depreciation Using the real data for Slovak economy for the year 1994 we get this SAM: 94

3 Table 2: Social Accounting Matrix, Slovakia, 1994, bill. Sk Firms Households Govern ment Net foreign paymen ts Net saving National income Indirect busines s taxes Deprec ation Total Firms 285,20 27,47 14,03 326,70 36,23 35,07 398,00 Households 251,89 46,17 14,03 321,09 Government 79,48 26,88 1,75 1,75 109,86 Net export 4,09 4,09 Net investm. 27,47 2,34 29,81 Net nat. produ. 362,93 Ind. bus. taxes 36,23 Deprecation 35,07 Total 398,00 312,08 109,87 4,09 29,81 (Husár, June, 1995) Now we are in a position to create several equations that algebraically describe the state of the economy. First of all, from column 1 of Table 1 and Table 2 we see that GDP C + G + (X M) + I d + D (1) , ,48 + 4,9 + 27, ,07. Gross domestic product is the sum of the expenditures by all sectors in the economy. Again from the same column 1 we can write or Y n GDP D Y n C + G + (X M) + I d (2) 362,93 = 251, ,48 + 4, ,47 The net national product total represents the net addition to the flow of goods and services to individuals, either directly from business (domestic and foreign) or through the government., and to the capital stock. That is, net national product is gross domestic product less depreciation or, alternatively, the expenditures by the personal and government sectors and the net addition to the capital stock. 2 The principle of the SAM is that the row sum must equal the column sum. By this principle from row 1 we see: GDP R p + T b + S b + T i + D (3) but from column 2 and row 2 we see that 2 Both the change in inventory and net exports are given in net terms. 95

4 or R p + T r C+ T p + S p R p C+ T p + S p - T r (4) and from column 3 and row 3, or T b + T p + T i G + T r + T f + S g T b + T i G + T r + T f + S g - T p (5) Now we made o good preparation for statement that follows. Our next ideas are an important information needed for macroeconomic analysis. Substituting (4) and (5) into (3), we have: GDP C + T p + S p T r + G + T r + T f + S g T p + S b + D or GDP C + S p + G + T f + S g + S b + D (6) Now we can equate the expression (1) and (6). We get: + (X M) + I d + D S p S g + T f + S b + D Remembering that (X M) T f I f, we have + I f + I d + D S p S g + S b + D (7) 2, , ,07 14,03 + 1, , ,07. This identity represents both sides of the gross saving and investment account as it is known from the system of national accounts. In equations (6) and (7) we got compleetly new picture on the GDP identity and identity for import. What is needed is a systematic and coherent framework whixh can accomodate the main bodies of data needed for macroeconomic description of the functioning of an economy. Netting depreciation out of identity (7), we have I f + I d S p + S g + S b 2, ,47 14,03 + 1, ,03 and finally 29,81 29,81. This represents the equality of net saving and net investment. The identity of saving and investment plays a large role in economic analysis and economic policy. The policy makers should insist on accepting this result of the SAM theory 96

5 and the macroeconomics. That part of final output not purchased by consumers and government has been called investment and must by definition be equal to that amount of receipts not paid out for final goods or services by persons, government, or firms (business). National income may also be obtained by subtracting indirect taxes from Y. Y T i NI 362,93 36,23 326,70. National income may olso be obtained by adding total personal income payments to direct business taxes and net saving. Accordingly, from row 1: NI R p + T b + S b 326,70 285, , ,03. Further, from column 2 and row 2, R p + T r T p + S p (8) 285,2 + 26,88 251, , ,03 The left side of (8) lists personal income (factor payments plus transfers to persons from government); the right side shows the way persons dispose of their income: consumption expenditures for goods and services, direct taxes, and saving. If personal taxes are transposed in identity (8), the left side becomes personal disposable income. e. i., total income receipts of persons minus their tax payments. R p + T r - T p C +S p Y d 285, ,88 46,17 251, ,03 265,92 Disposable income, as shown by this identity, can be either spent (C) or saved (S p ). In some cases people can send some of their income to foreigners. Disposable income can be derived from the net national product total by subtracting from Y that part which does not accrue to persons and adding government transfer payments to persons. Thus Finally, let Y d Y (T i + T p + T b ) + T r - S b 265,92 362,93 (36, , ,47) + 26,88 14,03 T i + T p + T b T r T 36, , ,47 26,88 82,99 where T is defined as net taxes, so that Y Y T - S b 97

6 265,92 362,93 82,99 14,03. We would like to stress, moreover, that the government surplus can be calculated by subtracting government expenditures and transfers to foreigners from net taxes. Thus S g (G + T f ) 1,75 82,99 (79,48 + 1,75). As we can see, we have highlighted several important identities in the Slovak economy. They result from the frame of the SAM, that is the construction based on macroeconomics and our attempt to create a new form of SAM. The entries in a matrix, as we have seen, can be presented in an equations form which help us to find new aspects of an economy functioning. Or better, if something is valid, what else must me valid too. Our SAM provides a data base for economic analysis, different way of looking at it. In this explanation we have presented a fairly detailed picture of the national economy generally and the Slovak economy particularly. We showed how rhe transaction in the economy can be organize in matrix form. This form allows us to formulate a set of identities that help a policy maker to analyze the functioning of an economic system. 3. Conclusion Our discussion indicated that the volume of output is determined by the expenditures for final goods and services (column 1), which, in turn, are related in part to the income received by the same units making expenditure decisions. Therefore, the GDP account is broken down by this method in terms of income receipts by economic units and expenditures by the same unit. From Table 1 and 2 we can read of other important relationships using the requirement of the SAM that total of the first row should be equal to the total of first column. By making different substitutes one can get new information on an economy and so one can design a coherent economic policy. Data are always incomplete and rarely consistent; different bodies of statistics are often collected by a variety of agencies which do not all make use of an agreed set of definitions and classifications; different methods of collecting give rise to sampling and other errors of many kinds. So the strategy is required in order to extract the best possible quantitative description of the economy from the statistical data available. We showed how to cope with this problem. 98

7 References 1. E.G. Dolan and D.E. Lindsey, Economics, The Dryden Press, New York, R. Dornbusch and S. Fisher, Macroeconomics, McGraw Hill, New York, J. Husár, Rozumieme makroekonómii?, Elita, Bratislava, 1993 prof. Ing. Jaroslav Husár, CSc., Mgr. ek. Fakulta hospodárskej informatiky, Ekonomická univerzita, Dolnozemská 1b, Bratislava, e- mail: 99