Real National Accounts as a Money Flow System

Transcription

1 Real National Accounts as a Money Flow System Matti Estola 1 and Alia Dannenberg 2 The analogy between a money and a water flow system is demonstrated in Figure 1, where the difference between inflow and outflow of water (money) during time unit t corresponds to the profit and loss statement of a firm, and the amount of water (money) in the vessel corresponds to the net wealth in the balance sheet of the firm. The inflow of water (liter/ t) or the flow of income of the firm ( / t). The amount of water (liter) in the vessel or the net wealth of the firm ( ). The outflow of water (liter/ t) or the flow of expenditures of the firm ( / t). Figure 1. A water (money) flow system The System of National Accounts (SNA) and a circular money flow diagram are two ways to describe the real and the money flows between macro-economic sectors. In every trade there are two partners: the buyer and the seller. The expenditures of the buyer equal the gross revenues of the seller of which sales and product taxes are delivered to the state. The total value of production in an economy in a time unit can thus be measured by the gross expenditures of all buyers, or by the gross revenues of all sellers in the time unit according to the principles of accounting. Every bought good causes a money flow (its payment) in one direction, and a real flow (its delivery) in the opposite direction. The production process of an economy can thus be modelled by the money or the real flow process that have parallel events in both processes. Private and public consumption and investment are expenditures of the private and the public sector, respectively. The aggregate expenditures in an economy deviates from the aggregate value of production by the value of imports and domestic produced and unsold goods. If increased values of inventories are booked as inventory investment, then the aggregate expenditures in an economy equal the aggregate value of domestic production plus imports. The aggregation of production of various firms can be made in monetary units. The nominal GDP of an economy is obtained by adding the value-added of all firms in the economy in a time unit at current prices. By the nominal GDP we can approximate the real GDP the aggregate flow of production in the economy as follows. Let all production be measured in mass units,, and let the unit price of the product of firm i be denoted by ( ) and the 1 University of Eastern Finland, Faculty of Social Sciences and Business Studies, P.O. Box 111, FIN-80101, Joensuu, Finland. matti.estola@uef.fi (corresponding author). 2 University of Eastern Finland, Department of Business, P.O. Box 111, FIN-80101, Joensuu, Finland alia.dannenberg@uef.fi 1

2 real value-added of the firm by ), where is a time unit. Suppose one-product firms exist in the economy. Then =, where ( / ) is the arithmetic average of = 1,,. An approximation for the real, ), is thus obtained by dividing the nominal by the average price level in the economy. Thus by the money flow system to be introduced later we can analyse both the nominal and the real flow process of an economy. 4. Money Flows between Economic Units Originating from Production We study the money and the asset flows in an economy in one year. Every economic unit has an opening balance sheet that registers the assets and the liabilities of the unit at the initial time moment, several current (flow) accounts that register the incomes, the expenditures, and the transfers received and paid by the unit during the year, and a closing balance sheet that registers the stocks of the assets and the liabilities at the ending time moment Firm i as a Node in the Money Flow System of Production Here firm i can be a financial or a non-financial firm, but later these two kinds of firms are sometimes treated separately. The opening balance sheet of firm i is: Assets ( ) Liabilities and net worth ( ) + where the net worth defines the wealth of the firm as the difference between its assets and liabilities. In the first flow account of firm i the production account (PA) intermediate consumption is subtracted from the value of output ( 1) (the official abbreviations of the items are in brackets). This gives the value added of the firm. The gross value added (= ) of firm i is:, where ( 2) is the intermediate consumption of the firm on the products of other domestic firms. The reason for subtracting intermediate consumption from the value of output is that in aggregating the gross value added of an economy, firms productions would otherwise be added in several times. The net value added (= ) of firm i is obtained by subtracting from the consumption of the fixed capital ( 1) of the firm:. The consumption of fixed capital corresponds to the depreciation bookings of the firm of its capital goods. In SNA, the consumption of fixed capital is not made on the basis of firms depreciation bookings, however, but by the estimated consumption of firms capital goods. In SNA, the valuation is made in gross and in net terms. We apply here the net valuation where the consumption of fixed capital is taken into account. In SNA, two kinds of pricing principles are used. If production is valued at basic prices, taxes and subsidies on products are not included, and if production is valued at producers prices, all taxes and subsidies on products are included in prices. For example, value added tax is 2

3 collected as a fixed percentage of sales of goods (SNA 2009 pp ). Here we value production in producers prices, and so taxes and subsidies on products are included in production values. We aggregate current transfers in three items: 1) Net current taxes on income, wealth, etc. ( 5), 2) Social contributions and benefits ( ), and 3) Capital transfers ( 9). Transfer is a transaction where an institutional unit provides a good, service or asset to another unit without receiving from the latter any good, service or asset in return as a direct counterpart (SNA 2009 p. 161). Social benefits can be divided in two classes: pensions and other social benefits. Other social benefits are mostly related to medical or old age care, child allowances, or education. The fees are collected either voluntarily or obligatory from households or firms, and are paid as transfers to the beneficiaries. Current transfers may also take place between resident and non-resident households, like regular remittances between the members of one family. Social transfers in kind contain, for example, final consumption expenditures undertaken by government on behalf of households (ibid. pp ). With these assumptions, firm i faces the following annual money flows with unit /. Revenues: Households ( 31) and government s ( 31) individual final consumption expenditures on the products of firm i, Government s collective final consumption expenditures ( 32) on the products of firm i, Firms gross fixed capital formation ( 5) on the products of firm i, Sales of intermediate goods to domestic firms ( ), Exports of goods and services ( 6) of the products of firm i, Property income ( 4), Subsidies on production ( D3, 31, 39), Social contributions and benefits ( ), and Capital transfers ( ) received by firm i. is an auxiliary variable, sub-index R refers to revenues, 3 is Subsidies, 31 Subsidies on products, and 39 Other subsidies on production. Costs: Expenditures on intermediate goods of domestic firms ( ), Compensation on employees ( 1), Taxes on production and imports ( 2, 21, 29), Current taxes on income, wealth, etc. ( ), Own gross investment in fixed capital and changes in inventories ( ), Social contributions and benefits ( ), Capital transfers ( ), Imports of goods and services ( 7), Net acquisitions of non-financial non-produced assets ( 2), and Property costs ( ). Sub-index P refers to payments, 2 is Taxes on production and imports, 21 Taxes on products, and 29 Other taxes on production. Every firm does not face all these money flows, however; all firms do not import goods, get government subsidies, or government does not buy their products. For example, if firm i does not produce investment goods, then =0.In SNA in imports and exports, no distinction is made between consumption and investment goods, and between final and intermediate goods. We assume that all imports are carried out by the firms in the home country that sell the goods forward to domestic customers. Taxes on production and import contain, for example, value added tax. The operating surplus plus mixed income (net) of firm i is denoted by 13. Mixed income is the balancing item of unincorporated enterprises in the household sector that corresponds to remuneration for work carried out by the owner or members of his family including profits gained as entrepreneur (SNA 2009 p. 132). We define the of firm i by subtracting the consumption of fixed capital and the values of imported goods and intermediate consumption from sales: = +. The imported goods sold by firm i are subtracted from the market output to get the value of domestic production. In the generation of income account (GIA), from the net value added is subtracted the primary income components that 3

4 are paid to the corresponding economic units. The resulting item is operating surplus plus mixed income of firm i,, that is transferred to the allocation of primary income account APIA. In the APIA, is adjusted by property incomes and costs. The result is the balance of primary income of firm i ( ) that corresponds to the part of the net National Income created by firm i. In the secondary distribution of income account SDIA, is adjusted by current transfers (SNA 2009 pp. 159). This gives the disposable income of firm i,. These accounts and their connections are shown in Figure 2. GIA of firm i APIA of firm i SDIA of firm i Figure 2. The GIA, the APIA, and the SDIA of firm i Primary incomes accrue to economic units due to their involvement in processes of production or ownership of assets that may be needed for production. This may contain compensation of employees, taxes on production and imports less subsidies, operating surplus or mixed income, and property income (SNA 2009 p. 131). The equations for the accounts are:,,. Now, can either be saved or used in final consumption. Notice that the final consumption of goods that consumers and government participate in is separated from the intermediate consumption of goods in firms production processes (H i defined earlier), see SNA (2009 pp ). Because firms do not participate in final consumption, the whole disposable income of firm i is saved, i.e.. Net saving (= ) links the use of disposable income account (UDIA) and the capital account (CA) of firm i, and here we omit the item Adjustment for the change in pension entitlements ( 8), see SNA (2009 p. 181). The reason for omitting this marginal item is that pension contributions are included in social contributions (ibid. p. 168). UDIA of firm i CA of firm i FA of firm i Figure 3. The UDIA, the CA, and the FA of firm i The UDIA, the CA, and the financial account (FA) of firm i and their connections are shown in Figure 3. The inflow of the consumption of capital in CA can be explained in two ways: 1) CA accounts changes in the capital stock in net terms, and because investments increase the capital stock, the consumption of the stock must enter in the account from the opposite direction as increases in it. Actually firms do not pay anything of the consumption of their capital stock, and because enters as an expenditure item in the GIA, it must enter as a 4

5 revenue item in another account (CA) so that in the consolidation of the firm s accounts, cancels. Thus the capital stock of firm i accumulates according to the firm s net investment,. 2) Firms make savings that correspond to the consumption of their capital stock (depreciation). may thus be understood as the savings of the firm to replace its capital goods after their wearing out. The net capital transfers firm i receives are denoted by (through this study refers to net), is the (own) gross investments including changes in inventories, ) the net lending/borrowing, the net issuing of financial liabilities, and the net acquiring of financial assets of the firm in the year; the last two are asset flows with = 1. Notice that if <0, firm i has earned money by selling non-financial non-produced assets more than buying them. The equations corresponding to the accounts in Figure 3 are:,,. Net lending/borrowing links the CA and the FA of the firm. If >0, firm i has a surplus after its investments in fixed capital, and can invest this money in financial assets or repay its loans. However, if <0, this deficit must be financed by borrowing or issuing liabilities; notice that and may be negative too. The acquiring of financial assets and liabilities is treated in another article. Now, FA is the last flow account of firm i, and changes in stocks and with unit are added, respectively, in the initial assets ( ) and liabilities ( ) in the opening balance sheet. This results the closing balance sheet of the firm at the end of the year. We omit here the Other changes in the volume of assets account and the Revaluation account. These accounts correct the amounts and the values of assets due to non-intentional events that may occur in the year, see SNA (2009 pp ) Consolidated Account of the Firms Sector In consolidating aggregate sectors from individual units, the mutual money flows between the units cancel. For example, in the Firms Sector (FS) only those money flows remain visible FS pays to or receives from other kinds of economic units. This is shown in Figure 4 where Firm 1 and Firm 2 are consolidated into Firm 1+2 that receives all the incomes and pays all the expenditures of the two firms, and saves the rest. Firm 1 buys goods from Firm 2 by. Firm 1 Firm 2 Firm 1+2 Figure 4. The consolidation of Firm 1 and Firm 2 into Firm 1+2 5

6 The consolidation of Firms 1 and 2 is made mathematically as follows. The incomeexpenditure equations of the firms are: and. Adding the left and the right hand sides of these equations, the income-expenditure equation of Firm 1+2 becomes the following:, where are the aggregate money flows faced by the consolidated firm. In this consolidation, the mutual money flow cancels while other stay. By consolidating all non-financial and financial firms in the home country into the sector FS, the GIA, the APIA, and the SDIA of FS become as ( ): GIA of FS APIA BPI of FS N SDIA of FSD Figure 5. The GIA, the APIA, and the SDIA of FS The aggregate money flows faced in the accounts are explained in the Appendix. Next we show that our modeling is consistent with the Finnish NA data in million /year at year The data corresponding to Non-Financial Firms Sector (NFS) is: + = ( 1). Further, = , = 16855, = 61269, = 510, and = 1276, while are included in the value of production and are not reported in SNA. These give = Now, = and = give = Still = 2491, = 1853, and = Thus = 5916, as is correct for NFS. Quantities and are aggregated from those of individual firms, and the UDIA, the CA, and the FA of the FS are as follows: UDIA of FS CA of FS N FA of FS Figure 6. The UDIA, the CA, and the FA of FS In Finland at 2011, = 5916, = 268, = 30, = 16855, = 121, and = Thus = 2509, that equals with the NA of NFS. The data for FFS (Financial Firms Sector) in Finland at 2011 is: = 8755, = 4223, = 400, = 2749, =3, and =1, while are not reported. These give = Then = and = give = Further, = 4620, = 4729, and = 637 give = Still = 1290, = 34, =3, = 400, 2, and = 278. Thus = 1496 that equals with Finnish NA of FFS, and FS=NFS+FFS. 6

7 4.2. Household j as a Node in the Money Flow System of Production We omit here the opening balance sheet of household j because it is similar to that of firm i, and define only the flow accounts for household j for the accounting time (one year). Household j may gain operating surplus plus mixed income due to working as an owner in an unincorporated firm (UF). As a market producer, household j faces similar revenue and cost components as firm i defined earlier with the only exception that the firms owned by households are assumed not to take part in international trade. These income and cost components are not repeated, however, but they appear in the GIA of household j. Household j faces the following other revenues and costs as compared with firm i with unit. Revenues: Compensation on employees ( ), Social contributions and benefits ( ), and Property incomes ( ). Costs: Expenditures on consumer goods ( ), Current taxes on income, wealth, etc. ( ), Social contributions and benefits ( ), Net acquisitions of non-financial non-produced assets ( ), and Property expenditures ( ). The GIA, the APIA, and the SDIA of household j are then as follows: GIA of hh j APIA of hh j SDIA of hh j Figure 7. The GIA, the APIA, and the SDIA of household j Now, is government s collective consumption expenditures on the products of the UFs owned by household j, is the individual final consumption of households and government on the products of the UFs owned by household j, and all the other factors in the GIA of household j are as in the case of firm i. Even though households may operate as producers, most households operate as labourers in firms and earn only wage income. Thus is the gross wages paid by the UFs owned by household j to their labourers, and is the possible wage income household j receives as a labourer in a firm. is the operating surplus plus mixed income household j receives as being an entrepreneur, the balance of primary income after the operating surplus plus mixed income has been adjusted by wage and property incomes and costs. The disposable income of household j,, is obtained after social transfers have been taken into account. Notice that if household j does not operate as an entrepreneur, all the items in the GIA of household j vanish. The equations for the GIA, the APIA, and the SDIA are:,,. The capital goods of households correspond to the fixed capital of the UFs owned by households, see SNA (2009 pp ). Now, is the net saving, the consumption of fixed capital of the UFs owned by household j, and the capital transfers received and paid, the (own) investments of the UFs owned by household j, the net 7

8 lending/borrowing, the net acquiring of financial liabilities, and the net acquiring of financial assets of household j in the year. The UDIA, the CA and the FA of household j are demonstrated in Figure 8, where is the individual consumption expenditures of household j. UDIA of hh j CA of hh j FA of hh j Figure 8. The UDIA, the CA and the FA of household j Changes,, respectively, are added in the liabilities and in the assets in the opening balance sheet of the household to get the closing one. By taking account the CA, the equation for FA in Figure 8 becomes the following: Consolidated Accounts of the Households Sector (HS) We consolidate the Non-Profit Institutions Serving Households (NPISHs) into the Households sector (HS) because these economic units behave almost equally as households. The aggregate money flows faced by Sector HS are described in the Appendix, and the consolidated accounts of the HS are as follows: GIA of HS APIA of HS SDIA of HS Figure 9. The GIA, the APIA, and the SDIA of HS UDIA of HS CA of HS FA of HS Figure 10. The UDIA, the CA, and the FA of HS In the GIA,, and HS compensates its laborers by W HP. In the APIA, HS gets employee compensations from other sectors as:, see section 4.3. The gross compensation of employees of HS is thus:, and,, and are obtained by adding over households. 8

9 The corresponding items in Finnish NA at 2011 in million /year are: = = 43736, = = 16409, =20+0, = = 8754, = , and = = 5496, where the first numbers refer to HS and the latter to NPISHs; and are not reported. Thus = = 14575, as is correct. Now, = , = = 9858, and = = 2253; thus = Also = = 42061, = = 29359, and = = Thus = Further, = = gives = = Because = 8754, = = 402, = = 461, = = 13987, and = = 104, then = 4263 as is consistent with Finnish NA at Government as a Node in the Money Flow System of Production Government sector contains all legal entities established by political processes that have legislative, juridical or executive authority over other institutional units within a given area. Such entities are government, local governments, social security funds etc., see SNA (2009 pp ). We assume, for simplicity, that government does not produce investment or export goods, and government produces goods mostly for its own use or as transfer goods to other domestic units. We omit here the opening balance sheet of government because it is similar to that of firm i, and define only the flow accounts for the government at the accounting time (one year). From the market production of the government sector, consumers consume, and the rest of it is used as intermediate consumption in firms ( ). The non-market output of the government sector is consumed partly by consumers (included in ) and mostly by the government sector itself, ( ). Government faces the following money flows with unit /. Revenues: Sales of market goods to consumers ( ) and firms ( ), Government s own consumption of public goods ( ), Taxes on production and import ( ), Current taxes on income, wealth etc. ( ), Social contributions and benefits ( ), Capital transfers ( ), and Property income ( ). Costs: Individual final consumption on goods ( ), Collective final consumption on goods ( ) ( 32), Intermediate consumption ( ), Subsidies to producers ( ), Taxes on production and import ( ), Current taxes on income, wealth etc. ( ), Social contributions and benefits ( ), Capital transfers ( ), Own investments in fixed capital ( ), Consumption of fixed capital ( ), Net acquisitions of non-financial non-produced assets ( ), and Property expenditures ( ). GIA of GS APIA of GS SDIA of GS Figure 11. The GIA, the APIA, and the SDIA of GS 9

10 UDIA of GS CA of GS FA of GS Figure 12. The UDIA, the CA, and the FA of GS The essential accounts of GS are displayed in Figures 11 and 12. The net savings of government is denoted by. If <0, government is a net borrower and vice versa. By taking account the APIA, the SDIA, and the CA, the equations for the UDIA and the FA of GS become the following:, A. The corresponding data of Finnish NA at 2011 in million /year are: = 52653, = 21250, =5, = 4067, = 26853, and =0, while are not reported. These give = 496, as is correct. Now = = 26754, = = 2719, = 7393, and = These give = Also = 50129, = 65289, = 30919, and = 20. Then = 44830, as is correct. Now = and = give 1149, and = 4067, = 804, = 826, = 4655, and =7 give 1766, as is correct Rest of the World as a Node in the Money Flow System of Production In international trade, capital and intermediate goods are included in imports and exports and are not separated from consumer goods, and the capital stock of the rest of the world sector (RS) is not a part of the SNA of the home country. The financial account of RS, on the other hand, defines the change in net lending position between the home country and RS. Excluding the acquirement of financial assets and liabilities that are treated in another article, the home country and RS face the following money flows with unit treated from the point of view of RS. Revenues: Import revenues ( ), Compensation on employees ( ), Taxes on production and imports ( ), Social contributions and benefits ( ), and Property income from the home country. Costs: Export expenditures ( ), Compensation on employees ( ), Subsidies ( ), Social contributions and benefits ( ), Net acquisitions of non-financial non-produced assets ( ), and property expenditures ( ) to the home country. The production account of RS is omitted because the production of RS is not a part of the SNA of the home country. The balancing item of the GIA of RS - the external balance of goods and services (EB) - measures the difference in the sales of goods and services between the home country and RS. The balancing item of the consolidated account ASUA = 10

11 APIA+SDIA+UDIA of the RS is the balance of payments ( ) between RS and home country, and it equals with the disposable income of RS. GIA of RS ASUA (= APIA+SDIA+UDIA) of RS Figure 13. The GIA and the ASUA of RS The corresponding equations for the GIA and the ASUA of RS are:,. The equals with the savings of RS, and after is adjusted by net capital transfers and net acquisitions of non-financial non-produced assets, we get the net lending/borrowing of RS to/from the home country,. The final flow account of RS is the FA that adds into the flow of net acquisition of liabilities of RS from the home country,. This gives the flow of net acquisition of financial assets of RS from the home country,. These accounts are shown in Figure 14. CA of RS FA of RS Figure 14. The CA and the FA of the rest of the world By taking account the GIA, the APIA, and the SDIA, we get the equation for FA of RS as: =. Adding changes and in the opening balance sheet of RS gives the closing one. The Finnish NA data in million /year at 2011 is: = 78342, = 77075, which give = Further, = 392, = 627, = 451, = 0, = = 776, = 14280, = 14745, = 3249, = Thus = 2167, that equals with Finnish NA at Now, = 11, = 199, and = 12. These give = 1967, that is consistent with the Finnish NA at Gross Domestic Product The GIA of the home country is defined by consolidating the GIAs of FS, HS, and GS. The corresponding equation is obtained by adding the inflows of money in the consolidated GIA of all domestic sectors, and setting this equal to the sum of outflows of money from the consolidated GIA: 11

12 (2) Because GS does not produce investment goods ( =0) but only buys them ( >0), the aggregate investment in the economy is:. The other aggregate quantities are:,,, =,, +,,, and. By using aggregate quantities we can write Eq. (2) as +( )+. (3) On the left hand side of the latter form of Eq. (3) is the aggregate value of domestic production +( )+ including revenues from intermediate goods, and from this is subtracted the expenditures on intermediate goods. Thus the left hand side of Eq. (3) equals with the GVA of the home country. Net exports are in parenthesis to separate the international and the domestic trade. In this consolidation, the revenues and expenditures on intermediate goods vanish, because they are mutual money flows between the domestic sectors, see Figure 4. Thus, and then the left hand side equals with GDP calculated on the basis of expenditures: +( ).On the right hand side of the latter form of Eq. (3) is GDP calculated on the basis of income generated in production. Thus the three ways of calculating GDP are obtained from Eq. (3), see SNA (2009) pp Equation (3) is demonstrated in Figure 15: The consolidated GIA of FS, HS, and GS Figure 15. The consolidated GIA of the domestic sectors We check our modeling by the data of Finnish NA at 2011 in million /year. There = 77075, = 78342, = 15019, and =( ) = , where the first two numbers refer to HS and NPISH, and GS takes part in Individual consumption (P31) by Further, =( ) = 39541, = ( ) = 18086, =( ) = 30076, = ( ) = 39233, and = ( ) = , where the numbers refer to (HS+NPISH), NFS, FFS, and GS. Still, = (20+0) = 27205, = ( ) = 3495, and = ( ) =

13 We can now express the GDP of Finland at 2011 as: +( )= ( ) 57 = , where -57 is the statistical discrepancy between demand and supply. To check that Eq. (3) is correct, we calculate the GDP on the basis of income: = = Disposable National Income The second fundamental macro level identity is obtained in the system by adding the inflows of the UDIAs (disposable incomes) of all domestic sectors, and setting this equal with the sum of outflows of the corresponding UDIAs. This gives:, (4) where is the net property income of sector k,,,, and. The latter form of Eq. (4) is demonstrated in Figure 16. The consolidated UDIA of FS, HS, and GS Figure 16. The consolidated UDIA of sectors FS, HS, and GS. Because is the aggregate final consumption and the aggregate savings of the domestic sectors, the latter form of Eq. (4) shows that in the system money does not vanish; on the left hand side is total disposable income, and on the right hand side total final consumption and saving of the home country We check Eq. (4) by the data of Finnish NA at 2011 in million /year. There = 39233, = 78487, = 18097, = 26754, = = 1879, 46, = 15019, = , = 2719, = 465, and = ( ) = 7241, where the numbers in brackets refer to HS and NPISHs. These numbers fulfill Eq. (4). References: System of National Accounts New York. 13

14 Appendix FS: : Aggregate revenues of firms from exported goods, : Aggregate government consumption on the goods of firms, : Aggregate households consumption on the goods of firms, : Aggregate fixed capital formation on the goods of firms, : Aggregate sales of intermediate goods by firms, : Aggregate consumption of intermediate goods by firms, : Aggregate government subsidies to firms, : Aggregate operating surplus plus mixed income of firms, : Aggregate gross compensations on employees paid by firms, : Aggregate expenditures of firms on imported goods, : Aggregate own fixed capital formation of firms, : Aggregate net property incomes of firms, : Aggregate current taxes on income, wealth, etc. of firms, : Aggregate depreciation of capital goods of firms, : Aggregate net capital transfers received by firms, : Aggregate net social contributions and social benefits of firms, : Aggregate taxes on production and imports of firms, : Net acquisitions of non-financial non-produced assets of firms. 14