5. Investments, export and import

1999-06-29
To Chap 4.
Model S2

  1. The economic circular flows
  2. Tax rate and import fractions
  3. Production and expenditure on the GDP in Sweden
  4. References

5.1 The economic circular flows

The model is now extended by the investments of the companies. The companies buy equipment from other companies and use own labor for investments in production resources. This gives a payment flow from the private sector which returns to the same sector.

We also add foreign trade. It is assumed that the companies (not the households) do all the trading with foreign countries. The companies earn export incomes and pay for the imports. The difference between export income and import cost gives a balance of trade, which results in financial savings abroad.

Figure 5.1:1, Payment flows between sectors of society, model S2.

We get the following payment balances:

Public sector:-X(1) + X(3)=0 eq. (1)
Households:X(1) + X(2) - X(3) - X(4) = 0 eq. (2)
Private sector:-X(2) + X(4) - X(6) - X(7) + X(8) = 0 eq. (6)
Abroad:X(6) + X(7) - X(8) = 0 superfluous

Table 5.1:1 Payment balances Model S2

The equations follow the rules proposed in chapter 4:

The equations are given the numbers that they will have when all eight equations are finished. Eight equations are needed in order to determine eight unknowns. Equation (6) for the private sector does not include the flow X(5) because it both leaves and enters the private sector, -X(5) + X(5) cancels from the equation.

We have to add model equations:

Taxes:hs*X(1) + hs*X(2) - X(3) = 0 eq. (3)
The consumption of households:X(4) = hK eq. (4)
Investments of the companies:X(5) = pInv eq. (5)
Imports:pi4*X(4) + pi5*X(5) - X(7) + pi8*X(8) = 0 eq. (7)
Exports:X(8) = uExp eq. (8)

Table 5.1:2 Model equations Model S2

The imports X(7) are assumed to depend upon the production of goods and services, investments and exports according to equation (7). A nomenclature is introduced with the first letter indicating the sector to which the quantity belongs: o = public sector, h = households, p = private sector, u = abroad. The other letters indicate the type of quantity, small letter for parameter, capital letter for state variable. (The nomenclature will later be revised and translated into English).

hsTax rate based on the total income of the households. Only the part of the taxes that is used for public consumption is considered. Transfers will be considered in a later model.
hKThe total consumption of the households.
pInvThe investments of the companies (in the private sector).
pi4The import share generated by the private production of goods and services X(4) = the consumption of the households, as a fraction of X(4).
pi5The import share generated by the investments X(5) of the companies, as a fraction of X(5).
pi8The import share generated by the export X(8) of the companies, as a fraction of X(6).
uExpExport

Table 5.1:3 Parameters and state variables model S2

A certain state variable can arbitrarily be attributed to one of two sectors. In this case the export uExp is considered to belong to abroad because the decisions to buy our goods are taken abroad. It is also possible to consider export as belonging to the companies and name it pExp (prefix p). It will become more clear when we try to formulate a model for the corresponding quantity. It will soon be clear what other parameters determine the quantity in question and to which sector they belong.

A closer look reveals that this model has a very simple structure. The equations for the payment balances can be rewritten as follows:

.

Public consumption:-X(1) + X(3) = 0 eq. (1)
Consumption of households:X(2) - X(4) = 0 eq. (2) + eq. (1)
Investments:-X(5) + X(5) = 0
Foreign trade:X(6) + X(7) - X(8) = 0

Table 5.1:4 Rewritten payment balances Model S2

We get four independent equations without common flows.

Note that these equations only model the magnitude of the flows and not how the payments really flow through the sectors.

Figure 5.1:2, Flows as separated circular flows.

In reality, all flows within a sector are mixed. The separated flows depend on another as stated by the model equations for taxes and import.

Taxes: X(3) = hs*X(1) + hs*X(2)

Private consumption: X(4) = (1-hs)*X(1) + (1-hs)*X(2)

Import: X(7) =

pi4*X(4) + pi5*X(5) + pi8*X(8)

The figure suggests that one part of the demand is satisfied through imports. Imported goods are also part of the goods manufactured by the industry. All possible routes inside the private sector are not shown in the figure.

Figure 5.1:3, Mixing of payment flows.

5.2 Tax rate and import fractions

The parameters hs, pi4, pi5 and pi8 can be estimated according to historical data. The data are found in the Financial accounts of Statistics Sweden (SCB) ref. (1). The diagram below shows tax rate hs = X(1) / (X(1)+X(2)) .

Figure 5.2:1. Tax rate calculated as (public consumption) / (sum of private and public consumption).

At present one third of all consumption in Sweden is public consumption (education, medical service, justice etc.).

The economist Per Gunnar Berglund has estimated how the import depends upon the demand (2). His table is reproduced below:

Kind of demandInfluence upon import volume
Private domestic demand0,336
Public domestic demand0,154
Export0,513

Table 5.2:1 Constants for import volume according to Per Gunnar Berglund

An increase of private domestic demand by 1000 kronor would increase the import by 336 kronor.

The model S2 does not consider public domestic demand when calculating the magnitude of the import. It is not because it should have no influence, but because the equations only include flows that belong to the sector under consideration (in this case the private sector). This may seem to be a limitation now, but it will turn out to be a correct principle for the future model design. The larger models include the purchases of the public sector of goods and services from the private sector, that in turn imports goods. Thus the public demand will ultimately be included in the calculation of the import.

The constants pi4, pi5 and pi8 are calculated from SCB data (1). The following equation for the import has a constant term also. It is not possible to determine the constants of the equation X(7) = Konst + pi4*X(4) + pi5*X(5) + pi8*X(8) from data of a single year. If the values of X(7), X(4), X(5) and X(8) for all years from 1950 to 1994 are used, then we get 25 equations with four unknowns. This is an overdetermined equation system which is solved by linear regression, a method from the statistics. In order to avoid that the latest years have a bigger influence than the years after 1950, the whole equation is divided by the gross domestic product before the calculation. x(.) = X(.)/BNP. This gives:

Kind of demandInfluence upon import volume Standard deviation of pi_
Constant importkonst = 0,02 0,09
Domestic private consumptionpi4 = -0,05 0,08
Gross investmentspi5 = 0,17 0,14
Exportpi8 = 0,88 0,10

Table 5.1:2 Constants for import volume, Model S2

88 percent of the export should generate import. How can this strong influence be explained? First the exported goods are made from a large share of imported components, second the income from the export generates liquidity that is used for other kinds of import. In the long run, the trade balance with foreign has to even out which imposes a strong dependence between import and export. According to the figures, the domestic demand should have very small influence upon the import, which is contradictory to all economic theory. The small value of the constant term konst means that it can be omitted. The linear regression method only shows how different variables vary simultaneously, not the cause of the interaction.

The coefficients of the table above gives a very good agreement with historical data for the years 1950 - 1994, as can be seen in the diagram below:

Figure 5.2:2. Actual import/GDP as compared to a fitted curve calculated from domestic consumption, investments and export.

A comparison with only export gives a curve fit that is nearly as good. In contrast, a curve fit against domestic consumption and investments gives a poor agreement.

5.3 Production and Expenditure on the GDP in Sweden

The model S2 has been designed to include exactly those payment flows that constitute the most simple tables of the production and expenditure on the GDP in Sweden (1).

Public production, X(1)Public consumption, X(3)
Private production, X(2)+X(5)+X(6) Private consumption, X(4)
Import, X(7) Gross investments + increase in stocks, X(5)
Export, X(8)
Total supply, =X(1)+X(2)+X(5)+X(6)+X(7) Total usage, =X(3)+X(4)+X(5)+X(8)

Table 5.3:1 GDP balance, Model S2

The public production is priced to the costs of wages and salaries in the public sector. The private production is priced to the costs of wages and salaries plus the total profits. One part of the total profits is used for investments, an other part becomes financial savings abroad. The dividends are in this case included among the private wages and salaries.

The balance of production and usage can also be obtained from the payment balances (1) and (6) in paragraph 5.1 if the investments are added. The equations are shown below, a bit altered. By adding the equations, left members and right members separately, the balance is obtained.

Public sector:X(1) = X(3) eq.(1)
Private sector:X(2) +X(6) + X(7) = X(4) + X(8) eq.(6)
Investments:X(5) = X(5)
Supply = UsageX(1)+X(2)+X(5)+X(6)+X(7) = X(3)+X(4)+X(5)+X(8) Totals

Table 5.3:2 Derivation of the GDP balance, Model S2

The gross domestic product, GDP, is the total of all domestic production. The GDP can be expressed in payment flows as GDP = =X(1)+X(2)+X(5)+X(6), i.e. earnings in public sector + earnings in private sector + investments + financial savings. The textbooks write GDP = C + I + G + (X - IM), i.e. private consumption + investments + public consumption (government) + difference between export and import. Rearranging the terms of the latter equation gives the same expression ( BNP = G + C + I + (X - IM) ) as the first one.

The historical process shown in figure 5.2:1, increasing share of public consumption, and figure 5.2:2, increasing share of export and import, can also be seen in the diagram below showing the relative distribution of the expenditure on the GDP. It can also be seen that the share of investment has decreased after the year 1970. Many trends changed during the year 1970. Lars Ingelstam has shown in his book "Ekonomi för en ny tid" (3) (Economy for a new age) that the employment in the industrial sector (in 9 OECD-countries) increased until 1965 and decreased after 1970 despite that the industrial production increased all the time. Statistics for the years 1978 - 1996 in the diagram "Increasing production, less employment" confirms that the same kind of development also applies to Sweden.

Figure 5.3:1. Expenditure on the GDP, relative shares 1950 - 1994.

As a whole, the Swedish economy has grown very much. The expenditure on the GDP, measured as current prices, almost disappears in the year 1950 as compared to the year 1994. Current prices are used because the analysis works with nominal values. Inflation and the development of the real economy will be treated in later chapters.

Figure 5.3:2. Expenditure on the GDP, current prices 1950 - 1994.

The yearly nominal growth has been around 10 % except for two short periods when it plunged to approximately zero. In the year 1975 the wages and salaries increased by 14 %. The diagram below shows the development of the household consumption, hK in eq. (4) above, and GDP.



Figure 5.3:3, Economic growth in current prices 1950 - 1994.

5.4 References

  1. Statistiska meddelanden, N 10 SM 9501, Nationalräkenskaper 1980-1994, SCB 1996. Tabell 1, Försörjningsbalans i löpande priser. (National accounts 1980-1994, Expenditure on GDP, Current prices).
  2. Per Gunnar Berglund: Konsten att avskaffa arbetslösheten, Ordfront 1996. Tabell 4.2 sid 65, Effekter på importvolymen av en kronas (i 1991 års priser) ökning av respektive efterfrågekomponent. (The art of abolishing the unemployment).
  3. Lars Ingelstam: Ekonomi för en ny tid, Carlssons Bokförlag, Stockholm 1995. Figur 3.5 sid 147. (Economy for a new age).

The Excel calculus that corresponds to Model S2 and that contains the diagrams above can be downloaded here.

Back to home page or contents. Next chapter Chap 6 .