7. Different households, profits of enterprises

1. Model S3
2. Historical data
3. References

7.1 Model S3

Figure 7.1:1. Payment flows of model S3.

Traditionally, households in macro economy have been treated as one category, aggregated without distinction between how the people earn their living. This model divides the households into four different categories in order to analyze the occupation in different sectors of the society, unemployment and transfer payments. Children are not included in this first division, they are assumed to be supported by their parents.

• Pensioners
• Not working, a remainder that represents the unemployed. Includes unemployed busy in different activities such as studies and other "labor market policy measures", students and housewives. (I have not investigated the statistics as deeply so all groups can be separated).
• Public employees. People privately employed and paid by public finance are provisionally included. More extended models will have the purchases of the public sector from the private sector as a separate payment flow.
• Private employees. Private undertakers are included here.

The single households may consist of one or more persons from the four categories listed above. This model does not consider the composition of the single households.

Capital owners have been added to these four categories. A capital owner gets incomes in the form of compensation or dividends from the private sector due to his/hers ownership of fixed capital, land, minerals, shares etc. A capital owner may simultaneously be employed, unemployed or pensioner.

The value added by the companies consists of wages, salaries and gross profits. The gross profits are, in this simple model, shared between investments, financial saving abroad and dividends. The wages and salaries include also taxes on the labor force and subsidies. All taxes are eventually included in the taxes of the households. Even sales taxes are included in the taxes of the households. Later models will show how different taxes are paid.

The payment flows of this model are shown in the figure 7.1:1 above.

A similar diagram can be made for the flows of labor. These are measured as man-years / year, i.e. number of persons. Unemployed and pensioners are included in a similar manner as the labor force. The unemployed kind of get paid for not to work, the pensioners get their pension without having to work.

Figure 7.1:2. Flows of labor of model S3.

The equations for this system are described below sector by sector. The equations of payment balances are not explained, they follow the same principles as described before.

The public sector

Table 7.1:1.

Equations 3, 5 and 6 describe how many persons can be paid with a certain amount of money. The factor 1/1000 converts from millions kr / year to billions kr / year. Equation 3 states that the total earnings X(2) of the public employees equals the annual salary of ow thousand kr / year times the number of public employees X(3). Pensioners have the annual pension twp and the unemployed (not working) receive an annual compensation of twa thousand kr / year .

Households

Table 7.1:2.

The number of pensioners hNp and the number in the total potential work force hNw are given quantities at any time. The number in the potential work force, people between the age of 16 and 65 years, is the sum of the privately employed X(13), the publicly employed X(3) and not working X(9). A average tax rate hs gives the total tax X(10). The private consumption hK is given as a known state variable. This model says nothing about the influence on consumption from other quantities. This simple equation (11) has been chosen because it can be assumed the consumption level is rather slow-changing.

Private sector, the enterprises

Table 7.1:3.

The annual earnings of the privately employed are pw. The value added by the companies is shared between wages and salaries and gross profits. The profit ratio pv is the share of the gross profit in relation to the total value added. The gross profit X(14) is, according to eq. 16, divided between investments X(17), dividends X(7) and financial saving abroad X(16). The imports X(15) consist of different parts, each proportional to the consumption of the households (factor pik), the investments (piinv) and the exports (piex). The proportionality factors do not reflect a direct casual relation but are, as pointed out in chapter 5, the result of a statistical correlation between historical data. The large factor for the exports (piex = 0.88) does no tell that exported goods contain 88 percent imported goods, but only that several equilibrium mechanisms (e.g. floating exchange rate) tends to balance the values of the exports and the imports. The magnitude of the investments pInv is assumed to be given.

Abroad

Table 7.1:4.

The exports uExp are determined by the demand abroad. The imports were treated above in connection to the private sector, because they depend in principle upon the domestic demand.

7.2 Historical data

In order to simulate a realistic case, a reference case for a certain year has to be found with the help of historical data. The payment flows used here are taken from the national accounts of Sweden, years 1980-1994 (1).

The model has 18 flows, 14 of which are payment flows, 4 are labor flows. By adding public finances, public production and transfers to a single public sector, the flows X(1) and X(4) cancel.

Remain 12 payment flows to be determined. They are mutually dependent according to the balance equations. There are 5 balance equations, for the public sector (eq. 1,2 and 4 added), households (eq. 7), private sector (eq. 12 and 16) and abroad (superfluous equation). Because the trade balance follows from the other equations, only four balance equations remain. In order to determine the 12 payment flows, 8 quantities from the tables are needed. 5 quantities are taken from the expenditure on the GDP and 3 quantities from the sector balances.

By tabulating the payment balances for each sector and successively filling in the table values, an other value is automatically obtained for an other payment balance, because the expenditures of one sector are the incomes of the other sector. When all values except one are entered in a payment balance, the last one is given by the balance condition. This method gives a consistent description of the flows, however simplified as the model is a simplified picture of the real world. The simplification implies that some flows consist of several flows, e.g. all taxes are summarized as a single flow.

The appended Excel calculus has tables for the years 1980-1994. The payment flows for 1994 are shown in the figure below:

Figure 7.2:1. Payment flows in Sweden during 1994, billion SKr/year. Reference: Statistics Sweden.

The four "flows of labor" are related by the equations 8 and 9. Not working and pensioners enter the equations in the same way as the labor force (eq. 3, 5, 6 and 13). For that reason, the concept "flow of labor" has been generalized (who can find a better name?). Six variables minus two equations implies that four table values are needed: the number of pensioners hNp=X(8), the number of the total potential work force hNw, the number of employees in the private sector X(13) and the number of employees in the public sector X(3). The not working X(9) are the remainder, that includes more people than just the unemployed.

The data have been taken from the Statistical Yearbook of Sweden ´96 (2). It has only limited time series of data, mostly for the years 1989 - 1994. A combination from several tables give different totals, deviations by 200 thousand people may result. Other sources may have longer time series. Data that separate the not working into unemployed, people occupied by "labor market policy measures", students and housewives (-husbands) etc., would give more insight.

The present interpretation of the statistics gives the following generalized "flows of labor":

Figure 7.2:2. Flows of labor etc. in Sweden 1994. Thousands of persons. Reference: Statistics Sweden.

As mentioned before, the employees of the private sector that are working for the public production are counted as publicly employed. This accounting makes the flow of tax money to correspond to the amount of labor paid by taxes.

When all flows are known, the parameters of the equations can be calculated, e.g. the wages and salaries to the public employees ow = 1000 * X(2) / X(3) from eq. 3. By rearranging the model equations, all parameters and state variables can be calculated:

Table 7.2:1.

Substituting the calculated parameters and state variables into the original equations and solving the equation system gives the original flows back. This is no proof of the correctness of the model. It only proves that the equations are correctly written and that the equation system is correctly solved.

One test of the validity of the model, may be to make independent estimations of the parameters and compare with the values above. It can also be tested if the model is plausible by varying a parameter at a time and study how the flows change. If these changes agree with accepted experience, the model can be considered verified. Note that it is not possible to demonstrate more details than are included in the model. Therefore it is important to start with the largest flows of the economy and include the smaller flows in the big ones.

The model equations 3, 5, 6, 10, 13 and 14 can not be verified because they are in fact definitions of the parameters. The definitions are good if the parameters vary slowly and little as other quantities vary. The equation 15 can be said to be verified if the calculated imports agree with the historical data (Figure 5.1:5 in chapter 5).

The historical variations of some parameters are shown in the following diagrams. The balance of expenditures on the GDP was shown in figure 5.2:1 in chapter 5.

Figure 7.2:3. Tax rate and gross profit ratio (Sweden).

The tax rate has increased slowly from 1980 to 1989. It has decreased a little during 1990 - 1994 and the tax rate is now back to the level of the year 1980. The profit ratio has increased substantially from 36 % in 1980 to 44 % in 1994.

These observations are verified by an article in the Swedish newspaper Dagens Nyheter 1997-10-14 (3): "Share holders earn money, but the wages and salaries are kept low. Lennart Schön, professor of economic history at the university of Lund, Sweden, has investigated the share of wages and salaries during different cycles of the economic history and point out the fact that the share of wages and salaries today is as low as 80 years ago. The share of wages and salaries in relation to the value added in the industrial sector has decreased since the end of the 70:es".

Figure 7.2:4. The share of wages and salaries in the industry, Dagens Nyheter 1997-10-14.

The part that is not used for wages and salaries, is distributed between investments, dividends to the shareholders and financial saving.

Figure 7.2:5. The use of the total profits.

An decreasing share of the total profits are used for investments while dividends have increased since 1990.

Figure 7.2:6. Distribution of the incomes of the households.

The incomes of the households consist since 1990 ever more of dividends. The share for the unemployment costs has decreased while the pensions have increased.

7.3 References

1. Statistical reports, N 10 SM 9501, National accounts 1980-1994, Statistics of Sweden 1996.
   Table 1, Expenditure on the GDP, current prices.
   Table 4, GDP as the sum of … value added.
   Table 7, The consolidated public sector.
2. SCB: Statistical Yearbook of Sweden, Statistics of Sweden 1996.
   Table 33, Population by age.
   Table 192, Labor force participation of the population.
   Table 197, Employed by industry.
   Table 288, Finances of the municipalities.)
   Table 293, Finances of the county councils.
   Table 348, Basic pensions and supplementary pensions …
3. Torbjörn Pettersson: Kapitalet leder stort efter 80 års kamp…, Dagens Nyheter 1997-10-14.
   (The capital has the lead after 80 years of struggle …)

More statistics are found in the Excel calculus that describes the model S3. It can be downloaded here.
Back to home page or contents. Next chapter Chap 8.