Using the numerical data from the production account (Table 10.3) efficiency (e) comes to:

The results presented support the hypothesis that the German economy can be characterized as a throughput economy (Strassert 2000a). The transformation capacity of the

= total primary input, = secondary input, = secondary output, = final production A, = final production B.

economy is still so low that the total primary input is almost totally transformed into residuals. This is true even if water is neglected.

With regard to national accounting, a complementary calculation is of interest. When we calculate the gross national production (GNP), according to the SNA definition as consumption plus investment plus exports, for the residuals we receive a share about 12 times higher than GNP. From this point of view, the focus is now on the transformation matrix, to find some characteristics of the pathways of the secondary (intermediate) production. In brief, because we are dealing with a highly linear order of production activities we have a straight pathway of material transformation where cycles are largely absent.

In general, cycles can be understood as a deviation from a strictly triangular input-output table (transformation matrix). In practice, the structure of input-output tables is a mixtum compositum ranging between two extremes, from the totally linear case on the one hand to the totally circular case on the other hand. It is assumed that a certain degree of linearity can be seen as a necessary working condition of a production system. A linear structure is inherent in almost every empirical input-output table and can be made visible (through 'triangularization'). Conversely, the same can be said of the degree of interdependence or circularity.

A triangular matrix is the result of the so-called 'triangularization'; that is, a systematic reordering of the j sectors such that out of a set of p =j! (in our casep = 6! = 720) orders, in the matrix of the final order, the total of the values above the main diagonal is maximal. The triangularization method is generally applicable to quadratic matrices, say an input-output matrix or a voting matrix. This method has a long tradition in the context of economic input-output analysis. In a totally triangular matrix there are only zeros below the main diagonal, a situation which Roubens and Vincke (1985, p. 16) denote as 'total order structure'.

This case corresponds to a (strong) transitive overall final order of activities. Normally, the activities of a given input-output table are not ordered optimally for purposes of revealing the order structure. Thus triangularization can be understood as a method for testing and displaying the degree of achievement of a (strong) transitive overall order of activities.

After triangularization this degree, X, called 'degree of linearity' in the context of input-output matrices, is defined as follows:

As 8 is the degree of 'feedback' or 'circularity', we have to take the complementary value (1 -X). The factor 2 is chosen because the minimum value of X is 0.5.

If we have only zeros below the main diagonal, then X= 1. In this case, the complementary 'degree of interdependence', 8, is minimized: 8 = 0. The degree of linearity, X, and the degree of interdependence, 8, combine as follows:

The degree of interdependence is defined as

The German PIOT yields the following degrees:

degree of linearity: \ = 0.96, degree of interdependence/circularity: 8 = 0.08.

These measures are near their extreme values (maximum/minimum); that is, the degree of linearity is very high and, conversely, the degree of interdependence/circularity is very low.3 To present these results in a more meaningful form, the triangularized PIOT is filtered and transformed into Boolean form. Its elements are set equal to 1, if x,, > x„ , and

J Jl equal to 0, otherwise. Table 10.4 shows the extremely linear organization of the production system; that is, when the activities are presented in the order E, C, M, I, H, P, the result is a complete triangular matrix. That means that the primary material input is transformed along this activity chain without any feedback circuits. Not even environmental protection services (activity 6) creates a feedback.

Table 10.4 Filtered triangularized PIOT

2 E 1111

This result, which is incompatible with the common idea of a recycling economy (at least in Germany), underlines the crude fact that the German economy is a typical throughput economy (see below).

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