A PIOT is a tabular scheme in which nactivities (‘production processes’ or ‘sectors’) are represented by both their material inputs and outputs in physical units (for example, 1000 tons). The inputs are detailed by origin categories in the columns and the outputs are detailed by destination categories in the rows. Normally the same categories are used for both rows and columns, but it is possible to construct (non-square) matrices with different
102
source and destination categories. Only the square matrix case is considered here. For ease of illustration, the input and output sides are considered separately. When the two parts (Tables 10.1a and 10.1b) overlap what results is the typical rectangular scheme of an input–output table with three quadrants (Table 10.1c). The fourth quadrant is omitted because it does not correspond to any ‘real’ economic transformation according to the intention of exclusive representation of activities with respect to the composition either of inputs or of outputs (formally speaking, it contains only so-called ‘counter-bookings’).
Table 10.1 can be explained as follows. As compared with a traditional monetary input–output table (MIOT) in a PIOT the quadrants II and III are subdivided into two components, A and B, respectively. One may suppose that the components I, IIA and IIIA correspond to a MIOT (for modifications see below). Then, for a PIOT it is essential to add the material/energy components IIB and IIIB, which are omitted in a MIOT.
To be complete in terms of a material balance and to show the total production on the input side and the output side as well, in a PIOT it is necessary to include two compo- nents, primary input and final disposal. The direct inputs from nature may be in gaseous, Table 10.1(a) Components of the input side of a PIOT
P1 Pn
• Secondary
• (intermediate) Primary inputs A Primary inputs B Total input
• inputs Pn
(b) Components of the output side of a PIOT
P1 Pn
• Secondary
• (intermediate) Final output A Final output B Total output
• outputs Pn
(c) Scheme of a PIOT with five components (I, IIA, IIB, IIIA, IIIB)
I II
Transformation matrix Final production
A B
III Primary input
A B
ActivitiesActivities
solid or fluid form. These inputs are typical primary inputs because they are natural resources not produced within the economy (quadrant IIIB). The outputs of residuals, in terms of solid,fluid and gaseous residuals (quadrant IIB) are then added to the output side.
The extension of the primary input component to include the primary natural resources component (quadrant IIIB) is due to the fact that the products of the economic production system are only transformation products which require a corresponding pro- vision of primary natural resources of low entropy. Without such a supply of energetic and material inputs the economic production system would not be viable, because it is not able to create these products itself. As these primary inputs cross the boundary of the eco- nomic production system, one can speak of quasi-imports.
In physical terms, economic production is defined as the transformation of a set of energetic and material inputs by a specific production activity into another set of ener- getic and material outputs. These outputs are either main products, included in the final output component (IIB), or joint by-products, so-called ‘waste’ (gaseous, solid, fluid residuals), included in the final production component IIB. As these final outputs cross the boundary of the economic production system back to the environment, one can speak of quasi-exports.
In a MIOT these inputs and outputs, although representing the greatest portion of total production, are excluded. From this it follows that a MIOT generally can only represent a relatively small part of total material production. Of course, it cannot meet the condi- tion of a material balance.
A PIOT, as described above, represents the idea that in the economic production system, which is an open subsystem of a finite and non-growing ecosystem (environment), the economy lives by importing low-entropy matter energy (raw materials) and exporting high-entropy matter energy (waste) (Daly 1991a, p. xiii). Capital proper and labor are con- ceived of as funds or agents that transform the flow of natural resources into a flow of products. The added components on the input and on the output side represent the one- way flow beginning with resources and ending with waste, and can be thought of as the digestive tract of an open biosystem that connects them to their environment at both ends (Daly 1995, p. 151). In this sense, a PIOT is a descriptive scaffold for the one-way flow or
‘entropic flow’ through the economic production system (ibid.).
There are three other quadrants of a MIOT to consider: the transaction or transforma- tion matrix (quadrant I),final production A, normally called final demand accounting (quadrant IIA) and primary input A, normally called value-added accounting (quadrant IIIA). In terms of the System of National Accounts (SNA) final demand corresponds to the gross national product account (consumption plus gross investment plus exports minus imports) and primary input A to the gross national income account including wages, interests, rents and profits and depreciation and public transfers.
In this physical context, instead of the monetary value-added accounting we have, as its physical counterpart, a physical fund-oriented accounting which includes the material inputflows needed for maintaining the funds intact.2In the broader context of a PIOT, the services of the funds used as inputs for economic production can be recorded, even though they are not material. From this point of view, Stahmer introduced time units into physical input–output accounting (see Stahmer 1999).
A PIOT, because it incorporates materials balances, overcomes the conventional bias
of national accounting which is based on the vision of the economic process as an iso- lated circular flow from firms to households and back again, with no inlets or outlets, (Daly 1995, p. 151). Hence the accounting is concentrated on the completeness of the materials balance and not on the correspondence of the final demand component (IIA) to the value-added component (IIIA) as in conventional (monetary) national accounting.
Consequently, in a PIOT, households play a different role and can be included in the trans- action matrix as a quasi-production activity.
EXAMPLE: A PIOT FOR GERMANY, 1990; A FUNCTIONAL SIX-SECTOR VERSION
An aggregated version of the original PIOT has been used to create Table 10.2. It has been modified to reflect aspects of a bioeconomic approach proposed by Georgescu-Roegen (1971, 1984) and modified by Strassert (1993, 1997). A general outline of this approach is shown here.
The transaction matrix includes the following six production activities:
M: procurement of raw materials for processing through extraction of matter in situ;
E: procurement of effective (available) energy (fuel) through extraction of energy in situ;
I: production of new capital goods (investment), capital fund (assets) and maintenance goods (servicing);
C: production of consumer goods for manufacturing and private households;
H: household consumption activities, transformation of consumer goods;
P: environmental protection services, collection and recycling of residuals in the same establishment and further treatment in external protection facilities or storage in controlled landfills.
For a first characterization of the physical production system of West Germany (‘Old Länder’, 1990) we look at the characteristic relations/shares which are represented in the total input column and total output row or, equivalently, in the corresponding (aggre- gated) production account (Table 10.3).
On the input side, starting from the bottom, we see that 78.8 per cent of the total con- sists of primary (raw) material inputs from nature; that is, natural resources in solid,fluid and gaseous condition, which are transformed by all production activities (including private households) into a set of outputs. Since the de-accumulations of stocks and fixed assets are only a tiny percentage, the total primary material input amounts to less than 79 per cent of total input. The remainder (about 21 per cent of total input) belongs to total secondary or transformation production; that is, the intermediate production of all pro- duction activities including that of private households.
What is the result? Starting now from the top on the output side,first comes interme- diate production (about 21 per cent). Next comes final main products in terms of accu- mulation of stocks and fixed assets (material gross investment) plus exports minus imports, with a share of less than 1 per cent, and, third, total final by-production of material residuals or waste, in solid,fluid and gaseous condition, with a share of about 79.0 per cent.
106
M E I C H
Output Extraction Extraction Production Production Household of matter of energy of capital of consumer consumption
in situ in situ goods goods
Input 1 2 3 4 5
1 M Extraction of matter in situ 295.1 0.1 551.8 189.3 22.5
2 E Extraction of energy in situ 3.8 38.1 0.6 292.9 2.5
3 I Production of capital goods 0.2 0.2 8.3 7.7 4.6
4 C Production of consumer goods 268.2 81.4 210.8 3 661.5 3 052.4
5 H Household consumption 0.0 0.0 0.0 0.0 0.0
6 P Environmental protection 20.4 0.0 21.1 35.7 0.2
7 II Intermediate input 587.7 119.8 792.6 4 187.1 2 082.2
8 PI-A Primary input A: de-accumulation 0.0 0.0 0.0 0.0 0.0
9 PI-B Primary input B: materials from nature 1 705.4 1 985.2 389.3 41 627.2 280.4
Gaseous 640.0 1 151.5 168.9 0.7 0.0
Solid 702.7 825.2 197.1 41 142.5 59.0
Fluid 362.7 8.5 23.3 484.0 221.4
10 TI Total input 2 293.1 2 105.0 1 181.9 45 814.3 3 362.6
107
P IO FO-A FO-B TO
Output Environmental Intermediate Final output Final output Total protection output A: accumulation B: residuals output
(investment) (gaseous, solid, and net exports fluid)
Input 6 7 8 9 10
1 M Extraction of matter in situ 41.8 1100.6 10.3 1 182.2 2 293.1 1
2 E Extraction of energy in situ 40.4 378.3 115.7 1 842.4 2 105.0 2
3 I Production of capital goods 214.2 235.2 603.7 343.0 1181.9 3
4 C Production of consumer goods 1 579.5 8 853.8 10.1 36 950.4 45 814.3 4
5 H Household consumption 2 647.6 2 647.6 12.6 702.4 3 362.6 5
6 P Environmental protection 14.1 91.5 12.0 7 976.9 8 080.4 6
7 II Intermediate input 4 537.6 13 307.0 533.6 48 997.3 62 837.3 7
8 PI-A Primary input A: de-accumulation 19.9 19.9 9 PI-B Primary input B: materials from nature 3 522.9 49 510.1
Gaseous 0.0 1 961.1
Solid 3 501.1 46 427.6
Fluid 21.8 1 121.7
10 TI Total input 8 080.4 62 837.3
To get an overall picture, an efficiency indicator (e) can be used (for an ecological context, see Ulanowicz 1986; for an economic context, see Strassert 2000c). From the pro- duction account (Table 10.3) one can derive the gross production equation,
TPISISOFPAFPB (10.1)
where
TPItotal primary input, SI secondary input, SO secondary output, FPAfinal production A, FPBfinal production B.
So
1FPA /TPIFPB/TPI (10.2)
or
1yr (10.3)
Efficiency (e) is defined as
e1–ry. (10.4)
Using the numerical data from the production account (Table 10.3) efficiency (e) comes to:
e148.997/49.51010.990.01 (10.5) The results presented support the hypothesis that the German economy can be charac- terized as a throughput economy (Strassert 2000a). The transformation capacity of the Table 10.3 Production account of the German PIOT, 1990, million tons
Input Output
Type MT % MT %
Intermediate production 13 307 21.2 13 307 21.2
Primary input A: de-accumulation (stocks, 20 0 533 0
fixed assets)
Primary input B: (raw) material from nature 49 510 78.8 48 997 78.8
Solid 1 961 3.1 1 648 3.1
Fluid: process water 6 041 9.6 6 125 9.6
throughput water 40 387 64.3 40 387 64.3
Gaseous 1 122 1.8 1 122 1.8
Total 62 837 100 62 837 100
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, tofind some characteristics of the pathways of the secondary (intermediate) pro- duction. In brief, because we are dealing with a highly linear order of production activ- ities 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 compositumranging 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 jsectors such that out of a set ofpj! (in our case p6!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 overallfinal order of activities. Normally, the activities of a given input–output table are not ordered optimally for purposes of reveal- ing 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, , called ‘degree of linearity’ in the context of input–output matrices, is defined as follows:
ij(Cij) / ij(Cij) 0.5 1 (10.6) The degree of interdependence is defined as
2(1). (10.7)
As is the degree of ‘feedback’ or ‘circularity’, we have to take the complementary value (1). The factor 2 is chosen because the minimum value ofis 0.5.
If we have only zeros below the main diagonal, then 1. In this case, the complemen- tary ‘degree of interdependence’,, is minimized:0. The degree of linearity,, and the degree of interdependence,, combine as follows:
1 and 0 0.5 and 1
The German PIOT yields the following degrees:
degree of linearity:0.96,
degree of interdependence/circularity: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.3To present these results in a more meaningful form, the triangularized PIOT is fil- tered and transformed into Boolean form. Its elements are set equal to 1, ifxij> xji, and equal to 0, otherwise. Table 10.4 shows the extremely linear organization of the produc- tion 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 trans- formed along this activity chain without any feedback circuits. Not even environmental protection services (activity 6) creates a feedback.
Table 10.4 Filtered triangularized PIOT
E C M I H P
2 4 1 3 5 6
2 E 1 1 1 1 1
4 C 0 1 1 1 1
1 M 0 0 1 1 1
3 I 0 0 0 1 1
5 H 0 0 0 0 1
6 P 0 0 0 0 0 0
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).