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The energy cost of goods and services in the Federal Republic of Germany
The energy cost of goods and services in the Federal Republic of Germany
Richard V. Denton
Recent studies of energy costs in national economies have tended to concentrate on the UK and t h e US. This study applies i n p u t - o u t p u t analysis t o t h e economy of t h e Federal Republic of Germany, It indicates that foreign trade in n o n e n e r g y products has a great i m p a c t on t h e n a t i o n a l energy balance w i t h energy contained in exports b e i n g l a r g e r t h a n i m p o r t s by about 2 5 % . It is h o p e d t h a t t h e general results s h o u l d be useful in comparing energy costs in various economies although explicit comparisons between countries of energy costs per final demand are complicated by t h e f a c t t h a t currency exchange rates do not correspond t o t h e rates which should be used w h e n m a k i n g energy comparisons. The a u t h o r is w i t h the Institute for Systems Analysis (ISI), D 75 Karlsruhe-Waldstadt, Breslauer Str. 48, Federal Republic of G e r m a n y The research was supported by Siftung Volkswagenwerk and conducted in association with the Mesarovic-Pestel World Model Project.
* 1 tSKE" 108 kilocalories - 8139.5 kWh. 1 Deutsches Institut fihr Wirtschaftsforschung (DIW), Quarterly Report 1-74, Dunckner & Humblot Press, Berlin, 1974. z DIW Weekly Report, Berlin, 10 January 1974. Provisional results for 1970, using a different classification than the one in the DIW tables, are available in 'Wirtschaft und statistik', Statistische~ Bundesamt Wiesbaden, March 1974.
In calculating sectoral energy cost per final demand, the 1967 inputoutput tables, at 1967 prices, computed by the German Institute for Economic Research (DIW), have been applied. 1 Although these tables are now eight years old they do represent the most recent complete tables available at the present time. 2 The D I W tables for 1970 should be available towards the end of 1975. Data on the energy flows have been taken from Energy Balances of the Federal Republic of Germany? Their use is convenient since all the energies have been converted to a common energy unit - tonnes of coal equivalent (tSKE*). Furthermore, the raw data contributed by the member organizations in the 'Working Group for Energy Balances' has been analysed and refined in order to remove inconsistencies due to differences in the data collection bases. However, economic data compilation is not necessarily the same as energy data collection. As a result, directly matching up the energy data with the sectors in the input-output tables is no trivial task. One way of proceeding is to aggregate the input-output tables so that they correspond to the available energy data. Here the 56 sector D I W input-output table has been aggregated to 26 sectors. In spite of this aggregation there are still a number of difficulties. The usual problems relating to coupled production processes have to be dealt with, such as when coal is consumed both to produce briquettes, to be sold by the coal sector, and gas, to be delivered to the gas sector. Although the overall energy consumption is accounted for, the actual sectoral energy cost results depend upon the allocations chosen for each sector. Secondly, the sector household-commercial invariably represents a very heterogeneous set of end users, and in fact is a 'catch-all' for energies not accounted for elsewhere in the statistics. Finally, the import coefficient AMk of Equation (9) (See Appendix for Equations (1)-(10)) can be obtained readily from the input-output table, but unfortunately this is not the case for the matrix elements mk which describe the composition of imports going into each sector. At present we have contented ourselves with making plausible estimates of a mk based upon the German economy; the resulting total energy costs ef will be seen to increase considerably from the initial values ej for some sectors, ie energy costs associated with imports are significant for some sectors. Specific details are available elsewhere. 4
ENERGY POLICY December 1975
279
The energy costs of goods and services in ~he I:R G 'Energiebilanzen der Bundesrepublik Deutschland' Verlags und
Results
The initial sectoral energy costs, obtained with the use of Equation (5). are displayed as the diagonally lined area in Figure 1. The energy Working paper, ISI, July 1 9 7 5 sectors generally have a high energy intensiveness, the coal sector be(unpublished). ing highest with 31.3 kWh per German mark of 1967. We note that most of the contribution to the energy costs of the coal mining and petroleum refining sectors are due to the fairly large quantities of energy supplied directly to final demands, the terms Eh/Y~ and E~y/Y5 of Equation (4) being large. The apparently low value shown for domestic petroleum and natural gas extraction is a result of'allocating away' the energy in this sector to the petroleum refining sector, in order to avoid the problem of double-counting. F i g u r e 1: Energy costs per sectoral The gas and water sector also has a lower energy intensiveness final d e m a n d in k w h per 1 9 6 7 than the remaining three energy sectors. The gas and water works are Wirtschaftsgesellschaft Elektrizit~itswerke mbH Frankfurt (Main), 1971.
der VWEW,
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ENERGY
POLICY
December
r~
1975
The energy costs of goods and seta,ices in the FRG
lumped together in the DIW input-output tables and were not disaggregated in the present implementation. If this disaggregation were carried out, with water works properly being included among the other energy user sectors, then the gas sector by itself would presumably have an energy intensiveness comparable to the other energy producing sectors. Nevertheless, effects related to the energy sectors do not significantly affect the energy costs obtained for the remaining sectors. Of these, iron and steel production has the highest energy intensiveness (14.9 kWh/German mark), while the two sectors, electrical engineering, precision and optical goods and wood working, musical instruments, etc, have the lowest (2.16 kWh/German mark). Energy costs associated with consumption of energy for nonenergy purposes, such as chemical feedstocks, lubrication of machinery, etc, can also be included. Data on the distribution of these energies to the various sectors are not generally available, but a reasonable estimate for the German economy is that 15% goes to transport, 60% goes into chemicals, and the remaining 25% is distributed roughly proportionally into the other production sectors (excluding the energy sectors, which have already been accounted for), with these latter proportions being determined by their consumption of petroleum fuels. The resulting energy costs are also shown in the histogram Figure 1. Comparison with the initial energy costs shows, as one would expect, that the energy costs associated with chemicals have been most affected with a relative increase of 44%. The next largest change is for plastics manufactures, due to the large share of chemicals going into plastics production. In the final part of the calculation the energy costs ej were inserted into Equation (10) in order to obtain the total energy costs per final demand ef, which include the energies hidden in imported products. It can be seen in Figure 1 that the non-ferrous metals sector has the largest relative increase (64%). This is due to the inclusion of the relatively high energy costs associated with the foreign mining operations. Although the iron and steel production sector also had additional costs associated with foreign mining operations, relatively more of these costs are allocated to the final demands in other sectors. As a result there is only a relative increase of 10% for the iron and steel sector itself. Whether or not the additional costs due to imports should be counted in an energy analysis depends, as emphasised elsewhere, 5 on the purpose to which the energy analysis is being put.
Import-export energy balance
s See for example the series of articles in Energy Policy: P.F. Chapman, 'Energy costs: a review of methods', Vol 2, No 2, June 1974; P.F. Chapman, G. Leach and M. Slesser, "The energy cost of fuels," Vol 2, No 3, September 1974; D.J. Wright, 'Goods and services: an input-output analysis', Vol 2, No 4, December 1974. CDie Wirtschaft 1973, Deutscher Taschenbuchverlag, 1973.
The energy costs from the last section can be used to examine an energy balance related to imported and exported products. For this purpose the sectoral trade balances of 1970, deflated to 1967 prices, have been u s e d . 6 Multiplication of product imports and exports with the energy cost ef results in the qualitative picture shown in Figure 2. The picture is only 'qualitative' because of the usual problems of associating each of the individual products with an appropriate sector. The situation is typical of a country not overly rich in raw materials, so that import purchases are greater than exports for most of the primary industries. The energy flows reflect this, with the excess of import over export energies also being shown in the histogram.
ENERGY POLICY December 1975
281
The energy costs of goods and services in the FRG 109kWh
-50
....
- 25
~:::::::~:::;:::::::~
-50
Figure 2 : Import-export balance of the FRG economy
energy
The chemicals sector is a major exception among the primary sectors, since the significant chemical imports are compensated by an even greater volume of exported finished chemical products. Investment goods, starting with the machinery sector, show net exports of energy. The transport sector is not shown since it was not included as a separate entity in the data. (Presumably transport costs were included within the individual import and export product prices, and a more accurate treatment would disaggregate this information.) The relatively large imports shown for the last sector, household and commercial, is mainly due to the inclusion of most agricultural products. West Germany has large net imports of agricultural products. The histogram shows a net energy export of about 107x109 kWh, energy exports being larger than imports by about 25%. There is no reason to expect an exact balance between the two, since this section has dealt only with the energies allocated to products. T h e actual net energy imports into the energy sectors in 1970, which are not shown in the figure, amounted to 1390x 109 kWh.
Concluding remarks No explicit comparisons have been made of the energy costs obtained for other countries. Considerable care is required, since currency exchange rates do not necessarily correspond to the rate which should be used in making energy cost comparisons. For example, the energy costs calculated for household appliances in the US in 1963 were 18.8 kWh/196352 In terms of the exchange rate in 1963, which was 4 marks -- 1 dollar, this would be 4.7 kWh/1963 mark. Since that time there has been a clear recognition that the dollar was overvalued 282
ENERGY POLICY December 1975
The energy costs of goods and services in the FR G
compared with the mark. For the purpose of making a comparison with similar German household appliances of 1963 the value 4.7 would probably be too low a value to use. Conversely, a calculation in real terms (ie inflation corrected), using the present exchange rate, could well be too favourable to the mark. Related problems arise when one tries to correct for inflation. A complete correction would involve inflators for each sector. However, reasonable average corrections can be obtained by reducing the results given in the present paper by 1.5, since 1 mark of 1967 = 1.50 marks of 1975 as measured by the price index of the Gross Domestic Product. 7 This of course does not mean that the energy costs are reduced in real terms! We have also included the imports in the energy cost calculation, and the procedure above glosses over the differences between the domestic inflation rate and the generally higher inflation experienced by other countries. On the one hand, it can be argued that the domestic price levels respond to import price increases, and thus the domestic price index eventually accounts for higher import prices. On the other hand, sufficiently large price increases will tend to induce substitution effects wherever possible; this, however, is outside the realm of the present static calculation. Appendix: The method In the standard input-output formalism the interrelationships of an n-sector economy in any given year are described through the equation
Eik Elk = - - X k Xk Eik n = --Z
[(1
Vp
A) - 1 ]
Xkp= l
kp
H
Xi = Y" ]:1
Ai/Xj + Y i
(1)
where Xi is the total output of sector h Yi is the output of sector i sold to the
Ei = k = l p~=
sector final demand, and Aij is the sales of sector i to sector j divided by the total output of sector j. Because of the long time constants involved in the introduction of new technologies, the coefficients A/j, which to a certain extent reflect the underlying technologies of an economy, are assumed to be essentially constant. Thus to obtain A0 it suffices to collect data for a single year in the recent past. Herendeen s introduces energy by writing down the energy flows from each of the energy sectors:
+ E~K yi
/7
z 'Statistische Beihefte in den Monatsberichten der Deutschen Bundesbank,' seasonally adjusted, June
E i = ~Z Elk + Eiy k=1
(2)
edited by M.S, Macrakis, The MIT Press,
where Ei = total energy output in (kWh) of energy sector i, Ei/~ = energy sales (kWh) for i to k, Eiy = energy (kWh) of type i sold to final demand. He then writes for each Elk, with the use
1974.
of Equation (1),
1975.
s R.A. Herendeen, 'Use of Input-Output Analysis to Determine the Energy Cost of Goods and Services,' in Energy: Demand, Conservation and Institutional Problems,
Inserting this into E q u a t i o n (2), one has
ENERGY POLICY December 1975
E~i--kxz-[ ( l - A ) I ]kpYP
Yi
13)
He defines for convenience Rik = E i k / X k and _ E i y / Y i i = k = one of the energy sectors Sik - O, otherwise.
Written in vector notation his result is equivalently
E = [R ( l - A ) - / + S] Y= eY
(4)
which defines the energy matrix e. Once the data have been collected and the energy matrix e has been calculated according to Equation (3), the energy flows from each of the energy sectors for a given year are determined if the final demands are specified. In the present paper we are interested in calculating the energy costs ej for the economy of the Federal Republic of Germany, as obtained by summing the
283
The energy costs of goods and serviees in the FRG elements e/j of the energy matrix over all energy sectors i:
ej = Z el/ i = ~, Rip [ ( l - A ) 1] pj+ Sj k i,p
(5)
An element ej gives the total consumption of energy from all energy sectors necessary for the economy to deliver a unit monetary value of a product from sector j to final demand
vj. The terms of E# in Equation (3), where i=k, can be taken to be the consumption of energy within the energy sector i; this internal consumption is then allocated to the 'true' users, final demands, Yj in Equation (3). Also a direct application of Equation (3) would account for some energies twice, and therefore the sum of Equation (3) over all energy sectors i would add up to more energy than is actually consumed in the economy in any given year. For example, the coal sector provides (primary) energy for the generation of electricity m the electricity sector, and in turn the electricity sector supplies (secondary) energy back to the coal sector. Adding both of these flows would involve double-counting of energies. This problem can be avoided by following Herendeen's suggestion of initially allocating ~he relevant primary energies to the secondary energy producing sectors. In the example above any coal used in the electricity producing sector is to be included within the electricity sector itself, and the flow Ecoal --+ eleetriciO'is set equal to zero. After calculation of the energy matrix using the method, the primary energies which have been included in the secondary sectors must be allocated back to their original sectors by introducing a new allocation matrix C (for details see Herendeen). However, we are only interested here in calculating ei = Eeii ' and it turns out that this final reallocation is not necessary. The fact that the total energy must be conserved in the reallocation places certain mathematical constraints on the elements of C, and as a result the matrix C drops out in the sum over i in the calculation of ej. So far this procedure allocates all energies used in the domestic market to
284
final demands. For some purposes it is reasonable to include, in addition, the energy costs associated with products which are imported into the domestic market. (It would be misleading to state a low energy cost associated with some final demand item if all energy intensive operations in its manufacture have been transferred outside the country.) In the following we describe a procedure which allocates these additional energies associated with imports to their respective final demands. Total imports XM are distributed to the various manufacturing sectors Xk and to final demand for imports YMf according to
XM = ~k AMk Xk + YMf where Amk is the sales of imports to sector k divided by total output of sector k (for energy sectors 'sales of imports' excludes actual energy imports, since these have already been counted in Equation (3); it refers only to the 'non energy' products). In turn, an added energy flow is to be associated with these imports:
EM = 2 ek AMk Xk + eM[ YMf k =EekAMk
k.p
+ eMf YMf
[(l-A)
1] kp yp (6)
Here the energy cost factor ~k is the energy per unit monetary value of the products which are imported into sector k, and eMf is a similar factor corresponding to final demand for imports. The previous results, Equations (4) and (5), are then combined with Equation (6) to give the total energy cost (including imports) of a sector p, here denoted by eT ; epT=ep + ~-"ek AMk [ ( 1 - A ) - I ] k p k (7) To calculate epT we require the energy cost factors ~k, which have not yet been given. Obviously, if Ek had to be determined for all countries which contribute to imports, the calculation would be somewhat time-consuming. A way to avoid this unpleasantness is to assume that the sectoral energy costs of other countries is the same as the corresponding sector of the Federal Republic. Then the simplest
approximation to ~k would be a single weighted average of the ej values calculated from Equations (4) and (5), with the weighting related to the sectoral composition of the imports, and then to set all the ~k equal to this result. Averages however can be misleading and, at the expense of adding a distribution matrix O~pk the energy cost factors ~k can be expressed in a better approximation as
ek = ~, e ; apk
(8)
The matrix element O~pk gives the fractional share of the imports going into sector k which have the energy cost of sector p of the domestic market. Since the total of the fractional shares for a branch k must add up to I, one has ~; 1. Also, we note again that p apk ~k for an energy sector k refers to nonenergy imports into k, since energy imports are already counted in Equation =
(4). The use of ~eT instead of just ep from Equation (5) can be interpreted fairly simply. In order to calculate the total energy cost of the sectoral final demands, including the energy hidden in imports, one must treat the energy cost of the imports themselves with the same convention. (Another country would calculate its own total energy costs including its imports, say epT!, and a closed solution is obtained by our assumption e
1 = eT P
Combination of Equations (7) and (8) results in the following expression for
eT : p eT = e p + E e T m G m p rn
(9)
where
Gmp =Y~amkAMk [(1
A)-l]kp
g?l
The solution in vector notation is e T =e. (l~J) -1
(1 O)
In the above e is the sectoral energy cost excluding imports as obtained in Equation (5). Multiplication with the inverse matrix (l-G) -I provides the additional energy costs hidden in imports which must be added to the sectoral final demands, to give the total energy costs.
E N E R G Y P O L I C Y December 1975
Richard V. Denton
Recent studies of energy costs in national economies have tended to concentrate on the UK and t h e US. This study applies i n p u t - o u t p u t analysis t o t h e economy of t h e Federal Republic of Germany, It indicates that foreign trade in n o n e n e r g y products has a great i m p a c t on t h e n a t i o n a l energy balance w i t h energy contained in exports b e i n g l a r g e r t h a n i m p o r t s by about 2 5 % . It is h o p e d t h a t t h e general results s h o u l d be useful in comparing energy costs in various economies although explicit comparisons between countries of energy costs per final demand are complicated by t h e f a c t t h a t currency exchange rates do not correspond t o t h e rates which should be used w h e n m a k i n g energy comparisons. The a u t h o r is w i t h the Institute for Systems Analysis (ISI), D 75 Karlsruhe-Waldstadt, Breslauer Str. 48, Federal Republic of G e r m a n y The research was supported by Siftung Volkswagenwerk and conducted in association with the Mesarovic-Pestel World Model Project.
* 1 tSKE" 108 kilocalories - 8139.5 kWh. 1 Deutsches Institut fihr Wirtschaftsforschung (DIW), Quarterly Report 1-74, Dunckner & Humblot Press, Berlin, 1974. z DIW Weekly Report, Berlin, 10 January 1974. Provisional results for 1970, using a different classification than the one in the DIW tables, are available in 'Wirtschaft und statistik', Statistische~ Bundesamt Wiesbaden, March 1974.
In calculating sectoral energy cost per final demand, the 1967 inputoutput tables, at 1967 prices, computed by the German Institute for Economic Research (DIW), have been applied. 1 Although these tables are now eight years old they do represent the most recent complete tables available at the present time. 2 The D I W tables for 1970 should be available towards the end of 1975. Data on the energy flows have been taken from Energy Balances of the Federal Republic of Germany? Their use is convenient since all the energies have been converted to a common energy unit - tonnes of coal equivalent (tSKE*). Furthermore, the raw data contributed by the member organizations in the 'Working Group for Energy Balances' has been analysed and refined in order to remove inconsistencies due to differences in the data collection bases. However, economic data compilation is not necessarily the same as energy data collection. As a result, directly matching up the energy data with the sectors in the input-output tables is no trivial task. One way of proceeding is to aggregate the input-output tables so that they correspond to the available energy data. Here the 56 sector D I W input-output table has been aggregated to 26 sectors. In spite of this aggregation there are still a number of difficulties. The usual problems relating to coupled production processes have to be dealt with, such as when coal is consumed both to produce briquettes, to be sold by the coal sector, and gas, to be delivered to the gas sector. Although the overall energy consumption is accounted for, the actual sectoral energy cost results depend upon the allocations chosen for each sector. Secondly, the sector household-commercial invariably represents a very heterogeneous set of end users, and in fact is a 'catch-all' for energies not accounted for elsewhere in the statistics. Finally, the import coefficient AMk of Equation (9) (See Appendix for Equations (1)-(10)) can be obtained readily from the input-output table, but unfortunately this is not the case for the matrix elements mk which describe the composition of imports going into each sector. At present we have contented ourselves with making plausible estimates of a mk based upon the German economy; the resulting total energy costs ef will be seen to increase considerably from the initial values ej for some sectors, ie energy costs associated with imports are significant for some sectors. Specific details are available elsewhere. 4
ENERGY POLICY December 1975
279
The energy costs of goods and services in ~he I:R G 'Energiebilanzen der Bundesrepublik Deutschland' Verlags und
Results
The initial sectoral energy costs, obtained with the use of Equation (5). are displayed as the diagonally lined area in Figure 1. The energy Working paper, ISI, July 1 9 7 5 sectors generally have a high energy intensiveness, the coal sector be(unpublished). ing highest with 31.3 kWh per German mark of 1967. We note that most of the contribution to the energy costs of the coal mining and petroleum refining sectors are due to the fairly large quantities of energy supplied directly to final demands, the terms Eh/Y~ and E~y/Y5 of Equation (4) being large. The apparently low value shown for domestic petroleum and natural gas extraction is a result of'allocating away' the energy in this sector to the petroleum refining sector, in order to avoid the problem of double-counting. F i g u r e 1: Energy costs per sectoral The gas and water sector also has a lower energy intensiveness final d e m a n d in k w h per 1 9 6 7 than the remaining three energy sectors. The gas and water works are Wirtschaftsgesellschaft Elektrizit~itswerke mbH Frankfurt (Main), 1971.
der VWEW,
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A d d i t i o n a l e n e r g y costs d u e to i m p o r t s
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ENERGY
POLICY
December
r~
1975
The energy costs of goods and seta,ices in the FRG
lumped together in the DIW input-output tables and were not disaggregated in the present implementation. If this disaggregation were carried out, with water works properly being included among the other energy user sectors, then the gas sector by itself would presumably have an energy intensiveness comparable to the other energy producing sectors. Nevertheless, effects related to the energy sectors do not significantly affect the energy costs obtained for the remaining sectors. Of these, iron and steel production has the highest energy intensiveness (14.9 kWh/German mark), while the two sectors, electrical engineering, precision and optical goods and wood working, musical instruments, etc, have the lowest (2.16 kWh/German mark). Energy costs associated with consumption of energy for nonenergy purposes, such as chemical feedstocks, lubrication of machinery, etc, can also be included. Data on the distribution of these energies to the various sectors are not generally available, but a reasonable estimate for the German economy is that 15% goes to transport, 60% goes into chemicals, and the remaining 25% is distributed roughly proportionally into the other production sectors (excluding the energy sectors, which have already been accounted for), with these latter proportions being determined by their consumption of petroleum fuels. The resulting energy costs are also shown in the histogram Figure 1. Comparison with the initial energy costs shows, as one would expect, that the energy costs associated with chemicals have been most affected with a relative increase of 44%. The next largest change is for plastics manufactures, due to the large share of chemicals going into plastics production. In the final part of the calculation the energy costs ej were inserted into Equation (10) in order to obtain the total energy costs per final demand ef, which include the energies hidden in imported products. It can be seen in Figure 1 that the non-ferrous metals sector has the largest relative increase (64%). This is due to the inclusion of the relatively high energy costs associated with the foreign mining operations. Although the iron and steel production sector also had additional costs associated with foreign mining operations, relatively more of these costs are allocated to the final demands in other sectors. As a result there is only a relative increase of 10% for the iron and steel sector itself. Whether or not the additional costs due to imports should be counted in an energy analysis depends, as emphasised elsewhere, 5 on the purpose to which the energy analysis is being put.
Import-export energy balance
s See for example the series of articles in Energy Policy: P.F. Chapman, 'Energy costs: a review of methods', Vol 2, No 2, June 1974; P.F. Chapman, G. Leach and M. Slesser, "The energy cost of fuels," Vol 2, No 3, September 1974; D.J. Wright, 'Goods and services: an input-output analysis', Vol 2, No 4, December 1974. CDie Wirtschaft 1973, Deutscher Taschenbuchverlag, 1973.
The energy costs from the last section can be used to examine an energy balance related to imported and exported products. For this purpose the sectoral trade balances of 1970, deflated to 1967 prices, have been u s e d . 6 Multiplication of product imports and exports with the energy cost ef results in the qualitative picture shown in Figure 2. The picture is only 'qualitative' because of the usual problems of associating each of the individual products with an appropriate sector. The situation is typical of a country not overly rich in raw materials, so that import purchases are greater than exports for most of the primary industries. The energy flows reflect this, with the excess of import over export energies also being shown in the histogram.
ENERGY POLICY December 1975
281
The energy costs of goods and services in the FRG 109kWh
-50
....
- 25
~:::::::~:::;:::::::~
-50
Figure 2 : Import-export balance of the FRG economy
energy
The chemicals sector is a major exception among the primary sectors, since the significant chemical imports are compensated by an even greater volume of exported finished chemical products. Investment goods, starting with the machinery sector, show net exports of energy. The transport sector is not shown since it was not included as a separate entity in the data. (Presumably transport costs were included within the individual import and export product prices, and a more accurate treatment would disaggregate this information.) The relatively large imports shown for the last sector, household and commercial, is mainly due to the inclusion of most agricultural products. West Germany has large net imports of agricultural products. The histogram shows a net energy export of about 107x109 kWh, energy exports being larger than imports by about 25%. There is no reason to expect an exact balance between the two, since this section has dealt only with the energies allocated to products. T h e actual net energy imports into the energy sectors in 1970, which are not shown in the figure, amounted to 1390x 109 kWh.
Concluding remarks No explicit comparisons have been made of the energy costs obtained for other countries. Considerable care is required, since currency exchange rates do not necessarily correspond to the rate which should be used in making energy cost comparisons. For example, the energy costs calculated for household appliances in the US in 1963 were 18.8 kWh/196352 In terms of the exchange rate in 1963, which was 4 marks -- 1 dollar, this would be 4.7 kWh/1963 mark. Since that time there has been a clear recognition that the dollar was overvalued 282
ENERGY POLICY December 1975
The energy costs of goods and services in the FR G
compared with the mark. For the purpose of making a comparison with similar German household appliances of 1963 the value 4.7 would probably be too low a value to use. Conversely, a calculation in real terms (ie inflation corrected), using the present exchange rate, could well be too favourable to the mark. Related problems arise when one tries to correct for inflation. A complete correction would involve inflators for each sector. However, reasonable average corrections can be obtained by reducing the results given in the present paper by 1.5, since 1 mark of 1967 = 1.50 marks of 1975 as measured by the price index of the Gross Domestic Product. 7 This of course does not mean that the energy costs are reduced in real terms! We have also included the imports in the energy cost calculation, and the procedure above glosses over the differences between the domestic inflation rate and the generally higher inflation experienced by other countries. On the one hand, it can be argued that the domestic price levels respond to import price increases, and thus the domestic price index eventually accounts for higher import prices. On the other hand, sufficiently large price increases will tend to induce substitution effects wherever possible; this, however, is outside the realm of the present static calculation. Appendix: The method In the standard input-output formalism the interrelationships of an n-sector economy in any given year are described through the equation
Eik Elk = - - X k Xk Eik n = --Z
[(1
Vp
A) - 1 ]
Xkp= l
kp
H
Xi = Y" ]:1
Ai/Xj + Y i
(1)
where Xi is the total output of sector h Yi is the output of sector i sold to the
Ei = k = l p~=
sector final demand, and Aij is the sales of sector i to sector j divided by the total output of sector j. Because of the long time constants involved in the introduction of new technologies, the coefficients A/j, which to a certain extent reflect the underlying technologies of an economy, are assumed to be essentially constant. Thus to obtain A0 it suffices to collect data for a single year in the recent past. Herendeen s introduces energy by writing down the energy flows from each of the energy sectors:
+ E~K yi
/7
z 'Statistische Beihefte in den Monatsberichten der Deutschen Bundesbank,' seasonally adjusted, June
E i = ~Z Elk + Eiy k=1
(2)
edited by M.S, Macrakis, The MIT Press,
where Ei = total energy output in (kWh) of energy sector i, Ei/~ = energy sales (kWh) for i to k, Eiy = energy (kWh) of type i sold to final demand. He then writes for each Elk, with the use
1974.
of Equation (1),
1975.
s R.A. Herendeen, 'Use of Input-Output Analysis to Determine the Energy Cost of Goods and Services,' in Energy: Demand, Conservation and Institutional Problems,
Inserting this into E q u a t i o n (2), one has
ENERGY POLICY December 1975
E~i--kxz-[ ( l - A ) I ]kpYP
Yi
13)
He defines for convenience Rik = E i k / X k and _ E i y / Y i i = k = one of the energy sectors Sik - O, otherwise.
Written in vector notation his result is equivalently
E = [R ( l - A ) - / + S] Y= eY
(4)
which defines the energy matrix e. Once the data have been collected and the energy matrix e has been calculated according to Equation (3), the energy flows from each of the energy sectors for a given year are determined if the final demands are specified. In the present paper we are interested in calculating the energy costs ej for the economy of the Federal Republic of Germany, as obtained by summing the
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The energy costs of goods and serviees in the FRG elements e/j of the energy matrix over all energy sectors i:
ej = Z el/ i = ~, Rip [ ( l - A ) 1] pj+ Sj k i,p
(5)
An element ej gives the total consumption of energy from all energy sectors necessary for the economy to deliver a unit monetary value of a product from sector j to final demand
vj. The terms of E# in Equation (3), where i=k, can be taken to be the consumption of energy within the energy sector i; this internal consumption is then allocated to the 'true' users, final demands, Yj in Equation (3). Also a direct application of Equation (3) would account for some energies twice, and therefore the sum of Equation (3) over all energy sectors i would add up to more energy than is actually consumed in the economy in any given year. For example, the coal sector provides (primary) energy for the generation of electricity m the electricity sector, and in turn the electricity sector supplies (secondary) energy back to the coal sector. Adding both of these flows would involve double-counting of energies. This problem can be avoided by following Herendeen's suggestion of initially allocating ~he relevant primary energies to the secondary energy producing sectors. In the example above any coal used in the electricity producing sector is to be included within the electricity sector itself, and the flow Ecoal --+ eleetriciO'is set equal to zero. After calculation of the energy matrix using the method, the primary energies which have been included in the secondary sectors must be allocated back to their original sectors by introducing a new allocation matrix C (for details see Herendeen). However, we are only interested here in calculating ei = Eeii ' and it turns out that this final reallocation is not necessary. The fact that the total energy must be conserved in the reallocation places certain mathematical constraints on the elements of C, and as a result the matrix C drops out in the sum over i in the calculation of ej. So far this procedure allocates all energies used in the domestic market to
284
final demands. For some purposes it is reasonable to include, in addition, the energy costs associated with products which are imported into the domestic market. (It would be misleading to state a low energy cost associated with some final demand item if all energy intensive operations in its manufacture have been transferred outside the country.) In the following we describe a procedure which allocates these additional energies associated with imports to their respective final demands. Total imports XM are distributed to the various manufacturing sectors Xk and to final demand for imports YMf according to
XM = ~k AMk Xk + YMf where Amk is the sales of imports to sector k divided by total output of sector k (for energy sectors 'sales of imports' excludes actual energy imports, since these have already been counted in Equation (3); it refers only to the 'non energy' products). In turn, an added energy flow is to be associated with these imports:
EM = 2 ek AMk Xk + eM[ YMf k =EekAMk
k.p
+ eMf YMf
[(l-A)
1] kp yp (6)
Here the energy cost factor ~k is the energy per unit monetary value of the products which are imported into sector k, and eMf is a similar factor corresponding to final demand for imports. The previous results, Equations (4) and (5), are then combined with Equation (6) to give the total energy cost (including imports) of a sector p, here denoted by eT ; epT=ep + ~-"ek AMk [ ( 1 - A ) - I ] k p k (7) To calculate epT we require the energy cost factors ~k, which have not yet been given. Obviously, if Ek had to be determined for all countries which contribute to imports, the calculation would be somewhat time-consuming. A way to avoid this unpleasantness is to assume that the sectoral energy costs of other countries is the same as the corresponding sector of the Federal Republic. Then the simplest
approximation to ~k would be a single weighted average of the ej values calculated from Equations (4) and (5), with the weighting related to the sectoral composition of the imports, and then to set all the ~k equal to this result. Averages however can be misleading and, at the expense of adding a distribution matrix O~pk the energy cost factors ~k can be expressed in a better approximation as
ek = ~, e ; apk
(8)
The matrix element O~pk gives the fractional share of the imports going into sector k which have the energy cost of sector p of the domestic market. Since the total of the fractional shares for a branch k must add up to I, one has ~; 1. Also, we note again that p apk ~k for an energy sector k refers to nonenergy imports into k, since energy imports are already counted in Equation =
(4). The use of ~eT instead of just ep from Equation (5) can be interpreted fairly simply. In order to calculate the total energy cost of the sectoral final demands, including the energy hidden in imports, one must treat the energy cost of the imports themselves with the same convention. (Another country would calculate its own total energy costs including its imports, say epT!, and a closed solution is obtained by our assumption e
1 = eT P
Combination of Equations (7) and (8) results in the following expression for
eT : p eT = e p + E e T m G m p rn
(9)
where
Gmp =Y~amkAMk [(1
A)-l]kp
g?l
The solution in vector notation is e T =e. (l~J) -1
(1 O)
In the above e is the sectoral energy cost excluding imports as obtained in Equation (5). Multiplication with the inverse matrix (l-G) -I provides the additional energy costs hidden in imports which must be added to the sectoral final demands, to give the total energy costs.
E N E R G Y P O L I C Y December 1975