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Resources and Energy 6 (1984) 129-163. North-Holland
EMBODIES ENERGY AND ECONOMIC VALUE XN THE UNITED STATES ECONOMY: 1963, 1967 and 1972
Robert COSTANZA*
Louisiana State University, Baton Rouge, LA 70803, USA
Received October 1983, final version received February 1984
An economy con be said to operate on an energy theory of value if economic value can be shown to be proportional to an appropriate energy indicator. We have investigated this hypothesis for an 87 sector breakdown of the U.S. economy for the years 1963, 1967 and 1972. Input-output (I-G) models of the economy, modified to include households and government as endogenous sectors, were used to calculate each sector’s direct plus indirect (embodied) energy ~nsumption based on various estimates of the dist~bution of direct energy inputs to tbe sectors. Dollar value of sector output is higbiy correlated with this energy indicator (though not with direct energy ~nsum~tio~ or with embodied energy calculated exctuding labor and ~ove~m~t energy costs). We also test explicitly the criticism that this rest& is merely a ~the~ti~ artifact of in#~mting hou~hold and govor~ent sectors, thus making the system more ‘closed’. Application of these tests to a 4-sector example implies that the mathemat~~l artifact argument is not valid (except for a specific, bmited case). Application of tbe tests to the full 87 sector modef also indicates that the mathemati~l artifact argument is not valid. We conclude that embodied energy, calculated in the way we suggest, is a good predictor of economic value, at least for the relatively large aggregates of marketed goods and services that appear in I-G tables.
1, Intr~~tion
An economy can be said to operate on an energy theory of value if economic value can be shown to be proportionaf to an appropriate energy indicator. One of us previously found evidence of such proportionality [Costanza (1980)], while the other challenged that result [Herendeen (1981)]. This paper represents a partial resolution of our differences.
We present further analysis of the type used in Costanza (1980), and address s~~~~y the major remanning technical criticism raised in Herendeen (1981): that the observed proportionality is merely a mathemat- ical artifact of the ma~pulation of the data. The other major technical criticism, having to do with double counting [Huettner (1982)], has aheady
*This research was funded, in part, by the National Science Foundation under Grant PRA- 8003845, and by the Bhnois Department of Energy and Natural Resources under Grant ENR- 80.260. We thank B.M. Hannon, C.J. Cleveland, MJ. Lavine, 11.T. Butler and HE. Daly for reviewing eartier drafts and providing useful comments.
~165~572/84~~3.~ Q 1984, Elsevier Science Publishers B.Y. (North-Holland)
130 R, Cnstanza and &!.A. Herendeen, bandied energy and economic due
been disposed of [Costanza (f982)J. We find that the ‘mathematical artifact argument’, while h$ding in one limited situation, is in general invalid. This conclusion is based on empirical calculations. We have not been successful at finding a closed form proof.
The basic idea behind the analysis is: if proportionality is found to result from acceptabie manipulations and computations with acceptable data, then it is a valid “revealed’ result. The major issue is that of data manipuIation~
Our energy indicator is embodied energy, calculated using the energy input-output (I-O) method developed by Bullard and Herendeen (1975). This method uses the standard assumptions [linearity, constant coefficients, etc., cf. Carter and Brody (1970)] of I-O analysis, and is applied to an 87- sector breakdown of the U.S. eeonomy for the years 1963, I967 and 1972.
Features of this analysis are: (1) the energy costs of labor and government services are included by considering households and government to be endogenous sectors [&stanza (1980, 1982)-j; (2) analysis of the mathemati~l artifact argument; and (3) use of two alternative measures of the distribution of direct energy inputs to the system. The first measure follows previous practice and assumes energy enters the economy only through the ‘energy sectors’. The second measure assumes direct energy input occurs at the point of consumption, not the point of physical entry. The second method is more consistent with the treatment of transportation sectors in I-O analysis.
Embodied energy costs are calculated for each year and compared with the corresponding dollar value of output of the sectors. The accuracy of embodied energy as a predictor of sector dollar output is investigated. The differences between the results based on the two measures of direct energy input are interpreted, both from an empirical and a theoretical perspective.
Any economic or ecological system can be divided into a number of interacting components or processes that consume, produce and exchange energy, organized material, information and services (or ‘commodities’ for
Fig. 1. Process j consumption and production relations for a specikd time interval. iJfj is the consumption or ‘use’ of internally produced commadity i by process j. E, is the use of external& produced eo~~iti~ by process j. k$ is the pr~uct~on or ‘make’ of commodity i by process j.
‘sector’ and ‘process’ are synonyms.
R. Cosranza and R.A. Herendeen, ~rn~od~ed energy and economic value 131
short). Fig. 1 is a diagram of a typical process, J, which uses or consumes internally produced commodities (Ui,) and externally produced commodities [l”;$) in order to produce or make its output commodities (I’&. Various mathematical formulations are possible starting with this picture [cf. Ritz (19791, Carter and Brody (1970), Harmon et al. (1983), Costanza and Neil1 (1984)]. These approaches all share the assumptions of scale and time independent production functions. Costanza (1980) and Bullard and Nerendeen (1975) did not alfow for ‘joint products’, produced when an individual process has more than one output commodity. Our approach allows for joint products. For the purposes of this study the following formulation is employed. An embodied energy balance equation can be written for each process in the form:
where ei represents the embodied energy intensity of each of the n com- modities in the system and EJ represents the direct energy input to process J. It is assumed that the energy intensity for a commodity is a single number representing the average over the processes which produce it.
In matrix notation for a system with n commodities and m processes one can write:
EfsU=sVr, where (21
E = m d~ensio~al row vector of direct energy inputs, U = n x m matrix of the use of commodities by processes, Y T = n x m matrix of the production of commodities by processes, & =PZ Dimensions row vector of embodied energy intensities.
Given data on U, V and E we wish to solve eq. 2 for the embodied energy intensity vector, B. If m= n this is possible using standard matrix manipu- lation techniques:
ezzE(VT.-v)-‘=r EVr=-“(I-- UP+“> - I. (3)
There are potential problems with this formulation, in that it can yield negative energy intensities. We believe (as will be pointed out) that these arise mainly as a result of deficiencies in the data, and are best handled by using preliminary runs to pinpoint problems. For example, preliminary runs on the U.S. economy produced negative intensities for three sectors (out of 88), one of which was Radio and TV broadcasting. On closer inspection it was discovered that this sector consumed al1 of its own output, according to the Bureau of Economic Analysis I-O data base we used. This was obviously done as an accounting convenience and does not reflect the real situation. This sector was aggregated with communications to eliminate the problem. Similar steps were taken for the other two problem sectors (business services and state and Iocal government enterprises).
132 R. Cosmnzu und R.A. Heremieen, ~mbodjed energy and economk zaiue
Most energy I-O modeling assumes the standard I-O accounting conven- tion that places households and government outside the boundaries of the economic system (they are assumed to be exogenous). This accounting stance can tead to major distortions of energy cost calculations since labor and government provide services to the economy whose energy costs would be ignored. In this study we employed I-O models which included ho~eholds and government as endogenaus sectors (rosvs and columns in U and y) in order to capture their energy cost contributions. Specific methods for doing this followed Costanza (1980) and will be discussed in detail further on.
Once modified U and V matrices were formed that included households and government as endogenous sectors and ‘proMem’ sectors were rectified, the matrix (VT-- v) was inverted and energy ~te~sities were calculated as a function of various estimates of the direct energy input vector, E. The different E vectors reflected different measures of the dist~bution of direct energy inputs to the economy. The resufting energy intensities were then evaluated in terms of their relationship to market prices for the sectors. Since U and V are measured in constant 1972 dollars for the economy, and direct energy inputs are in Btu’s, the energy intensities have the units Btu/$. If the energy embodied in a commodity (3tu/physical unit) is proportions to its price (~/physical unit) then the energy intensities expressed as Btu/S shoufd all be constant.
To test for this, the total energy embodied in sector inputs was regressed on dollar vaIue of sector outputs. A high degree of chelation between these variables indicates a relatively constant energy intensity (~tu/~~ and a high correlation between embodied energy and economic value across sectors.
3. I-O data
Eighty~ight sector U and V matrices were obtained From the Energy Research Group (ERG), University of Xltinois, for the years 1963, 1967 and 1972. These data were aggregated and modified from the originat I-O data available through the Bureau of Economic Analysis (BEA). Staff at the ERG invested considerable time and effort making the three year’s data as compatible as possible, so that valid ~ornpa~so~s between years could be made. As mentioned earfier, three problem sectors remained in the data and these were first eliminated by aggregation to an 85 sector model household and government sectors were then added yielding revised 87 sector matrices for all three years.
Inputs to the government and Household sectors (coiumns 86 and 87 of the revised 0 matrix) were developed from data on government expenditures (GE) and personal consumption expenditures (PCE) avaiIable as components of final demand. Inputs of government services to househoIds (Us6,& were estimated as personal taxes (PT) and household services to government
R. Casranza and R.A. Rerendeen, ~mb5d~ed energy and economic value 133
Table 1 Government salaries, personal taxes, and household and government
gross investment for 1963, 1967 and 1972 ( x 10’ 1972s).
1963 1967 1972
Government salaries” 73.76 92.34 1t9.40 Personal taxes’ 68.22 84.26 95.70 Household investmentb gross 280.82 338.76 471.66 Government investmentb gross 129.14 151.94 213.58
Y%orn US. Bureau of the Census (1976). bValues for 1963 and 1967 based on estimates in Kendrick (1976).
Values for 1972 based on Eisner et al. (1981) and Kendrick (1976). See table 2.
(Us7.a6) as government salaries (GS). Values for these components for all three years are listed in table 1. ‘Self sales’ of households and government
W 86,86 and U87,87) were assumed to be zero, since these values have no effect on the energy intensities. The inputs of government and household services to the other sectors (rows 86 and 87 of the revised ZJ matrix) were estimated as indirect business taxes (fB7’) and employee compensation (EC) respectively, both of which are also available in the I-O data base as components of value added. These modi~cations leave property type income (PTI) as the financial net input and gross capital formation (GCF), plus net inventory change (NIC), plus net exports (NE), plus estimates of household and government capital formation as the net output in financial terms. This net output will be referred to simply as revised net output (RNO) henceforth.
In a zero growth economy with no net exports this boundary definition would leave gross capital formation (including human and government capital formation) as the only non-zero components of RNO, At steady state, RN0 is just enough to counteract depreciation, the system’s tendency (by the second law of thermodynamics) to evolve toward a higher state of entropy if net energy inputs were cut off. It is worthwhile to note the magnitude of these adjustments to GNP. The ratio of RN0 to ‘normal’ GNP was 63.1% 63.8% and 75.0% in the three years, respectively.
Only two additional entries in the V matrix were required, Pa,,, and &,,a,. These represent the total output of the Gove~ent and Household sectors, respectively, exclusive of ‘self-sales’. These values include estimates of gross househoId and government investment (capital formation), which were available in Kendrick (1976) and Eisner et al. (1981) (table Z), as well as data on ISZ P7; EC, and GS. The estimated total outputs of the government and household sectors are listed in table 3. The complete revised 87 sector U and V matrices in 1972$ for 1963, 1967 and 1972 are available from the first author on request.
134 R. Costanza and R.A. Herendeen, Embodied energy and economic value
Table 2
Total gross investment for 1963, 1967 and 1972 (lo9 1972.S)”
Kendrick Eisner
Year Business Government Households Total Total
1963 115.48 129.14 280.82 525.44 512.95 % of total 21.98 24.58 53.44 - -
1967 155.05 151.94 338.76 645.75 667.41 % of total 24.01 23.53 52.46 - -
1972 204.68 213.58 471.66 - 889.93 % of total 23.00 24.00 53.00 - -
“Kendrick (1976) provides business, government, and household components for gross investment, but his series stops at 1969. To extend the series to 1972, data on total gross investment from Eisner et al. (1981) was used. Eisner’s totals agree well with Kendrick’s for 1963 and 1967, but sector breakdowns were not provided. The average percent of total for each sector from the 1963 and 1967 Kendrick data was therefore used to estimate the breakdown of the Eisner total for 1972.
Table 3
Total government and household output, 1963, 1967 and 1972 (lo9 1972%).’
1963 1967 1972
Government Indirect business taxes (IBT) Personal taxes (PT) Gov’t gross investment (GGI)
69.32 68.22
129.14
Government total 266.67
Households Employee compensation (EC) Government salaries (GS) H’hold gross investment (HGI)
433.40 71.76
280.82
Household total 785.98
89.14 106.94 84.26 95.70
151.94 213.58
325.06 416.22
494.21 692.35 92.34 119.40
338.76 471.66
925.31 1283.41
“Source: See tables 1 and 2.
The remaining data necessary to complete the analysis were estimates of the direct energy input from nature to the 87 sectors (E vectors) for each of the three years. There is considerable debate on the appropriate E vector for this analysis. In this analysis we used E vectors containing only fossil fuel, hydro and nuclear energy inputs, ignoring direct environmental energy inputs. The alternate E vectors used in this study for all three years are listed in table 4, along with the revised sector definitions in terms of their BEA I-O codes. Alternative 1 (DIRECT) consisted of fossil, nuclear and hydro energy
Tab
le
4
Alte
rnat
ive
dire
ct
ener
gy
inpu
t ve
ctor
s us
ed
in
this
st
udy.
D
IRE
CT
as
sum
es
dire
ct
ener
gy
inpu
t at
th
e po
int
of
phys
ical
en
try
into
se
ctor
s,
whi
le
DE
C
assu
mes
di
rect
en
ergy
co
nsum
ptio
n as
th
e po
int
of e
ntry
in
to
sect
ors.
U
nits
ar
e B
tu
per
year
.
I-0
No.
C
ode
Sect
or
nam
e
1963
19
67
1972
-
DIR
EC
T
DE
C
DIR
EC
T
DE
C
DIR
EC
T
DE
C
(1)
700
(2)
800
(3)
3101
(4
) 68
01
(5)
6802
(6)
(7)
::
(8)
300
(9)
400
(10)
50
0 (1
1)
600
(12)
90
0 (1
3)
1000
(1
4)
1100
(1
5)
1200
(1
6)
1300
(1
7)
1400
(1
8)
1500
(1
9)
1600
(2
0)
1700
(2
1)
1800
(2
2)
1900
(2
3)
2000
(2
4)
2100
(2
.5)
2200
(2
6)
2300
(2
7)
2400
(2
8)
2500
(2
9)
2600
Coa
l m
inin
g 0.
1247
68+
17
O.l1
557E
+14
Cru
de
petr
o ga
s 0.
3038
4E
+ 17
0.
2027
28
+ 14
Pe
tro
refi
n.
prod
. O
.l065
4E+
16
O.l4
101E
+15
Ele
ctri
c ut
ilitie
s O
.l698
7E+
16
0.32
7828
+ 15
G
as
utili
ties
0.71
6408
+ 15
0.
7007
98+
14
Liv
esto
ck
0.43
9548
+
15
Mis
c.
ag.
prod
ucts
0.
6703
7E
+ 15
Fo
rest
, fi
sh
prod
ucts
0.
3173
38+
14
Ag.
, fo
r.,
lish
serv
ices
0.
9409
58+
13
Iron
or
e m
inin
g 0.
8567
78
+ 14
N
onfe
rr.
min
ing
0.86
759E
+
14
Ston
e cl
ay
min
ing
O.l2
6OlE
+ 15
C
hem
. m
iner
al
min
ing
O.l1
624E
+l5
New
co
nstr
uctio
n 0.
7719
8E+
15
Mai
nt.
rep.
co
nst.
0.48
258E
+
15
Ord
nanc
e 0.
4950
6E
+ 14
Fo
od
0.11
2928
+ 16
T
obac
co
0.21
757E
+ 14
Fa
bric
an
d m
ills
0.33
952E
+
15
Tex
tile
good
s 0.
4172
3E+
14
App
arel
0.
9389
9E
+ 14
Fa
b.
text
ile
prod
. 0.
1079
28+
14
Woo
d pr
oduc
ts
O.l5
084E
+ 15
W
ood
cont
aine
rs
0.36
5558
+ 13
H
’hol
d fu
rnitu
re
0.37
908E
+ 14
Fu
rn.,
fixt
ures
0.
1921
28+
14
Pape
r pr
oduc
ts
0.12
5208
+ 16
Pa
perb
oard
co
nt.
0.48
485E
+
14
Prin
ting,
pu
blis
hing
0.
1025
28+
15
O.l4
794E
+ 17
O
.l239
8E+1
4 0.
3745
98+1
7 0.
3501
2E+1
4 O
.l252
3E+
16
O.l6
994E
+ 15
0.
2390
2E
+ 16
0.
4556
9E
+ 15
O
.l173
0E+1
6 0.
9936
6E+1
4 0.
5360
4E+
15
0.71
9768
+ 15
0.
4935
28
+ 14
o.
l161
0E+
14
0.93
147E
+ 14
0.
8002
78
+ 14
0.
1444
28+
15
O.l5
588E
+ 15
O
.l194
6E+
16
0.26
876E
+
15
O.l1
523E
+ 15
O
.l269
9E+
16
0.26
066E
+
14
0.39
455E
+
15
0.63
472E
+
14
O.l1
505E
+ 15
0.
2919
48+
14
0.27
445E
+
15
0.62
667E
+
13
0.39
658E
+ 14
0.
2464
1E+
14
0.14
284E
+
16
0.78
269E
+
14
0.13
8068
+ 15
O.l4
172E
+ 17
O
.l905
3E+
14
0.42
336E
+
17
0.46
075E
+
14
0.17
3098
+ 16
0.
2347
0E+
15
0.34
343E
+ 16
0.
8329
7E+
15
O.l4
512E
+ 16
0.
1331
58+
15
0.34
7778
+
15
O.l2
962E
+ 16
O
.l174
3E+
15
0.60
442E
+
14
O.l5
258E
+ 15
O
.l425
5E+
15
0.22
5768
+ 15
0.
1954
58+
15
0.17
3658
+ 16
0.
7991
6E+
15
0.86
1698
+ 14
O
.l458
2E+
16
0.29
803E
+
14
0.46
058E
+ 15
O
.l062
7E+
15
0.22
885E
+ 15
0.
3330
38+
14
0.44
330E
+
15
0.82
064E
+
13
0.63
837E
+ 14
0.
4665
9E
+ 14
0.
1786
98+
16
O.l1
506E
+ 15
0.
2180
9E+
15
Tab
le
4 (c
ontin
ued)
I-O
N
o.
Cod
e Se
ctor
na
me
1963
19
67
1972
DIR
EC
T
DE
C
DIR
EC
T
DE
C
DIR
EC
T
DE
C
(30)
27
00
Che
m.
prod
ucts
(3
1)
2800
Pl
astic
s (3
2)
2900
D
rugs
, to
il.
prep
. (3
3)
3000
Pa
ints
(3
4)
3102
Pa
ving
(3
5)
3103
A
spha
lt (3
6)
3200
R
ubbe
r pr
oduc
ts
(37)
33
00
Lea
ther
pr
oduc
ts
(38)
34
00
Foot
wea
r (3
9)
3500
G
lass
pr
oduc
ts
(40)
36
00
Ston
e cl
ay
prod
ucts
(4
1)
3700
Pr
im.
ir.,
stl.
man
ufac
t. (4
2)
3800
Pr
im.
nonf
err.
met
als
(43)
39
00
Met
al
cont
aine
rs
(44)
40
00
Hea
ting,
pl
umbi
ng
(45)
41
00
Scre
w
mat
h.
prod
ucts
(4
6)
4200
Fa
b.
met
al.
prod
ucts
(4
7)
4300
E
ngin
es,
turb
ines
(4
8)
4400
Fa
rm
mac
hine
ry
(49)
45
00
Con
st.,
min
ing
eq.
(50)
46
00
Mat
. ha
ndlin
g eq
. (5
1)
4700
M
etal
wor
king
eq
. (5
2)
4800
Sp
ec.
ind.
m
ath.
(5
3)
4900
G
en.
ind.
m
ath.
(5
4)
5000
M
ach.
sh
op
prod
ucts
(5
5)
5100
O
TC
. com
put.
mat
h.
(56)
52
00
Serv
ice
ind.
m
ath.
(5
7)
5300
E
lec.
in
d.
appa
rat.
(58)
54
00
H’h
old
appl
ianc
e (5
9)
5500
E
lec.
lig
ht
eq.
(60)
56
00
R-T
V
com
mun
. eq
.
0.37
8218
+ 16
0.
4694
0E
+ 15
0.
2717
5E+
15
0.79
557E
+ 14
0.
2110
3E+
15
0.22
2138
+ 15
0.
2251
4E+
15
0.28
141E
+ 14
0.
1592
68+
14
0.28
714E
+ 15
O
.l003
9E+
16
0.42
0338
+
16
O.l0
206E
+ 16
0.
2024
6E
+ 14
O
.l142
1E+
15
0.65
586E
+
14
0.13
2798
+ 15
0.
4580
28
+ 14
0.
4438
38
+ 14
0.
5400
5E
+ 14
O
.l075
1E+
14
0.50
0828
+
14
0.29
132E
+ 14
0.
6776
08
+ 14
0.
2394
5E
+ 14
0.
2403
2E
+ 14
0.
1534
98+
14
0.80
8198
+ 14
0.
5316
48+
14
0.27
9758
+
14
0.84
5898
+
14
0.38
2548
+
16
0.68
7428
+
15
O.l2
015E
+ 15
0.
5158
68+
14
0.28
7918
+ 15
0.
2305
0E
+ 15
0.
2933
OE
+
15
0.21
437E
+ 14
0.
2416
28+
14
0.31
809E
+ 15
0.
1217
88+
16
0.44
632E
+
16
O.l2
944E
+ 16
0.
3878
4E
+ 14
0.
1464
98+
15
O.l1
460E
+ 15
0.
1798
18+
15
0.43
3598
+ 14
0.
5219
2E+
14
0.75
505E
+ 14
0.
1504
78+
14
0.73
236E
+ 14
0.
4129
28+
14
0.79
1038
+ 14
0.
5098
7E
+ 14
0.
3075
5E
+ 14
0.
3457
7E
+ 14
O
.l094
8E+
15
0.63
704E
+
14
0.43
128E
+ 14
0.
9524
4E
+ 14
0.43
613E
+ 16
0.
9489
9E
+ 15
O
.l850
3E+
15
0.65
851E
+ 14
0.
3916
2E+
15
0.35
914E
+ 15
0.
4501
38+
15
0.22
528E
+ 14
0.
3072
68
+ 14
0.
4136
98+1
5 0.
1365
08+
16
0.43
9798
+
16
O.l5
481E
+ 16
0.
5875
3E+
14
0.18
6748
+ 15
O
.l515
8E+
15
0.23
877E
+
15
0.49
350E
+
14
0.64
6808
+
14
0.94
025E
+
14
0.24
343E
+ 14
0.
9170
8E+
14
0.60
5298
+
14
0.10
5588
+ 15
06
0141
E+
14
0.55
097E
+
14
0.84
5078
+
14
O.l4
726E
+ 15
0.
7377
88+
14
0.62
908E
+
14
0.12
2828
+ 15
(61)
(6
21
(63j
(W
(6
5)
(66)
I:;;
(6
9)
(70)
(7
1)
(72)
(7
3)
(74)
(7
5)
(76)
(7
7)
(78)
(7
9)
(80)
(8
1)
(82)
(8
3)
(84)
(8
5)
(86)
(8
7)
5700
E
lect
roni
c ca
mp.
58
00
Ele
ctri
cal
equi
pmen
t 59
00
Mot
or
veh.
an
d eq
. 6O
w
Air
craf
t an
d pa
rts
6100
T
rans
port
eq
uipm
ent
6200
Pr
of.
scie
nt.
supp
lies
6300
O
ptic
al
supp
lies
6400
M
isc.
m
anuf
act.
6501
R
ailr
oad
6502
L
ocal
tr
ansp
ort
6503
M
otor
fg
t. tr
ansp
ort
6504
W
ater
tr
ansp
ort
6505
A
ir
tran
spor
t 65
06
Pipe
lin
e tr
ansp
ort
6507
+ 7
3 T
ran.
bu
snss
. se
rv.
661-
67
Com
mun
icat
ions
68
03
Wat
er
sani
t. se
rv.
6900
W
hole
, re
tail
trad
e 70
00
Fina
nce,
in
sura
nce
71O
il R
eal
esta
te
7200
H
otel
s,
pers
. se
rv.
7500
A
uto
repa
ir
7600
A
mus
emen
ts
7700
M
ed.,
educ
. se
rvic
es
78+7
9 G
ovt.
ente
rpri
ses
Gov
ernm
ent
Hou
seho
lds
0.55
087E
+ 14
0.
2178
38+
14
0.32
010E
+ I5
O
.l305
1E+
15
0.53
549E
+ 14
0.
2344
88
+ 14
0.
3764
5E+
14
0.66
2048
+
I4
0.74
905E
+
15
0.30
822E
+
15
0.56
182E
+ I5
0.
6735
6E
+ 15
0.
6705
68
+ 15
O
.l406
4E+
15
0.42
1OO
E+
15.
0.21
3188
+ 15
0.
1666
48+
I5
0.26
494E
+
16
0.47
596E
+
I5
0.11
7898
+ 15
0.
2934
1E+
15
O.l0
802E
+ I5
0.
6958
6E
+ 14
0.
8156
0E+l
5 O
.l970
lE+
I5
0.23
369E
+
16
0.18
9938
+ I7
_
0.83
169E
+ 14
0.
3176
4E+
14
0.35
97lE
+ I5
O
.l756
8E+
15
0.66
796E
+
14
0.35
886E
+ I4
0.
2843
3E
+ 14
0.
6065
3E
+ 14
0.
6842
18+
15
0.23
8728
+
15
0.51
4678
+ 15
0.
7065
9E
+ I5
O
.l271
7E+
16
O.l4
865E
+ 15
0.
3800
6E
+ 15
0.
2236
1E+1
5 0.
1087
58+
I5
0.34
762E
+
16
0.37
788E
+
I5
0.29
6158
+ I5
0.
6143
68+
15
0.29
49lE
+ I5
0.
8482
2E
+ I4
O
.l372
7E+
16
0.35
080E
+
I5
0.39
163E
+ 16
0.
2203
7E
+ I7
O.l1
75lE
+l5
0.46
196E
+ I4
0.
4523
08
+ 15
O
.l659
6E+
15
0.99
986E
+
I4
0.57
473E
+ I4
0.
6126
7E+
I4
0.12
0288
+ 15
0.
8149
08+
15
0.23
257E
+
I5
0.86
26O
E
+ 15
0.
9169
9E+
I5
O.l6
780E
+ 16
O
.l636
2E+
15
0.37
657E
+
15
0.22
7588
+
15
0.61
2268
+ I4
0.
4510
5E+
I6
0.57
1438
+ 15
0.
6348
2E
+ I5
0.
6239
28
+ I5
O
.l542
0E+
I5
O.l3
009E
+ 15
O
.l561
9E+
I6
0.31
099E
+ 15
0.
4381
3E+
16
0.27
140E
+ 17
Y
138 R. Costanza and R.A. Herendeen, Embodied energy and economic o&e
Table 5 Domestic primary fossil fuel, hydro and nuclear energy use (10 I5 Btu/yr). Prod. is gross output by sector, primary is total primary energy use based on w, which is a factor that prevents double
counting, e.g., when adding crude and reftned petroleum. Primary is production times w.’
1963 1967 1972
Sector Prod. w Primary
(1) Coal mining 12.48 1 12.48 (2) Crude petro, gas 30.38 1 30.38 (3) Refined petro 19.86 0.054 1.07 (4) Electric util. 3.13 0.543 1.70 (5) Gas utilities 13.19 0.054 0.72
Total 44.34
Prod. w. Primary Prod. w. Primary
14.79 1 14.79 14.17 1 14.17 37.75 1 37.75 42.34 1 42.34 23.19 0.054 1.25 27.56 0.063 1.73 4.16 0.575 2.39 5.99 0.573 3.43
17.35 0.064 1.12 20.85 0.070 1.45
57.30 63.12
“Sources: Production: Harmon and Casler (1981). w: Hannon et al. (1983).
Table 6 Weighting factors for energy types for 1963, 1967 and
1972 (Btu primary/Btu energy type delivered for use).’
Sector 1963 1967 1912
(1) Coal mining 1.0141 1.0116 1.0227 (2) Crude petro, gas 1.0578 1.0564 1.0601 (3) Refined petro 1.1497 1.1192 1.1487 (4) Electric util. 3.8181 3.7542 3.7714 (5) Gas utilities 1.1684 1.1515 1.1496
“Source: Hannon and Casler (1981).
into the ‘primary’ energy sectors (sectors l-5). No other sectors receive energy input from nature under this alternative. Estimates for total primary energy use for the three years are derived in table 5. The weighting factor w is necessary in table 5 to avoid double counting, since most refined petroleum and natural gas utilities output is made from crude, and a large part of electricity is made from coal or crude (see Bullard and Herendeen (1975)J. Alternative 2 (DEC) uses estimates of direct fossil fuel, hydro and nuclear consumed (burned) by sector. All sectors use such energy, and the total use by sector is a weighted sum of the five fuel types used in this model. The weighting factors used were calculated previously by Hannon and Casler (1981). They reflect, for example, the primary (i.e., coal or crude) fossil energy required to produce a unit of refined petroleum (about 1.15 Btu/Btu in 1972). The weighting factors for each of the three years are given in table 6.
4. Results of I-O analysis
One question to answer at the outset is: what is a proper index of
R. Costonza and R.A. Herendeen, Embodied energy and economic value 139
proportionality in this case? There are several possible measures of disper- sion of the energy intensities that could be used to measure the ‘constancy’ of energy intensities across sectors, and there are several ways of regressing total dollar output on total embodied energy input across sectors to test for ‘proportionality’. In the results given below, we calculate and discuss both the coefficient of variation (CO% equal to the standard deviation divided by the mean) of the equally-weighted entries of the energy intensity vector, and a simple linear regression (including an intercept term) of total dollar output on embodied energy input. We manipulate the regressions to determine the effects of the high magnitudes of some observations on the results.
Tables 7, 8 and 9 list the results of the I-O energy analysis for 1963, 1967 and 1972, respectively for the alternative E vectors listed in table 4. Each table hsts the calculated energy intensity vector (in Btu/l972~), the total energy embodied in sector inputs (in Btu, calculated by multiplying the calculated energy intensity by total dollar input), and the dollar output from the sector (in 1972%) for each of the three years. The total dollar output was regressed on total embodied energy input both including and excluding the primary energy sectors (sectors l-5), and the household and government sectors (sectors 86-87). The results are plotted in fig. 2, and are summarized in table 10, which lists the RZ statistic for each alternative along with the coefficient of variation for the energy intensity vector. Ah regressions were significant at the 0.001 level. Fig. 2 is a log-log plot because the range of values for dollar output and embodied energy input spanned over four orders of magnitude (the regressions were run on the untransformed data). The R2 statistic is reported both including and excluding the government and household sectors (86-87) in the regression, since these sectors are much Iarger than the other sectors and could unduly weight the R2 values. R2 values excluding these sectors are also more directly comparable with previously calculated R2 values based on an X-O model with exogenous household and government sectors.
The results of the present analysis confirm and expand previous studies [Costanza (1980)] and generally provide evidence supportive of a strong cross-sectional relationship between embodied energy and dollar value, especially if the DEC energy input vector is used. A precondition for this conclusion is the accounting for government and household energy costs by making them endogenous sectors. Exclusion of the household and govern- ment sectors from calculation of energy intensities [the treatment used by Bullard and Herendeen (1975) and others] yields much poorer values for R2 and COV both here and in the previous study [Costanza (1980)]. While the use of endogenous household and government sectors has been criticized [Herendeen (1981), Huettner (1982)], we now feel that the criticisms are less valid based on previously published arguments [Costanza (1982)], and the tests presented in a following section.
Tab
le
7
I-O
en
ergy
an
alys
is
resu
lts
for
1963
. I-
O
code
re
fers
to
th
e B
EA
se
ctor
de
fini
tions
in
clud
ed
in
our
87
orde
r se
ctor
s.
Res
ults
fo
r bo
th
dire
ct
ener
gy
inpu
t ve
ctor
s lis
ted
in t
able
4
are
give
n.
I-O
No.
Cod
e
(1)
700
(2)
800
(3)
3101
(4
) 68
01
(5)
6802
(6)
(7)
::
(8)
300
(9)
400
(10)
50
0 (1
1)
600
(12)
90
0 (1
3)
1000
(1
4)
II00
(1
5)
1200
(1
6)
1300
(1
7)
1400
(1
8)
1500
(1
9)
1600
(2
0)
1700
(2
1)
1800
(2
2)
1900
(2
3)
2000
(2
4)
2100
(2
5)
2200
(2
6)
2300
(2
7)
2400
Sect
or
nam
e
Coa
l m
inin
g C
rude
Pe
tro,
G
as
Petr
o re
lin.
prod
. E
lect
ric
utili
ties
Gas
ut
ilitie
s L
ives
tock
M
ist
ag.
prod
ucts
Fo
rest
, fi
sh
prod
. A
g.,
for.,
fi
sh
serv
. Ir
on
ore
min
ing
Non
ferr
. m
inin
g St
one
clay
m
inin
g C
hem
. m
iner
al
min
N
ew
cons
truc
tion
Mai
nt.,
rep.
co
nst.
Ord
nanc
e Fo
od
Tob
acco
Fa
bric
an
d m
ills
Tex
tile
good
s A
ppar
el
Fab.
te
xtile
pr
od.
Woo
d pr
oduc
ts
Woo
d co
ntai
ners
H
’hol
d fu
rnitu
re
Furn
., fi
xtur
es
Pape
r pr
oduc
ts
DIR
EC
T
DE
C
Dol
lar
outp
ut
($19
72)
Em
b.
ener
gy
Em
b.
ener
gy
inte
nsity
in
put
(Btu
/S)
(Btu
)
Em
b.
ener
gy
Em
b.
ener
gy
inte
nsity
in
put
(Btu
/S)
(Btu
)
0.45
192
E +
10
O.l2
704E
+ll
0.21
345E
+ II
0.
1811
9E+
11
0.12
8308
+ 11
0.
3990
9E
+ 11
0.
2997
8E
+ 11
0.
3247
5E+
10
O.l8
513E
+ IO
0.
9575
lE+0
9 O
.l740
8E+
10
0.21
678E
+ IO
0.
5360
1E+0
9 0.
9919
3E+
1 I
0.31
773E
+ 11
0.
6257
1E+
10
0.93
125E
+ I
I 0.
9489
58
+ IO
O
.l463
4E+
11
0.29
7888
+
10
0.21
3288
+ 11
0.
2683
48
+ 10
O
.l549
8E+l
l 0.
5077
1E+0
9 0.
5017
lE+
10
0.22
884E
+
10
O.l3
932E
+ I1
0.33
4828
+07
0.26
358E
+ 16
0.
2568
0E+0
7 O
.l502
1E+l
6 0.
1590
78+0
7 0.
3118
0E+
17
0.46
0958
+
06
0.66
390E
+
I6
0.80
180E
+
06
0.95
969E
+
16
0.70
934E
+
05
0.27
976E
+
I6
O.l0
849E
+O6
0.30
880E
+ 16
0.
4071
3E+0
5 O
.l322
2E+
15
0.72
427E
+05
O.l3
371E
+ 15
O
.l214
6E+O
6 O
.l165
4E+
15
0.87
019E
+05
O.l5
426E
+ 15
0.
1023
98+0
6 0.
2330
1E+
15
O.l1
531E
+06
0.67
799E
+ 14
0.
9508
4E+O
5 0.
9431
7E+
16
0.84
607E
+0
5 0.
2688
2E
+ 16
0.
8208
5E+0
5 ()
.517
98E
+ 15
0.
8635
0E
+ 05
0.
8036
3E
+ 16
0.
6362
7E
+ 05
0.
6039
9E
+ 15
O
.l023
0E+0
6 O
.l494
6E+
16
0.31
3978
+06
0.33
650E
+ 15
0.
8496
9E+0
5 O
.l811
3E+
16
0.98
741E
+05
0.26
509E
+ 15
0.
7016
18+0
5 O
.l095
1E+
16
0.97
659E
+05
0.48
474E
+ 14
0.
8854
5E+0
5 04
4433
E+
15
0.98
974E
+
05
0.22
470E
+
I5
O.l3
647E
+O6
O.l8
848E
+ 16
0.63
087E
+O5
0.27
396E
+ 15
0.
3943
78+0
5 0.
4919
2E+
15
0.57
309E
+05
0.14
8578
+ 16
0.
6317
7E+0
5 0.
8254
88+
15
0.48
425E
+
05
0.56
882E
+
15
0.68
612E
+05
0.22
717E
+l6
0.86
7138
+05
O.l8
217E
+ 16
0.
3416
lE+0
5 0.
7920
58+1
4 0.
7875
0E+0
5 O
.l358
8E+
15
0.16
260E
+
06
0.68
676E
+
14
0.13
715E
+06
0.15
3448
+15
O.l2
294E
+06
O.l4
9OO
E+
15
0.24
915E
+06
0.44
278E
+ 14
0.
998l
OE
+05
0.91
285E
+ 16
0.
9867
8E+0
5 0.
2652
7E+
16
0.92
019E
+05
0.53
170E
+ 15
0.
9196
3E+0
5 0.
7456
7E+
16
0.64
8348
+05
0.59
328E
+ 15
O
.l488
5E+0
6 O
.l819
5E+
16
O.l6
321E
+06
0.43
986E
+ 15
O
.l062
9E+0
6 0.
2169
5Ef
16
O.l2
543E
+06
0.32
698E
+ 15
0.
7444
68+0
5 O
.l012
8E+
16
O.l0
588E
+O6
0.48
877E
+ 14
O
.l025
2E+0
6 0.
4771
9E+
15
0.11
358E
+06
0.23
889E
+l5
0.20
013E
+06
O.l5
097E
+16
ri8)
(29)
(3
0)
(31)
(3
2)
2330
P
abei
boar
a ‘c
bnt.
P
rin
tin
g, p
ubl
. C
hem
. pr
odu
cts
Pla
stic
s D
rugs
, to
il,
prep
. P
ain
ts
Pav
ing
Asp
hal
t R
ubb
er p
rodu
cts
Lea
ther
pro
duct
s F
ootw
ear
Gla
ss p
rodu
cts
Sto
ne
clay
pro
d.
Pri
m.
ir.,
stl.
man
u.
Pri
m.
Non
ferr
. m
et.
Met
al c
onta
iner
s H
eati
ng,
plu
mbi
ng
Scr
ew m
ath
. pr
od.
Fab
. m
etal
pro
d.
En
gin
es,
turb
ines
F
arm
mac
hin
ery
Con
st.,
min
ing
eq.
Mat
. h
andl
ing
eq.
Met
al w
ork
ing
eq.
Spe
c. i
nd.
mat
h.
Gen
. in
d. m
ath
. M
ach
. sh
op p
rod.
O
ft.
com
put.
m
ath
. S
ervi
ce i
nd.
mat
h.
Ele
c. i
nd.
app
arat
. H
’hol
d ap
plia
nce
E
lec.
lig
ht
eq.
R-T
V
com
mu
n.
eq.
Ele
ctro
nic
cam
p.
Ele
ctri
cal
equ
ip.
Mot
or
veh
. an
d eq
. A
ircr
aft
and
part
s T
ran
spor
t eq
uip
.
u.53
1(//~
+1u
0.22
277E
+ 1
1 0.
1507
0E+
11
0.
4851
5E+
10
0.
9206
78 +
10
0.29
374E
+ 1
0 0.
4799
0E +
09
0.67
291E
+O
9 O
.l02
58E
+
11
0.92
649E
+05
0.
9617
5E+
15
O
.l37
17E
+
10
0.87
659E
+05
O
.l20
10E
+
15
U.ll
ZiY
E+
Uti
U
.6W
U1~
+15
0.72
12O
E+
O5
O.l
4813
E+
16
O
.l49
27E
+06
0.
2264
48+
16
0.
1533
78+
06
0.72
501E
+
15
0.80
633E
+05
0.
7794
48+
15
O
.l45
12E
+06
0.
4278
2E+
15
0.
5325
8E+
06
0.24
151E
+
15
0.33
115E
+06
0.
2130
5E+
15
U.lJ
Yb
5t+U
b
U./U
JY3l
z++1
5 0.
9925
28+
05
O.l
7472
E+
16
0.
4158
7E+
06
0.21
898E
+
16
0.32
036E
+06
O
.l05
19E
+
16
0.12
8068
+06
0.
9574
78+
15
0.
1619
38+
06
0.41
728E
+
15
0.55
9178
+06
0.
4206
6E+
14
0.
4516
8E+
06
0.64
656E
+
14
O.l
4142
E+
O6
0.12
365E
t 16
0.
1052
0EtO
6 0.
1160
7Et
15
0.91
168E
t05
0.40
189E
t 15
0.
1586
7E t
06
0.32
7668
t
15
0.17
774E
tO6
0.10
711E
t 16
0.
2511
3E+
06
0.35
003E
t 16
0.
1691
OE
tO6
0.18
883E
t 16
0.
1555
6Et0
6 0.
4826
4Et
15
0.14
537E
t06
0.13
785E
t 16
0.
1183
7Et0
6 0.
6794
5Etl
5 0.
1196
1EtO
6 0.
1049
2Et
16
O.l
1682
E+
O6
0.27
769E
+
15
0.12
389E
t06
0.41
871E
t 15
0.
1145
1Et0
6 0.
5359
78+
15
0.10
5818
+06
0.
1828
8Et
15
0.96
5868
t 0
5 0.
5469
08 t
15
0.
9945
78+
05
0.
4144
OE
t 15
0.
1077
8EtO
6 0.
5938
48+
15
0.
9378
0E t
05
0.26
8878
t
15
2600
27
00
2800
29
00
3000
31
02
3103
32
00
3300
34
00
3500
36
00
3700
38
00
(33)
(3
41
i35j
(36)
(3
7)
(38)
(3
9)
(40)
(4
1)
(42)
(4
3)
(44)
(4
5)
(46)
(4
7)
(48)
(4
9)
(50)
(5
1)
(52)
(5
3)
(54)
0.45
717E
+
10
0.78
989E
tO5
0.36
151B
+
15
0.39
0348
t
10
0.95
633E
tO5
0.37
249E
+l5
0.
1184
4Etl
l 0.
1469
5EtO
6 0.
1716
3Et
16
0.31
470E
t 11
0.
2017
8Et0
6 0.
6205
5Et
16
0.17
338E
t 11
0.
9319
7Et0
5 0.
1644
5Et
16
3900
4c
@O
0.
3255
9E t
10
O
.l30
25E
+06
0.
4209
6Et
15
0.10
454E
t 11
O
.l18
06E
+06
0.
1219
9Et
16
4100
0.
6278
48 +
10
0.98
934E
t05
0.62
118E
t 15
42
00
4300
0.
9842
98 +
10
0.95
259E
t 0
5 0.
9459
7E +
15
0.27
7828
+ 1
0 0.
9893
1E+
05
0.27
535E
+
15
4400
0.
3728
28 t
10
0.
1061
2EtO
6 0.
3970
1Et
15
4500
46
00
0.51
551E
t 10
0.
9819
6Et0
5 0.
5073
6Et
15
0.18
1648
+
10
0.96
104E
t05
O.l
7484
E+
15
47
00
0.59
703E
+
10
0.90
545E
t 0
5 0.
5523
0E t
15
48
00
4900
0.
4454
9E t
10
0.
9601
5Et0
5 0.
4240
3Et
15
0.60
436E
t
10
0.98
349E
t 0
5 0.
5943
3E t
15
50
00
5100
52
00
5300
0.30
583E
t
10
0.38
9OlE
t 10
0.
3134
8Et
10
0.69
020E
+ 1
0
0.82
801E
+05
0.
2573
5Et
15
(55)
(5
6)
0.75
530E
t 0
5 0.
2929
6E t
15
0.
8414
4EtO
5 0.
3009
7Et
I5
0.10
576E
t06
0.
3276
38+
15
O
.l20
44E
+06
0.
3588
7Et
15
i57j
(58)
(5
9)
(60)
(6
1)
(62)
(6
3)
(64)
(6
5)
0.97
717E
tO5
0.67
844E
t 15
0.
1114
3EtO
6 0.
7024
7Et
15
5400
55
00
0.43
252E
t
10
0.11
635E
tO6
0.48
735E
+
15
0.14
461E
t06
0.54
528E
t 15
0.
3576
OE
+ 1
0 0.
9884
0E t
05
0.35
2368
+ 1
5 O
.l05
64E
+06
0.
3552
08+
15
56
00
0.12
866E
t 11
0.
8415
6E t
05
0.10
918E
t
16
0.94
874E
t05
0.11
527E
t 16
0.
3264
3E t
10
0.
1161
3EtO
6 0.
3702
9Et
15
0.14
826E
t06
0.41
406E
t 15
0.
2646
5E t
10
0.
7263
0Et0
5 0.
2009
7Et
15
0.95
951E
t05
0.24
174E
t 15
0.
4881
2E t
11
0.
101O
OE
t06
0.49
309E
+
I6
0.12
024E
t06
0.55
516E
t 16
0.
1789
5Etl
l 0.
8463
3EtO
5 0.
1516
6Et
16
0.93
023E
tO5
0.15
447E
t 16
0.
5952
98 t
10
O
.l10
39E
+06
0.
6508
8E+
15
0.
1280
7E t
06
0.70
176E
+ 1
5
5700
58
00
5900
60
00
6100
6
Tab
le
7 (c
ontin
ued)
No.
(66)
(6
7)
(68)
(6
9)
(70)
(7
1)
(72)
(7
3)
(74)
(7
5)
(76)
(7
7)
(78)
(7
9)
(80)
I::;
(83)
1::;
(86)
(8
7)
DIR
EC
T
I-O
C
ode
Sect
or
nam
e
Dol
lar
outp
ut
($19
72)
Em
b.
ener
gy
Em
b.
ener
gy
inte
nsity
in
put
(Rtu
/%
(Rtu
)
DE
C
Em
b.
ener
gy
Em
b.
ener
gy
inte
nsity
in
put
(Rtu
/%)
(Rtu
)
6200
Pr
of.,
scie
nt.
supp
. 63
00
Opt
ical
su
pplie
s 64
00
Mis
c.
man
ufac
t. 65
01
Rai
lroa
d 65
02
Loc
al
tran
spor
t 65
03
Mot
or
fgt.
tran
sp.
6504
W
ater
tr
ansp
ort
6505
A
ir
tran
spor
t 65
06
Pipe
lin
e tr
ansp
. 65
07 +
73
Tra
n.
busn
ss.
serv
. 66
+ 6
7 C
omm
unic
atio
ns
6803
W
ater
sa
nit.
serv
. 69
00
Who
le,
reta
il tr
. 70
@0
Fina
nce,
in
sura
nce
7100
R
eal
esta
te
7200
H
otel
s,
pers
. se
rv.
7500
A
uto
repa
ir
7600
A
mus
emen
ts
7700
M
ed.,
educ
. se
rv.
78 +
79
Gov
t. en
terp
rise
s G
over
nmen
t -
Hou
seho
lds
0.47
672E
+
IO
0.25
0668
+
10
0.77
4098
+
10
O.l3
29O
E+
11
0607
62E
+ 10
0.
2088
1E+
11
0.51
844E
+ 10
0.
5165
3E+
10
0.86
8488
+
09
0.41
016E
+ 11
O
.l846
3E+
11
O.l8
64O
E+
10
O.l6
029E
+ 12
0.
5388
2E
+ 11
0.
9783
48
+ 11
0.
2119
2E+
11
0.15
9628
+ 11
0.
1116
8E+l
l 0.
5420
5E
+ 11
O
.l522
3E+
11
0.26
667E
+
12
0.78
598E
+
12
0.76
1588
+05
0.37
245E
+ 15
0.
7896
OE
+05
O.l9
892E
+ 15
0.
8755
58
+05
0.67
0378
+
15
O.l1
620E
+06
O.l5
338E
+ 16
O
.l199
8E+O
6 0.
7273
1E+
15
O.l0
288E
+06
0.21
4088
+ 16
O
.l049
7E+O
6 0.
5441
7E+
15
O.l9
475E
+06
O.l0
027E
+ 16
0.
2093
88+0
6 O
.l813
9E+
15
0.58
045E
+
05
0.23
767E
+
16
0.53
7388
+
05
0.10
068E
+
16
0.97
664E
+05
O.l8
180E
+ 15
0.
7868
28+0
5 O
.l255
3E+
17
0.69
144E
+05
0.36
737E
+ 16
0.
3698
68+0
5 0.
3618
8E+
16
0.70
5948
+05
O.l4
829E
+ 16
0.
6683
58+0
5 O
.l062
7E+
16
0.63
041E
+05
0.69
84O
E+
15
0.66
29O
E
+ 05
0.
3590
4E
+ 16
0.
3646
4E+0
5 0.
1099
88+
16
0.61
5728
+05
O.l6
419E
+ 17
0.
7848
48+0
5 0.
6168
7E+
17
0.85
691E
+05
0401
00E
+15
0.11
3138
+06
0.24
1928
+ 15
O
.l063
2E+0
6 0.
7479
1E+
15
O.l3
297E
+O6
O.l0
012E
+ 16
O
.l026
4E+O
6 0.
3169
88+1
5 0.
8838
88+0
5 O
.l277
6E+
16
0.20
519E
+
06
0.39
006E
+
15
O.l9
566E
+06
0.33
679E
+15
0.23
3528
+06
0.61
644E
+ 14
06
0623
E+0
5 0.
2053
6E+
16
0.53
487E
+
05
0.79
9268
+
15
0.13
494E
+0
6 0.
8446
4E+
14
0.75
686E
+
05
0.94
214E
+
16
0.72
121E
+05
0.33
454E
+ 16
0.
3194
3E+0
5 0.
3007
8E+
16
0.71
6638
+05
O.l2
108E
+16
0.62
136E
+05
0.87
967E
+ 15
0.
6597
2E+0
5 0.
6600
3E+
15
0.69
334E
+0
5 0.
2939
0E
+ 16
0.
3892
9E
+05
0.76
945E
+
15
0.64
4018
+05
0.14
8378
+17
0.78
159E
+05
0.42
438E
+ 17
Tab
le
8
I-O
en
ergy
an
alys
is
resu
lts
for
1967
. I-
O
code
re
fers
to
th
e B
EA
se
ctor
de
fini
tions
in
clud
ed
in
out
87
orde
r se
ctor
s.
Res
ults
fo
r bo
th
dire
ct
ener
gy
inpu
t ve
ctor
s lis
ted
in
tabl
e 4
are
give
n.
I-O
N
o.
Cod
e Se
ctor
na
me
(1)
700
(2)
800
(3)
3101
(4
) 68
01
(5)
6802
(6)
(7)
::
(8)
300
(9)
400
(10)
50
0
(11)
60
0 (1
2)
900
(13)
10
00
(14)
11
00
(15)
12
00
(16)
13
00
(17)
14
00
(18)
15
00
(19)
16
00
(20)
17
00
(21)
18
00
(22)
19
00
(23)
20
00
(24)
21
00
(25)
22
00
(26)
23
00
(27)
24
00
(28)
25
00
Coa
l m
inin
g C
rude
pc
tro,
ga
s Pe
tro
relin
. pr
od.
Ele
ctri
c ut
il.
Gas
ut
ilitie
s L
ives
tock
M
isc.
ag
. pr
oduc
ts
Fore
st,
lish
prod
. A
g.,
for.,
fi
sh
serv
. Ir
on
ore
min
ing
Non
ferr
. m
inin
g St
one
clay
m
in.
Che
m.
min
eral
m
in.
New
co
nstr
uctio
n M
aint
., re
p.
cons
t. O
rdna
nce
Food
T
obac
co
Fabr
ic
and
mill
s T
extil
e go
ods
App
arel
Fa
b.
text
ile
prod
. W
ood
prod
ucts
W
ood
cont
aine
rs
H’h
old
furn
iture
Fu
rn.,
fixt
ures
Pa
per
prod
ucts
Pa
perb
oard
co
nt.
Dol
lar
outp
ut
($19
72)
DIR
EC
T
DE
C
Em
b.
ener
gy
Em
b.
ener
gy
Em
b.
ener
gy
Em
b.
ener
gy
inte
nsity
in
put
inte
nsity
in
put
(Btu
/S)
(Btu
) (B
tu/.V
(B
tu)
0.51
574E
+ 10
0.
1563
48+1
1 0.
2478
5E
+ 11
0.
2338
08
+ I 1
0.
1654
68
+ 11
0.
4027
08
+ 11
0.
3162
5E+
11
0.24
5608
+
10
0.27
762E
+
10
O.l1
899E
+ 10
O
.l47O
OE
+ 10
0.
2487
5E
+ 10
0.
754O
OE
+ 0
9 O
.l094
3E+
12
0.32
9338
+
11
0.11
058E
+11
O.l0
418E
+ 12
0.
9419
8E+
10
0.17
4698
+ 11
0.
4111
2E+
10
0.25
402E
+
11
0.36
096E
+
10
O.i7
440E
+ 11
0.
6561
98
+ 09
0.
5843
0E
+ 10
0.
3073
4E
+ 10
o.
l666
6E+
11
0.67
423E
+
10
0.33
649E
+
07
0.25
460E
+
16
0.25
915E
+07
O.l7
124E
+ 16
O
.l582
8E+0
7 0.
3524
9E+
17
0.47
244E
+
06
0.86
409E
+
16
0.79
26O
E+0
6 O
.l196
4E+
17
0.71
002E
+05
0.28
273E
+ 16
O
.l013
1E+0
6 0.
3080
1E+
16
0446
82E
+05
O.l0
971E
+ 15
0.
5371
1E+0
5 O
.l488
1E+
15
0.96
0588
+05
O.l1
417E
+15
0.94
7928
+05
O.l3
913E
+ 15
O
.l216
9E+O
6 0.
3078
4E+l
5 0.
9193
1E+O
5 0.
7667
4E+
14
0.93
495E
305
O.l0
231E
+ 17
0.
89O
OO
E+0
5 0.
2931
08+
16
0.89
455E
+
05
0.98
7548
+
15
0.85
2538
+
05
0.88
694E
+
16
0.67
196E
+05
0.63
303E
+ 15
0.
9494
4E+0
5 O
.l652
9E+1
6 0.
9698
48
+ 05
0.
3967
8E
+ 15
0.
8396
38+0
5 0.
2129
88+
16
0.89
649E
+05
0.32
411E
+ 15
0.
7654
7E+0
5 O
.l339
4E+l
6 0.
7885
6E+0
5 0.
5164
6E+
14
0.85
94O
E
+ 05
0.
5024
OE
+
15
0.92
535E
+
05
0.28
4228
+
15
O.l2
518E
+06
0.20
6078
+16
0.10
4838
+06
0.70
571E
+ 15
0.64
5628
+
05
0.32
083E
+
15
0.35
719E
305
0.54
261E
+ 15
0.
4850
3E+0
5 O
.l578
7E+
16
0.62
285E
+O5
O.l0
074E
+ 16
0.
4067
78
+05
0.59
3988
+
15
0.76
724E
+
05
0.25
093E
+
16
0.92
440E
+
05
0.20
9608
+
16
0.43
337E
+05
0.57
043E
3 14
0.
5870
9E+0
5 0.
1508
98+
15
O.l5
435E
+06
0.90
050E
+ 14
0.
1454
8E+0
6 O
.l332
2E+
15
O.l2
349E
+06
O.l6
793E
+ 15
0.
2667
28+0
6 0.
5530
4E+
14
O.l0
278E
+06
O.l0
052E
+ 17
0.
9606
78+
05
0.28
95O
E
+ 16
O
.l054
4E+0
6 0.
1043
68+
16
0.94
688E
+
05
0.85
897E
+
16
0.71
669E
+O5
0648
88E
+ 15
O
.l404
7E+O
6 0.
2034
2E+
16
O.l4
448E
+06
0.52
6468
+ 15
O
.l051
7E+O
6 0.
2550
4E+
16
O.l1
629E
+06
0.39
206E
+ 15
0.
8289
78+0
5 0.
1179
28+1
6 0.
8620
28+0
5 0.
5016
5E+
14
0.97
078E
+05
0.52
876E
+ 15
0.
1028
28+0
6 0.
2917
2E+1
5 O
.l934
4E+0
6 0.
1742
98+
16
0.13
8948
+06
0.85
535E
+ 15
Tab
le
8 (c
ontin
ued)
I-0
No.
C
bde
(29)
26
00
(30)
27
00
(31)
28
00
(32)
29
00
(33)
30
00
(34)
31
02
(35)
31
03
(36)
32
00
(37)
33
00
(38)
34
00
(39)
35
00
(40)
36
00
(41)
37
00
(42)
38
00
(43)
39
00
(44)
40
00
(45)
41
00
(46)
42
00
(47)
43
00
(48)
44
00
(49)
45
00
(58)
46
00
(51)
47
00
(52)
48
00
(53)
49
00
(54)
5O
tlO
(55)
51
00
(56)
52
00
157)
53
00
Sect
or
nam
e
Dol
lar
outp
ut
($19
72)
DIR
EC
T
DE
C
Em
b.
ener
gy
Em
b.
ener
gy
Em
b.
ener
gy
Em
b.
ener
gy
inte
nsity
in
put
inte
nsity
in
put
(Btu
/S
(Btu
) (B
tu/S
) (B
tu)
Prin
ting,
pu
bl.
Che
m.
prod
ucts
Pl
astic
s D
rugs
, to
il.
prep
. Pa
ints
Pa
ving
A
spha
lt R
ubbe
r Pr
oduc
ts
Lea
ther
pr
oduc
ts
Foot
wea
r G
lass
pr
oduc
ts
Ston
e cl
ay
prod
. Pr
im.
ir.,
stl.
man
u.
Prim
. no
nfer
r. m
et.
Met
al
cont
aine
rs
Hea
ting
plum
bing
Sc
rew
m
ath.
pr
od.
Fab.
m
etal
pr
od.
Eng
ines
, tu
rbin
es
Farm
m
achi
nery
C
onst
., M
inin
g eq
. M
at.
hand
ling
eq.
Met
alw
orki
ng
eq.
Spec
. in
d.
mat
h.
Gen
. in
d.
mat
h.
Mac
h.
shop
pr
od.
Oft
. co
mpu
t. m
ath.
Se
rvic
e in
d.
mat
h.
Ele
c.
ind.
an
nara
t.
0.27
299E
+
11
O.l9
596E
+ll
0.69
9128
+
10
O.l2
466E
+ll
0.33
135E
+ 10
0.
6807
1E+O
9 0.
7317
28+0
9 O
.l400
2E+l
l O
.l401
4E+
10
0.50
479E
+
10
0.47
454E
+
10
O.l3
149E
+ll
0.37
787E
+
11
0.20
903E
+
11
0.41
825E
+ 10
O
.l386
OE
+ 11
0.
1069
7E
+ 11
O
.l27O
OE
+ 11
0.
3892
38+
10
0.51
8978
+ 10
0.
6969
58
+ 10
0.
2734
4E+
10
0.87
13O
E+
10
0.61
3708
+ 10
0.
8211
9E+
10
0.50
4528
+
10
0.61
7268
+ 10
0.
4723
5E
+ 10
%
9?92
9E+
10
0.63
553E
+05
0.16
7418
+ 16
O
.l338
8E+O
6 0.
2689
0E+
16
O.l3
876E
+O6
0.95
225E
+ 15
0.
7487
3E+0
5 0.
9801
2E+
15
O.l0
702E
+O6
0.35
5608
+ 15
0.
4245
1E+O
6 0.
2728
4E+
15
0.25
845E
+O6
O.l8
563E
+ 15
0.
8919
4E+O
5 0.
1255
48+
16
0.80
810E
+05
0.11
3378
+15
0.79
040E
+0
5 0.
3993
3E
+ 15
09
0319
E+O
5 0.
4279
OE
+ 15
0
1291
88+0
6 0.
1686
28+
16
0.21
4058
+06
0.78
4188
+ 16
0.
9052
5E+0
5 O
.l934
8E+
16
0.13
0948
+06
0.52
817E
+ 15
O
.l190
4E+O
6 O
.l630
4E+
16
O.l1
123E
+06
O.l1
765E
+16
0.95
6OO
E+O
S O
.l217
6E+
16
O.l0
116E
+06
@.3
9351
E+
15
O.l0
551E
+O6
0.54
770E
+ 15
0.
1015
88+0
6 0.
7048
78+1
5 0.
9680
7E
+05
0.26
395E
+
15
0.93
225E
+05
0.81
896E
+ 15
0.
9309
38
+ 05
0.
5664
9E
+ 15
0.
9705
3E
+05
0.79
875E
+
15
0.94
66O
E+0
5 0.
4779
5E+
15
0.79
552E
+05
0.48
305E
+ 15
0.
9473
9E
+05
Ct4
4937
E
+ 15
09
5199
E+“
,5
O.?
246O
E+
15
0901
60E
+05
O.l9
956E
+ 16
0.
3470
6E
+06
0.26
6998
+
16
0.28
107E
+O6
O.l2
454E
+ 16
0.
9960
8E+0
5 O
.l188
2E+
16
O.l4
830E
+O6
0.45
1198
+15
0.52
987E
+O6
0.54
190E
+ 14
0.
4206
OE
+O6
0.61
5998
+ 14
O
.l331
3E+O
6 O
.l571
0E+
16
0.96
3808
+05
O.l1
381E
+15
0.91
822E
+05
0440
06E
+15
O.l4
439E
+06
0.36
3318
+15
0.18
5708
+06
O.l1
874E
+ 16
0.
2320
68
+ 06
0.
4058
7E
+ 16
O
.l753
3E+0
6 0.
2336
4E+
16
0.14
6828
+06
0.56
0908
+ 15
O
.l360
2E+O
6 0.
1714
78+
16
O.l2
507E
+O6
O.l2
097E
+ 16
O
.l123
5E+O
6 0.
1251
48+1
6 O
.l115
0E+0
6 0.
3898
5E+
15
O.l1
603E
+O6
0.54
9518
+15
O.l0
94O
E+0
6 0.
6853
1E+
15
O.l0
412E
+06
0.26
949E
+ 15
0.
9487
2E+O
5 0.
7681
9E+
15
0.95
897E
+05
0.54
928E
+ 15
0.
1045
38+0
6 0.
7865
7E+
15
0.90
3738
+05
0.41
0628
+ 15
0.
8898
68
+ 05
0.
5080
3E
+ 15
O
.l101
9E+0
6 0.
4863
98+
15
q.t0
663E
+O6
0.93
304E
+ 15
(58)
(5
9)
(60)
(6
1)
(62)
(6
3)
(64)
(6
5)
(66)
(6
7)
(68)
(6
9)
(70)
(7
1)
i74j
(75)
(7
6)
(77)
(7
8)
(79)
U
-4
f8ll
5400
55
00
5600
57
00
5800
59
00
6000
61
00
6200
63
00
6400
65
01
6502
65
03
6504
65
05
6506
65
07 +
7
66+
67
6803
69
00
7000
71
00
7200
75
00
7600
77
00
78+
79
-
H’h
old
appl
ian
ce
Ele
c. l
igh
t eq
. R
-TV
co
mm
un
. eq
. E
lect
ron
ic c
amp.
E
lect
rica
l eq
uip
. M
otor
ve
h.
and
eq.
Air
craf
t an
d pa
rts
Tra
nsp
ort
equ
ip.
Pro
f. s
cien
t. s
upp.
O
ptic
al
supp
lies
Mis
c. m
anu
fact
. R
ailr
oad
Loc
al
tran
spor
t M
otor
fg
t. t
ran
sp.
Wat
er t
ran
spor
t A
ir t
ran
spor
t P
ipe
lin
e tr
ansp
. ‘3
Tra
n.
busn
ss.
serv
. C
omm
un
icat
ion
s W
ater
san
it.
serv
. W
hol
e, r
etai
l tr
. F
inan
ce,
insu
ran
ce
Rea
l es
tate
H
otel
s, p
ers.
ser
v.
Au
to r
epai
r A
mu
sem
ents
M
ed.,
e&c.
se
rv.
Gov
t.
ente
rpri
ses
Gov
ern
men
t H
ouse
hol
ds
0.55
475E
+ 1
0 0.
4463
0E +
10
O.l
786O
E+
il
0.70
304E
+ 1
0 0.
3322
2E +
10
0.50
531E
+
11
0.25
355E
+ 1
I 0.
9126
2E+
10
0.
6221
4E+
10
04
4417
E +
10
0.95
030E
+ 1
0 O
.l58
29E
+
11
0601
68E
+
10
0.24
930E
+ 1
1 0.
5477
2E +
10
0.99
192E
+
10
0.12
297E
+ 1
0 0.
5691
1E+
11
0.
2523
9E +
11
O.l
9664
E+
10
O
.l95
87E
+
12
0.64
8108
+ 1
1 0.
1218
5E+
12
0.
2553
5E +
11
O.l
9938
E+
11
O
.l19
93E
+ll
0.
6549
9E +
11
0.18
5448
+
11
0.32
506E
+
12
0.92
53lE
+
12
O.l
0094
E+
O6
0.55
317E
+
15
0.81
8638
+05
0.
3705
28+
15
0.
757O
OE
+05
0.
1367
68+
16
0.
9556
7E +
05
0.65
919E
+ 1
5 0.
7613
4E+
05
0.26
054E
+
15
0.98
568E
+05
0.
4988
8E +
16
0.88
363E
+ 0
5 0.
2242
2E+
16
0.
1035
88+
06
0.94
193E
+
15
0.78
362E
+O
5 0.
4937
2E+
15
0.
6399
5E+
05
0.29
171E
+
15
0.83
480E
+ 0
5 0.
7829
68 +
15
O.l
0838
E+
O6
O.l
6642
E+
16
0.91
023E
+05
0.
5469
4E+
l5
O.l
1922
E+
06
0.29
615E
+
16
0.12
4688
+06
0.
6791
2E+
15
O
.l60
93E
++
O
.l59
23E
+
16
O.l
9262
E+
O6
0.23
638E
+
15
0.57
173E
+ 0
5 0.
3249
4E +
16
0.50
929E
+O
5 O
.l31
lOE
+16
0.
8104
5E+
05
O.l
5910
E+
15
0.
7834
78+
05
O.l
5274
E+
17
0.
6603
5E+
05
0.42
150E
+
16
0.37
1618
+05
0.
4528
1E+
16
0.
7969
4E+
05
0.20
009E
+
16
0.72
4878
+05
O
.l44
10E
+
16
0.65
1748
+05
0.
7728
1E+
15
0.
7398
0E+
05
0.48
42lE
+
16
0.36
668E
+05
O
.l29
46E
+
16
0.65
952E
+05
0.
2143
8E+
17
0.79
136E
+05
0.
7322
6E+
17
O.l
2188
E+
O6
0.59
980E
+
15
0.98
723E
+05
04
0352
E+
15
0.
8488
4E+
05
0.14
4298
+
16
O.l
1964
E+
O6
0.73
4698
+15
0.
9950
5E+
05
0.30
86O
E+
15
O.l
1167
E+
06
0.52
9228
+16
0.
9260
9E+
05
0.21
948E
+
16
O.l
1562
E+
06
0.98
377E
+l5
0.
8847
0E +
05
0.52
386E
+ 1
5 0.
8822
68 +
05
0.36
673E
+ 1
5 0.
9797
18+
05
0.86
005E
+
15
O.l
1586
E+
O6
0.10
8588
+16
0.
9295
3E +
05
0.32
009E
+ 1
5 0.
8452
0E t
05
O.l
5856
E+
16
0.
2227
4E t
06
0.50
519E
+
15
0.19
190E
tO6
0.62
647E
+l5
0.
1907
2E t
06
0.85
387E
+ 1
4 0.
6116
6Et0
5 0.
3083
lE+
16
0.
5373
3Et0
5 0.
1162
3Et
16
0.97
541E
t 0
5 0.
8264
68 +
14
0.80
762E
+05
0.
1225
7Et
17
0.70
166E
t 0
5 04
0825
E +
16
0.31
341E
t05
0.35
228E
t 16
0.
8512
6Et0
5 0.
1517
6Et
16
0.75
280E
t 0
5 0.
1200
7E +
16
0.69
126E
t 0
5 0.
7328
9E t
15
0.
8059
8E t
05
0.39
017E
t
16
0.59
465E
+ 0
5 0.
9459
3E +
15
0.71
659E
+05
0.
1937
7Et
17
0.79
741E
tO5
0.51
7488
+
17
Tab
le
9
1-O
en
ergy
an
alys
is
resu
lts
for
1972
. I-
O
code
re
fers
to
th
e B
EA
se
ctor
de
tiniii
ons
incl
uded
in
ou
r 87
ord
er
sect
ors.
R
esul
ts
for
both
di
rect
en
ergy
in
put
vect
ors
liste
d in
tab
le
4 ar
e gi
ven.
I-O
N
o.
Cod
e Se
ctor
na
me
Dol
lar
outp
ut
($19
72)
DIR
EC
T
DE
C
Em
b.
ener
gy
Em
b.
ener
gy
Em
b.
ener
gy
Em
b.
ener
gy
inte
nsity
in
put
inte
nsity
in
put
(Btu
/%)
(Btu
) (B
tu/%
) (B
tu)
(1) $1
(4
) (5
) (6
) (7
)
I:;
(10)
(1
1)
(12)
(1
3)
(14)
(1
5)
(16)
(1
7)
(18)
(1
9)
(20)
(2
1)
(22)
(2
3)
(24)
(2
5)
I:;;
l3
RI
700
800
3101
68
01
6802
10
0 20
0 30
0 40
0 50
0 60
0 90
0 10
00
1100
12
00
1300
1500
16
00
1700
18
00
1900
20
00
2100
2300
24
00
35nn
Coa
l m
inin
g 0.
5442
4E
+ 10
C
rude
pe
tro,
ga
s O
.l781
9E+
11
Petr
o re
lin.
prod
. 0.
2958
1E+
11
Ele
ctri
c ut
il.
0.31
6658
+11
Gas
ut
ilitie
s 0.
2013
8E+l
l L
ives
tock
0.
4333
9E
+ I1
M
isc.
ag
. pr
oduc
ts
0.35
08O
E
+ 11
Fo
rest
., lis
h pr
od.
O.l9
705E
+ 10
A
g.,
for.,
lis
h se
rv.
0.35
657E
+
10
Iron
or
e m
inin
g 0,
1232
5E+
10
Non
ferr
. m
inin
g 0.
227O
OE
+ 1
0 St
one
clay
m
in.
0.28
4718
+ 10
C
hem
. m
iner
al
min
. 0.
7746
08
+ 09
N
ew
cons
truc
tion
0.12
9588
+ I2
M
aint
. re
p.
cons
t. 0.
3641
7E+
I1
Ord
nanc
e 0.
7084
1E+
IO
Food
O
.l183
0E+
I2
Tob
acco
0.
9226
9E
+ IO
Fa
bric
an
d m
ills
O.l7
632E
+ 1
I T
extil
e go
ods
0.59
5848
+ 10
A
ppar
el
0.30
1838
+ I1
Fa
b.
text
ile
prod
. 0.
4922
6E
+ IO
W
ood
prod
ucts
0.
215l
lE+l
l W
ood
cont
aine
rs
0.46
570E
+
09
H’h
old
furn
iture
0.
7281
68+
IO
Furn
., lix
ture
s 0.
3727
5E
+ IO
Pa
per
prod
ucts
O
.l983
3E+
II
ParK
XhU
ard
cml,
0.79
0978
-t
10
0.30
608E
+
07
0.24
739E
+
I6
0.69
555E
+0
5 0.
3597
7E
+ I5
0.
2579
1E+0
7 0.
2303
5E+
I6
0.35
763E
+05
0.61
237E
+ I5
O
.l604
7E+O
7 0.
4330
4E3
17
0.57
363E
+05
0.18
7448
+ I6
0.
5619
OE
+06
0.14
3368
+ 17
0.
7090
7E+O
5 O
.l601
3E+1
6 0.
8926
5E+O
6 0.
1652
68+
17
0.46
244E
+O5
0.81
828E
+ I5
0.
7693
8E+0
5 0.
3357
7E+
16
0.78
979E
+O5
0.31
169E
+ I6
0.
8462
8E
+ 05
0.
2984
6E
+ 16
0.
9565
7E
+ 05
0.
2065
7E
+ I6
0.
8987
8E+0
5 O
.l77l
OE
+l5
O.l1
603E
+O6
O.l1
120E
+l5
O.l1
432E
+O6
0.40
732E
+ 15
O
.lOllO
E+O
6 0.
2999
88+
I5
O.l2
528E
+O6
O.l5
425E
+ 15
O
.l940
4E+O
6 0.
8625
9E+
14
0.94
867E
+05
0.21
7438
+ 15
0.
1346
38+0
6 O
.l670
9E+1
5 O
.l197
9E+O
6 0.
3605
78+
15
O.l3
7OO
E+O
6 O
.l846
6E+
I5
O.l3
102E
+O6
O.l0
612E
+l5
0.32
819E
+O6
0.50
899E
+ I4
0.
9737
5E+0
5 0.
1261
88+
17
O.l0
996E
+06
O.l2
513E
+ I7
O
.l011
7E+0
6 0.
3684
38+
I6
O.I
1196
E+0
6 0.
3278
08+1
6 0.
9318
78+0
5 0.
6603
58+
15
0.10
010E
+06
0.62
904E
+ I5
0.
8254
38
+ 05
0.
9780
9E
+ I6
0.
9381
7E+0
5 0.
9664
0E+
I6
0.61
078E
+05
0.56
3568
+ I5
0.
6643
4E+0
5 0.
5831
88+
I5
O.l0
556E
+O6
O.l8
508E
+ I6
O
.l588
1E+0
6 0.
2301
38+
I6
O.l0
304E
+O6
0.61
396E
+ I5
O
.l484
7E+0
6 0.
7780
2E+
15
0.90
078E
+
05
0.27
220E
+
I6
O.l1
295E
+06
0.31
89O
E+
16
0.95
5068
+05
0.47
19O
E+
I5
0.12
0818
+06
0.56
762E
+15
0.10
9218
+06
0.23
495E
+ 16
O
.l052
3E+O
6 0.
1827
48+1
6 0.
1037
38
+ 06
0.
4846
9E
+ 14
O
.l104
0E+0
6 0.
4317
5E+
I4
0.91
088E
+
05
0.66
5078
+
15
O.l0
152E
+06
0.67
988E
+ 15
0.
9973
4E+0
5 0.
3712
88+1
5 O
.l127
3E+O
6 0.
3740
18+1
5 0.
I34
85E
+
06
0.26
4148
+
16
O.l9
738E
+06
0.20
739E
+16
“t13
5OE
tQ6
0.89
645E
+lS
0.14
349E
+0
6 0.
KQ
Q\E
+ t6
(4
LbW
(30)
27
00
(31)
28
00
(32)
29
00
(33)
30
00
(34)
31
02
(35)
31
03
(36)
32
00
(37)
33
00
(38)
34
00
(39)
35
00
(40)
36
00
(41)
37
00
(42)
38
00
(43)
39
00
(44)
40
00
(45)
41
00
(46)
42
00
(47)
43
00
(48)
44
00
(49)
45
00
(50)
46
00
(51)
47
00
(52)
48
00
(53)
49
00
(54)
50
00
(55j
51
00
(56)
52
00
(57)
53
00
(58)
54
00
(59)
55
00
(60)
56
00
(61)
57
00
(62)
58
00
(63)
59
00
(64)
60
00
(65)
61
00
(66)
62
00
l’rm
tmg
, p
ubl.
Che
m.
prod
ucts
Pl
astic
s D
rugs
. to
il.
prep
. Pa
ints
Pa
ving
A
spha
lt R
ubbe
r pr
oduc
ts
Lea
ther
pr
oduc
ts
Foot
wea
r G
lass
pr
oduc
ts
Ston
e cl
ay
prod
. Pr
im.
ir.,
stl.
man
uf
Prim
. no
nfer
r. m
et.
Met
al
cont
aine
rs
Hea
ting,
pl
umbi
ng
Scre
w
mat
h.
prod
. Fa
b.
met
al
prod
. E
ngin
es,
turb
ines
Fa
rm
mac
hine
ry
Con
st.,
min
ing
eq.
Mat
. ha
ndlin
g.
eq.
Met
alw
orki
ng
eq.
Spec
. in
d.
mat
h.
Gen
. in
d.
mat
h.
Mac
h.
shop
pr
od.
Oft
. co
mpu
t. m
ath.
Se
rvic
e in
d.
mat
h.
Ele
c.
ind.
ap
para
t. H
’hol
d ap
plia
nce
Ele
c.
light
eq
. R
-TV
co
mm
un.
eq.
Ele
ctro
nic
cam
p.
Ele
ctri
cal
equi
p.
Mot
or
veh.
an
d eq
. A
ircr
aft
and
part
s T
rans
port
eq
uip.
Pr
of.
scie
nt.
supp
.
U.L
Yb_
iSh+
11
0.
2404
lE+
11
0.96
8408
+
10
O.l7
228E
+ll
0.36
lOlE
+ 10
0.
9026
08
+ 09
0.
9470
08
+ 09
0.
2064
8E
+ I 1
0.
1052
48+
10
0.45
2918
+ 10
0.
5583
48+
10
O.l5
267E
+ I1
0.
3644
08
+ 11
0.
2387
48
+ 11
0.
4823
6E
+ 10
O
.l530
4E+l
l O
.l113
5E+l
l O
.l414
1E+
11
0.54
095E
+
10
0.55
662E
+
10
0.78
886E
+
10
0.28
0908
+
10
0.71
48O
E+
10
0.58
6338
+
10
0.81
3208
+ 10
04
4433
E+
10
0.80
508E
+
10
0.84
9548
+
10
0.10
3928
+
11
0.66
5898
+
IO
0.55
221E
+ 10
0.
1795
08+
11
0.83
929E
+ 10
0.
4276
7E
+ 10
0.
6508
OE
+
11
O.l7
021E
+ II
0.
1276
38+
11
0.69
807E
+
10
U.6
676U
E +
05
U20
634E
+
16
O.l4
883E
+06
U36
042E
+ 16
O
.l369
0E+0
6 0.
1298
18+
16
0.78
111E
+05
O.l4
007E
+16
O.l1
988E
+O6
U43
596E
+ 15
0.
4939
8E
+ 06
U
4252
6E
+ I5
0.
3399
3E
+ 06
t-
t.330
958
+ 15
0.
9474
18+0
5 O
.l976
2E+
16
0.98
5378
+05
O.l0
363E
+ 15
0.
8635
4E+0
5 0.
3916
OE
+lS
O.l0
568E
+O6
0.58
988E
+15
O.l3
26O
E+0
6 0.
2028
3E+
16
0.19
2378
+06
U68
477E
+ 16
O
.l070
9E+O
6 0.
2578
88+
16
O.l2
594E
+06
0603
82E
+15
0.11
4678
+06
0.17
4848
+ 16
0.
1156
68+0
6 O
.l276
6E+1
6 0.
1022
38+0
6 O
.l448
3E+
16
0.97
906E
+O5
0.53
047E
+ 15
0.
9267
2E
+ 05
0.
5250
4E
+ 15
0.
9536
7E
+ 05
0.
7605
0E
+ 15
0.
9843
8E+0
5 0.
2767
98+
15
0.96
626E
+
05
0.70
102E
+
15
0.95
709E
+0
5 0.
5665
1 E
+ 1
5 O
.l044
7E+0
6 0.
8454
1E+
15
0.10
850E
+0
6 0.
4811
4E
+ I5
0.
7652
3E
+05
0.62
7028
+
15
0.90
2OO
E +
05
(I.7
6970
8 +
I5
0.95
838E
+
05
0.99
3788
+
15
0.88
2728
+
05
0.59
2498
+
I5
0.81
8448
+05
0.46
8238
+15
0.80
753E
+O5
U.l4
589E
+ 16
0.
8898
28
+ 05
U
.741
43E
+
15
0.81
532E
+05
0.35
898E
+ I5
0.
9003
88
+05
U58
9OO
E +
16
0.90
362E
+O5
0.15
4298
+ 16
0.
9994
1 E
+ 0
5 0.
1276
48
+ I6
0.
8331
4E+0
5 0.
5863
3E+
15
0.99
577E
+
05
0.23
375E
+
16
0.31
147E
+06
0.29
0668
+ 16
0.
2599
8E+0
6 0.
1489
18+
16
0.89
680E
+05
O.l4
551E
+ 16
O
.l571
7E+O
6 0.
5195
8E+1
5 0.
5412
8E+O
6 0.
7683
OE
+ 14
0.
4924
5E
+06
0.88
694E
+
14
O.l3
244E
+06
0.23
236E
+ 16
0.
1234
08+0
6 O
.l072
6E+
15
0.10
1338
+06
0.42
9498
+ 15
O
.l591
3E+0
6 0.
4739
2E+
15
0.18
3808
+06
0.14
3538
+ 16
0.
2456
1E+0
6 0.
4323
8E+
16
0.19
4678
+06
0.30
6978
+ 16
O
.l60l
OE
+06
0.70
933E
+15
O.l3
787E
+O6
O.l9
174E
+ 16
0.
1394
28+0
6 O
.l383
9E+1
6 O
.l248
6E+0
6 O
.l526
5E+
16
O.l1
380E
+06
0.56
7898
+ 15
O
.l077
0E+0
6 0.
5472
18+
I5
O.l0
937E
+06
0.78
0558
+ 15
O
.l101
2E+0
6 0.
2858
48+
15
O.lU
OlO
E+0
6 0.
6449
78+
15
O.l0
375E
+06
0.55
945E
+ 15
O
.l106
7E+0
6 0.
8032
lE+
15
O.l0
450E
+06
0.41
OO
lE+
15
0.84
9038
+
05
0.64
6638
+
15
O.l0
334E
+O6
0.80
278E
+ I5
O
.l110
7E+0
6 O
.lOU
96E
+l6
O.l1
020E
+06
0.66
218E
+ I5
O
.l007
8E+0
6 0.
5156
5E+
15
0.91
074E
+05
O.l5
286E
+ 16
O
.l083
2E+0
6 0.
7801
3E+
15
O.l0
419E
+O6
0.41
254E
+ 15
O
.l061
6E+0
6 0.
6499
58+
16
0.98
020E
+05
O.l5
118E
+ 16
0.
1144
88+0
6 0.
1363
08+
16
0.90
597E
+
05
0.58
6788
+
I5
Tab
le 9
(co
ntin
ued)
I-O
N
o.
Cod
e Se
ctor
na
me
Dol
lar
outp
ut
($19
72)
DIR
EC
T
DE
C
Em
b. e
nerg
y E
mb.
ene
rgy
Em
b. e
nerg
y E
mb.
ene
rgy
inte
nsity
in
put
inte
nsity
in
put
(Rtu
/S)
(Rtu
) (R
tu/S
) (R
tu)
(67)
(6
8)
(69)
(7
0)
(71)
(7
2)
(73)
(7
4)
I:;
(77)
(7
8)
(79)
(8
0)
(81)
I::;
(84)
(8
5)
(86)
(8
7)
6300
O
ptic
al
supp
lies
6400
M
isc.
man
ufac
t. 65
01
Rai
lroa
d 65
02
Loc
al t
rans
port
65
03
Mot
or
fgt
tran
sp.
6504
W
ater
tr
ansp
ort
6505
A
ir t
rans
port
65
06
Pipe
lin
e tr
ansp
. 65
07 +
73
Tra
n. b
usns
s. s
erv.
66
+ 6
7 C
omm
unic
atio
ns
6803
W
ater
sa
nit.
ser.
6900
W
hole
. re
tail
tr.
7000
Fi
nanc
e,
insu
ranc
e 71
00
Rea
l es
tate
72
00
Hot
els,
per
s. s
erv.
75
00
Aut
o re
pair
76
00
Am
usem
ents
77
00
Med
., ed
uc.
serv
. 78
+ 7
9 G
ovt.
ente
rpri
ses
- G
over
nmen
t -
Hou
seho
lds
0.65
269E
+ 1
0 O
.l197
9E+
11
O
.l506
7E+
11
0.
7406
3E +
10
0.29
993E
+ 1
1 0.
7307
5E +
10
O.l3
134E
+
11
O.l6
167E
+ 1
0 0.
7034
6E +
11
0.36
078E
+ 1
1 0.
2582
2E +
10
0.26
493E
+ 1
2 0.
7788
6E +
11
0.17
4588
+
12
0.30
504E
+ 1
1 0.
2434
OE
+ 1
1 O
.l274
5E+
11
0.
8490
08 +
11
O.l8
919E
+ll
0.
4162
28+
12
0.
1283
48+
13
0.69
182E
+05
0.
4599
5E+
15
0.93
679E
+05
O
.l112
1E+
16
O.l0
987E
+06
O
.l660
7E+
16
0.13
8748
+06
0.
1023
28+
16
O
.l062
9E+
O6
0.31
862E
+ 1
6 O
.l526
5E+
O6
O.l0
977E
+
16
O.l6
748E
+O
6 0.
2198
3E+
16
0.16
596E
+ 0
6 0.
2682
9E +
15
0.72
104E
+05
0.
5098
8E+
16
0.43
236E
+05
O
.l716
1E+
16
0.
9556
5E +
05
0.24
677E
+ 1
5 0.
7737
18+
05
0.20
498E
+ 1
7 0.
6565
6E+
05
0.51
122E
+ 1
6 0.
3260
5E+
05
0.56
923E
+ 1
6 0.
8663
08 +
05
0.26
303E
+ 1
6 0.
7906
OE
+05
O
.l924
3E+
16
0.
7353
5E +
05
0.93
693E
+ 1
5 0.
7776
9E +
05
0.66
0268
+ 1
6 0.
4123
7E+
05
O.l5
3OO
E+
16
0.55
567E
+05
0.
2312
8E+
17
0.71
033E
+05
0.
9116
3E+
17
0.81
939E
+05
0.
4872
08+
15
O
.l065
2E+
O6
O.l1
485E
+
16
O.l2
441E
+06
O
.l064
7E+
16
0.
9578
2E +
05
0.47
643E
+ 1
5 09
0985
E+
05
O.l8
652E
+
16
0.24
4948
+06
0.
8338
4E+
15
O.l9
162E
+O
6 0.
8368
6E+
15
O.l6
157E
+06
0.
9755
9E+
14
0.67
547E
+05
0.
4407
9E +
16
0.47
483E
+05
O
.l594
6E+
16
0.
9843
3E+
05
O.l9
295E
+
15
0.79
248E
+05
O
.l648
5E+
17
0.47
30lE
+05
0.
4666
4E+
16
0.31
021E
+05
0.
4780
7E+
16
0.82
911E
+O
5 O
.l893
4E+
16
0.77
3338
+05
O
.l728
1E+
16
0.75
9768
-I- 0
5 0.
8366
38 +
15
0.79
8148
+05
0.
5214
3E+
16
0.57
458E
+05
0.
1057
68 +
16
0.58
533E
+05
0.
1998
18+
17
0.
6980
4E +
05
0.62
447E
+ 1
7
R. Cosranza and R.A. Herendeen, Embodied energy and economic value 149
Table 10
Summary statistics for embodied energy estimates calculated using the alternative direct energy input vectors shown in table 4. RZ estimates are for a linear regression of dollar output by sector on embodied energy input (see tables 7-9 for listings of these series and fig. 2 for plots). All R2 values are significant at the 0.001 level. Coefficient of variation (COV) estimates are for the
embodied energy intensity vectors listed in tables 7-9.
Year Sectors included in statistics
DIRECT DEC
R2 COV R2 cov
1963 l-87 0.800 2.35 0.981 0.67 6-87 0.986 0.69 0.981 0.67 l-85 0.239 2.34 0.858 0.67 685 0.884 0.69 0.858 0.67
1967 l-87 0.814 2.43 0.984 0.64 6-87 0.987 0.69 0.984 0.64 1-85 0.251 2.42 0.866 0.64 6-85 0.873 0.69 0.866 0.64
1972 l-87 0.805 2.25 0.978 0.64 6-87 0.986 0.61 0.978 0.64 l-85 0.247 2.24 0.851 0.64 6-85 0.876 0.61 0.851 0.64
The present study also indicates the relative merits (as a predictor of market value) of calculations of embodied energy based on alternative treatments of the direct energy input vector, E. We also find that the results for the three different years are very similar, indicating a stable pattern over the time interval of the data.
Comparison of the various alternatives in table 10 brings out some interesting points. The R2 values for alternative 1, (DIRECT) including only sectors 687 or 6-85 in the regression, are much higher than with the primary energy sectors (l-5) included, and are very close to those for alternative 2 (DEC) with or without the primary energy sectors. Alternative 1 represents direct energy input to the economy (specifically to the primary energy sectors) while alternative 2 represents consumption of that energy distributed through the economy. Distribution is the key word here, since this is the major difference between the two alternatives. The primary energy sectors distribute energy to the rest of the economy, and if this distribution function is factored out by excluding the primary energy sectors from the regression or by predistributing the energy by looking at consumption rather than production (i.e., alternative 2), then higher correlations result. The degree of departure of the energy sectors from the regression line in alternative 1 (fig. 2) can thus be viewed as a measure of the net energy input to the system.
A -1963
28
f
Direct
26
J--J--J Kl--J-d 35 40 30 35 40
Log Embodied Energy Input
9 -1967
28
26 - - _ .- .
*. 24 - +.F
Log Embodied Energy Input
26 ; P - s 0 24-
;I = 0
o 22- : _I i
20 I
. Direct .
. .- 5
P’: - .” -
1’ . . .
c - 1972
26 .
D@C
. 26
. .
Log Embodied Energy Input
Fig. 2. Log-log plots of embodied energy inputs vs. dollar output for the 87 sector data, for three years and two alternative direct energy input vectors.
R. Costanza and R.A. Herendeen, Embodied energy and economic value 151
The primary energy sectors functions are like the transportation sectors, which alse require special treatment in I-O analysis based on the difference between the services they provide and their physical inputs and outputs. If a strictly physical interpretation were applied to the transportation sectors, they would receive almost all goods produced in the whole economy as inputs and redistribute them as output, masking information on transfers of goods between sectors. For this reasun, the transportation sectors in I-O analysis are thought of as providing transportation services that are pur- chased by the producing sector, preserving the connection between the producing and consuming sector but adding a ‘transportation margin’. For analogous reasons, the primary energy sectors should be thought of as providing a ‘transportation service” in moving primary energy from nature to the consuming sectors. The DEG energy input vector incorporates this interpretation.
In a previous article [Herendeen (1981)j it was shown that the necessary and sufficient conditions for constant energy intensities in an I-O analysis are that the direct energy input vector be proportional to the dollar value of net input (the remaining components of value added). With the boundaries and approximations used in this study, the dollar value of net input is equal to property type income (PT~), and there is, in fact a relatively high correlation between PTf and direct energy consumption (DEC) across sectors. This explains the relatively constant energy intensities calculated for alternative 2. For alternative 1, however, this correlation is very low, since only the energy sectors (l-5) have direct energy inputs under this alternative. The energy intensities are still relatively constant, however, except for the energy sectors (I-5). The distributive function of the energy sectors is responsible for this phenomenon, In the appendix we prove that if and only if the sum of the energy rows (1-5 in our case) of U is proportional to net dollar input (PTX in our case) then E is constant except for the energy sectors.
5. The effects of adding labor and government sectors: The mathematical artifact argument
Several critics of this approach have argued that closing the input-output matrix as we do here must inevitabIy lead to a reduction in the variance of the energy intensities, or, in the terms of this paper, an inevitably high correlation between economic value and embodied energy [Herendeen (1981), Huettner (1982), Reister (personal comment)]. (This is not worrisome, of course, if inclusion of the household and government sectors is uncontroversial.) In this section we present the mathematicaf artifact argument in some detail, establish several theorems which aim in the right direction, and finally present results of some empirical tests.
The manipulations we have performed %lose’ the matrix by converting two parts of final demand to producing sectors whose outputs (labor and
152 R. Costanza and R.A. Herendeen, Em~died energy and eccmomie v&e
government services), previously a part of value added, are now listed as a consumed input bye all sectors. The rank of the I-O matrix is increased by two, while the “closedness’ increases, We define closedness as
where
6 =net output of sector i, Xi =gross output of sector i.
Closedness thus varies between 0 (possible only for a trivia1 one-sector system) and 1 (for a system with no net output at all)_
The new inputs (labor and ~o~e~ment services) tend to be fairly large fractions of all inputs, and are non-zero for almost ivery sector. Therefore one suspects a homogeni~ng effect on the energy intensities (s’s), which has been stated thus [~er~deen (1981, p. 67i)j:
‘The intuitive argument that inclusion of labor and government as producing as well as consuming sectors ought to force the s’s in the direction of a ~mmon value is this: every economic sector Rays wages (and practically every one pays taxes), and these expenditures are a large fractiun of the expenditures for all inputs. (Labor costs are typically 300$--500/;; of the tota& Bureau of Economic Analysis, 1980). Thus the inclusion of labor requires every sector to have a large input flow from the same sector. Referring to fig. 1, we see that the reason that the E’S can be different is that each sector can, in principle, have a different input mix. Inclusion of the (necessarily large) labor input to a11 sectors reduces that possibility.’
To demonstrate this argument, we will use the 4 x 4 example shown in table f 1. In the language of table I I, we ask what happens to the coefficient of variation (standard deviation divided by the mean) of E,, ezl and Ed as L1, ,?+ and L, increase from zero up to their maximum allowable values, equal to total vaiue added before the inclusion of labor. In this example we make endogenous only one sector (labor), vs. two (labor and government) in the actual data, since this simplifies the discussion and does not cause any loss of generality. The inputs to the labor sector (person& ~ns~mption~ expand in such a way that their total just equals the production of labor. For discussion, we will use the normalized labor (t=LP- *) and energy input (e=Ep- “) vectors. We can test the foilowing hypotheses:
Hypothesis I (the ‘strong hypothesis’). Starting with fl = 1, = i3 =0, use of any admissable positive Ii will always decrease the coeficient of variation of the 3 E’S. We will calf the coefficient of variation of the E’S ‘COVE’. Thus COVE3 is the coefficient of variation of the 3 E’S in our example-
R. Costanza and R.A. Herendeen, Embodied energy and economic value
Table 11
Example 4 x 4 input-output table. All units are dollars except for the direct energy inputs, which are Btu’s.
Sector
Personal consumption Net Total
1 2 3 (PC) output output
1 1 1 2 0.3(L,+L,+La) 6-(PC,) 10 2 1 2 1 0.4(Lt+L,+L,) 6-(PC,) 10 3 1 3 1 0.3(L, + L, + Ls) 5-(P&) 10
Wages LI La Ls 0 0 L,+L,+L,
Profits 7-L, 4-L2 6-L, 0 0 17-(L,+L,+L,)
Energy E, Es Es E,
For above: (I=L/lO, G=lJVT-‘Ae=EVT-‘)
I-G = 0.9 -0.1 -0.2 -0.3 -0.1 0.8 -0.1 -0.4 -0.1 -0.3 0.9 -0.3
1, 1, 1, 1 e = O.lE, O.lE, O.lE, O.lE,
Table 12
Coefficient of variation of the first three epsilons (COVEE3) for various combinations of the normalized direct energy input vector (e) and the normalized labor vector (I). See
table 11 for details.
Normalized energy input (e= Eve’)
Labor input Closed- Proportional to 1 1 1 1 1 2 3 4 ness (1111) (1000) (0100) (0010) 1st row ofG
(1) No labor 0000 0.43 0.1300 0.7425 0.9688 0.6886 0.2066
(2) ‘Actual’ 0.5 0.2 0.2 0 0.79 0.1043 0.4573 0.4189 0.2516 0.0744
(3) Prop. to VA 0.37 0.21 0.32 0 0.79 0.0458 0.3600 0.4251 0.3282 0.0582
(4) Constant 0.3 0.3 0.3 0 0.79 0.1300 0.3108 0.4929 0.3349 0.1320
(5) Mirror image 0.1 0.4 0.4 0 0.79 0.2927 0.1663 0.5975 0.4500 0.3272
153
Conclusion 1. This hypothesis is false by counter-example. In table 12 we see that it is violated for e=(l, 1, 1, l), and l=(O.l, 0.4, 0.4, 0). However, from table 12 the hypothesis appears true for the restricted case of e having just one non-zero element and also not satisfying Hypothesis 3 below.
154 R. Costanza and R.A. Herendeen, Embodied energy and economic value
Hypothesis 2. Use of a labor vector 1 such that normalized profits are proportional to e, results in CO VE3 = 0.
Conclusion 2. This hypothesis is true in general, and was proved previously [Herendeen (198 l)].
Hypothesis 3. Use of any 1 whose first three entries are proportional to the first three entries of e results in the same value for COP’E3.
Conclusion 3. This hypothesis is true in general, and is proved in the appendix.
Hypothesis 4. By examining certain values from G( = UVT- ‘), I, and e it is possible to predict when COVE3 will decrease without actually calculating it.
Conclusion 4. This hypothesis is as yet unproven.
Hypothesis 5 (the ‘weak hypothesis’). While it can be shown by hypothesis l-3 above that COVE3 can be reduced to zero, remain unchanged, or increase on the addition of some positive Z, and while Hypothesis 4 is unproven, it is still true that for a wide class of reasonable 1 it will very likely decrease.
Conclusion 5. This is the strongest statement that can now be made of the mathematical artifact argument, and is obviously sensitive to the definitions of ‘wide class’, ‘very likely’, and ‘reasonable I’. At this point we see no way to proceed except by empirical test applied to the 4 x4 example and to the actual 87-sector data.
What, then, are reasonable values for 1, besides those obtained by the analysis of the first section of this paper? We choose several options and illustrate them by reference to the 4 x 4 example. We then proceed to the 87- sector data.
(1) I=0 This is the base case. The labor sector is assumed to be exogenous. (2) I= actual values used, as in the previous section. For the 4 x 4 example,
we (arbitrarily, in this case) pick 1=(0.5, 0.2, 0.2). (3) 1 proportional to the normalized value added (profit, including labor
costs). In the example this would give I proportional to (0.7, 0.4 0.6). This assumes that labor is a constant fraction of value added, sector by sector.
(4) Z=constant fraction of total inputs. This assumes that a fixed fraction of the value of output is spent on labor. Both 3 and 4 have some justification in reality. Labor is usually the largest component of value added.
(5) C=mirror image of the actual I in 2. This is an attempt to use an 1 which is ‘opposite’ from or inversely correlated with the actual one. This could be done in many ways. By mirror image we mean that li,mirror is set
R. Costanza and R.A. Herendeen, Embodied energy and economic value 155
equal to lmean-(li,actual- I,,,,), where I,,,, denotes the average labor input. In the example, I,,,, =(0.5+0.2+0.2)/3=0.3. Then Il,mirror=0.3- (0.5 -0.3) = 0.1, 12, mirror = 0.3 - (0.2 -0.3) = 0.4, etc. Caution is needed to avoid allowing the I. I, mirror to get too large. In this particular example this doesn’t happen.
In the example (table 12) we have constrained all ‘options’ so that L, + L, + L, = 9, which corresponds to a constant closedness of 1 - 8/(30 + 9) =0.79 vs. l-17/30=0.43 for L,=L,=L,=O.
In fig. 3 we present the results shown in table 12. In fig. 3a there seems to be only one systematic pattern: that for any non-zero values of I the coefficient of variation of all the E’S (COVE3) decreases relative to that for I, = I, = l3 =O, as long as only one entry in e is non-zero. However, for e= (1, 1, 1, l), this is no longer true. Otherwise, there is apparently no con- nection between the options. The ‘mirror image’ can produce a COVE3 that is greater or smaller than that for the ‘actual’.
A - COVE 3 B - COVE 85
1.25
1 F \ /
g :ii 1 2 3 4 5
Labor Input Alternative Labor Input Alternative
Fig. 3. Coefficients of variation (COV) for alternative labor input vectors for the 4 x 4 example (A) and the 87 sector model using 1967 data (B). Labels on A are the normalized direct energy input vector used for each plot. Labor input alternatives are: (1) no labor (labor sector is exogenous); (2) the ‘actual’ labor vector; (3) labor proportional to value added, (4) labor proportional to total input; (5) labor is the mirror image’ of actual labor input. Note that the
order of these alternatives is arbitrary.
Based on this limited example, we come to the following empirical conclusion: For e containing only one non-zero element, COVE3 is reduced as I is increased from 0. Otherwise, no conclusion can be made about COVE3 based, on the relationship of the two 1 vectors, unless they satisfy hypothesis 2 (in which case COVE3 =0) or hypothesis 3 (in which case COVE3 is unchanged). Thus, for a general e with many non-zero elements,
156 A. Co.mnzu and hi. ~~e~ee~, unbodied energy and economic ualue
even the weak hypothesis is not true, and the mathematical artifact argument appears false.
One additional aspect needs mention. The most general formulation of the energy intensity problem allows for the possibility that energy inputs can occur for any sector, so that E is not constrained. In the U.S. economy there are several energy seetors (e.g., coal, refined petroleum), which are the only ones with E+O. However, these sectors consume little energy (usually an exception is electric utilities) and pass the bulk of their input on as energy to be consumed or sequestered by their customers. If the purpose of E is to show where energy is finally consumed, then E should actually be the same as the energy rows of U, or DEC in the g7-sector examples, which includes non-zero entries for all sectors.
In this case it is pa~tieul~ly easy to calculate E. In the appendix we prove that if and only if e=kG, (where C;, means the energy row of G), then
di[(Z-Gp-Z]. 69
Except for the -Z in the bracket this is identical to calculating s when c is zero for all sectors except an entry k in the eth column.
For this special case, one might suspect a connection with the case of having only one non-zero element in e, for which we can make a definite statement about the behavior of COVE3 as I increases from zero. However, applying eq. 5 to the 4 x 4 example quickly shows that for e equal to the first row of G, COVE3 is 0,327 for the mirror image labor case vs. 0.207 for I= 0 (see table 12). Even for this special case, the mathematics artifact argument does not hold.
6. 87-s&w tests
We performed the tests outlined in the previous section for the full 87- sector model Since there was little variation in the overall findings between the three years, we limited our tests to only one year’s I-O model: 1967. The results of using labor input vectors l-5 above for the 1967 87-sector data are given in table 13, and plotted in fig. 3b. Table 13 indicates that adding a labor vector does not in itself guarantee a lower coefficient of variation of the E’S, or a higher RZ between embodied energy and dollar output. The mirror image labor vector, for example, produced a lower Rt (0.013) and a higher COV (1.22) than vector 1 (r=U, R 2=0.394, COVE85 = 1.02). Labor vectors 3 and 4 produced less variation in the s’s than vector 1, but more than vector 2 (the actual input). Vector 4 was not a significant improvem~t on vector 1, but vector 3 (labor input proportional to total value added) was. This is to be expected since the actual labor vector is a relatively large and constant component of value added.
R. Costanzu and R.A. Herendeen, ~rnbo~~ed energy and economic vahe
Table 13
Results of alternative labor vector tests on the full 87 sector model. Tests were performed on the 1967 data with DEC energy input vector. For comparison with the 4 x4 system,
statistical indicators are calculated for sectors l-85 only.
Labor vector R2 CO ?E8S
157
(1) I=0 0.394 1.02 (2) I=actual 0.866 0.64 (3) I a value added 0.832 0.65 (4) 1 a total input 0.457 0.97 (5) I u mirror image 0.013 1.22
We conclude from this analysis that the mathematical artifact argument is not valid for a ‘reasonable’ set of labor vectors. The reduction in COVE85 and the high degree of correlation between embodied energy and dollar value found using the “actual’ labor vector are therefore representative of real relationships and constraints in the economy and are not simply artifacts of the method used to incorporate labor and govermnent energy costs. If they were artifacts, we would expect COVE to decrease dramatically on addition of any large labor vector, which tables 12 and 13 and fig. 3 show is not the case.
It seems that the only remaining objections to this analysis are philo- sophical ones concerning the propriety of removing humans from their ‘controlling’ position outside the economy aid making them endogenous and therefore themselves %ontrolled’ to a larger extent [cf. Daly (19gt)3. This is analogous to the ‘positive vs. normative’ debate in economics. We believe that there is no one universally correct position on either of these questions, but that the answer is dependent on the intended uses of the analysis. In the case of calculating a static measure of total energy cost it seems appropriate to consider humans to be endogenous, since they have already made their energy consumption choices and we merely want to look at the repercussions of them. For making projections into the future, however, it is still debatable whether humans should be considered endogenous, exogenous, or some complex combination of the two.
In any case, our analysis has definitely strengthened the case that embodied energy (calculated the way we suggest) is a good, non-trivial, static correlate of the economic value of the ‘relatively large aggregates of goods and services that make up the entries in I-Q tables. This does not imply that: (1) the market is perfect; (2) this relationship would continue to hold at the level of individual microeconomic transactions; or (3) absolutely no improve- ments in energy efficiency are possible. It is a relationship that applies to
158 R. Costanza and R.A. Herendeen, Embodied energy and economic value
large aggregates, analogous to the way that the gas laws apply only to large assemblages of molecules. The gas laws are, nonetheless, very powerful tools when used to predict the overall behavior of ideal gasses, and we think that embodied energy may be an equally powerful tool to help predict the overall behavior of economic systems.
Appendix
Two theorems regarding predicting certain attributes of the energy inten- sities from propertiesof EY r- l and G.
Theorem 1. Zf and only if EV T-1 is proportional to the pth row of G then
where c is the constant of proportionality and the subscript p means the pth row.
Proof of sufficiency. Assume (EY T-1)1, = Cam, c = constant.. Substituting in eq. (3):
(4 =-?EVT-‘),(Z-C)il =c~(G),,V-G-L
(4t =mz-G)-‘l,t.
For any invertible matrix (Z-G),
(I-G)(Z-G)-‘=I and G(Z-G)-‘=(I-G)-‘-I. 64.3)
Substituting eq. (A.3) into (A.2) proves sufficiency.
Proof of necessity. Rewrite eq. (3):
EVT-l=e(Z-G).
Assume
(s)l =W-G)-‘-K&r, d = constant.
Substituting eq. (A.5) in eq. (A.4):
(A.21
64)
(A-5)
(EVT-‘),=d{[(Z-G)-‘-ZJ(Z-C)),,. 64.6)
Substituting eq. (A.3) in eq. (A.6):
EPkl(G),, which was to be proved.
lkorem 2. F5r G of the form
Fur rn = n OY n f 1 the fu~low~~g is true: If the first m entries of EV ’ - ’ are proport~o~u~ to the first m entries of I
(i.e., to 1,,12 ,..., I,), then the coeficient of variation of the first m elements Of
g=EV=-‘(z-q-’ (A.71
Proof (of su~c~~cy onliy). We wifl prove that under the conditions above, when ls,lz..+ 1, are multiplied by a constant, the first M elements of e are multiplied by a constant. Therefore any normalized dispersion index of the ai, including the coeffkient of variation1 is unchanged.
Assume that the first n elements of E V ‘- ’ are equal to the corresponding elements of Z, i.e., of the (n+ 1)th row in G (there is no loss of generality of assuming equality rather than just proportionality, as we will show below).
We can then write
Using eq. (3) and applying Theorem 1 to the first term on the right-hand side,
The second term on the right-hand side is just a scalar times the In+ 1)th row of (Z-G)-‘.
Now assume that the first n elements of i are multj~lied by @. Following the same steps as above leads to
r+z-q-1 --rJm+l
where the primes refer to this second case. G is identieaI to G except that ali nt 1 elements of the (n-t- 1)th row have been multiplied by /3. Rewriting eq. (A. 10):
(A.11)
The term A is a scalar and can be factored out of the first term on the right-hand side of eq. (A.ll). The question which still remains is how
C(Z--GP - ZJ and [(Z-G’)- 1 -ZJ are related, It turns out that their terms are proportional.
We show this by brute force examination of the elements of the inverses. For an ~~~r~~ie matrix (I-G),
f~-C’L%r~=det(;_C) (-lfn+l+j*det of(Z-G’)
wjth jtll ‘Ow (n -I- 11th eofumn >
removed (A.121
moble (1969, pp. 200, 210)]. For j<n, the numerator of the right-hand side of eq. (A.12) is just p times
the n~erator of the expression for the inverse of (Z-G). Using eq. fA.12), and expanding det (Z-X?) by its (n-f- 1)th raw:
R. Gostanza and R.A. ~~endeen, Embodied energy and ecanomic v&e
Cf~-w’-4l+1,..~
i61
1
=det(Z-G)
det of (Z-G’) with (n-t- l)th row
( (n-i- I)th column > removed
- C
j$I ( - 1)” * 1 ‘j@Ij+det of (Z-G’)) with ($,‘~~n~~) removed
-i-(1 -pr,,,) det of (Z-G”) with n+ lth row
n + 1 th column > removed
(A. 13)
In eq. (A.l3), none of the determinants inside the brackets contains the (n + 1)th row of Z-G, therefore all terms are the same as the corresponding ones of Z-C. In addition, the only terms not linear in fl cancel out. The results is that numerator of eq. (A.131 is also just fi times the numerator for a similar expansion of [(Z-G)-’ -ZJ,+l, “+ 1.
This establishes that the n + 1 elements of [(Z-G)- ’ -I] and [(Z-G’) - ’ - Zl are proportional. Combining this with the fact that the factor A in eq. (A.11) is a constant inde~ndent of column, proves the theorem for M= n. The existence of the second term on the right-hand side of eq. (A. 111, which is non-zero only for the n+ lth element of e, prevents the theorem from appIying to m=n-$- i if the (n+ 11th elements of EYTWt and t are not proportional.
On the other hand, if ali n+ 1 entries in EVT-” are proportional to those of 1, the second term on the right-hand side of eq. (A,ll) is zero and the theorem applies for M=II+ 1. This completes the proof.2
One can wonder why the theorem applies only for m= n ot FE+ 1, but not a smaller number. The reason seems to be that there would be more than one non-zero element in the second term of eq. (A.8) and that other rows af fZ-G)- ’ besides the (n+ 11th would be involved in the right-hand term of eq. (AM}, which would then not be easily factorable.
The case of m = n corresponds exactly to the notion of
(1) starting with an n x n system to which labor is exogenous, (2) adding a labor sector which has fixed input coenicients (i.e., fixed values
of the (n + 11th column of (G), (3) constraining the values of the labor input ~~ffl~ents (the Ii) to the
proportional to EV T-X as states, and yet to vary in absolnte magnitude.
%ince we chose our initial 1 to have its first n elements equal to those of EYT-‘, the theorem is only strictly proved when we note that the above arguments could be used to compare the results of using two rnu~tipl~~tive factors, say /& and j&. Compa~~g the results for the two values of fi would yield the same conclusion as we quote here.
162 R. Costanza and R.A. Herendeen, ~rnb~~~d energy and economic value
David Reister [personal communication (25 April 1983)] has obtained a similar but more limited result. In the language of our proof, he
(1) assumes that G, + r, G, + i = 0, (2) looks at one row of (Z- G,l- ’ at a time, which is equivalent to EYT- ’
having only one non-zero entry, (3) assumes that (ZWr-‘)j is proportional to the jth column sum of (Z-G).
He finds in this case that for the first n rows of (Z--C)-‘, the fractional deviation of each entry from the row mean decreases as the constant of proportionality in his assumption 3 increases.
This result is what is claimed in the mathematical artifact argument, but Reister’s assumptions are too restrictive. In particular, use of EVT-’ containing many non-zero elements is common. But, all of these proofs, his and ours, admittedly cover special cases.
*This research was funded, in part, by the National Science Foundation under Grant PRA- 8003845, and by the Illinois Department of Energy and Natural Resources under Grant ENR- 80.260. We thank B.M. Harmon, C.J. Cleveland, M.J. Lavine, T.J. Butler and H.E. Daly for reviewing earlier drafts and providing useful comments.
References
Bullard, C.W. and R.A. Herendeen, 1975, The energy costs of goods and services, Energy Policy 3,268278.
Carter, A.P. and A. Brody, eds., 1970, Input-output analysis (Elsevier, New York). Costanza, R., 1980, Embodied energy and economic valuation, Science 210, 1219-1224. Costanza, R., 1982, Economic values and embodied energy: reply to D.A. Huettner, Science 216,
1141-I 143. Costanza, R. and 6. Neill, 1981, The energy embodied in the products of the biosphere, in: W.J.
Mitsch. R.W. Bosserman and J.M. Klonatek, eds., Energy and ecological modeling (Elsevier, New York) 745-755.
-.
Costanza, R. and C. Neil& 1984, Energy intensities, interdependence, and value in ecological systems: A linear progr arnming approach, Journal of Theoretical Biology 106,41-57.
Daly, H.E., 1981, Unresolved problems and issues for further research, Postscript in: H.E. Daly and A.F. Umana, eds.. Energy, economics, and the environment: conflicting views of an essential interrelationship (We&ew, Boulder, CO) 165-186.
Eisner. R.. E.R. Simons. P.J. Piener and S. Bender, 1981, Total incomes in the United States, 1946 to 1976: A summary report (International Association for Research in Income and Wealth. Gouvieux. France).
Harmon, Band S. ‘Casler, ‘1981, Calculation of the energy and labor intensities of U.S. ~~oditi~, 1974, and a comparison to 1963, 1967, and 1972, Document no. 315, Energy Research Grout3 Kbtiversity of Illinois, Champaign, IL).
Hannon, It., T. B&eck, D. &nnedy and R. Iilyes, 1983, A comparison of energy intensities 1963, 1967, and 1972, Resources and Energy 5, no. 1,83102.
Herendeen, R.A., 1981, Energy intensities in economic and ecological systems, Journal of Theoretical Biology 91, 607620.
Herendeen, R.A. and C.W. Bullard, 1974, Energy costs of goods and services, 1963 and 1967, CAC document no. 140, Energy Research Group (University of Illinois, Urbana, IL).
Huettner, D.A., 1982, Economic values and embodied energy, Science 216,1141-1143. Kendrick, J.W., 1976, The formation and stocks of total capital (National Bureau of Economic
Research, New York). Leontief, W.W., 1941, The structure of American economy, 1919, 1929: An empirical application
of equilibrium analysis (Harvard University Press, Cambridge, MA).
R. Costanza and R.A. Herendeen, Embodied energy and economic value 163
Nobel, B., 1969, Applied linear algebra (Prentice-Hall, Englewood Cliffs, NJ). Ritz, P.M., 1979, The inputoutput structure of the U.S. economy, 1972, Survey of Current
Business, Feb., 34-72. Searle, S., 1966, Matrix algebra for the biological sciences (Wiley, New York). U.S. Bureau of the Census, 1976, Statistical abstract of the United States (U.S. Government
Printing Office, Washington, DC).