5. Empirical investigation
This section tests the conditions developed in the previous section using data from the US agri-
cultural sector. The reason for using this example is the ready availability of relatively high quality
and comprehensive time series data.
5
.
1
. Data Data for direct and indirect energy used in
agriculture are taken from Cleveland 1995a. To the indirect energy data, energy used in extracting
the petroleum directly used in the industry
7
, and embodied energy associated with labor, using co-
efficients described in Cleveland and Stern 1993 and Stern 1994. The deficiency of this approach
is that the energy cost of the labor used in pro- ducing the other inputs to agriculture is ignored.
This energy associated with labor includes some of the energy used in acquiring and maintaining
knowledge and incorporating it in the inputs. Thus this omission reduces my ability to test the
neoclassical theory regarding the embodiment of knowledge in factors of production described in
Section 2. Data on inputs, outputs, and prices are taken from Ball et al. 1995. Data on the value
added implicit price deflator are from National Income and Product Accounts 1929 – 1982 US
Department of Commerce, 1986 and updated from Survey of Current Business US Department
of Commerce, various issues. The latter data were used in the computation of the Barnett and
Morse unit cost indicator Fig. 1.
Fig. 1. Generalized unit cost GUC, energy cost, and Barnett and Morse unit cost for US agriculture. All indicators are
indexed to 100 in 1948. Indicators defined in the text.
5
.
2
. Econometric models and tests This section tests whether the neoclassical
model of energy cost in Eq. 8 fits the data. Note that the biophysical model Eq. 14 cannot be
estimated as it is unidentified. There are several different augmentation trends to estimate but only
one equation with which to do so. A typical assumption about the technical change trends A
i
is that they could be second order integrated I2 stochastic processes Harvey and Marshall,
1991. An I2 process is a random walk which has a drift term that is itself a random walk. I2
processes cannot be estimated using a linear re- gression based on Eq. 8 as their first differences
are random walks. However, it is possible that the different trends CI2,1 cointegrate into an I1
process whose first difference is a constant and a stationary I0 noise process. In this case the
drift term can be estimated by including a con- stant in the regression. If the individual technical
change trends are I1 processes then a model that includes the revenue shares of each input as re-
gressors can be estimated. Such a model was estimated, but the estimates of these coefficients
Table 1 Energy intensities of inputs
a
Mean Standard deviation
s Mean
0.273 31 904
116 958 Capital
45 256 Labor
9055 0.200
Energy 671 711
131 166 0.195
84 654 Fertilizer
301 037 0.281
206 371 33 285
Pesticide 0.161
30 485 5712
0.187 Other
a
Energy Intensities in BTU per 1990 dollar value using the GDP deflator.
7
No coal is used directly in agriculture.
were all very large in absolute value 10s or 100s per year and so this model was rejected.
Three models are estimated. In all the models the technical change trend is represented by a
constant, the other variables are the changes in the logarithms of the relevant variables. The first
model estimates Eq. 8 with no restrictions or modifications. The output elasticities are esti-
mated as constant regression parameters. The condition U
E
= U
G
is tested by the exclusion of all the relevant terms. This ‘non-substitutability test’
is the closest that can be got to a test of whether Eq. 14 might fit the data. If the null hypothesis
is accepted then energy cost is a function of only the state of technology, the resource stock, and
the uncontrolled inputs. The other two models assume that there is substitutability. The second
model allows a test of whether the relevant output elasticities are proportional to shares of embodied
energy. If the restrictions can be accepted, then despite the presence of substitutability energy cost
can still be an accurate indicator of resource quality. The third model is used to test whether
price-taking profit-maximization holds and mar- ginal products are proportional to prices. If the
restrictions are accepted then generalized unit cost calculated using revenue shares will accurately
measure resource quality.
5
.
2
.
1
. Model
1
D ln U
Et
= − a − S a
i
D ln X
it
− a
E
D ln E
t
− S a
j
D ln N
jt
− a
R
D ln R
t
+ a
T
D ln T
t
+ y
t
8a The non-substitutability test sets all parameters
except a , a
R
, and the a
j
to zero and computes an F-statistic to test whether the resulting increase in
the error sum of squares is statistically significant. If the input – output model is correct, changes in
quantities of inputs and total energy use should not be expected to have a systematic effect on
energy cost.
5
.
2
.
2
. Model
2
This model is the same as Model 1 except that the energy and other non-resource inputs elastic-
ities are replaced with the relevant share of em- bodied energy multiplied by the returns to scale
described in association with Eqs. 10 and 11: D
ln U
Et
= − b − S b
i
o
it
D ln X
it
− b
E
o
Et
D ln E
t
− S b
j
D ln N
jt
− b
R
D ln R
t
+ b
T
D ln T
t
+ 6
t
8b where o
i
and o
E
are the RHS of Eqs. 10 and 11. Then a direct test of Eqs. 10 and 11 sets
b
i
= b
E
= b
T
= 1 and again the F-statistic for the
restriction is computed. If the restriction is re- jected then energy cost may give misleading indi-
cations of changes in resource quality as marginal products are not proportional to embodied
energy.
5
.
2
.
3
. Model
3
In this model the elasticities are replaced with the relevant revenue share:
D ln U
Et
= − g − S g
i
S
it
D ln X
it
− g
E
S
Et
D ln E
t
− S g
j
D ln N
jt
− g
R
S
Rt
D ln R
t
+ g
T
D ln T
t
+ v 8c
The coefficients are tested to see whether g
i
, g
E
, g
R
, and g
T
are equal to unity — a test of whether price-taking profit-maximization is an accurate
assumption. Cost is calculated as the sum of the costs of all
inputs apart from land, capital, and self labor. To calculate the revenue shares of land, capital, and
self labor their shares in factor services as esti- mated by Ball et al. 1995 are found first. Then
these shares are multiplied by the share of profit in revenue as proposed by Berndt et al. 1993.
Returns to scale for Model 2 are computed by deducting the revenue share of land from unity.
The models are estimated using OLS.
5
.
3
. Econometric results All three models fit the data well both in terms
of the adjusted R
2
and the Durbin – Watson and Box – Pierce diagnostic statistics for serial correla-
tion Table 2. The Dickey – Fuller cointegration test is intended to test whether the technical
change trend is adequately represented by the constant and random error. The result rejects the
hypothesis of non-cointegration which indicates
that the aggregate trend is at most I1 so that its first difference is stationary. The coefficients and
individual t-statistics are presented in Table 3. The coefficients have the expected sign with the excep-
tion of energy, fertilizer, and temperature in all three models and other services in Model 1. All the
incorrectly signed coefficients are insignificantly different from zero.
The time trend has about the expected magnitude in all three models. The index number based growth
rate of multi-factor productivity was about 1.7 p.a. over this period. The econometric estimates are
1.5, 1.5, and 1.8 for the three models, respectively. The mean rate of change in energy cost is 1.0. So
the time trend does track generalized unit cost while the other variables explain the deviation of energy
cost from generalized unit cost.
The coefficient on total energy is not significantly different from unity in Models 2 and 3 as expected
but is significantly different from unity at the 5 level in Model 1. In Model 1 the coefficient on total
energy under the substitutability hypothesis is ex- pected to be one and zero under the non-substi-
tutability hypothesis. Many of the other regression coefficients in the three models are not significantly
different to zero.
The results of the three joint hypothesis tests are presented in Table 2. Both the non-substitutability
and ‘marginal products proportional to embodied energy’ hypotheses are strongly rejected. The full
neoclassical price-taking profit-maximization is also rejected at the 5 level. But at a 3.5 level the
neoclassical model would be accepted. So, while neither the energy analysis model nor the strong
neoclassical model fits the data very well, the neoclassical model may diverge less from reality.
The individual t-statistics in Table 3 allow an investigation of which variables may be most
important in causing the rejection of the restric- tions. For Model 1 the t-statistics for capital and
total energy − 3.37 and 8.47 show that their coefficients diverge very significantly from their
expected values zero in both cases under the null. The coefficient for pesticides is significant at the
10 level. Total energy is probably most important in causing the restrictions to be rejected. For Model
2 the coefficients for capital, energy, and fertilizer all diverge significantly from their expected values
under the restrictions. Energy and fertilizer are the most energy intensive inputs Table 1 and, as
expected, their coefficients are greater than − 1 and in fact positive. Capital has a coefficient that is
significantly less than − 1 as expected for a less energy intensive input. However, this pattern is not
very clearcut. Both labor inputs have coefficients of less than − 1 but not significantly so and other
services — the least energy intensive inputs — in fact have a coefficient insignificantly greater than
−
1. For Model 3 the coefficients for capital and other services are significantly different from − 1
Table 2 Energy cost models diagnostic statistics and joint hypothesis tests
a
Model 1 Model 2
Diagnostic Model 3
R
2
0.7753 0.7660
0.7595 1.7573
Durbin–Watson 1.8203
1.7619 Box Pierce Q statistic
7.2055 6.0400
7.3808 0.6891
Significance level 0.7059
0.8119 −
5.42748 −
5.6893 Dickey–Fuller
− 5.4166
Joint hypothesis test 16.6266
Nonsubstitutability 0.0000
Marginal products proportional to embodied energy 5.9408
0.0002 2.4281
Price-taking profit-maximization 0.0350
a
For the joint hypothesis tests the first figure is the F-statistic and the second in parentheses the significance level.
at the 5 level and the coefficient of land is different from − 1 at close to the 10 significance
level. The ex post rents of the two non-labor primary factors — capital and land — diverge
substantially from the estimates of Ball et al. 1995 of their ex ante factor services. Therefore,
divergence of the coefficients from the shares of ex post rents in revenue is not surprising.
5
.
4
. Time paths of the indicators Fig. 1 presents three different ‘classical’ Cleve-
land and Stern, 1999 scarcity indicators: general- ized unit cost U
G
, energy cost U
E
, and Barnett and Morse’s unit cost U
B
. U
B
is calculated with value added as the output and capital and labor
as inputs. Data sources are described above. An increase in any of the indices indicates an increase
in scarcity. The GUC indicator almost forms a lower envelope for the other indicators. Both U
E
and U
B
show large movements in both directions. From about 1948 to 1973 both U
E
and U
B
are fairly stable, reaching a minimum in the mid
1960s and rising slightly thereafter. This was a period of falling real energy prices and energy was
substituted for capital and labor. U
B
rises steeply from 1975 on. The capital stock continued to
increase with apparently decreasing returns until 1983 from whence it declined sharply Fig. 2.
Value added rose slowly and became more volatile. The peak in U
B
in 1983 occurs when the peak in the capital stock coincides with poor
weather. Energy cost also moves up steeply through
1973, peaking in 1975 because direct energy use increased despite rising prices Fig. 3. Indirect
energy use also rose. The apparent reason for this behavior is that output prices rose sharply in
1972 – 1974 as part of the global commodity price boom. The increase in crop prices was bigger than
that in energy. Farmers rushed to buy capital and use intermediate inputs in order to increase pro-
duction. High energy prices began to have an impact from 1976 onwards. Energy use leveled
out and from the second oil shock in 1979 it declined sharply. Crop and livestock output con-
tinued to increase at about the same rate as previously. Since 1982 output has fluctuated
Table 3 Energy cost models: regression coefficient estimates, standard
errors and t-statistics
a
Model 1 Model 2
Variable Model 3
− 0.01493
Time trend −
0.01457 −
0.01825 [0.006801]
[0.00687] [0.007695]
0 2.6831 0 −1.94009 0 −2.1221
0.04055 Energy
0.2216 1.2548
[0.1177] [0.3327]
[2.0652] −
1 1.0918 0 0.3444
− 1 3.6718
− 0.7431
− 7.0609
− 6.9949
Capital [2.2051]
[2.2482] [0.2205]
− 1 −2.6665
0 −3.3702 −
1 −2.7486 −
0.001952 −
1.9307 −
1.0793 Self labor
[0.2174] [2.6925]
[1.2442] −
1 −0.06374 0 −0.00898 −1 −0.3457
− 0.1474
Hired labor −
1.9975 −
0.5906 [3.1107]
[1.5965] [0.1473]
0 −1.0012 −
1 −0.6421 −1 0.2564 0.001161
Fertilizer 0.03588
0.3466 [0.05373]
[0.3270] [0.9330]
− 1 1.4433
0 0.02161 −
1 3.1678 −
0.06830 Pesticides
− 1.3805
− 2.0509
[0.0006254] [0.9085]
[1.4898] 0 −1.8564
− 1 − 0.4188 −1 −0.7054
Other 0.03647
− 0.3807
− 0.07971
[0.1836] services etc.
[1.1457] [0.3843]
0 0.1987 −
1 0.5405 −
1 2.3947 −
0.5657 Land
− 0.4965
− 4.3938
[0.2399] [0.2097]
[2.0675] 0 −2.3576
0 −2.3677 −
1 −1.6415 −
0.03160 Precipitation
− 0.02729
− 0.009413
[0.03353] [0.03530]
[0.03479] 0 −0.2706
0 −0.9423 0 −0.7732
Temperature 0.08474 0.04301
0.09294 [0.2229]
[0.2317] [0.2291]
0 0.3801 0 0.4012
0 0.1877 1.3114
Total energy 1.2363
1.2325 [0.1549]
[0.1627] [0.1498]
0 8.4666 1 1.5774
1 1.4290 1 2.0103
a
The first of each group of figures is the estimated coeffi- cient. The second [in square brackets] is the standard error.
The third in parentheses is the t-statistic for equality of the coefficient to the number stated to its left.
Fig. 2. Output, real value added, and capital stock in US agriculture. All indicators indexed to 100 in 1948.
and 1970s, GUC does not. Similar results have been found by other studies. Researchers who
made projections on the basis of the energy cost trend at the time e.g. Gever et al., 1986 have
been shown to have been overly pessimistic Cleveland, 1995b.
6. Conclusions
Kategori