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TECINOLOGICAL CHN:CE, TAX POLICY, AND THE
N S T.
TEc8 .
AUG 161983
DERIVED DE.l-AND FOR ENERGY
LIBRARmW
by
Ernst R-- Berndt
David 0. Wood*
Energy Laboratory Report No. MIT-EL-75-019
First Draft
.Comments Welcome
Not for Citation
*University of British Columbia and Massachusetts Institute of Technology.
The theoretical development in this paper has drawn heavily on E.R. Berndt
In addition, we gratefully acknowledge the
and D.W. Jorgenson [1975].
Byron...
Neil
of
research assistance
AUG 16 1983
L' /
AR
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__~~__ _
__
__
_~___
~--- ~.~------.. 1 ~b
_____
IntrAteuct ion
The aszuription of Hicks-neutral factor aucmnenting technical change has prcved to be extremely useful to empirical
researchers
interested in applying production theory.
technical change is
Hicks-neutral,
~z:
en
the analytical. task is con-
siderably simplified; for example, substitution possibilitieamong inputs are independent of the level of technology.
There have been a number of studies which have attempted
to test whether the Hicks-neutral technical change (HTC) asJumption is valid.
Almost all of these studies have dealt with
traditional two input CES
duction models.
or
Cobb-Douglas capital-labour pro-
In recent years more flexible functional foraTms
with multiple (more than two) inputs have been estiated, although almost all such studies have assumed Ricks-neutral technical change.
The single published exception is
P. Binswanger [1974a3,
that of HanZ
who estimated a multiple-input t anslog
"cost function using U.S. agricultural data.
Binswanger did not
derive his functional form and estimating equations from an explicit statement on the forn
of technical change; rather, he
simply inserted 'time' into his cost share equations and, baSed
on the sign of the estimated coefficient, observed whether
technical change was input i share-saving, share-neutral, or
input i share-using.
In the first part of this paper we develop an explicit
theory of factor augmenting (input price diminishing) technical
change ard
inc.orate it
into the trianzlc
func;-ical
We test whether technical change is -actor augmenzing;
_
d-=-
-2that technical change is of the constant factor augmenting
form, we assume constant returns to scale and simultaneouslf
identify and estimate the techn:ological substitution parmameters and the rates of factor augmentation for each input.
Finally, we test
trather technical change is Hicks-neutral.
The data we use in this study is that on capital (1-),
!a-
bour (L), energy (E), and other interediate materials (M) for
total U.S. manufacturing 1948-71.
This data was eimployed i;
our earlier study which assumed H -TC.
The data is
of consid-
erable interest: for a salient result we obtained in our earlier study was that energy and capital tended to be cmplewentary rather than substitutable inputs.
In the present study-
we test for INTC and assess the reliability of our earlier re-entarity.
sult on capital-energy co.pr
We find that over the
1948-71 time period in U.S. raanufacturing,
technical change
has been energy-using and labour-saving; further, the energrcapital complementary relation persists when non-noutral ten:Ch-
nical change is allowed.
We cannot, however, reject the n'ull
hypothesis that thichnical chang. has been Hicks-neutral.
Thus
D= results provide some rather weak support for the hypoth.-esis
that the post-war increase in demand for energy is d:.e Partly
to the energy-neing bias of technical change.
:
si :e
we cannot reject HNTC, applied researchers may feel justified
in continuing to simplify their work by assuming ENTC.
An additional reason we provide for the increase in zostwar encrgy demand is that it
.icy.
Specifically,
is due partly to federal tax pl-
since energy and capital are complement.ary,
federal investment incentives have tended to lower the price
074674
of capital and thecrby increas
both the capital and energy in-
tensiveness of U.S. manufacturing.
In the final portion of the
paper we produce simulation results which attempt to depict what
the pattern of energy demand would have been like had the postm
war inves- t .ent
incentives not been implemented.
-
111M,
-3m
II.
The Translo. Function with Factor Auamentina Technical
Change
Assume there exists a twice differentiable aggregate pro-
duction function characterized by constant returns to scale,
(1) Y = F(K*,L*,E*,M*)
where
Y = gross output
K* = capital services measured in augmented units
L* = labour services measured in augmented units
= energy services measured in augmented units
E
M* = services of all other intermediate goods measured
in augmented units.
Corresponding to (1) there exists a cost functicn which reflects the production technology:
(2)
C
G(YrP*P,,P'P
where C is total cost and P*, Pf, P* and P
the augmented inputs K*; L*, E* and M*,
are prices of
__
_n_____
I
~
______~Z=~;~~_______q_____S__
4We now assume that the cost function (2)
2
approximated by the translog function:
(3)
In C = In a
+
+ hBKK (in
I n Y + aKln P* + aLln P* + aEln P*
0K
P
L
In
+
TPIn P!S +
i
xf
.
+ hLL~nhL
2
.-
-q
k
Liri4
- i
,-
LE
KE
4 in P*
"AM
P1i
-in P* -i e
1
*M
E
+ 8IEln P-ln P* +
+ ~iS
Linear homgen:
can be closely
BE
(ln P*)
E
2
in
In
A.
T
Kt
P*~n P*
+ B
n P*In P*
+ 4e
(In P.)
EM
4M
E
.
es imposes the following restrictions
.ri
on (3):
(4)
L +
aK +
C +
E + CM =1
OM
+
OL
+ BLL + BLE +
KE + BE+
BKM + 8M+
= + '
E +
-=0
l = 0
M = 0
0
EY + 0B. I 4 = 0.
From the point of view of the production function, it
has
been traditional to specify certain types of technical change
as factor augmenting.
Viewed from the vantage of the cost func-
tion, such factor augmenting technical change corresponds with
S
.
.-
I
(-,
*CC% C.5
..
'- ,
g4,,.
-5-
input price diminishing technical change.
Let us assume that
factor augmenting technical change occurs at a constant exponential rate:
(5)
...
Xit =
where
X
=- services of input j at time t measured in augmsnted
units,
Xjt
= services of input j at time t measured in n atural
units,
S constant e-ponential rate of augmentation f cr in-
put j
T
,= t-to, where to is an initial point in time.
The corresponding specification for input price dimlinishing
technical change is
(6)
P3t =Pjte
where Pjt and Pjt are the prices associated with Xjt and ::,
respectively, and Xj is the constant rate of price dinminution
for input j.
..
-6"It
is
of course desirable that Pt X
= P X , i.e.,
jt jit
t jt
that input value be invariant to units of augmentation mea3ure-
ment.
1A
For this to hold, it is necessary and sufficient that
=-Pj, i.e., that the rate of factor augmentation is the
negative of the rate - f -df
Inserting (6)
5-rZL-n
into (3)
and utilizing the restrictions in
(4), we rewrite the cost function taking account of technical
change:
(7)
In C = In
o
+
In Y + aKln P
+ %$,(in
2 +
+
in PIl
aLln PL + an
P
an
+
iT
PL + SBln PK n PE +
11
I
"
+ 14L(In P
)2
BLE n
n
+
Ln PE
+ h4B (In P,)
LM n PL
2
(9)
*T =
KK
LL + OE'E +
= S~kK +K LL
-
SKK0K1)
M +KL
+
MM
OKE E
(AL
M
PM
+ BITT In P. + 4
where
(8)
n
+ BEM+ln P 1n PM
P
gE(
+
n PKI n PM
+
RMxEE
KE
E
M
+
0
+
LT
E
1"2
T
In PK
in PL
In PE
I
.
KLE (XK-M)
SLT
+
7
-
s(LL(A-M)
)
LE (ILLT +
!BT +
PT
and
0
)
4 0E(XE-
ET)'
-
(10)
+ BLE(E-XM)
U
= KTA1K
TTT + BLT L + $ET E + BIT M
BKT(AK-M) + BLT(L-XM) +O ET0(E-AM)
-
We now derive.estima'ting equations.
If input prices and
output level are fixed, cost minimizing input demand functions
are obtained by logarithmically difsrentiating (7),
8an C
-81- P I
aJ
+
jk
S In Pk + 0 jT
= KL,E,M.
UsingShephard's Lemma, we obtain
(.1)
QM
C
M ax + .=
BK1n PK +
RL
1n
SPL
5r'---= ,,,. + BELn PK $.
+
a.
Eaa
aE +
PEE
-
- -
E +
=
PL
+
n PL
KE I n PE .+ B0KMln
0 LE1n
PE + 8LIn
2
M +
KTT
M + BLTT
XKEln PK + O:T.ln PL +
KE1 n PR +OLEIn
PL + BEEln PE + 8EL4In PM +
KM
PL +
PD +
in
BEMI n PE
+
Oin P.+8111
ETT
BMM1n PM + 'T
M
4-' PMT
-8-
where the total cost C = P
+ PL
+ PM.
+PE
The M are of
course the cost shares of the inputs in the total cost of producing Y.
We now differentiate (7) with respect to T:
(12)
nC
aT
T
+
P +
XT n K
Tn PL + 8
LT
L
PIT
I n PE
+
8b
In
P
+ 6T
Equation (12) can be rewritten by taking account of the relations (),
(I),
and (10):
a1n C
S ~e
erate of total cost dimisnution (output fixed) is e..al
to a weighted average of .the rates of input price diminution,
the weights _einfictor shares.
In practice, we shall mea-
sure a1n C/at as the negative of the rate of total factor productivIty.3
If rates of input price diminution are equal for all factors, i.e.,
KT
0LT
if
-
8ET
j = Ak, j,k = K,L,E,M,
MT
=
TT
0.
then by (
and (10)
a)
We term this form of tech-
U%
nical change Ilicks-neutral.
From (11) it
is obvious that when
v."
technical change is Hicks-neutral, cost shares are independent
of time; further, the rate of total cost diminution will then
-
d"
bic~
~
a
TT-
111,11111111911
-9simply be the common rate of input price diminution, i.e.,
aT =
j = Ak , J,k = K,L,E,M.
Thus Hicks-neutral technical
change involves a set of testable parametric restrictions.
If one interprets the cost function %7) as a function in
its own right, it
is possible to test for a weaker form of
technical change, namely that technical change is simpl
tor augmentiLg.
This is so. because factor augmentation in-
volves repararmeterizations
restriction in
fac-
(8) and (9), but imposes the single
(10).
The above framework
allows us to test for other
types of technical change as well.
4
For example, Harrod-
neutral change implies Ag = AE = )N = O, IL 4 0; Solowneutral change implies AL = AE = I M = O,
Kr
0.
Other
forms can easily bu developed.
To our knowledge, the first published empirical study
of technical change biases with many factors of production
and 'flexible'
functional forms is that of Hans Binswanger
[1974a1; he also uses a translog function.
Binswanger esti-
sates only the share equations (11) and defines technical
change as input j-saving if
and input j-using if
8T > 0.
T < O neutral if
jT = 0,
Thus his definition of biases
is in terms of factor shares, not in terms of factor augmentation (input price diminution).
Because Binswanger esti-
iates only the share equations (11), he can only obtain
- I0 -
estimates of differences in rates of augmentation; from (s),
for example, it is clear that XK , AL'
AE , and XM cannot be
separately identified, only the differences XK-XI,
and I ').1 are estimable.
Identification of-
M
L-M'
and thus of
the remaining Ai can be attained, however, by estimating
in the rate of total coSt diminution ecr -
(see eluation (8)
tion (12)
T
AZ
,
.
a t E3----
returns to scale in input.quantities )
constant
ct
o simultaneousiv
estimate and identify technological parameters and rates of
augmentation for each input. 5
Estimates of the Allen partial elasticities of substitution (AES)
bet 1 ;.een inputs j and k are obtained from the
translog parameters and the data:
. + M -M
(13)
. jj
(14)
°jk
,'
,
6A9 + M M.
,
jJ
K,L,E,M,
Jrk D
- ,LE,M.
The corresponding price elasticities, E jk
are computed as Mj
al
Xj/ amn P ,
k.
A useful interpretation of the translog parameters
8jk
is obtained by defining a share elasticity.
The first
partial derivative of In C with respect to in P
equation (see (11)).
is the share
The croas partial derivative,
22 1n C/8ln P jln Pk is a constant share elasticity equal to
Bjk.
Thus the translog parm.eters
0 jk
sunm-marize the response
of cost share Ij. to a chang3 in In Pk"
We now turn to a discussion of econometric concerns.
We propose to estimate parazmeters in the cost share aquatic-s
(11) and the total cost diminution equation (12) subject tc
the restrictions (4).
To each of the equations in (11) and
(12) we append an additive distu rbanc
ts-.
in.
e
of the four equations in (11) are 2±depenen
drop the M share equation.
A
o
t're
we arbitrar_:y
We specify that the distuizbarnces
from the remaining three share egiations and (12) form a 421l
disturbance vector c(t) swhich is teciporally independently and
identically normally distribu=ed with muean vector zero and
non-singular covariance imatrica 1l, t=l,... ,T.
The final issue on stochastic specification concerns the
issue of simlntaneity,
Two considerations suggest that the
aggregate prices PK' PL' PE and PM may be ccrrelated with
components of the disturbance vector r(t).
First, although
input prices may be fisd at the level of an individual firm,
the extent of aggregation in this study (total U.S. manufacturing) is considerable; at this industry level, it is less
likely that the supply of inputs is perfectly elastic.
Second, even if,
for example, the supply of er.
i -It , coal,
- 12
natural gas, crude and refined oil were perfectly elastic at
the industry level, the price index of aqqregate energy would
be endogenous,
for it would vary with changes in the mix of
energy inputs demrnded.
Similar arguments could be made for
the endogeneity of PK' PL and PM.
veloped by Fuss [19753.
This argument has been de-
If our estimation procedure is to
provide consistent estimates of the parmeters in
(12),
(11) and
account rust be tJaken of this possible simultaneity.v
As in Berndt-l.ocd E19753, we again use an instrumental vaziable estimator.
Our estimator is the iterative nonlinear
minimum distance estinator for simultaneous equations; when
the model is linear in the parameters,
theqminimu'm distance
estimator is simply the iterative th-ree stage least squares
estimator.7
Statistical inference is based on the Wald test
procedure.
Before presenting epirzical results, we refer back again
to the estimated Allieu partial elasticities of substitution
(AES); see (13) and (14).
Since the etimated
S are a
function of the estimated parzn.eters and data, it
possible to
a-;
should be
derive their estimated standard errors.
The problem, however, is that the fitted Mj depend on the
parameters a ,
jk and the data.
The foimula for the stan-
dard error therefore is rather complicated.
9
Estimates of
these standard errors could be quite useful, however, for
11116
-I
- 13 -
they would provide insight into the precision of the estimated
AES.10 Thus it appears useful to e:pend some e eet in obtaining standard errors for the estimated AES.
= PL
Suppose we scale our data so that P
T = 0, in som,-year (say, 1947).
PE
P
= 1.0,
The fitted or predicted M
in that year would then simply be the estimated a j, for all the
12 Pj and T terms would be zero (see (11)). Now substitute cj
for M. in (13) and (14):
=(13a) ~jj ("3"
jk
"
-
k k + ajo
K,L,E,M
= KoLEI .
+
Gja,
S(14a)
Thus for the year 1947, the estimated AES would only be a function of the estimated parameters.
Denote.the column vector
of first partial derivatives of the AES in
(13a, 14a) with re-
spect to the parameters c~, jk as SB --and the estimated variancecovariance matri .. of the parameter estimates as V(B).
Follow-
ing: Ementa [1971, p. 4443, a first order Taylor series approximation to the variance of the estimated AES is then computed as
(15)
SV (B)S .
- 14 -
Since fitted M. and estimated AES are invariant to data scal.ing, the data could be appropriately rescaled at any an-nual
observation
in order to obtain estimates -* the standard
errors for the AES at that point.
bo
.L.
•
-
-.
-
Il
nllh
- 15 -
III.
Data and
mri-rical Results on Technical Chance
The data used in this study is the same data used by us
in our earlier analysis.11
The additional data required here,
however, is a time series on total factor productivity. Based
12
we separately compute Divisia indexes
on the Faucett data,
of total output (sales of total manufacturing to all sectors
of the U.S. economy, including final demand) and total factor
input (purchases of total manufacturing from all sectors of
the U.S. economy, plus labour and capital services).
Follow-
ing Jorgenson-Griliches [1967, 19723, we obtain a measure of
total factor productivity as
a Divisia index of inputs.
*
Since the Divisia index is a chained
-index,we lose one observation.
therefore "
Divisia index of output minus
The data for this study is
the period 1948-71.
In Table 1 below we pre-
sent the index of the rate of total cost diminution for U.S.
manufacturing A
is computed simply as the negwhich
;,
ative of the rate of tctal factor productivity.
If technical
"progress" has taken place, the expected sign of the rate of
total %ost diminution is negative.
Table 1
Rate of Total Cost Dimrinution in U.S. Manufacturing, 1948-71'
(Denoted as C/C)
Year
1948
1949
1950
1951
1952
1953
Year
YC
-.01525
-.00500
-.01124
-.01700
-.00029
-.00759
We first
1951
1955
1956
1957
1958
1959
Year
-~Q.,555
-.02376
.0115
.00782
.00667
-.00893
1960
1961
1962
1963
1964
1965
6c/
-.01639
-. 00939
-.02443
.00077
-.03181
-.00815
Year
;/C
1966
1967
1958
1969
1970
1971
-.0095
.00577
-.00376
-.01406
.01241
.01256
directly estimate parameters in three of the four
share equations (11)
(12).
/C
plus the total cost diminution ecuation
Although there are twenty-four parameters in these four
equations, numerous restrictions must be imposed.
For examrGe,
*KL in the K-share equation must equal KL in the L-share
equation; similarly, 0B in the X-share equation must ecual
8KT in the total cost dimLinution equation.
There are ten such
symmetry restrictions; this reduces to fourteen'the nnmber of
free parametersto be estimated.
13
In the first
2 we present parameter estimates and t-ratios
with these ten sjymetry resqAbctions imposed.
col-n of Toble
for the model
It
should be
noted that this model does not impose the restriction that
technical change is of the factor augmenting (price diminuting) form.
~ I ~I^
_~ _____
^
--
~gill
Table 2
Parameter Estimates fcr Translog Model with Technical Ch.ange
U.S. Manufacturing, 1948-71
(t-ratios in parentheses)
Factor Au ymentation
and Svrett;r7
Parm n~t r
.0593
(34.002)
.2587
(65.100)
14*
K
BKL
OKE
OKM
SLL
OEE
EMI
Sp
'*~' -
.0433
(28.555)
.6387
(114.624)
.0381
(4.708)
.0163
(1.151)
-. 0073
(1.612)
-. 0471
(1.979)
.1449
(2.021)
-. 0267
(1.329)
-. 1345
.(1.574)
.0429
(3.378)
-.0090
(.432)
.6
.1906
(1.765)
-. 0005
(1.518)
.0594
(35.348)
.2589
(65.742)
.0434
(28.850)
.6382
(116.724)
.0381
(4.735)
.0162
(1.148)
-.0073
(1.622)
-. 0470
(1.997)
.1435
(2.014)
-.026
(1.334)
-. 1331
(1.576)
.0429
(3.394)
-.0090
(.437)
.1891
(1.772)
-. 0005
(1.453)
Hicks Teutral Techiical
Change and S,-nt:i
.0589
(37.654)
.2541
(99.950)
.0443
(33.375)
.6427
(155.139)
..0329
(4.781)
-. 0052
(1.257)
-. 0083
(1.982)
-. 0193
(1.679)
S .0721
(9.143)
-.0045
(1.370)
-.0624
(4.983)
.0265
(3.096)
-. 0136
(1.015)
.0953
(3.342)
.0
Paraee'ter
S-~ etrv
-. 0018
(1.175)
.0005
(1.160)
.0018
tLT
BMT
(.958)
ON
-.0018
.0005
(1.068)
.0018
(.975)
.oooo
-. 0059
(1.891)
(2.071)
I
UI
UI
R2 -m Share
.5953
-L Share
S-E Share
.8007
.7347
;-14 Share
-t/C
.6177
.0383
fqicks Neutral Tecynical
Change and S retr_.0
(1.093)
.0004
(.976)
.0101
Ul
itote:
Table 2-continued
Factor Augmentation
S
znd Sremetr
.0
.0
t.911)
-. 0105
(1.909)
-. 0137
(2.840)
.0018
(.299)
-. 0028
-. 0060
(2.321)
-. 0060
(2.321)
-. 004o
(2.32.)
-. 0060
(2.321)
-.0060
(.888)
(2.321)
.5950
.8005
.7344
.6175
.0005
.6057
.7824
.6980
.0000
UI denotes unidentified.
''
-
S-19 To impose and test for factor augmenting technical change,
we reparwneterize the Sjt in terms of the Sjk and
j,
T in
terms of the aj and Aj, and then impose the additional nonlin-ear restriction (.C,
TT in terms of the
The chi-square test statistic for the-single
Zjk and the 1j.
restriction in
which reparaeterizes
(10) is
is 3.841 (6.635).
4, while the .05 (.01) critical value
Thus we cannot reject the null hypothesis
of factor augmenting technical change.
It
is of considerable interest to examine the estimated
rates of factor augmentation (input price diminution).
From
the second column of Table 2 we obtain estimated annual rates
of factor augmentation (the negative of the estimated XA) as
1.05% for K, 1.37% for L, -.18% for E, and .28% for M.
The
estimated
is significantly different from zero, and AK is
marginally significant. The high estimate for labour is
somewhat surprising, because the hours worked data series has
already been adjusted for changes in educational attainment
over time.1 6
An intriguing result we obtain is that the rate
of factor augmentation is larg*-st for labour, the input whcse
•price has risen the most, and is lowest fnr energy, the input
whose price has risen the least.
Indeed, the estimated AE
suggests that factor augmentation for energy over the 1948-71
period has actually been negative (-.18%),
2
timateis insignificantly different from zero.
this esThus our re.-
sults suggest that part of the post-war increase in industrial
demand for energy is due to the fact that technical change
augmented capital, labour, and other intermediate material
- 20 materials more rapidly than it augmented energy.
In this sense
;
the historical technical change can he characterized sonmew;hat
.
loosely as labour saving and energy using.
An alternative mizthod for analyzing
is
c
ical
change bias
to measure the effsct of technical change on equilibrium
factor cost shares.
This method is more involved than the
simple measurement of rates of augmentation, because the net
effect of technical change depends on the technological substitution parcmeters and differences in rates of factor augmentation.
For example, the parameter
L (=SX 0-
M)
sunmarizeS the effect of technical
XLL(AL-M) + 8LE(X'E-M))
change on the labour share, taking into account differences
in rates of augmentation and technological possibilities for
factor substitution.
Fronma Table 2,
Coltun
2, we note that
the estimate of 0 LT is -. 0018 (labour share saving) which is
.insignificantly
1
is
statistically
different from zero,
sigrnificant.
(and t-values) fcr ST,
SET'
(1.068), and .001(.975).
even though the estimat d
The corresponding esti.ate3
and a
are-.0005(1.453),
r
.0003
Thus the pattern of technical cnange
appears to have been labour share saving and senergy share
using.
It
is
tempting to suggest that our results lend supportc
to the induced innovaticn hypothesis, which states that factor
prices significantly affect the rate and bias of technical
change.
We tend to resist this temptation,
simply because we
ii
- 21 -
believe that the process of research, innovation, and technical
change is extremely complex.
Hans P. Einswanger [1974b2, for
example, has considered invention possibilities on the basis
of potential payoffs to alternative research lines. In his
type of model, the biases and rates of technical change are determined jointly by (i) the relative productivity of alternative research lines (for example, If labour saving research results'are easier to achieve than e._ y saving ones, then technical change will tend to be labour saving),
the relative
(ii)
costs of alternative research lines, (iii) the size of the research budget (which may be affected by scale of output),
and
(iv) the relative present values of expected factor costs.
Although our results suggest that technical change in U.S.
manufacturing 1948-71 has been labour saving and energy using,
it does not seem reasonable to attribute this bias to a simple
induced innovationIypothesis.
Indeed, since our model assmes
that factor augmenting t2chnical change has constant rates and
biases, we cannot really address ourselves satisfactorily tc
the empirical issues concerning varying endogenous rates and
biases of technical change.7
We now examine in further detail the strength of our result that technical change appears to have been labour saving
and energy using.
To do this, we test the null hypothesis
that the rates of factor augmentation are equal, i.e., that
K =
L
=
E
=
Hicks neutral.
SLY
LT
ET =
, which implies that technical change is
Note also that when AK
=
AL
XE
=
XM' OKT
0 i.e., technical change is neutral with
, = 0,
MAT
r
'V
- 22 respect to factor shares.
the three restriction
The chi-square test statistic for
\.2_2 3
= A
=L
is
Ih,
hie
the
.05 (.01) critical value is
7.815(11.345).
Thus,
although
point estimates suggest that technical change has been labour
saving and anergy using, we cannot reject the null hypothesis
that techn-ical change has been neutral.
This result is
of
some comfort, however, for most e.pirical an.alyses (including
our Berndt-Wood [319753 study) have assumed that technical
change is
of the Hicks-neutral factor augmenting form.
Before leaving the topic of technical change, we note
briefly that when technical change is
assoumed to be
.icks
neutral, the estimate of the common rate of factor aumenk-tion (see column 3 of Table 2)
.a
is
2.321,
is
.60%; since the t-valuh
this rate of overall technical change is
icantly different from zero.
on
si-ni -
The figure of .60% as an annual
. rate of technical change may at first glance appear a bit lo.
Spencer Star
19074], however, has shown that previous stud.i
s
measuring technical change have tended to croduce somewhat
larger figures because they
-- "m
.t
v..
aded 'capita
.and labour), and ignorelintermediate materials.18
Specifi-
cally, in his study based on 1950 and 1960 census data for
seventeen U.S. manufacturing industries at the two digit
level,
Star found that the overall annual rate of technical
change was reduced from 1.51% to .59% when h/.ong other thin.,s,
.intermediate inputs were property taken into accunt.
__
IIIINIMIili fiYil
- 23 S.
.
Star's figure of .59% is remarkably close to
(=
our estimated
)
=
of .60%..
We now turn to a discussion of Allen partial elasticities
of substitutinn (.}S).
For the sake of brevity, we report esti-
*
uates o. the AS for ohly the most restricted model accepc'E
bby our data, i.e., the mrodel with Hicks-nautral technical
imposed.
h
. . ochange
mated a
We note in
passing, however,
that the estt-
basel on the syr.metry and symety pls fatrctor-
augmenting technical change parameter estimates always in
- ated that capital and enery were complementary inputs.
,;
The energy-capital complentarity was of course a salient
.-.;
result of our earlier paper, a study which assumed FHicks". neutral technical chanre.
-
".
In the first three column-s of Ta'1e 3 we present est-20
mated AES for selected years (1948, 1960,
971)
based on
he
the parameter estimates from column 3 of Table 2 --
model with Hicks-neutral technical change imposed.
Using
the linearized appro::ia-tion as discussed in Section II above,
we also corpute and present i. Table 3 estimated standard
errors and t-ratios for the AES.
The estimates of the own AES are all negative;
aM
21
the
and aLL estimates are significantly negative in all three
years, while
UKK
and a.
estimates tend to become less sig-
nificant statistically tow;ards the end of our sample.
The
_ , estimates (around .64) are significantly different from
zero, but not significantly different from unity.
%A
EstLma-tes of aKE becor.e increasingly negative and statistically significant towards the end of our samzple; a 953
.
confidene interval, h-oweer, wsculd inzlude zero and slightly
nificartly
of aLE and aI are sig-
tU.es
&
.
cr
positive val'jUs!
ositive, while
tites
St
fica n .y dlfrent
.tcii
itive but
and a,
.22
" zero.22
" from
o~
finajlly, we copare our przent r. u~s
reported in c-
are pos-
-with ho:e .~_-
n the fout h 2olumn of
ea.-ier effor'.:
Table 3-we rep~acca estimat4d 1 S for 1971 frcm Table 4 o
Berndt-ood [19753.
esults are sub-stant'.ally the
T1he
atimUates of o 7 OLL
and
0o.
in the pre3snt study are sli...-
ly smaller (in absol'ute value) than thori
the same t3:sad is obs 2ved fo
ard L~
same.
of our first stu.
the estimates of cuL, tKE' 9..i'
Th-q're-nt eutimates of
and
..... .,
- are slightly la:ge_- than those of the earlier analys;.'.
DL.-*
ferences in the -wo sz::; of r-e.lts can Ib attributed to t ;.:
variationz: '(1)
In the present study we add a total cost
bninuti
,n
if
dutonr
disturba.nces
in ~ltis equation are
*correlatid with .i3sturbances 2
ge~neralWT
"t e s harc eqvatios,
""rical estimates will diff r when the total c..
dimjiution equauion is .added.
in presient.and if
toto- efficienc
.f such residuia
e sarple s:.~za
were the se,
corre..ti.'
the asp:.
of results in this paper would be greater
stady. 2 3
than those of our -arlir
The simpe correlation
between re-iduals in the total cost diminution amd th
equations is
, 2.162
,
-. 0S(L),
*216(E),
the residual correlatioas are largest (in
in the
ir
end E equation-.
shar :
and -. 047 ().
Tht.:
absolute value)
(2) Because tho present study
- .25 -
employs a total cost
.iminwutionr
measlure based 3n log-diff-er-
enced Divisia indeig procedures,
drop one obseri- atin.
it h-a
been necassary to
Che reLults in this pap3r aze based
on 1948-71 data, iwhile those in our earlier study were base-d
on the years 1947-71.
This small change in data base coul
produce a slight var-ation in the parameter and. 1E
estimates
"'
"T-.ble 3
Esim.ted
A
..
.ate
Translog Kodzi -:
(,.
E.".st'c.5tiS3 of
c" --..- -:n
ms the C
,-? itU-
posed
.tanda-d
%.zor)
197.
1948
* 8E.
t-ratio
960
.2.77.7
-8.33
(2.3 =)
2.657
(3.45)
-. 55.
-1 73 C
8 .E.
*
(.11.)
-1.53
'.110)
. t-rciti
15.570
15.2 i3
AE
-8.403
-0.03
"
(4.63)
I T: 7
8.E.
t-'ratio
8.E.
(3.E62)
2.3~.I
-. 338
(.070)
a.i t-ratio
S.E. c
,5 33
.658
2.142
I.Co c 7
2.2S4
-2.040
(1.731)
-10
"-.355 -. S2
(.073)
(.C74)
4,835
t-rad&
(..07)
1.955
-2.420
-3.53
.447
.438
.327
t-ratio
(,2323)
1.32
(.333)
1.317
.626
S.E.
S.649
(.272)
2.375
(.2L8)
2.178
(.20)
2.452
.622
.637
.655
(.073;
(.0059)
(.075)
-. 39
.530
(:.973)
t-ratio
.
5.152
(1.CI6)
1,311
Ciz
S.E.
s;tim ts4
1971
-6. 3:!3
(2.3 2)
1.433
.49
.68
.61
S.762
.511
(.4-2'
1. :..
-Ion
1.C -$
3..3 )
.510
.S
t
-.
.. 73
i
- ----lr-- ~
__-
-~--~.p-------;;
~-~C=-iSi-i~---
----
-- ~--il~L__
.5
- 27 -
• • •
IV.
Simulated
Effects of Variations in Tax Policy on Enercy
_
---
Demand
In the previous section we presented empirical evidence
rWhich provided some weak support for the h: _thesis that the
. posTar increase in industrial demand for energy was due in
.
This result
part to biased (energy-using) technical change.
S s not conclusive,
for we
are unable to reject the hypothesis
that technical change was Hicks-neutral.
.
We now assune that technical change is
• 'nd-i
::
examine the effects of certain tax policies on the deand for energy in U.S.
"..
.
Hicks-neutral,
manufacturing.
Specifically, we
investigate the effects on energy demand of:
---
(i)
.-
removal
.* f the investment tax credit (w-hich took place in 1962) and
..a return to the pre-1954 accelerated depreciation allowances
S.on producers'
.
..- tures; and (ii)
--
*
" -Our
durable equipment and non-residential struc-
''
imposition of a 5% tax on energy.
simulation procedure is similar to that of Hall-
S orgenson L1967).
Specifically,
using the formulae for cap-
:ital service prices as presented in Berndt, Kesselman and
-Williamson 119753, we estimate the capital service price
S(denoted as PK) had the investment tax credits and post-1954
5
-changes
c.
'
in depreciation allowances not taken place.
.Table 4 below, we compare the two price series.
*
fN'
In
''i
There it
r
is
~,
seen that removal of these investment incentives would have
implied a sizable increase in the price of capital services.
r
~
..
;
55 ~
;. i~r
75 ~ ~
6'.
5;
~-.
2,
r
r
.
Table 4
P ) and Tax-Adjusted (PI) Capital Service Prices
amnufacturing, 1948-71
,U.S.
Actual
Px
Year
.
1948
S.-1949
1950
1.00270
1951
1.04877
.99744
1.00654
1.08737
-1953
1954
1.10315
1956
.99607
1.06321
1.15619
1.30758
9-57
2959
. "195
.
Tear
1.00270 " "
.74371
.92497 .
1.04877
.99744
1.C0H54
1.18321
1.20993
1.10043
o1.1S42
1.30087
1.50035
.74371
.92497
.-1952
p...
i
.
-
_i
1960
1.25413
1961
1962
1963
1964
1965
1966
1967
19681969
1970
1971
1.26329
1.26525
1.32294
1.32798
1.40659
1.45100
1. 33618
1.49901
1.44957
1.32465
.'1.20178
•3.
. ..
"**.
.
-
°..
1. 43750
1. 43 401
1. '5724
53838
.
*
1.1
1. 71959
1. 75797
1. 65735- ",
1.
1. 7-625
1. 53204
1. 43467 •
**
-
-
3
:: :0k.
.
.J
•
T.o sIbalate the effec-ts of this input price change, we
se parameter estimates from Column 3, Table. 2 and insert them
sIt
...
.
t
n
.with the new input price data into (7).
.
This provides
s with
A new price of output 'since with zero profits and consist
- returns to scale, marginal cost = average cost = price of ct-..
put) z ries.
We then solve the share equations (11) for K. L,.
' , and M in terms of the new P, historical output V, the ero:. "genous input prices, and the parame-ers.
-.
- eat result
S.....
years.
centives
-.
.mandj
~~
In Table 5 we pre-
from this simulation (Simulation I)
In 1971,
for examp
for selectd
removal of the investment in-
Awou
haBM resulted in
a 2.4% decrease in
a use of the energy-capital compleentaitt
energy dci
capital
.
-
--
'~-Yull
---
- 29 -
K,)~
demand would have decrease 5.0%, while the quantities of L
and M demanded would have increased .6 and .3 of 1%, respectively. Thus removal of the investment incentives would
have resulted in a less energy and capital intensive produc-tion process.
In our second siauilation, we obtain derived demands un-'er the ass,~mticn that in addticn to removal of the invest--ent incentives, a 5% tax was imposed on energy.
tive scenario which might hfave ~
to
An alterna-
increase in P
is the renmoval of price ceilins s on cert in energy types (e.g.,
na&ural gas).
The joint effect of th---
:o
tax policies
in
1971 is to decrease the quantity of E demanded by 4.1%, de. crease K by 5.6%, increase L by .7% and increase M by .4%.
In our final simulation (Simulation III), we take acScount of output demand conditions.
Specifically, the effect:
of the removal of investment incentives and the 5% energy
Stax is to increase the cost of producing output.
Given zea.ro
profits, this implies an increase in the price of output
('.
-(denoted
aP).
If output cqantity d-mandd is price sensi-
tive, the effect of the two tax policies is to reduce the
quantity of output demanded.
For convenience, we assume an
output price elasticity of -1, which implies that revenue
would be unaffected.
Taking account of these output price
effects, we find that in 1971 the effect of the two tax
r;-
S 30 policies is
,
to -
.
--
..--.--.
.
d---
-
.
.
. . -
-~
.....
.,
e
-i=Pase
'."
price
of output by? 1. % and reduce output demand by 1.0%.
The de-
rived demands for E, K, L, and M fall by 5.1%,
.3%
6.5%,
and .6% respectively.
We conclude that because of the energy-capital ccmplementarity, investmrent incentives have contributed sig-
nificamtly to the post-war
increase in industrial dmand.
for energy.
.1
Table 5
Effects of Changes in Tax. Policy on Price of Cutput
and Derived Demands for Inputs in U.S. Manufacturin-.
muirlation I:
Year
1954
1960
1966
1971
AP
AV
.005
.0
.003
.012
.0
.0
.009
.0
AK
A1
-. 029
-. 049
.003
-. 011
.C02
.005
.004
-. 074
.008
-. 018
-. 027
.-. 050
.006
-. 024
.A03
.003
.GC6
8iul2tion I i
. 1954
1960
1966
1971
.007
.010
.014
.011
.0
.0
.0
.0
-.
-.
-.
-.
034
054
078
056
.004
.007
.009
.007
-. 029
-. 008
-. 010
-.
-.
-.
-.
041
063
090
065
-. 003
-. 003
-. 004
-. 035
-. 044
-.-
-. 05 1
-. 051
-,.'06
.76
-. 035
-. 042
-. 041
.C4
Simzulation III:
1954
1960
1966
1971
.007
.014
-. 012
.011
-. 010
-. 003
C4
SmSimlation7I:
Removal of Post-1954 investment Incentives
using Eistorical Cutput
Smlation II: Rea.oval of Post-1954 In-estment Incnti -s
and IZiposition of 5 Energy Ta, Eis .ozfcal
Output
S&ulation III:
,.emcval of Post-154 -Invetment Incent:.ves
and I positTion of 5% EneiegyU
Tax, COttpu
Quntity Demanded Subject to Unitary Price
Elasticity.
Footnotes
i1. See, for example, P.A. David and Th. van de Klundert
[1965], and the references cited in Hans Binswanger
[1974a3.
S
~\
t
*
2.
The translog function can of course in interpreted as
a second o-rder approximation in logarithms to an arbitrary function.
For further discusicn of this, see
Berndt-Jozgenson [19753 and W.E. Diewert 119743.
3.
For further discussion. see W.E. Diewert (1975a,b),
Jorgenson-Lau [1975, Jorgenson-Griliches [19(7, 19723
ota ftor pr-AoducTh e i4,6x
and Nadiri [1970.
.neex of outtivity is typically co-mputd as a Livisa
puts (in constant dnllars' minus a Divisia index of
inputs.
4.
For further discussion, see Jorgenson-Lau
S5.
This reveals the error in Binswanger (p. 964): "The
substitution parameters of the production process have
to be estimated befoze any biases can be measured."
Binswanger's statement is true, however, if returns to
scale are unknown.
6.
For further discussion of share elasticities, see
Jorgenon-.Lau [1975].
7.
For f-uther discussion, see Berndt-Hall-Hall-Hausman
.1974).
19753.
..
8.
See A. Zellner and H. Theil [19623 and E. Malinvaud
[1970], ch. 9. It is worth noting that the Wald test
statistisLc. is asymptotically equivalent to the likellhood ratio cziterion.
j
The method used by Hunphrey-Moroney [1975] is incorrect,
for it fails to recognize that the M :are functions of
--tt.- stochastic parameters.
10.
**"11.
12.
The standard error -information would be particularly
useful in assessing, for example, if estimated own AES
which happen to be positive are "significantly nonnegative.
See Berndt-Wood [1975), Section III and Tables 1 and 2.
The prices are scaled to unity in 1947.
See Faucett [19733.
I
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Footnot-es
(corntinu. d)
21.
As noted in footnote 19, monotonicity and convexity conditions'are satisfied at all annual observations.
22.
To conserve space, we do not report estimates of the
price elasticities.
The interested reader can obtain
approxinrte estinates by multiplying our estimated AZS
by the cost shares,
Eij =
ij
The cst
share data
is found in Table 2 of 1erndt-Wood [1975].
23.
See Zellner-Theil [1962].
*
? ^~ -l^-~'~I^- '--
"" -"~
''~~~ ---~ - - i C-)--r -- --
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l
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" ~~~Tlx~nr
r e r -~-- ^--r,..,,,,.~,,
North-
,~.,,,~,.,~.,,.,~,~
.,,,,.~, ~..~._.,
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Reforerces
YIYII
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IYYIYIYIYIYIY
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i