Industrial Electricity Demand: S. M. Khalid Nainar University of … · 2008. 6. 26. · INDUSTRIAL...
Transcript of Industrial Electricity Demand: S. M. Khalid Nainar University of … · 2008. 6. 26. · INDUSTRIAL...
Industrial Electricity Demand:
New Results Using Bootstrapping Techniques
S. M. Khalid NainarResearch Associate
Public Utility Research CenterUniversity of Florida
February 1985
Acknowledgements. I am grateful to Professor Sanford Berg forsuggesting this topic to me and encouraging me along the way. I alsothank Professors Stephen Cosslett and Kim Sawyer for enlightening me onvarious methodological points. The usual disclaimer is invoked,however.
Abstract
This study examines the responsiveness of large industrial customers to time-of-use rate structures. The study set out to achieve twopurposes: (1) to replicate the Hirschberg-Aigner (H-A) analysis forFlorida data and (2) to introduce a correction in the H-A methodologywith regard to simultaniety bias between the output proxy and economicdemands, and to derive correct standard errors for estimates of variousprice elasticities.
The analysis corroborates the H-A analysis of Southern Californiadata, although the price elasticity estimates in our study are relatively higher. The analysis indicates that simultaniety bias did notsignificantly change the estimates.
When deriving price elasticity estimates from estimated cost-shareelasticities in a translog formulation, the variance of the priceelasticity estimates consists of two components: (1) variance due tovariations in observation and (2) variance due to the derivation of aprice elasticity estimate based on the estimated value of the cost shareelasticity. H-A analysis derives various price elasticity estimatestaking into account only the first component of the variance. Consequently, H-A underestimate the variance of their price elasticityestimates and, correspondingly, overestimate the significance of theseprice elasticity estimates. When we correct this analysis by takinginto account the second component of the variance of price elasticityestimates, some estimat~s that were significant earl ier becomeinsignificant.
INDUSTRIAL ELECTRICITY DEMAND:
New Results Using Bootstrapping Techniques
Introduction
Over the last few years, and particularly since the passage of PURPA,
electric utilities have shown interest in time-of-use (TOU) price
structures. Such pricing tries to mirror the opportunity costs of
producing electricity, which varies with the time of day, the day of the
week, and across seasons.
Many empirical studies have tested the responsiveness of industrial
customers to the new TOU rate structures. Notable among these are
Henderson [13] and Hirschberg and Aigner (H-A) [14]. H-A proposed a new
methodology to capture responsiveness to demand or capacity charges; they
found that the various price elasticities for different SrCtwo-diqit
classified group industries (except SIC 35 -- machinery except electrical)
were not significantly different from zero.
The purpose of this study is to apply t~e same type of analysis to
data for Florida provided by FP&L, to see whether we obtain the same
2
resul ts. H-A had assumed that a simul tanei ty bi as between tota1 energy
(used as output proxy) with economic demands Xi was insignificant, ensuring
consistency of estimates. We suggest a refinement to the H-A methodology
affecting how cost share elasticities translate into the relevant price
elasticities. Furthermore, we also allow for simultaneity bias.
The following section outlines the specification of the econometric
model used in our study. Next, we describe the data base. Then we present
the results, note the limitations of this study, and outline directions for
future research.
Economic Model and Econometric Specification
Fo11 owi ng H-A, we assume that a fi rm has the fo 11 owi ng type of
production function:
Y = f(K, L, NE, E), (1)
where Y is output, K is capital, L is labour, E is energy, and NE is other
non-energy input (materi a1s) . Energy coul d be subdi vi ded (fo11 owi ng H-A)
as consisting of electric and non-electric. Electric energy is further
subclassified according to time-of-day. The electricity input can be
broken into demand (KW) and energy (KWH); both are assumed to be sensitive
to time of use. The KW demand is defined as maximum instantaneous load
within the period under consideration, while the KWH energy is tt'E total
electricity IlS'ed within the same period. Formally, KW demand = max KW(t)
where KW(t) is the usual load curve and
KWH energy =
t 2f KW( t)dt.t 1
(2)
3
Assuming weak separability in the electricity inputs, we can write
Y = g(H(X), 8). (3)
where H is the electricity input function and 8 is a vector of all other
inputs and X is the vector of time-differentiated electricity inputs. This
characterization reflects a two-step optimization procedure. First, the
firm is assumed to determine its total electricity cost as a function of
the level of output and prices of all other inputs (both energy and
non-energy). Next, it allocates its electricity consumption (KWH) and
demand (KW) by time-of-use as a function of total electricity cost and
time-of-use pricing structure.
Further, given the duality of cost and production functions, we have
C = C(P,Z,E) (4)
where C is total electricity cost; P is the vector of prices of the various
electricity inputs; Z is a vector of exogenous factors, such as weather;
and E is the tota1 energy consumed, wh i ch is used as a proxy for total
output. Using Shepard I s Lemma, we get the input demand functions for
various electricity inputs:
dC.dP ~ = Xi and i s I
1
(5)
where Xi is the cost minimizing level of electric input i and I is the set
of all electric inputs.
4
The functional form that is used is the translog function
1nC = a + L: a,. ln P. + t L: L: S·· ln P. ln P.. , , ..,J , J, , J
+ L: y. 1n P. ln E + 1/J ln E (6). , ,where
,
r a,. = 1 L: S··· = (}\Lib b.. = O¥j L: y. = a [3.. = SJ.'. -\Li rj ( 7),. 1 . lJ ,.'J ,. 1 '.]J .
Equation (7) assumes that the cost function, (6) is positive linear
homogeneous in the elements of P (the electricity input price vector). The
underlying cost function (3) is assumed to be twice differentiable.
Although the input demand functions obtained from the translog cost
function are not linear in parameters, usingShephard1s Lemma (4) we have
·alnC . ac PiX ia1nP"": =(l/C) Pi ap. = -c-·_. :: Mi, . • , .
(8)
where Mi is the cost share of the i th electric input. After some
manipulation, we obtain:
(9)
With this specification, we have a problem with "simultaneity bias" between
E (output proxy) and "demands" Xi. H-A assume that because of highly
nonlinear relationships, the estimates obtained w'@lultlbe consistent1. This
assumption is testable, so later we consider a simultaneous equation
formulation to see if the bias is significant.
5
Next, the own-price and cross-price elasticities are estimated from
the parameters of the cost share equations in the following way:
(3 ••
Own price elasticity: ni ; =M~~~ + Mi - 111
Cross-price elasticity of i th input with respect to the
jth input price is:(3 ••
- 1J M 1· -J. J.n·· - M +. T1J i J i, j E: I
(10)
(11)
Since the price elasticities are functions of cost shares, they are
variable over observations. H-A assume normal distribution and obtain
standard errors that are not correct. We do bootstrapping for n iiestimates (see Efron [8, 9, 10, 11]) and generate a distribution for n iiand compute the mean value for 11 i i and the "ri ght" standard errors. The
bas i c problem is, when we get n'i from (3i values, we have to correct for
sample size in the sense that we are getting values of n based on one value
of 8. So, to control for that variance, we run our system regression
several times (say 50 times), after constructing residuals and artificial Y
(dependent variable vector). From these regressions we compute (3 and n
each time.- From this we will have 50 values for n i.e., n1' n2' n50 ·
Next, we compute the mean n as usual and the right standard error as:
50s . d = L
n i=l(12)
We should note here that we did not impose any distribution on n; i.e., it
was truly non-parametric. Even if we a·ssume a normal distribution for n as
H-A did, we should technically still construct residuals and use a random
normal generator on these residuals; and then get the artificial Y the
6
dependent variable vector and run system regressions several times and then
get the various n's and their standard errors. That way, we would have
controlled for the sample size. 2
As noted ea rl i er, H-A proposed an improved methodology of defi ni ng
demand for each good in terms of its characteristics, following Lancaster
[18]. We look at the results obtained by this approach. While earlier
studies, notably Chung and Aigner [5J defined inputs according to prices
paid for them, this analysis defines inputs with intrinsic characteristics
and varying prices. With that change in definition of a "good", the prices
of these goods also have to change. Thus,
Cost of energy = (KWH) [$/KWH + ~~~W]
where KWH is total energy used in the particular rating period, $/KWH is
the energy price, $/KW is demand charge; and #hr. are the hours in the
rating period under consideration. The term in brackets is the usual
effective energy price minus the capital charge plus the conventional
energy charge. The remaining portion of total electricity costs are called
potential energy consumption (PEC) and
Cost of PEC = [max KW - ~~~] [$/KW].
PEC is then interpreted by H-A as a measure of an average load curve shape
and hence of variations in the load. So the elasticity of PEC provides a
good indication of the load-levelling effect of demand charges. Again, the
PEC can be time-differentiated as we did for the energy input. The cost
7
share equations now become:
p -M,-t = a,- + L: B- - ln (-pJ)t + y- ln Et + e,-
, jfO' J 0 '
i = A, B, C, D t = 1, ... T. (13)
We consider only 3 equations, because of add-up restrictions; otherwise, we
will have a singular equation system, on account of the above add-up
restrictions, noted in (7), earlier in the paper. We estimate by Zellner's
SURE [22J and N3SLS [12J methods. We check for autoregression in errors,
as we did in the other approach. Following the others, we do not allow for
substitution across nonadjacent time-periods. Next, the various prices
were tri ed as numera ire pri ce and we selected the one that gave best
estimates -- implicitly minimizing condition index for relevant matrix. As
H-A note, this choice does not affect the properties of our estimators.
Data
The data used were provided by Load Research Group at Florida Power &
Light, Miami, Florida. The overall data base included about 22 companies
and the data on their electricity consumption. The companies belonged to
GSLDT-3 and CST-3 groups. These are companies with over 4,000 KW demands.
Due to data problems with some companies we included only 6 companies and
restricted ourselves only to GSLDT-3 class for this study. This still
provided 96 observations of which we left out about 6 observations on
account of some missing components. Also for some components (e.g., KWH)
the data were from rate systems while others were from load research
systems. To the extent that there are discrepancies of this sort, our
results will be affected. Also, exact start dates and closing dates of
8
bi 11 i ng peri ods for each company were not known and to that extent a
further errors-in-variables problem creeps into our results. The exact
tariff structure presented in table form is appended at the end of the
paper. While there were several price variations in energy charges, we had
only one price variation in the demand charges. This point also has to be
noted when we consider the results. The time series used was from
September 1982 to December 1983.
Results
The resul ts are presented in two sets: Fi rst we present the pri ce
elasticities computed with reference to commodities as usually defined
(i.e., on basis of price). Next, we present the price elasticities result
computed with reference to commodities defined on the basis of
characteristics [18J. The various commodities defined by the Lancaster's
characteristics approach [18J are illustrated in Figures 1 and 2. As can
be observed in Figure 2, A refers to peak energy commodity; D represents
off-peak PEC commodity; C represents on-peak PEC commodity, and B refers to
off-peak energy commodity. The values for elasticities with respect to B
off-peak energy commodity can be easily obtained from cost-share elastici
ties for other commodities using the add-up restrictions alluded to
earlier. It was found that there was no significant autocorrelation, hence
we did not use Zellner's SURE with AR method [4J.
The results are generally similar to the results obtained by other
authors [19, 15J, although the specifics are quite different and notable.
All elasticities are significantly positive in sign, a finding that
corroborates the H-A study. The key difference in our results is that the
values are relatively quite high. As H-A point out, this situation might
KWmaxkw
(AREA x no. of days x demand charge)= PEe cost
TIME OF DAY 24(AREA x no. of days x energy charge =ENERGY cost
Figure I
Distinction between energy and PEe fora firm subject to a demand and anenergy -chorg-e,._(nc>tfjQlrvoryln-gprices)
• ';-, .~'<: •.• -' . . -'. - --:---~. '" ,," ~," ",'.. ...,' ,'- • ',-
"Energycommodities:
A as
o
B
A
B
o
o
K~W i-----. .....__--. PEC
max kw C commodities:C aD
Figu re 2
Loodptottern With TOU Prices
9
be the result of several factors:
1) Misspecification of the cost function as being of translog nature.
2) Price changes due to fuel cost changes.
3) Violation of separability assumption noted earlier.
4) The elasticities are partial, for they are based on the first step
of a two-step optimization that allocates the amount to be spent on
electricity as opposed to other commodities. Hence these should also
depend on elasticity of electricity expenditure.
An important point to note is that the values of price elasticities
depend on the cost shares at which the particular elasticity is computed.
Moreover, the assumption of stochastic cost shares implies that the price
elasticity estimates have probability distributions defined by ratios of
normally distributed random variates. While Anderson and Thursby [2]
proposed that computation at mean cost share is more likely to result in
normally distributed price elasticities than at any other observation, it
should be noted that in these days of high-speed computers it is better to
check out the distribution by repeated sampling techniques such as
IIbootstrapping ll and derive correct standard errors. This takes on added
significance, particularly if computed elasticities are borderline cases on
significance level tests.
The relevant elasticities are presented in the following format. The
entries along the diagonal are own-price elasticities, while those off the
diagonal are cross-price elasticities. It can be seen that the elasti
cities have the wrong sign; and more notably they are quite significant at
1% and 5% levels of significance. The t-statistics are given below each
entry in parenthesis. As an example of how the table should be read, the
10
own-price elasticity of peak energy is 0.60, while the cross-price elasti
city of peak energy with respect to off-peak energy price is -0.50.
Table 1 presents the elasticities computed using Zellner's SURE
method, in an effort to duplicate H-A analysis for Florida data for GSLDT-3
customers.
Table 2 presents the elasticities computed using a technique called
nonlinear three-stage least squares (N3SLS) after Gallant [IIJ where we
take account of simultaneity bias between E (total energy) and the
individual components such as OKWH (off-peak kilowatt hours). The bias was
found to be present, in that residuals from different equations were
correlated relatively highly; and this is reflected in some of the
estimates obtained by N3SLS which are different from those obtained with
the SURE method. Only one simultaneous specification is given here, the
one we thought best in terms of R2 and parameter estimates; the others are
given in the appendix.
In Table 3 we present the standard errors computed by using the
bootstrapping technique alluded to in the earlier section of this report.
It can be seen that the values for various standard errors are different.
Notably, we can see that the value for own-price elasticity of peak energy
which was significant in earlier tables using H-A methodology of deriving
standard errors, is now not significant. Other such cases can be seen by
reading the table completely. So, we observe that significance of
estimates obtained is sensitive to the way the standard errors are derived.
To the extent that the "bootstrap" standard errors are closer to rea1i ty
(see Efron [7, 8, 9, 10, IIJ) we should use this method to arrive at con-
elusions regarding the significance of various estimates.
Table 1
Calculated Elasticities: Zellner's SURE Method
Peak Off-peak Peak Off-peakEnergy Energy Demand Demand
-
Peak 0.60 -0.44 -0.27 -0.36Energy (2.40) (-2.58) (-2.25) (-4.50)
Off-peak -0.20 0.36 -0.02 -0.06Energy (4.00) (6.00) (-0.66) ( ...1.50)
Peak -0.23 -0.04 0.32 0.01Demand (-2.87) (-0.80) (2.66) (-0.33)
Off-peak 0.24 0.21 0.01 0.29Demand (6.00) (2.62) (0.25) (1.70)
11
R2
M1: On peak .58energy
M2: Off peak . .50energyo : ..
M3: On peak .61demand
M4: Off peak .75demand
LC: Cost .82equation
Table 2
Nonlinear Three Stage Least Squares
Peak Off-peak Peak Off-peakEnergy Energy Demand Demand
Peak 0.59 -0.50 -0.24 -0.32Energy (2.45) (-2.77) (2.18) (-4.00)
Off-peak -0.23 0.36 -0.01 -0.04Energy {-4.60) (6.00) (-0.33) (-4.00)
Peak -0.20 -0.02 0.30 -0.01Demand {-2.50) (-0.40) (2.72) (-0.33)
Off-peak 0.28 0.22 -0.02 0.25Demand (7.00) (2.75) (-0.40) {1.56)
12
R2
Ml: .55
M2: .45
M3: .59
M4: .74
LC: .81
LE'109 (KWH.): .74
Table 3
Seemingly Unrelated Regression Estimates
with Bootstrapping
Peak Off-peak Peak Off-peakEnergy Energy Demand Demand
Peak 0.41 -0.72 -·0.06 0.43Energy (1.57 ) (-~4. 00) (~O.28) (3.90)
Off-peak -0.34 0.48 -0.05 --0.01Energy (-4.25) (4.80) c-O. 55} (-2.00)
Peak -0.05 -0.10 0.11 0.10Demand (-0.27) (-D.58) CO. 61) C1.00)
Off-peak 0.58 -0.05 0.16 0.32Demand (3.86) (-0.35) (1.06) (2.90)
13
14
Next we present the results computed for commodities defined according
to their characteristics rather than by price. Table 4 presents elasti
cities computed by the SURE method, while Table 5 relates to the N3SLS
technique. In particular we note the one that relates to the load
1eve11 i ng impact of pri ce changes. The value we get for on-peak demand
elasticity is low, 0.1, and is of the wrong sign, but is insignificant.
The other notable result here is that on-peak energy elasticity is of the
right sign and rather high -0.99, and is significant. The tables are to be
read as earlier ones.
Concl~sions and Implications
The purpose of this study was twofold: first, to duplicate the H-A
study for Florida data; and second, to extend the H-A study by correcting
for the simultaneity bias involved in the H-A analysis and outlining the
application of the bootstrap resampling technique to approximate the
IIcorrectll standard errors for the various price elasticities. Both these
purposes were more-or-l ess accompli shed. In 1i ght of the fi rst purpose,
this study corroborated the H-A study, in that we also get significant
own-price elasticities, the difference in the two studies being that we get
relatively higher values for the various elasticities. Also the cross
price elasticities had wrong signs and were significant.
With regard to the second purpose, our results with regard to simul
taneity bias was mixed, with residuals in various equations in the SURE
method correlated highly while the estimates for elasticities did not turn
out to be very different. Still, as long as a procedure such as N3SLS is
available, one should allow for the simultaneity bias that is present.
Table 4
Seemingly Unrelated~R~gression Estimates:
Characteristics Approach
0 C A
0 -0.55 0.34 -0.24(-0.06) (1.25) (-0.70)
C -0.06 0.10 -2.96(-6.00) (0.37) (-1.16)
A 0.00 -0.19 -0.99(0) (-2.37) (9.90)
B 0.0 0.07 0.17(0) (3.5) (4.2)
0: .84
C: .92
A: .11
15
Table 5
Nonlinear Three-Stage Least Squares:
Characteristics Approach
D C A
D -0.04 0.35 -0.33(-0.05) (1.25) (-0.80)
C -0.07 0.15 -3.13(-7.00) (0.51) (-1.17)
A (0.00) (-0.15) (-0.99)(0) (-2.50) (9.90)
B (0.00) 0.06 0.17(0) (3.00) (4.2)
. '~" i
D: .84
C: .90
A: .05
LE: .72
16
The various price elasticities computed in the study were all less
than 1 in absolute value, i.e., the various demands are price inelastic,
although the magnitudes are relatively higher as compared to the H-A study.
Nevertheless, these results conform to other results reported by Park and
Acton, where [18] at a disaggregated level of SIC four-digit code, a
greater price-related response was observed. It should be stressed that we
found this larger response for two-digits SIC code, while for the same
level of aggregation Park and Acton [18] found a relatively smaller mean
response.
All these differences in results suggest lines for future work. One
should be able to determine how much of this is specification sensitive
(translog approximation) [12]. Also, we did not include the various
weather-related factors, in an effort to keep the model simple.
Furthermore, how much of these differences may be due to peculiarities and
deficiencies in data sets employed in the various studies warrants
attention.
In conclusion, because of data limitations pointed out earlier, some
of the strength of our resul ts may be affected; probably one needs to
collect more data, in terms of years and industry specifics. But, in the
face of such strongly significant results, one is led to believe that not
all differences can be accounted for by data set idiosyncrasies: much more
is involved, and disentanglement of theoretical, methodological and data
limitation issues should be the focus of further work.
17
Endnotes
1. Consistency following Johnston [16] can be illustrated as follows: An
estimator xn(a random variate) of ~ is said to be consistent if:
n -+ 00
In other words, the probability of xn lying in an arbitrarily small
interval about ~ can be made as close to unity as we desire by letting
n become sufficiently large. A precise way to write this is:
where plim is an abbreviation of probability limits. The estimator xnis said to be a consistent estimator of~, some population
characteristic such as the mean.
2. We had a sample size of 90 observations. From that we estimated the
system 1.. = f(x,B) + .!! andS. Next, we construct the residuals
U= 1.. - f(x, B). Next, we take 50 drawingsof 90 values of LA in each"'-
selection with replacement and get sets of u. Next, construct
1=f(x, S) + Q. Then estimate the model system using the artificial
data generated.~y ~ f(x, 8) + u.
~ ~Get Ssfrom the above series of system estimation and we will get n
18
from these values.~,
So then we will have a set of 50n .; Next we
compute the mean and standard error in the usual way. This then will
control for the unknown distribution of n.
Bibliography
1. AMEMIYA, T., 1974. liThe nonlinear two-stage least squares estimator,"
Journal of Econometrics, £' pp. 105-110.
2. ANDERSON, R. G., and J. G. THURSBY, 1982. "Some evidence on distribu
tion of elasticity estimators in translog models," Proceedings of the
Business and Economic Statistical Section of the American Statistical
Association.
3. BERG, S., 1984. Topics in public utility economics, unpublished mono
graph, University of Florida.
4. BERNDT, E., and N.E. SAVIN, 1975. "Estimation and hypothesis testing
in singular equation systems with auto-regressive disturbances,"
Econometrica, September-November.
5. CHUNG, C. and D. J. AIGNER, 1981. "Industrial and commercial demand
for electricity by time-of-day: A California case study," The Energy
Journal, pp. 91-110.
6. EFRON, B., 1979a. "Bootstrap methods: another look at the jackknife,"
Annals of Statistics, I, pp. 1-26.
7. , 1979b. "Computers and the theory of statistics: Thinking
the unthinkable," SIAM Review, Q, pp. 460-480.
8. , 1981a. "Nonparametric estimates of standard error: The
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19
20
21. THEIL, H., 1971. Principles of Econometrics, John Wiley &Sons, New
York.
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21
Appendix
Table 1N3SLS (All in LE Equation;
tha tis, NKWH, OKWH, KKW, OKW)
Peak Off-peak Peak Off-peakEnergy Energy Demand Demand
Peak 0.58 -0.49 -0.23 -0.32Energy (2.41) (-2.72) (-2.09) (-4.00)
Off-peak -0.23 0.36 -0.01 -0.05Energy (-4.60) (6.00) (-0.33) (-1.25)
Peak -0.19 -0.03 0.30 0Demand (-2.37) (-0.60) (2.72) (0)
Off-peak 0.28 0.22 0.01 0.26Demand (7~OO) (2.75) (2.00) (1.62)
R2:M1 035M2 0.45M3 0.59M4 0.74LC 0.81LE 0.74
1
Table 2N3SLS (NKW, NKWH, OKW in LE Equation
Peak Off-peak Peak Off-peakEnergy Energy Demand Demand
Peak 3.07 -2.65 -1.78 -1.86Energy (4.03) (-4.27) (-4.13) (-4.65)
Off-peak -1.26 1.20 0.66 -0.54Energy (-7.00) (7.05) (8.25) (-5.40)
Peak -1.51 1.19 1.05 -0.66Demand (-5.80) (7.93) (4.77) (-6.00)
Off-peak 1.89 -0.26 -1.03 1.03Demand (5.90) (-1.73) (-4.68) (3.43)
R2:M1 0-:14M2 0.44M3 0.31M4 0.56LC 0.81LE 0.72
2
Table 3N3SLS (OKWH, OWK, NK~J in LE Equa ti on
Peak Off-peak Peak Off-peakEnergy Energy Demand Demand
Peak 0.58 -0.50 -0.23 -0.32Energy (2.41) (-2.77) (-4.60) (-4.00)
Off-peak -0.23 0.36 -0.01 -0.04Energy (-4.60) (6.00) (-0.33) (-1.00)
Peak -0.19 -0.02 0.30 -0.01Demand (-2.37) (-0.40) (2.72) (-0.33)
Off-peak 0.29 0.23 -0.03 0.25Demand (5.80) (2.87) (-0.6) (1.56 )
3
R2:Ml 034M2 0.45M3 0.59M4 0.74LC 0.81LE 0.74
Table 4N3SLS (OKWH, NKWH,OKW in LEEquation
Peak Off-peak Peak Off-peakEnergy Energy Demand Demand
Peak 0.59 -0.50 -0.24 -0.33Energy (2.36) (-2.77) (-2.18) (-4.12)
Off-peak -0.23 0.36 -0.01 -0.04Energy (-4.60) (6.00) (-0.33) (~1.00)
Peak -0.20 -0.02 0.30 -0.01Demand (-2.50) (-0.40) (2.72) (-0.33)
Off-peak 0.29 0.23 -0.02 0.25Demand (7.25) (2.87) (0.4) (1.56)
4
R2:M1 035M2 0.45M3 0.59M4 0.74LC 0.81LE 0.74
• •
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