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

jackknife, the bootstrap and other resampling methods," Biometrika.

9. , 1981b. "Nonparametric standard errors and confidence

intervals," Canadian Journal of Statistics, ~, pp. 139-172.

10. , 1982. "The jackknife, the bootstrap and other resampling

plans, "SIAM, Monograph #38, CBMS-NSF.

11. EFRON, B. and G. GONG, 1983. "A leisurely look at the bootstrap, the

19

20

21. THEIL, H., 1971. Principles of Econometrics, John Wiley &Sons, New

York.

22. ZELLNER, A., 1962. "An efficient method of estimating seemingly

unrelated regressions and tests for aggregation bias," Journal of the

American Statistical Association, June, pp. 348-368.

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

• •

I'

•

•

••

•

-J

...J

~

••

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