1

An Analysis of Monthly Power Demand in Korean

Industries1

Zulfikar Yurnaidi 1, Jayeol Ku2, Suduk Kim3,*

1,2,3Graduate School of Energy Studies, Ajou University,

San 5, Woncheon Dong, Youngtong Gu, Suwon, Suwon, Korea

* Corresponding Author, professor, Tel: 031-219-2689, Fax: 031-219-2969

E-mail: 1viczhoel@yahoo.com, 2ken9410@gmail.com, 3suduk@ajou.ac.kr

Abstract

An analysis of monthly power demand in 17 industrial contract types is conducted using least square

dummy variables (LSDV) model for the estimation of own and cross price elasticity of power demand.

The data set used for analysis is observed under the time of use (TOU) pricing system and the estimation

result would provide information for better understanding the power demand behavior in Korean

industrial sector.

Estimation result shows that own price elasticity of power demand is found to be negative for all

contract types ranging from 0.43 to 1.94 which is rather higher in terms of their magnitude than is usually

expected. Especially the contract type of the Industrial Service C, High-Voltage C with option III shows

the highest partial price elasticity of power demand with high statistical significance. It is noted that the

cross price elasticity of the base group exhibits both gas and oil as substitute with statistical significance.

When the partial cross price elasticity of power demand for each contract types are considered in addition,

however, the results are mixed. Contract types number 4, 5, 13, and 17 show plus sign implying

substitutes for oil, while others have negative sign. For gas, the negative price elasticity is found for the

contract types 3, 5, 12, 13, 14, 15, and 17, while other contract types’ result shows gas as a complement of

electricity. Further study may be required for a better understanding of the results observed in this study.

Keywords: power demand, own price elasticity, cross price elasticity, time of use (TOU) pricing, Least

Square Dummy Variables (LSDV) model

JEL classification: C23

1 We would like to express our deepest gratitude to Prof. C.G. Moon and Prof. Songnian Chen for their valuable

comments.

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1. Introduction

The price elasticity of demand is defined as the measure of percentage change of demand when price

changes in one percent. It is important to get the proper estimate of this price elasticity to better

understand the behavior of consumers in power market. It would also be interesting to estimate the cross

price elasticity of power demand, such as of gas and petroleum product. Using these parameter estimates,

one can analyze the characteristic of electricity market especially in response of the various energy prices.

In general, the consumers of electricity market can be divided into several sectors, such as residential,

service or commercial, and industrial. Although it is possible to analyze the market as a whole, the

difference of specific behaviors between sectors can disrupt the estimation process. For example, the

residential and industrial sector might response differently to the change of electricity price due to the

difference on demand shifting capability. Another problem is the difference of energy price change that is

applied to each sector. First, the tariff imposed on each sector’s usage of electricity and gas is different

one another. Also, the type of energies used is different, especially for gas and petroleum product case.

For example, industrial sectors use bunker-C or heavy oil more than any other petroleum product while

the residential sectors do not use it but kerosene instead. The difference in policy of price incentive could

produce different response and price elasticity, too. Thus, analyzing the power demand for specific sector

(in this case, industrial sector) is more promising than the analysis of the whole market. Although with

proper management of econometrics modeling, these problems could be sorted out.

Prior to this study, some researches on price elasticity of power demand estimation have been

published. In his paper, Fan and Hyndman (2011) summarizes a number of those studies. Most of the

studies are conducted in developed countries where power market reformation takes place, such as US,

Australia, and European countries. From these, it is observed that the estimated price elasticity of power

demand differs from one study to another. The most common numbers are ranging from -0.2 to -0.4 for

the short run elasticity and -0.5 to -0.7 for the long run elasticity. The inconsistency of result might be

caused by the difference of model used which in turn is heavily depends on the difference availability of

data. Interestingly, it is also reported that there is no significant difference between residential,

commercial and industrial price elasticity of demand.

The difference of model and data type utilized in estimation of price elasticity of power demand can

further be seen in a study by Lijesen (2007). For estimation of long and short run elasticity, various types

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of model such as trans-log, log-linear, and error correction model are summarized. The range and type of

data also varies; it can be quarterly or annual, time series or panel, with different period under study. In

his summary, the price elasticity for industrial sector ranges from -0.123 to -0.51 for short run and -0.311

to -1.76 for long run.

Patrick and Wolak (2002) analyzes the data from large and medium sized industrial and commercial

customers purchasing electricity under half-hourly spot prices and demand charges from the England and

Wales electricity market for the period of April 1991 to March 1995 (four years). This study shows that

the day-ahead price elasticity estimates vary substantially by time-of-use, industry and firms within

industries. The values of price elasticity are ranging from essentially zero to 0.89 in absolute value. The

sign of price elasticity of demand is negative, as in other reports, since a higher price would give incentive

to reduce the demand, and vice versa.

For Korean case, Korean Energy Economic Institute (KEEI, 2004) estimated the price elasticity of

electricity demand using OLS (Ordinary Least Square) and ARDL (Autoregressive Distributed Lag)

model. The determinants of electricity demand in this report include production index, price of electricity

and time trend. Using Ordinary Least Square (OLS) method, the price elasticity of power demand is

around -0.285 for the overall industrial sector. When using Autoregressive Distributed Lag (ARDL)

method, the price elasticity is lower, around -0.171 for overall. Meanwhile the price elasticity for

commercial and residential sector is found to be not significant.

The purpose of this study is to analyze the monthly power demand in Korean industrial sector using

econometrics method to estimate the price elasticity of power demand. In the case of Korea, although

there are previous researches on the empirical estimation of the price elasticity of power demand such as

those of KEEI (2004), recent empirical work on domestic power demand has not been reported since.

Also, different from the previous studies which only focused on the main parameter estimate of price

elasticity of power demand, this paper would also emphasize on the analysis of cross price elasticity of

power demand. The analysis of other energy prices (gas and petroleum product) such is in our study

would greatly improve the understanding of Korean power market especially in relation with the energy

market in general.

This paper is organized as follow: the second section elaborates the data gathering, data processing

and the econometrics method applied to those data; the results of estimation process would be

summarized in section three along with discussion of the results; then section four would provide

concluding remarks of insights from this study.

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2. Data and Method

2.1 Data

The data set used in our analysis is monthly electricity consumption for the period of 2004-2010

provided by KEPCO (Korean Power Electricity Company). Other than electricity consumption, the

database provided by KEPCO is also equipped with the electricity sales, number of households, contract

sizes, and other variables. It should be noted that the original raw data is categorized into several

dimensions—regions, contract types, and industrial codes—other than the time dimension.

There are fourteen regions in the KEPCO database, which are: Seoul, South Seoul, Incheon, North

Gyeonggi, Gyeonggi, Gangwon, Chungbuk, Daejon-Chungnam, Jeonbuk, Gwangju-Jeonnam, Daegu-

Gyeongbuk, Busan, Gyeongnam and Jeju. Further, the original samples are categorized into 99 industries

with their respective industrial codes, following the Korean Standard Industrial Classification (KSIC).

These can also be combined into 35 industrial groups, which ranging from agriculture, forestry, and

fishing to residential and street lights. The last dimension is the contract types, such as several types of

residential, educational, industrial, service, agriculture, and street light.

Although the richness of the database is tempting to analyze the power market in detail, the

complication of the econometrics model needed is also equivalent with the complexity of the data. In

addition to that, the data quality also shows that the analysis utilizing all dimensions available would be

difficult and could not provide the expected result. Based on those reasons, the analysis in this paper is

based on the contract type (especially the industrial type) while the other two dimensions (region and

industrial group) are aggregated.

As mentioned before, KEPCO divides the electricity pricing system in Korea into several contract

types, with various types of Residential, General, Educational, Industrial, Agricultural, and Street Lights

Services. But the present study is focused on just one big category of contract type – Industrial Service,

which is divided further into total of 17 pricing tariffs. Table 1 shows the complete disaggregation of

electricity tariffs for industries. To begin with, there are three classes of contract types based on the power

limit, which are “Service A” for less than 300 kW, “Service B” for between 300 and 1000 kW, and

“Service C” for more than 1,000 kW. Each class can be divided again depends on their connection to

power grid, “Low-Voltage” for those connecting with 100-380V (low voltage) power line, “High-Voltage

A” for those connecting with 3.3-66 kV (middle voltage) power line, “High-Voltage B” for those

connecting with 154kV (high voltage) power line and “High-Voltage C” for those connecting with 345kV

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(high voltage) power line. Last, there are also two to three tariff options that can be chosen by costumer.

Each option is differentiated with others by the level of base tariff (fixed) and usage tariff (variable,

depends on electricity consumption). Option I has a lower base tariff than Option II, but the usage tariff of

Option I is higher. Then the Option III has a higher base tariff but lower usage tariff than both Option I

and Option II.

Table 1 Industry Contract Types of Electricity Tariff

Group Number Contract Type Class Voltage Type Tariff Option2

1 3110 Industrial Service A Low-Voltage -

2 3211 Industrial Service A High-Voltage A Option I

3 3212 Industrial Service A High-Voltage A Option II

4 3311 Industrial Service A High-Voltage B Option I

5 3312 Industrial Service A High-Voltage B Option II

6 7211 Industrial Service B High-Voltage A Option I

7 7212 Industrial Service B High-Voltage A Option II

8 7261 Industrial Service C High-Voltage A Option I

9 7262 Industrial Service C High-Voltage A Option II

10 7311 Industrial Service B High-Voltage B Option I

11 7312 Industrial Service B High-Voltage B Option II

12 7361 Industrial Service C High-Voltage B Option I

13 7362 Industrial Service C High-Voltage B Option II

14 7363 Industrial Service C High-Voltage B Option III

15 7461 Industrial Service C High-Voltage C Option I

16 7462 Industrial Service C High-Voltage C Option II

17 7463 Industrial Service C High-Voltage C Option III

The electricity tariff currently used by KEPCO is already exercising time of use pricing (TOU)

system. It has three seasons and three time zones with different tariff for each season and time zone. For

example, since people tend to use electricity more during the night time of winter which is colder than the

day time, the electricity tariff during the night time of winter is higher than the day time. Meanwhile in

2 Tariff options differs one another in such a way that for the higher Option, the base tariff gets higher while the hourly (Time-of-Use) usage tariff gets lower.

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summer, the electricity during the day time is more expensive than the night time since the electricity

consumption during the day time of summer tends to be higher. The system is designed based on the load

curve of each season at specific time duration, which shows the off-peak, middle, and peak load of

electricity. The electricity tariff is set to be higher on peak load than off-peak time zone. Figure below

shows one example of time-of-use price (starting from August 1st, 2010) for contract type 7261. The three

lines show the change of electricity tariff during one day (24 hours) for each season type. As can be seen,

it intuitively follows the load curve of a typical consumer.

Figure 1 Daily Time-of-Use Tariff for The Contract Type of Industrial Service C High-Voltage A Option I (7261)

Even though the analysis in this study is on monthly basis, but the usage of TOU tariff system

with three different seasonal price tariffs could provide a better understanding of the consumer’s demand

response which is captured in the price elasticity of demand. Other than these seasonal price differences,

the overall pricing system in Korea also has been changed eight times during the period of this study

(2004-2010).

Other than collecting the electricity consumption data and electricity price data, which are the

independent and dependent variable needed to estimate the price elasticity, other exogenous variable

information is also gathered in order to properly analyze the power demand. Those variables includes the

price of other energy sources (gas and petroleum product), producer price index, production index,

number of customer, and temperature (to calculate Heating Degree Days and Cooling Degree Days),

which are gathered from various sources.

40

60

80

100

120

140

160

0 4 8 12 16 20 24

Summer(Jul-Aug)

Spring . Fall(Mar-Jun . Sep-Oct)

Winter(Nov-Feb)

7

Among several kinds of gas and petroleum product prices in the Korean market, the ones utilized

in this study are the industrial gas price and the bunker-C price. The data is gathered from Korean Gas

(KOGAS) and Korean National Oil Company (KNOC) database. The importance of these two energy

prices is to serve as substitute or complementary product to the electricity as an energy source. Then by

analyzing the sign of cross price elasticity of demand estimated, the nature of interaction between

electricity and gas or petroleum products can be observed.

As common practice in economics analysis, this study uses production price index (PPI) to

deflate all the price information in this study and eliminate the effect of changes in the price levels

(inflation). In other words, all prices should be converted into real term. The PPI data is taken from Bank

of Korea information system.

Since the size of each industry would have affected the electricity usage, this paper adds two

more variables to take care of that problem, which are production index and number of costumers. The

first variable—production index—would be useful to explain the changes in electricity demand due to the

change in overall level of production, like in an economic recession. Meanwhile, the number of costumers

is important to explain the difference in power demand due to the size of each industry on specific time.

These two variables are gathered from Bank of Korea and KEPCO database, respectively.

Following the previous studies on price elasticity of power demand estimation (for instance,

Patrick and Wolak, 2002) this study also utilizes the temperature information to explain the electricity

demand. The initial data is gathered from Korea Meteorological Administration (KMA). This data then is

transformed into two distinct variables, Cooling Degree Days (CDD) and Heating Degree Days (HDD).

CDD is defined as the number of days when the temperature (T) is higher than a certain limit, while HDD

is defined as the number of days with temperature lower than a certain limit. This limit is usually 18oC,

which is also used in this study. This information will take care of the power demand change due to the

different seasonal characteristics, for example the increasing electricity consumption due to cooling in

summer and heating in winter will be explained by a higher CDD and HDD, respectively. After collecting

hourly information of temperature from KMA, the monthly CDD and HDD can be calculated as follows:

CDDi =∑ (Tt − 18)24∗d

t=1

24, for Tt > 18 C

HDDi = ∑ (18 – Tt)24∗d

t=1

24, for Tt < 18 C

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where: i = month index; Tt = temperature at hour t; d = number of days on month i

First we calculate and aggregate the hourly Cooling Degree/Heating Degree for the whole month. Then

we divide this number with 24 hours/day to produce the CDD/HDD for the respective month. Using this

information, the increase of demand in summer and winter due to seasonal effect would be taken care of

CDD and HDD, respectively.

2.2 Model

As elaborated in the previous subsection, even after aggregating two dimensions from the original

raw data, there are still two dimensions in the dataset: contract type and time. In econometrics model, this

nature of data needs panel analysis—which combines cross section and time series type of

econometrics—in order to properly estimate the parameter. The panel model would be able to fully utilize

the data information from the sample which has a panel data structure with 17 different contract types for

the period of January 2004 to December 2010 (84 months).

For this study, a panel model with fixed effect is utilized to estimate the parameters. The general

model of this fixed effect is also called the Least Square Dummy Variables (LSDV). Utilizing the price of

electricity and other exogenous variables as discussed in the previous subsection, the estimation model for

this study is specified as follow:

yi,t = ∑ β1k

nl

k = 1

yi,(t−k) + ∑ β2k

nl

k = 1

PGi,(t−k) + ∑ β3k

nl

k = 1

POi,(t−k) + ∑ β4k

nl

k = 1

PIi,(t−k) + ∑ β5k

nl

k = 1

Housei,(t−k)

+ β6

PEi,t + β7

PGi,t + β8

POi,t + β9

Housei,t + β10

PIi,t + β11

HDDi,t + β12

CDDi,t

+ ∑ β13j

nsb

j = 1

SDj + ∑ β14j

12

j = 2

MDj + ∑ β15j

n

j = 1

PEi,tCDj + ∑ β16j

n

j = 1

PGi,tCDj

+ ∑ β17j

n

j = 1

POi,tCDj + ∑ β18j

n

j = 1

PIi,tCDj + αi

where yi,t : Electricity consumption for contract type i at time t

yi,(t-k) : Electricity consumption at time t-k (k-th lag)

PG i,(t-k) : Price of gas (real term) at time t-k (k-th lag)

PO i,(t-k) : Price of oil (real term) at time t-k (k-th lag)

PI i,(t-k) : Production index at time t-k (k-th lag)

House i,(t-k) : Number of household at time t-k (k-th lag)

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PEi,t : Price of electricity (real term)

PGi,t : Price of gas (real term)

POi,t : Price of oil (real term)

Housei,t : Number of household

PIi,t : Production index

HDDi,t : Heating Degree Days

CDDi,t : Cooling Degree Days

SDj : Structure break Dummy (SDj = 1 for specific structure periods)

MDj : Monthly Dummy (MDj = 1 for month j)

CDj : Contract type Dummy (CDj = 1 for contract type j)

αi : Fixed effect

From the model above, it should be noted that we used several lagged variables, for both the

dependent (electricity demand) and independent variables (price of gas, oil, production index and number

of household). When lagged dependent variable is included as regressor (autoregressive model), the

model becomes a dynamic panel linear regression model. Some econometrics studies argue that in this

case, the LSDV model no longer works because it produces bias on the estimated parameters. Thus it

must be solved by utilizing other method such as using simple instrumental variable estimator as

proposed by Anderson and Hsiao (1982) or using the first-differenced GMM estimation as proposed by

Arellano and Bond (1991). But it should be noted that the problem posited by Arellano and Bond is in the

condition of short time series (T) and long cross section (N), T > N. A case where the autoregressive

panel model could be a problem is the study by Filippini (2011). Since his data size is quite small (T = 6

and N =22) he undergoes two kinds of estimation, which is LSDV and corrected LSDV model proposed

by Anderson and Hsiao (1982) and Kiviet (1995).

However, the time dimension in this study is quite long in comparison to the number of contract types

(T = 84; N = 17). Given the results obtained from LSDV are quite acceptable, it can be argued that the

within estimator βWG(LSDV) does not have asymptotic bias when T→∞. Accordingly, we can still use

the LSDV covariance matrix, following Hahn and Kuersteiner (2002). A rigorous study by Alvarez and

Arellano (2003) analyzes the econometrics model for a pure autoregressive (AR) process for y. It then

shows that when N/T→0, the asymptotic bias 1

T(1 + α)disappears. It can be seen that in this study the

N/T is small enough, which is 17/84 ≈ 0.2

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To describe the consistency of within estimator, in general, the dynamic panel linear regression

model can simply be described as below. It can be seen that the lagged dependent variable (yi,t−1) is

included as regressor:

yi,t = λ yi,t−1 + x′i,tβ + ui,t, ui,t = αi + ϵi,t, i = 1, ⋯ , N, t = 1, ⋯ , T

yi,t − yi = λ (yi,t−1 − yi,t−1) + (xi,t − xi,t)′β + (ϵi,t − ϵi)

The correlation between (yi,t−1

− yi,t−1

) and (ϵi,t − ϵi) will decide the consistency of within estimator. The

asymptotic covariance between (yi,t−1

− yi,t−1

) and (ϵi,t − ϵi) is as below.

cov(yi,t−1

− yi,t−1

, ϵi,t − ϵi) ≈ −σϵ

2

T2 (T − 1) − Tλ + λT

(1 − λ)2

In the dynamic panel linear regression model described above, we assume (|λ| ≤ 1) to assure the

dynamic stability of the model. Then, as the size of T becomes large, the covariance converges to zero.

Because of no correlation between (yi,t−1

− yi,t−1

) and (ϵi,t − ϵi), it can be concluded that within estimator

satisfies the consistency.

3. Result and Discussion

In this study, the estimation process is done using a Least Square Dummy Variable procedure written

in GAUSS. Table below shows the estimation results several main independent variables such as

electricity price, gas and oil price, production index, household, lagged variables, HDD and CDD. The

complete results can be checked in the appendix. The statistical summary shows that there are 1359

observations (unbalanced panel data) with 1251 degrees of freedom. The R-square of this estimation

process is calculated as 0.882.

Table 2 Main Estimation Results

Variable Estimate Standard Error t-value p-value

y(-1) 0.33170 0.01549 21.40865 0.00000

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P_Elec -1.94376 0.23089 -8.41865 0.00000

P_Gas 2.12866 0.32614 6.52680 0.00000

P_Gas(-1) -0.34356 0.16944 -2.02758 0.04282

P_Oil 0.44839 0.22636 1.98086 0.04783

P_Oil(-1) -0.08890 0.15748 -0.56454 0.57249

Prdx 0.45937 0.33915 1.35448 0.17583

Prdx(-1) 0.12158 0.16317 0.74513 0.45633

Prdx(-2) 0.29937 0.14372 2.08304 0.03745

House 0.98060 0.08698 11.27441 0.00000

House(-1) -0.51617 0.11489 -4.49285 0.00001

House(-2) 0.19411 0.08680 2.23633 0.02551

HDD 0.00042 0.00021 1.98119 0.04779

CDD 0.00047 0.00042 1.09948 0.27177

From the table above, it is found that the price elasticity of power demand is proven to be negative

with the magnitude of 1.94376. As in economic theory, the negative sign shows that the increase in

electricity price would result in the decrease of electricity consumption, and vice versa. But please note

that this own price elasticity is not for all the data analyzed in this paper. Due to the model specification,

the results will have distinct price elasticity for each group of contract type. The number shown in table 2

is then called the price elasticity of power demand for the base group. In this paper, group 17 (Industrial

Service C, High Voltage C with option III) is chosen as the base group for three parameter estimation,

own price elasticity, gas price elasticity, and oil price elasticity of power demand. It is chosen due to the

high significance of its parameters. To find the estimates of other groups (not the base group) this base

group elasticity should be added to the partial elasticity, which will be analyzed later.

Both cross price elasticity of power demand are found to be positive (2.12866 and 0.44839 for gas

and oil, respectively), which shows a substitution effect between electricity and both oil and price. As in

the case of own price elasticity, these elasticity are only for the base group, which is group 17. As will be

discussed shortly after, the elasticity for other groups will show various relationships between electricity

and other energy prices.

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The significance of all price elasticity of power demand (own and cross) is quite high. The own and

gas price elasticity of power demand are found to be highly significant at 1% level, while the oil is at 5%

level. Other than the price elasticity of power demand, most of the lagged terms and main variables

shown here is significant (minimum at 10% level) , most notably the autoregressive term, lagged price of

gas, second lagged production index, lagged number of household, price of electricity, price of oil,

number of household, and HDD.

As mentioned before, since our model has group-wise partial elasticity of power demand, in order to

calculate the elasticity for groups other than the base group we need to add the base group price elasticity

with the respective group’s partial elasticity. The same procedure also goes for the gas and oil price

elasticity of power demand. The total elasticity for each group is shown in table below. For example, the

own price elasticity of power demand for group 1 (Industrial Service A, Low Voltage) is calculated by

summing -1.94376 (the own price elasticity for the base group) and 1.22228 (the partial own price

elasticity for the group 1) which results in -0.72149.

Table 3 Electricity, Gas and Oil Price Elasticity of Power Demand

Group

Number

Price Elasticity

of Group Electricity Demand

Gas Price Elasticity

of Group Electricity Demand

Oil Price Elasticity

of Group Electricity Demand

Partial Total Partial Total Partial Total

1 1.22228*** -0.72149 -2.16111*** -0.03245 -0.55190** -0.10351

2 1.48567*** -0.45809 -2.15478*** -0.02612 -0.59095** -0.14256

3 1.49498*** -0.44878 -2.03163*** 0.09703 -0.58277** -0.13438

4 1.24536*** -0.69840 -2.34125*** -0.21260 -0.43429* 0.01410

5 1.25829*** -0.68547 -1.90513*** 0.22353 -0.43355* 0.01484

6 1.35361*** -0.59015 -2.23957*** -0.11092 -0.60001** -0.15162

7 1.34919*** -0.59457 -2.19182*** -0.06317 -0.60263** -0.15424

8 1.50347*** -0.44030 -2.24355*** -0.11490 -0.66788*** -0.21949

9 1.50976*** -0.43400 -2.37909*** -0.25043 -0.60559** -0.15720

10 0.81150*** -1.13226 -2.94876*** -0.82010 -0.56926** -0.12087

11 1.35464*** -0.58912 -2.85308*** -0.72442 -1.03856*** -0.59017

12 0.33294 -1.94376 -1.46574*** 0.66292 -0.85860*** -0.41021

13

13 1.02842*** -0.91534 -1.66257*** 0.46609 -0.39424 0.44839

14 1.49078*** -0.45298 -2.07504*** 0.05361 -0.52868** -0.08029

15 0.66479*** -1.27897 -1.25774*** 0.87092 -1.04670*** -0.59831

16 0.67357*** -1.27019 -2.38533*** -0.25668 -1.22152*** -0.77313

17 - -1.94376*** - 2.12866*** - 0.44839**

Note: *, **, *** : significant at 10%, 5%, and 1% level, respectively.

Group 17 is selected for the base group of own and both cross price elasticity for our conveniences.

Total is obtained by adding the partial price elasticity which is statistically significant to base group price elasticity.

First, it must be noted that all of the partial price elasticity of power demand shown above (own and

cross, across all groups) are significant except for two cases: one from group 12 of own price elasticity

and the other from group 13 of oil price elasticity. Moreover, for own price and gas price elasticity of

power demand, all except one group is highly significant (1% or less). Please note that for non-base group,

the price elasticity of power demand depends on the significance of its partial elasticity. If the partial

elasticity is significant, then the total (price elasticity for a group) can be calculated as described before,

adding it with the base group’s elasticity. But if it is found that the partial elasticity is not significant, then

it should be rejected and the base group’s elasticity is used instead. Cases of group 12 for own price

elasticity and group 13 for oil price elasticity follow this process.

For all industrial contract types, the electricity (own) price elasticity of power demand is found to be

negative, with values ranging from 0.43400 (group number 9) to 1.94376 (group number 12 and 17, base

group). Please note that group 12 has the same own price elasticity as group 17, due to the insignificance

of partial elasticity of that group. It must be noted that these magnitudes are generally higher than what is

usually expected. Observing the significance of partial elasticity of power demand, all groups are

significant at 1% level. The negative results are interpreted as when electricity price changes one way, it

will cause electricity demand to move the other way, meaning higher price will cause lower electricity

demand, and vice versa.

As for the cross price elasticity of power demand, the signs are varies between positive and negative,

which explains substitute and complementary effect of the other energy prices (gas or petroleum product)

to electricity, respectively. Out of 17 industrial contract types, seven of them show positive sign, which

range from 0.05361 (group 14) to 2.12866 (group number 17, base group). Meanwhile the other groups

exhibit negative cross price elasticity of power demand, with magnitude ranging from 0.02612 (group 2)

14

to 0.82010 (group number 10). Based on the sign of gas price elasticity, for the group number 3, 5, 12, 13,

14, 15, and 17, the gas is considered as a substitute to electricity. Meanwhile for the other groups, gas acts

as a complement of electricity.

On the other hand, there are four groups which have positive estimate of oil price elasticity and 13

groups with negative sign. Also, group number 13 is found to have insignificant result for oil price

elasticity of power demand, thus the partial elasticity is rejected and regarded as zero. Then, the oil

elasticity for that group would be just the price elasticity of the base group, which 0.44839 (group number

17, base group). Based on the sign of oil price elasticity, for the group number 4, 5, 13, and 17, oil is

regarded as a substitute for electricity, with magnitude ranging from 0.01410 (group number 4) to

0.44839 (group 13 and 17, base group). Meanwhile for the other groups, oil becomes the complement of

electricity, with magnitude ranging from 0.08029 (group number 14) to 0.77313 (group 16).

In the end, further study may be required for better understanding of the results observed in this study

and its implication. As discussed above, some estimation results need to be examined in more detail.

Examples are the high magnitude of own price elasticity of power demand and the mixed results of cross

price elasticity of power demand.

4. Concluding Remarks

In this study, analysis of monthly power demand for all 17 industrial contract types in Korea has been

conducted. The analysis is done using econometrics model which estimates the price elasticity of demand

as well as the cross price elasticity of demand caused by other energy sources, gas and petroleum product.

Estimation result shows that own price elasticity of power demand is found to be negative for all

contract types ranging from 0.43 to 1.94 which is rather higher in terms of their magnitude than is usually

expected. Especially the contract type of the Industrial Service C, High-Voltage C with option III shows

the highest partial price elasticity of power demand with high statistical significance.

It is noted that the cross price elasticity of the base group exhibits both gas and oil as substitute with

statistical significance. When the partial cross price elasticity of power demand for each contract types are

considered in addition, however, the results are mixed. Contract types number 4, 5, 13, and 17 show plus

sign implying substitutes for oil, while others have negative sign. For gas, the negative price elasticity is

found for the contract types 3, 5, 12, 13, 14, 15, and 17, while other contract types’ result shows gas as a

15

complement of electricity. Further study may be required for a better understanding of the results

observed in this study and its implication.

References

1. Alvarez, J. and Arellano, M., The Time Series and Cross-Section Asymptotics of Dynamic Panel Data

Estimators, Econometrica, 71 (4), 2003, pp 1121-1159.

2. Arellano, M. and Bond S., Some Tests of Specification for Panel Data: Monte Carlo Evidence and an

Application to Employment Equations, Review of Economic Studies, 58, 1991, pp 277-297.

3. Bank of Korea, Economic Statistics System, http://ecos.bok.or.kr, accessed at August 2011.

4. Fan, S. and Hyndman R. J., The price elasticity of electricity demand in South Australia, Energy

Policy, 39, 2011, pp 3709-3719.

5. Filippini, M., Short- and long-run time-of-use price elasticities in Swiss residential electricity demand,

Energy Policy, 39, 2011, pp 5811-5817.

6. Hahn, J. and Kuersteiner, G., Asymptotically Unbiased Inference for A Dynamic Panel Model with

Fixed Effects when both n and T are Large, Econometrica, 70 (4), 2002, pp1639-1657.

7. Hsiao, C., Analysis of Panel Data, second edition, Cambridge University Press, 2003.

8. Korea Energy Economics Institute (KEEI), the Estimation of Power Price Elasticity of Demand and Its

Application, Final Report, Feb. 2004.

9. Korea Meteorological Administration, http://web.kma.go.kr, accessed at August 2011.

10. Lijesen, M. G., The real-time price elasticity of electricity, Energy Economics, 29, 2007, pp 249-258.

11. Patrick, Robert H. and Wolak, Frank A., Using Customer Demands Under Spot Market Prices for

Service Design and Analysis, EPRI Working Paper, 2001, WO 2801-11.

16

Appendix 1 Estimation Results

1.1 Statistical Summaries

Table 4 Statistical Summaries of Estimation

Observations : 1359

Number of Groups : 17

Degrees of freedom : 1251

Total SS (corrected) : 386.379

Residual SS : 45.696

R-squared : 0.882

Rbar-squared : 0.872

Std error of est : 0.191

F = 102.491 with 91, 1251 degrees of freedom

P-value = 0.000

1.2 Short Run Estimation Result

Table 5 Complete Estimation Result for the Short Rum

Variable Estimate Standard

Error t-value p-value

y(-1) 0.33170 0.01549 21.40865 0.00000

P_Elec -1.94376 0.23089 -8.41865 0.00000

P_Gas 2.12866 0.32614 6.52680 0.00000

P_Gas(-1) -0.34356 0.16944 -2.02758 0.04282

P_Oil 0.44839 0.22636 1.98086 0.04783

P_Oil(-1) -0.08890 0.15748 -0.56454 0.57249

Prdx 0.45937 0.33915 1.35448 0.17583

Prdx(-1) 0.12158 0.16317 0.74513 0.45633

Prdx(-2) 0.29937 0.14372 2.08304 0.03745

House 0.98060 0.08698 11.27441 0.00000

House(-1) -0.51617 0.11489 -4.49285 0.00001

House(-2) 0.19411 0.08680 2.23633 0.02551

HDD 0.00042 0.00021 1.98119 0.04779

CDD 0.00047 0.00042 1.09948 0.27177

SD1 -0.08449 0.03087 -2.73733 0.00628

SD2 -0.01860 0.02989 -0.62226 0.53389

D2 0.06131 0.03771 1.62600 0.10420

D3 0.06176 0.05446 1.13418 0.25694

17

D4 0.11684 0.08710 1.34143 0.18003

D5 0.06935 0.10996 0.63068 0.52837

D6 0.09449 0.12558 0.75244 0.45193

D7 0.18032 0.14157 1.27371 0.20300

D8 0.17427 0.14813 1.17647 0.23963

D9 0.09882 0.12470 0.79252 0.42821

D10 0.09124 0.10337 0.88266 0.37759

D11 0.08373 0.06546 1.27911 0.20110

D12 0.00557 0.03017 0.18466 0.85352

PE_GD1 1.22228 0.42642 2.86636 0.00422

PE_GD2 1.48567 0.37863 3.92380 0.00009

PE_GD3 1.49498 0.43780 3.41477 0.00066

PE_GD4 1.24536 0.27653 4.50354 0.00001

PE_GD5 1.25829 0.30083 4.18279 0.00003

PE_GD6 1.35361 0.33069 4.09328 0.00005

PE_GD7 1.34919 0.35211 3.83174 0.00013

PE_GD8 1.50347 0.32536 4.62092 0.00000

PE_GD9 1.50976 0.31577 4.78125 0.00000

PE_GD10 0.81150 0.23079 3.51624 0.00045

PE_GD11 1.35464 0.33966 3.98829 0.00007

PE_GD12 0.33294 0.25854 1.28779 0.19806

PE_GD13 1.02842 0.31395 3.27577 0.00108

PE_GD14 1.49078 0.31334 4.75768 0.00000

PE_GD15 0.66479 0.24102 2.75830 0.00590

PE_GD16 0.67357 0.24243 2.77838 0.00555

PG_GD1 -2.16111 0.40321 -5.35977 0.00000

PG_GD2 -2.15478 0.38844 -5.54722 0.00000

PG_GD3 -2.03163 0.39933 -5.08762 0.00000

PG_GD4 -2.34125 0.39268 -5.96233 0.00000

PG_GD5 -1.90513 0.40527 -4.70089 0.00000

PG_GD6 -2.23957 0.39652 -5.64807 0.00000

PG_GD7 -2.19182 0.40698 -5.38554 0.00000

PG_GD8 -2.24355 0.40594 -5.52687 0.00000

PG_GD9 -2.37909 0.40482 -5.87691 0.00000

PG_GD10 -2.94876 0.39105 -7.54067 0.00000

PG_GD11 -2.85308 0.41277 -6.91201 0.00000

PG_GD12 -1.46574 0.40606 -3.60969 0.00032

PG_GD13 -1.66257 0.39869 -4.17005 0.00003

PG_GD14 -2.07504 0.40089 -5.17607 0.00000

PG_GD15 -1.25774 0.49112 -2.56099 0.01055

18

PG_GD16 -2.38533 0.39636 -6.01812 0.00000

PO_GD1 -0.55190 0.24294 -2.27172 0.02327

PO_GD2 -0.59095 0.24330 -2.42886 0.01529

PO_GD3 -0.58277 0.24241 -2.40407 0.01636

PO_GD4 -0.43429 0.25291 -1.71722 0.08619

PO_GD5 -0.43355 0.24214 -1.79052 0.07361

PO_GD6 -0.60001 0.24360 -2.46311 0.01391

PO_GD7 -0.60263 0.24274 -2.48264 0.01317

PO_GD8 -0.66788 0.24238 -2.75555 0.00594

PO_GD9 -0.60559 0.24228 -2.49959 0.01256

PO_GD10 -0.56926 0.24275 -2.34503 0.01918

PO_GD11 -1.03856 0.24237 -4.28505 0.00002

PO_GD12 -0.85860 0.24300 -3.53339 0.00043

PO_GD13 -0.39424 0.24142 -1.63298 0.10273

PO_GD14 -0.52868 0.24187 -2.18582 0.02901

PO_GD15 -1.04670 0.27365 -3.82495 0.00014

PO_GD16 -1.22152 0.24773 -4.93092 0.00000

PI_GD2 -0.65208 0.42129 -1.54784 0.12191

PI_GD3 -0.35252 0.42315 -0.83309 0.40496

PI_GD4 -0.42513 0.42730 -0.99491 0.31997

PI_GD5 -0.07785 0.42087 -0.18498 0.85328

PI_GD6 -0.30720 0.42263 -0.72688 0.46743

PI_GD7 -0.49780 0.42406 -1.17389 0.24066

PI_GD8 -0.35505 0.42504 -0.83534 0.40369

PI_GD9 -0.09840 0.42314 -0.23255 0.81615

PI_GD10 -1.68856 0.41970 -4.02326 0.00006

PI_GD11 -0.73960 0.42035 -1.75949 0.07874

PI_GD12 -0.37193 0.41950 -0.88660 0.37546

PI_GD13 -0.61788 0.42116 -1.46709 0.14260

PI_GD14 -0.00814 0.42205 -0.01930 0.98461

PI_GD15 -0.55997 0.44941 -1.24601 0.21299

PI_GD16 -0.27418 0.43282 -0.63347 0.52654

PI_GD17 0.64875 0.42326 1.53275 0.12559

Ctr3110 10.94824 2.62320 4.17363 0.00003

Ctr3211 9.44677 1.94229 4.86372 0.00000

Ctr3212 9.24109 2.77118 3.33471 0.00088

Ctr3311 12.20813 1.31088 9.31297 0.00000

Ctr3312 11.42159 2.28393 5.00084 0.00000

Ctr7211 12.22242 1.37404 8.89525 0.00000

Ctr7212 11.58225 1.33310 8.68820 0.00000

19

Ctr7261 11.19008 1.25159 8.94069 0.00000

Ctr7262 11.85846 1.24733 9.50710 0.00000

Ctr7311 26.47049 1.23499 21.43387 0.00000

Ctr7312 22.80498 1.40040 16.28465 0.00000

Ctr7361 15.01620 1.15520 12.99879 0.00000

Ctr7362 12.23331 1.28835 9.49534 0.00000

Ctr7363 11.87943 1.23263 9.63751 0.00000

Ctr7461 14.49564 2.20975 6.55986 0.00000

Ctr7462 21.02703 1.30036 16.17012 0.00000

Ctr7463 -0.83861 1.31617 -0.63716 0.52414

1.3 Long Run Estimation Result

Table 6 Complete Estimation Result for the Long Run

Variable Estimate Standard

Error t-value p-value

P_Elec -2.90853 0.34160 -8.51448 0.00000

P_Gas 2.67111 0.44584 5.99119 0.00000

P_Oil 0.53792 0.27922 1.92653 0.05427

Prdx 1.31725 0.48281 2.72831 0.00646

House 0.98539 0.04170 23.63112 0.00000

HDD 0.00062 0.00032 1.97856 0.04809

CDD 0.00070 0.00063 1.09904 0.27196

SD1 -0.12643 0.04616 -2.73872 0.00626

SD2 -0.02783 0.04468 -0.62291 0.53346

D2 0.09174 0.05646 1.62485 0.10445

D3 0.09242 0.08157 1.13304 0.25742

D4 0.17483 0.13052 1.33949 0.18065

D5 0.10377 0.16460 0.63041 0.52854

D6 0.14139 0.18800 0.75210 0.45213

D7 0.26982 0.21193 1.27316 0.20320

D8 0.26077 0.22169 1.17627 0.23971

D9 0.14787 0.18665 0.79224 0.42837

D10 0.13652 0.15476 0.88218 0.37785

D11 0.12529 0.09803 1.27810 0.20145

D12 0.00834 0.04514 0.18465 0.85353

PE_GD1 1.82894 0.63828 2.86542 0.00423

PE_GD2 2.22306 0.56611 3.92693 0.00009

PE_GD3 2.23700 0.65461 3.41730 0.00065

PE_GD4 1.86348 0.41024 4.54239 0.00001

20

PE_GD5 1.88283 0.44936 4.19007 0.00003

PE_GD6 2.02547 0.49408 4.09951 0.00004

PE_GD7 2.01885 0.52611 3.83733 0.00013

PE_GD8 2.24970 0.48584 4.63049 0.00000

PE_GD9 2.25911 0.47071 4.79937 0.00000

PE_GD10 1.21428 0.34352 3.53478 0.00042

PE_GD11 2.02701 0.50712 3.99709 0.00007

PE_GD12 0.49819 0.38616 1.29011 0.19725

PE_GD13 1.53886 0.46679 3.29670 0.00101

PE_GD14 2.23072 0.46709 4.77575 0.00000

PE_GD15 0.99475 0.35917 2.76959 0.00570

PE_GD16 1.00789 0.36098 2.79212 0.00532

PG_GD1 -3.23375 0.59755 -5.41167 0.00000

PG_GD2 -3.22428 0.57604 -5.59736 0.00000

PG_GD3 -3.04000 0.59290 -5.12730 0.00000

PG_GD4 -3.50331 0.58290 -6.01017 0.00000

PG_GD5 -2.85072 0.60261 -4.73066 0.00000

PG_GD6 -3.35116 0.58828 -5.69650 0.00000

PG_GD7 -3.27971 0.60442 -5.42620 0.00000

PG_GD8 -3.35712 0.60306 -5.56684 0.00000

PG_GD9 -3.55992 0.60058 -5.92748 0.00000

PG_GD10 -4.41234 0.57968 -7.61172 0.00000

PG_GD11 -4.26918 0.60825 -7.01876 0.00000

PG_GD12 -2.19324 0.60183 -3.64430 0.00028

PG_GD13 -2.48777 0.59185 -4.20336 0.00003

PG_GD14 -3.10497 0.59566 -5.21269 0.00000

PG_GD15 -1.88201 0.72999 -2.57813 0.01005

PG_GD16 -3.56927 0.58375 -6.11440 0.00000

PO_GD1 -0.82583 0.36225 -2.27971 0.02279

PO_GD2 -0.88426 0.36281 -2.43725 0.01494

PO_GD3 -0.87203 0.36142 -2.41279 0.01597

PO_GD4 -0.64985 0.37723 -1.72267 0.08520

PO_GD5 -0.64874 0.36152 -1.79444 0.07298

PO_GD6 -0.89781 0.36322 -2.47182 0.01358

PO_GD7 -0.90173 0.36194 -2.49139 0.01285

PO_GD8 -0.99938 0.36136 -2.76559 0.00577

PO_GD9 -0.90617 0.36143 -2.50722 0.01229

PO_GD10 -0.85180 0.36356 -2.34295 0.01929

PO_GD11 -1.55404 0.35962 -4.32137 0.00002

PO_GD12 -1.28476 0.36188 -3.55026 0.00040

21

PO_GD13 -0.58991 0.36035 -1.63706 0.10187

PO_GD14 -0.79108 0.36096 -2.19162 0.02859

PO_GD15 -1.56621 0.40866 -3.83258 0.00013

PO_GD16 -1.82781 0.36772 -4.97062 0.00000

PI_GD2 -0.97574 0.63065 -1.54720 0.12207

PI_GD3 -0.52749 0.63329 -0.83294 0.40504

PI_GD4 -0.63614 0.63954 -0.99468 0.32008

PI_GD5 -0.11649 0.62980 -0.18496 0.85329

PI_GD6 -0.45968 0.63246 -0.72682 0.46747

PI_GD7 -0.74487 0.63454 -1.17388 0.24067

PI_GD8 -0.53127 0.63604 -0.83528 0.40372

PI_GD9 -0.14724 0.63314 -0.23256 0.81614

PI_GD10 -2.52666 0.63028 -4.00876 0.00007

PI_GD11 -1.10670 0.62854 -1.76074 0.07853

PI_GD12 -0.55654 0.62814 -0.88600 0.37579

PI_GD13 -0.92456 0.63090 -1.46547 0.14304

PI_GD14 -0.01219 0.63154 -0.01930 0.98461

PI_GD15 -0.83790 0.67289 -1.24523 0.21328

PI_GD16 -0.41027 0.64809 -0.63303 0.52683

PI_GD17 0.97076 0.63301 1.53355 0.12539

Ctr3110 16.38228 3.94352 4.15422 0.00004

Ctr3211 14.13557 2.92475 4.83309 0.00000

Ctr3212 13.82780 4.15900 3.32479 0.00091

Ctr3311 18.26751 2.00671 9.10320 0.00000

Ctr3312 17.09057 3.44043 4.96757 0.00000

Ctr7211 18.28888 2.09930 8.71192 0.00000

Ctr7212 17.33097 2.03484 8.51714 0.00000

Ctr7261 16.74415 1.91261 8.75460 0.00000

Ctr7262 17.74428 1.91122 9.28425 0.00000

Ctr7311 39.60883 2.06354 19.19459 0.00000

Ctr7312 34.12398 2.23984 15.23502 0.00000

Ctr7361 22.46933 1.80536 12.44590 0.00000

Ctr7362 18.30518 1.97397 9.27330 0.00000

Ctr7363 17.77565 1.88990 9.40558 0.00000

Ctr7461 21.69040 3.34456 6.48528 0.00000

Ctr7462 31.46356 2.07802 15.14111 0.00000

Ctr7463 -1.25485 1.96965 -0.63709 0.52418