The Estimation of Electricity Demand Function and Prediction of its ...
Danish Journal of Engineering and Applied Sciences, April, 2015, Pages: 7-13
The Estimation of Electricity Demand Function and Prediction of its Consumption in Iran Ali Changi Ashtiani Payame Noor University, Iran
Mehdi jalouli jihad daneshgahi, markazi province , Iran
Hadi Ghaffari (PhD) Payame Noor University Iran
Article Information Article history: Received: 20 April Received in revised form: 8May. Accepted: 28May Available online: April Keywords: aggregate electricity demandenergy price self-explanatory method with auto regressive distributed lag model (ARDL) targeting subsidies plan Jel Classification: C,E,L Corresponding Author: Ali Changi Ashtiani [email protected]
Abstract The history of electricity industry dates back to one hundred years ago. In Iran, the electricity industry is transiting from the typical monopoly to the competitive markets which the producers compete with each other to sell the energy. In the present research, the long-term and short-term models of electrical energy in Iran have been estimated using time-series data and correlational techniques specifically the dynamic self-explanatory models with auto regressive distributed lag model (ARDL) and error correction model (ECM). After estimating the electricity demand function, the prediction of the whole country electricity demand was carried out. The results confirmed the inelasticity of electricity demand in proportion to the electricity price indicated by other studies in Iran and other countries. According to the Power Ministry statistics, the aggregate electricity demand has been 176230 million kw/h in 2009 which after implementing the targeting subsidies plan in the first year, this number has been decreased to 170067 million kw/h with a 3.5 % decline in the electricity demand. Finally, the aggregate electricity demand is expected to increase to 240020 million kw/h by the year 2025.
© 2015 Danish Journals All rights reserved To Cite This Article: Ali Changi Ashtiani,Payame Noor University, Iran, Danish journal of psychology, 7-13, 2015
Introduction The econometrics models of energy demand generalize the rule governing the relationships among the variables of the model to the future. However, in Iran, there are not sufficient long run and short-run time-series studies in this regard. Thus, one of the advantages of the technical-economic models to the econometric models in Iran is that they do not require historical and time-series studies. The present study benefits from the self-explanatory model with auto regressive distributed lag model (ARDL) for estimating the electricity demand function in Iran. The Research Background There are numerous studies carried out in the recent decades for estimating the electricity demand. The study carried out by Hou Athker (1951) might be regarded as one of the initial researches in this regard. He indicated that the price elasticity and the income elasticity for electricity demand among Iranian families are low and high, respectively. Ang (1988) estimated the electricity demand function for four South- Eastern Asian countries including Malaysia, Singapore, Thailand, and Taiwan. The research demonstrated that in the countries where there is a higher annual per capita income, there is a lower electricity income elasticity of electricity demand. Eltony and Mohammad Yousef (1993) carried out estimation on the electricity demand among the Persian Gulf Cooperation Council states (Bahrain, Oman, Saudi Arabia, Emirates) using the ordinary least square model and indicated that there is no elasticity in electricity demand in proportion to its price and income in short-term and long-term. According to them the reason behind this was the subsidies paid by the government. Al Aziz and Hoedown (1999) estimated the energy demand in Jordan and concluded that the income elasticity for electricity demand is less than one. Also, Ettestol (2002) estimated the electricity demand for homes in Norway using the 1970-1999 electricity demand data. The results show that there is a low electricity demand elasticity in proportion to the price and there is a high electricity demand elasticity in proportion to the income. Also in Iran, there have been carried out several researches in this regard. Some of them are as follows: Fakhraei (1992) estimated the electricity model for homes in Iran using the time-series data during the years1968-1989 and concluded that there is no elasticity in the electricity consumption in proportion to its price. Moreover, Pazhooyan (2000) estimated the electricity demand in Iran and found that the price elasticity and the income elasticity for electricity demand are lower and higher than one. Aminifard (2002) estimated the electricity demand for homes using the Johanson and Joselius coefficient model, the error correction model and the time-series data for the years 1967-99. He found that the price and income elasticities and intersecting
7
Danish Journal of Engineering and Applied Sciences, April, 2015, Pages: 7-13
electricity demand is lower than one and that the elasticity ofnumber of electricity consumers in proportion to electricity demand is greater than one. Theoretical principles and the Electricity Demand Model According to micro-economic theory, the demand for different kinds of energies in various productive sectors derives from the production function. For example, the production function of a particular enterprise in a certain time can be defined as follows: Q= F (K, L, M, E1, E2, … En, T) Where M, L, K refer to the initial material, labor, and capital, respectively. E1 is the 1st type of energy such as electrical energy and T is a set of other factors such as technology variations. A firm selects a combination of necessary factors so that it spends the least possible costs for manufacturing a certain production. The demand function for production factors is reached through minimizing the cost function of the firm. If the demand for electricity as a production factor is regarded as follows: Xei= Xei (Pk, P1, Pm, Pi, Q, T) Where, the electricity demand in a certain time (t) is a function of electrical energy price (Pi) and other alternative sources of energies and the non-energy factors are (Pm, Pl, Pk), and the added value is (Q). In this case, other factors such as technology (T) can also be used. One of the recommended models for the electrical demand is the Bandaranaike and Munasinghe’s (1983) model which tries to provide a comprehensive model for electricity demand. The theoretical foundation of the present research relies on this model and its logarithm can be regraded as follows: LOGE= LOG K+ γ1 LOG Ps+ γ2 LOG Pe+ γ3 LOG Vi Electricity Demand Model First, the aggregate electricity demand function will be referred to in terms of the mentioned theoretical principles. A: Aggregate Electricity Demand Function LCBA= + LPBA+ LPE+ LY+ LPOPCO+ Where: LCBA= the aggregate electricity consumption logarithm LPBA= the consumed electricity price logarithm LPE= energy price index logarithm The energy price index has been calculated in terms of the average weight of energy factors: PE= (PB* CB+PNS* CNS* PNK* CNK+ PNG* CNG+ PGT* CGT+ PGM* CGM (CB+CNS+CNK+CGT+CGM) Where PE refers to the energy price index, and PGM, PG, PNG, PNK, PNS, PB refer to price index of petroleum, paraffin, mazut, gas oil, natural gas, and petroleum gas, respectively. The Cs in the above equation indicate the consumption of mentioned energies. LY: the income logarithm (gross domestic product in 1997 constant price). LPOPCO: the aggregate electricity subscribers’ logarithm. : intercept : Residual term The Stationary Test of Variables The stationary test is regarded as one of the significant requirements in the estimation of econometric models using time-series data. There are several ways to distinguish stationary time-series data from non-stationary among which Augmented Dickey-Fuller test is the most significant one. Table.1 the results of Dickey-Fuller Test for the electricity demand models’ variables Stationary rank
I(0) I(1) I(0) I(1) I(0)
8
Critical value of ADF %10 -3/22 -2/62 -2/59 -2/60 -2/60
%5 -3/57 -2/96 -2/92 -2/93 -2/93
%1 -4/32 -3/67 -3/57 -3/61 -3/60
Statistic
Function format
observed -4/92 -4/4 -6/87 -3/25 -8/99
Intercept, with trend Intercept, no trend Intercept, no trend Intercept, no trend Intercept, no trend Intercept, no trend
Danish Journal of Engineering and Applied Sciences, April, 2015, Pages: 7-13
Estimation of electricity demand function using ECM and ARDL models In order to benefit from ARDL and ECM models for estimation of electricity demand function, we need to consider appropriate time spans for model variables in terms of the Schwarz- Bayesian criterion. The procedure has been carried out using Mircofit 4.1 and the results are as follows: Table 2. Estimation of the self-explanatory model coefficients with widespread time spans using SchwarzBayesian criterion Regressor
Coefficient
Standard Error
LCBA(-1)
-0.465
0.121
LCBA(-2)
-0.016
0.12
LCBA(-3)
0.203
0.073
LPBA
0.032
0.019
LPBA(-1)
-0.082
0.025
LPBA(-2)
0.078
0.028
LPBA(-3)
-0.074
0.024
LPE
0.011
0.023
LPE(-1)
-0.012
0.022
LPE(-2)
0.055
0.016
LY
0.261
0.04
LY(-1)
-0.011
0.084
LY(-2)
-0.137
0.068
LPOPCO
0.332
0.089 1.05
INT
-3.26
R-Squared
0.99
D.W
2.6
Aggregate demand function To ensure that there is a correlational relationship between the models’ variables, we try to examine the correlational relation among variables and the validity of the estimation equation. The value of the statistic t is calculated as follows: p
∑α i =1 P
^ i
−1
∑ Sα
Where
^ 1
−1
Sα
^
I =1
=α
^
=
− 0.27778 − 1 = −4.06 0.31437
1
i
Sα refers to the standard deviation of the dependent variable in the model (right-hand) ^
i
Since the absolute value of the obtained statistic is higher than its critical value1 introduced by Banerjee, Dolado, and Mestre (1992), so the null hypothesis ( ) is rejected. Therefore, we can conclude that there is a long-run equilibrium relation among the variables of the model and the long-run relation for electricity demand is real. According to the above conclusions; we try to estimate the long run coefficients of the modelwhich have been illustrated in the Table 3:
1
(‐3.91)
9
Danish Journal of Engineering and Applied Sciences, April, 2015, Pages: 7-13
Table3. The long-run coefficients for aggregate electricity demand using ARDL and Schwarz-Bayesian criterion Dependent Varibale
Independent Variables
LCBA
LPBA
LPE
LY
LPOPCO
Intercept
Coefficient
-0.133
0.161
0.329
0.984
-9.67
Standard Error
0.068
0.064
0.085
0.066
1.436
T-Ratio
-1.95
2.48
3.86
14.89
-6.73
the long-run total electricity demand function estimated as follows: LCBA= -9.67 – 0.133 LPBA+0.161 LPE+0.329 LY+ 0.9854LPOPCO The coefficients symbols are as expected and according to the theoretical principles. The LPBA price elasticity equals -0.133. Consequently, the electricity is regarded as an inelastic commodity since electricity in comparison with other oil products is a cheap commodity of a high economic efficiency and it is less likely to substitute it with other oil products. Also, it is impossible to reduce electricity consumption through increasing its price and the pricing policy does not influence its consumption. The coefficient of variation of price index for other energy sources as substitutions for electricity, it can be said that the substitution is not effective. However, the income elasticity for electricity demand is greater and more influential than the other two elasticities. The quantitative value of this elasticity is 0.329. In the following, we estimate the model using the ECM in order to study the short-run dynamic behavior of variables and to illustrate the velocity of adjustment towards a log-run equilibrium among variables. The results of estimation can be seen in the Table 4. Error correction coefficient has been estimated to be -0.45 which indicates the relatively high velocity of adjustment. In addition, it shows that every year, 45% of disequilibrium in the electricity demand in one period is adjusted by the similar electricity consumption in the next period. Table 4. The short-run coefficients of aggregate electricity demand model using ECM Regressor
Coefficient
Standard Error
DLCBA1
-0.207
0.124
DLCBA2
-0.213
0.077
DLPBA
0.032
0.019
DLPBA1
-0.004
0.021
DLPBA2
0.073
0.024
DLPE
0.0109
0.023
DLPE1
-0.055
0.016
DLY
0.261
0.04
DLY1
0.137
0.068
DLPOPCO
0.332
0.089
DINT
-3.26
1.05
ECM(-1)
-0.45
0.075
R-Squared
0.935
D.W
2.31
Simulation and the aggregate electricity demand prediction The simulated and actual values of the mentioned variables can be seen in the 1. The diagram not only shows that the simulated values are approximately close to actual values but also it shows the trends in variables in an efficient way. The indexes of square root of mean square of partial error (RMSPE) and Tile un-equality index (U) for dependent variables have been calculated and illustrated in the figure. Aggregate electricity consumption(demand) simulation. U= 0.028 RMSPE= 3.12
10
Danish Journal of Engineering and Applied Sciences, April, 2015, Pages: 7-13
Figure. Aggregate electricity consumption simulation (million kw/h) As it can be seen, the simulated variables follow closely the movement of variables in the estimated range. The PMSPE and U statistics also confirm strongly this claim. Aggregate electricity demand estimation Table 5. shows the aggregate electricity demand predication (million kw/h) using the software Microfit 4.1 in terms of the estimation model for this function. Table 5.
Aggregate electricity demand predication (2010-2025) million kw/h
Year
2010
2011
2012
2013
2014
2015
2016
2017
Aggregate electricity demand predication
170067
174730
179394
184057
188721
193384
198048
202711
Year
2018
2019
2020
2021
2022
2023
2024
2025
Aggregate electricity demand predication
207375
212039
216702
221366
226029
230693
235356
240020
As it can be seen in the table, there is a reduction in the demand for electricity after implementing the targeting subsidies plan. According to the Power Ministry estimations, the state electricity demand has been 176230 million kw/h in 2009 which after implementing the targeting subsidies plan in the first year, this number has been decreased to 170067 million kw/h with a 3.5 % decline in the electricity demand. This value has been reached 174730 kw/h in 2011 which is still lower than the electricity demand in 2009. Finally, aggregate electricity demand will have an increasing trend with 240020 million kw/h consumption in the year 2025. Figure2 shows the predication of aggregate electricity demand for the years 2012-2025.
Figure2. Aggregate electricity demand estimation million kw/h
11
Danish Journal of Engineering and Applied Sciences, April, 2015, Pages: 7-13
Conclusion and Suggestions The results of the study confirmed the inelasticity of electricity demand in proportion to the electricity price indicated by further studies in Iran and other countries. In addition, the results indicate that all the coefficients at the levels 5 and 10 % are significant. The results also show that the pricing policy cannot be influential in controlling the electricity demand. Therefore, we should take actions to invest more and to increase the electricity production. On the other hand, we need to implement non-pricing policies such as using energy-saver lamps, informing people on how to use the electricity in an efficient way, and manufacturing products with low energy consumption (energy label: A) to reduce the increasing trend in energy consumption for homes. Another effective way for economizing electricity consumption is exerting various electricity prices and tariffs in terms of season, region, and consumption peak hours. For example, we can encourage the consumers to consume less in the peak hours using multi-tariffs electricity meters.
Refrences 1. Akay, D., Atak, M., 2007. Grey prediction with rolling mechanism for electricity demand forecasting of Turkey. Energy 32 (9), 1670–1675. 2. Aminifard, Abbas, (2002); The Estimation of Demand for Electricity at Homes in Iran: A Cointegration Approach (1967-1999), M.A Thesis(Economics), Shiraz University (in Persian). 3. Anderson .B, Damsgaard. N(2002) , Residential Electricity Use –Demand Estimation Using Swedish Micro Data, Stockholm School of Economics, Box 6501, S-11383 Stockholm, Sweden. 4. Asgari, A. (2000). Assessing electricity demand of different consuming sectors and investigating its pricing policy, PhD thesis, Faculty of Economy, University of Tehran. 5. Asgari, Mansour, (2001); The Estimation of Electricity Demand with Convergence Method in Iran, (2000-2004), 16th International Electricity Conference (In Persian). 6. Bentzen, J., Engsted, T., (1993). Short – and Long-Run Elasticities in Energy Demand: A Cointegration Approach. Energy Economics 15 (1), 9-16. 7. Bentzen, J., Engsted, T., (2001). A Revival of the Autoregressive Distributed Lag Model in Estimating Energy Demand Relationships.Energy 26 (1), 45-55. 8. Bidram, Rasoul, (2002); "Eviews" Together with Econometrics, 1st Edition, Productivity Prism, Tehran (In Persian). 9. Bjorner , T.B . Togeby , M and Jensen , H.H.(2001 ). " Industrial Companies ' demand for electricity : evidence from a micropanel . " Energy Economics, Volume 23 ( 5),sqs 595 – 617. 10. Darbellay Georges A, Marek Slama (2000)."Forecasting the short term demand for electricity :Do neural network stand a better chance?". International Journal of Forecasting 16,71-83. 11. Engle, R.F., Granger. C.W.J. (1987) Co–Integration and Error Correction: Representation, Estimation, and Testing; Econometrica, Vol. 55, No.2, PP: 251-276. 12. Erdogdu, E., (2007). Electricity Demand Analysis Using Cointegration and ARIMA Modelling: A Case Study of Turkey. Energy Policy, 35., 1129–1146. Energy Market Regulatory Authority, Ziyabey Cad. No: 19 06520Balgat/Ankara, Turkey. 13. Esiyok, U., (2007), Energy consumption and thermal performance of typical residential buildings in Turkey, Doctoral dissertation, University of Dortmund. 14. Ettestol, Ingunn (2002), Estimating Residential Demand for Electricity with Smooth Transition Ragression, NTNU, Trondheim, Norway. 15. Haas, R., Schipper, L., (1998). Residential Energy Demand in OECD Countries and the Role of Irreversible Efficiency Improvements. Energy Economics 20 (4), 421–442. 16. Hondroyiannis, George (2004) Estimating Residential Demand for Electricity in Greece; Energy Economic, Vol. 26, pp: 319-334. 17. Jebaraj, S., Iniyan, 2006, A review of energy models, Renewable and Sustainable Energy Reviews, Volume 10, Issue 4, pp. 281-31. 18. Kazemi, A. (1996). Electricity demand analysis and estimation in household and industrial sectors, MSc thesis, Faculty of Economics, University of Tehran. 19. Kmershen, D.R. and Porter, D.V.(2004 ). "The demand for residential,industrial and total electricity , 1973 – 1998 ". Energy Economics, Volume 26 , Issue 1 , PP:87-100. 20. Kumar Bose , R and Shukla , M . ( 1999). "Elasticities of electricity demand in India " . Energy policy, Volume 27 , Issue 3 , PP: 137 – 146. 21. Moradi, Alireza, (2005); Eviews Application in Econometrics, 1st Edition, Jahad Daneshgahi Organization, Tehran Branch (In Persian). 22. Noferesti, Mohammad, (1999); Unit Root and Cointegration in Econometrics, 1st Edition, Cultural Services Institute of Rasa (In Persian).
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23. Pesaran, M.Hashem & Pesaran, Bahram (1997) Working With Microfit 4 Interactive Econometric Analysis; Camfit Data Limited. 24. Rriss,P.C.and M.W.White,(2001) “Household Electricity Demand, Revisited”,University of Cambridge, Working Paper, No.8687. 25. Saab Samer, Badr Elie, Nasr George. (2001) "Univariate modeling and forecasting of energy consumption: the case of electricity in Lebanon". Energy 26, 1-14. 26. Sadeghi, N. (2003). Forecasting Electricity consumption through economics models, MSc thesis, Faculty of Economy, University of Tehran. 27. Saffaripour Isfahani, Masoud, (1999); Electricity Demand View &Country's Required Potential Competence of Powerhouse in 3rd Plan, 3rd National Congress of Iran's Energy (In Persian). 28. State Utility Forecasting Group. Industrial Econometrics Model. Indiana Electricity Projections. 1999. 29. Tabrizian, B. (1997). Estimation of electricity consumption in Iran and comparing it with that of OECD countries, MSc thesis, Faculty of Economy, University of Tehran. 30. Zhang G Peter. (2003) "Time series forecasting using a hybrid and neural network model". Neurocomputing 50, 159-175.
13
The Estimation of Electricity Demand Function and Prediction of its Consumption in Iran Ali Changi Ashtiani Payame Noor University, Iran
Mehdi jalouli jihad daneshgahi, markazi province , Iran
Hadi Ghaffari (PhD) Payame Noor University Iran
Article Information Article history: Received: 20 April Received in revised form: 8May. Accepted: 28May Available online: April Keywords: aggregate electricity demandenergy price self-explanatory method with auto regressive distributed lag model (ARDL) targeting subsidies plan Jel Classification: C,E,L Corresponding Author: Ali Changi Ashtiani [email protected]
Abstract The history of electricity industry dates back to one hundred years ago. In Iran, the electricity industry is transiting from the typical monopoly to the competitive markets which the producers compete with each other to sell the energy. In the present research, the long-term and short-term models of electrical energy in Iran have been estimated using time-series data and correlational techniques specifically the dynamic self-explanatory models with auto regressive distributed lag model (ARDL) and error correction model (ECM). After estimating the electricity demand function, the prediction of the whole country electricity demand was carried out. The results confirmed the inelasticity of electricity demand in proportion to the electricity price indicated by other studies in Iran and other countries. According to the Power Ministry statistics, the aggregate electricity demand has been 176230 million kw/h in 2009 which after implementing the targeting subsidies plan in the first year, this number has been decreased to 170067 million kw/h with a 3.5 % decline in the electricity demand. Finally, the aggregate electricity demand is expected to increase to 240020 million kw/h by the year 2025.
© 2015 Danish Journals All rights reserved To Cite This Article: Ali Changi Ashtiani,Payame Noor University, Iran, Danish journal of psychology, 7-13, 2015
Introduction The econometrics models of energy demand generalize the rule governing the relationships among the variables of the model to the future. However, in Iran, there are not sufficient long run and short-run time-series studies in this regard. Thus, one of the advantages of the technical-economic models to the econometric models in Iran is that they do not require historical and time-series studies. The present study benefits from the self-explanatory model with auto regressive distributed lag model (ARDL) for estimating the electricity demand function in Iran. The Research Background There are numerous studies carried out in the recent decades for estimating the electricity demand. The study carried out by Hou Athker (1951) might be regarded as one of the initial researches in this regard. He indicated that the price elasticity and the income elasticity for electricity demand among Iranian families are low and high, respectively. Ang (1988) estimated the electricity demand function for four South- Eastern Asian countries including Malaysia, Singapore, Thailand, and Taiwan. The research demonstrated that in the countries where there is a higher annual per capita income, there is a lower electricity income elasticity of electricity demand. Eltony and Mohammad Yousef (1993) carried out estimation on the electricity demand among the Persian Gulf Cooperation Council states (Bahrain, Oman, Saudi Arabia, Emirates) using the ordinary least square model and indicated that there is no elasticity in electricity demand in proportion to its price and income in short-term and long-term. According to them the reason behind this was the subsidies paid by the government. Al Aziz and Hoedown (1999) estimated the energy demand in Jordan and concluded that the income elasticity for electricity demand is less than one. Also, Ettestol (2002) estimated the electricity demand for homes in Norway using the 1970-1999 electricity demand data. The results show that there is a low electricity demand elasticity in proportion to the price and there is a high electricity demand elasticity in proportion to the income. Also in Iran, there have been carried out several researches in this regard. Some of them are as follows: Fakhraei (1992) estimated the electricity model for homes in Iran using the time-series data during the years1968-1989 and concluded that there is no elasticity in the electricity consumption in proportion to its price. Moreover, Pazhooyan (2000) estimated the electricity demand in Iran and found that the price elasticity and the income elasticity for electricity demand are lower and higher than one. Aminifard (2002) estimated the electricity demand for homes using the Johanson and Joselius coefficient model, the error correction model and the time-series data for the years 1967-99. He found that the price and income elasticities and intersecting
7
Danish Journal of Engineering and Applied Sciences, April, 2015, Pages: 7-13
electricity demand is lower than one and that the elasticity ofnumber of electricity consumers in proportion to electricity demand is greater than one. Theoretical principles and the Electricity Demand Model According to micro-economic theory, the demand for different kinds of energies in various productive sectors derives from the production function. For example, the production function of a particular enterprise in a certain time can be defined as follows: Q= F (K, L, M, E1, E2, … En, T) Where M, L, K refer to the initial material, labor, and capital, respectively. E1 is the 1st type of energy such as electrical energy and T is a set of other factors such as technology variations. A firm selects a combination of necessary factors so that it spends the least possible costs for manufacturing a certain production. The demand function for production factors is reached through minimizing the cost function of the firm. If the demand for electricity as a production factor is regarded as follows: Xei= Xei (Pk, P1, Pm, Pi, Q, T) Where, the electricity demand in a certain time (t) is a function of electrical energy price (Pi) and other alternative sources of energies and the non-energy factors are (Pm, Pl, Pk), and the added value is (Q). In this case, other factors such as technology (T) can also be used. One of the recommended models for the electrical demand is the Bandaranaike and Munasinghe’s (1983) model which tries to provide a comprehensive model for electricity demand. The theoretical foundation of the present research relies on this model and its logarithm can be regraded as follows: LOGE= LOG K+ γ1 LOG Ps+ γ2 LOG Pe+ γ3 LOG Vi Electricity Demand Model First, the aggregate electricity demand function will be referred to in terms of the mentioned theoretical principles. A: Aggregate Electricity Demand Function LCBA= + LPBA+ LPE+ LY+ LPOPCO+ Where: LCBA= the aggregate electricity consumption logarithm LPBA= the consumed electricity price logarithm LPE= energy price index logarithm The energy price index has been calculated in terms of the average weight of energy factors: PE= (PB* CB+PNS* CNS* PNK* CNK+ PNG* CNG+ PGT* CGT+ PGM* CGM (CB+CNS+CNK+CGT+CGM) Where PE refers to the energy price index, and PGM, PG, PNG, PNK, PNS, PB refer to price index of petroleum, paraffin, mazut, gas oil, natural gas, and petroleum gas, respectively. The Cs in the above equation indicate the consumption of mentioned energies. LY: the income logarithm (gross domestic product in 1997 constant price). LPOPCO: the aggregate electricity subscribers’ logarithm. : intercept : Residual term The Stationary Test of Variables The stationary test is regarded as one of the significant requirements in the estimation of econometric models using time-series data. There are several ways to distinguish stationary time-series data from non-stationary among which Augmented Dickey-Fuller test is the most significant one. Table.1 the results of Dickey-Fuller Test for the electricity demand models’ variables Stationary rank
I(0) I(1) I(0) I(1) I(0)
8
Critical value of ADF %10 -3/22 -2/62 -2/59 -2/60 -2/60
%5 -3/57 -2/96 -2/92 -2/93 -2/93
%1 -4/32 -3/67 -3/57 -3/61 -3/60
Statistic
Function format
observed -4/92 -4/4 -6/87 -3/25 -8/99
Intercept, with trend Intercept, no trend Intercept, no trend Intercept, no trend Intercept, no trend Intercept, no trend
Danish Journal of Engineering and Applied Sciences, April, 2015, Pages: 7-13
Estimation of electricity demand function using ECM and ARDL models In order to benefit from ARDL and ECM models for estimation of electricity demand function, we need to consider appropriate time spans for model variables in terms of the Schwarz- Bayesian criterion. The procedure has been carried out using Mircofit 4.1 and the results are as follows: Table 2. Estimation of the self-explanatory model coefficients with widespread time spans using SchwarzBayesian criterion Regressor
Coefficient
Standard Error
LCBA(-1)
-0.465
0.121
LCBA(-2)
-0.016
0.12
LCBA(-3)
0.203
0.073
LPBA
0.032
0.019
LPBA(-1)
-0.082
0.025
LPBA(-2)
0.078
0.028
LPBA(-3)
-0.074
0.024
LPE
0.011
0.023
LPE(-1)
-0.012
0.022
LPE(-2)
0.055
0.016
LY
0.261
0.04
LY(-1)
-0.011
0.084
LY(-2)
-0.137
0.068
LPOPCO
0.332
0.089 1.05
INT
-3.26
R-Squared
0.99
D.W
2.6
Aggregate demand function To ensure that there is a correlational relationship between the models’ variables, we try to examine the correlational relation among variables and the validity of the estimation equation. The value of the statistic t is calculated as follows: p
∑α i =1 P
^ i
−1
∑ Sα
Where
^ 1
−1
Sα
^
I =1
=α
^
=
− 0.27778 − 1 = −4.06 0.31437
1
i
Sα refers to the standard deviation of the dependent variable in the model (right-hand) ^
i
Since the absolute value of the obtained statistic is higher than its critical value1 introduced by Banerjee, Dolado, and Mestre (1992), so the null hypothesis ( ) is rejected. Therefore, we can conclude that there is a long-run equilibrium relation among the variables of the model and the long-run relation for electricity demand is real. According to the above conclusions; we try to estimate the long run coefficients of the modelwhich have been illustrated in the Table 3:
1
(‐3.91)
9
Danish Journal of Engineering and Applied Sciences, April, 2015, Pages: 7-13
Table3. The long-run coefficients for aggregate electricity demand using ARDL and Schwarz-Bayesian criterion Dependent Varibale
Independent Variables
LCBA
LPBA
LPE
LY
LPOPCO
Intercept
Coefficient
-0.133
0.161
0.329
0.984
-9.67
Standard Error
0.068
0.064
0.085
0.066
1.436
T-Ratio
-1.95
2.48
3.86
14.89
-6.73
the long-run total electricity demand function estimated as follows: LCBA= -9.67 – 0.133 LPBA+0.161 LPE+0.329 LY+ 0.9854LPOPCO The coefficients symbols are as expected and according to the theoretical principles. The LPBA price elasticity equals -0.133. Consequently, the electricity is regarded as an inelastic commodity since electricity in comparison with other oil products is a cheap commodity of a high economic efficiency and it is less likely to substitute it with other oil products. Also, it is impossible to reduce electricity consumption through increasing its price and the pricing policy does not influence its consumption. The coefficient of variation of price index for other energy sources as substitutions for electricity, it can be said that the substitution is not effective. However, the income elasticity for electricity demand is greater and more influential than the other two elasticities. The quantitative value of this elasticity is 0.329. In the following, we estimate the model using the ECM in order to study the short-run dynamic behavior of variables and to illustrate the velocity of adjustment towards a log-run equilibrium among variables. The results of estimation can be seen in the Table 4. Error correction coefficient has been estimated to be -0.45 which indicates the relatively high velocity of adjustment. In addition, it shows that every year, 45% of disequilibrium in the electricity demand in one period is adjusted by the similar electricity consumption in the next period. Table 4. The short-run coefficients of aggregate electricity demand model using ECM Regressor
Coefficient
Standard Error
DLCBA1
-0.207
0.124
DLCBA2
-0.213
0.077
DLPBA
0.032
0.019
DLPBA1
-0.004
0.021
DLPBA2
0.073
0.024
DLPE
0.0109
0.023
DLPE1
-0.055
0.016
DLY
0.261
0.04
DLY1
0.137
0.068
DLPOPCO
0.332
0.089
DINT
-3.26
1.05
ECM(-1)
-0.45
0.075
R-Squared
0.935
D.W
2.31
Simulation and the aggregate electricity demand prediction The simulated and actual values of the mentioned variables can be seen in the 1. The diagram not only shows that the simulated values are approximately close to actual values but also it shows the trends in variables in an efficient way. The indexes of square root of mean square of partial error (RMSPE) and Tile un-equality index (U) for dependent variables have been calculated and illustrated in the figure. Aggregate electricity consumption(demand) simulation. U= 0.028 RMSPE= 3.12
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Danish Journal of Engineering and Applied Sciences, April, 2015, Pages: 7-13
Figure. Aggregate electricity consumption simulation (million kw/h) As it can be seen, the simulated variables follow closely the movement of variables in the estimated range. The PMSPE and U statistics also confirm strongly this claim. Aggregate electricity demand estimation Table 5. shows the aggregate electricity demand predication (million kw/h) using the software Microfit 4.1 in terms of the estimation model for this function. Table 5.
Aggregate electricity demand predication (2010-2025) million kw/h
Year
2010
2011
2012
2013
2014
2015
2016
2017
Aggregate electricity demand predication
170067
174730
179394
184057
188721
193384
198048
202711
Year
2018
2019
2020
2021
2022
2023
2024
2025
Aggregate electricity demand predication
207375
212039
216702
221366
226029
230693
235356
240020
As it can be seen in the table, there is a reduction in the demand for electricity after implementing the targeting subsidies plan. According to the Power Ministry estimations, the state electricity demand has been 176230 million kw/h in 2009 which after implementing the targeting subsidies plan in the first year, this number has been decreased to 170067 million kw/h with a 3.5 % decline in the electricity demand. This value has been reached 174730 kw/h in 2011 which is still lower than the electricity demand in 2009. Finally, aggregate electricity demand will have an increasing trend with 240020 million kw/h consumption in the year 2025. Figure2 shows the predication of aggregate electricity demand for the years 2012-2025.
Figure2. Aggregate electricity demand estimation million kw/h
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Danish Journal of Engineering and Applied Sciences, April, 2015, Pages: 7-13
Conclusion and Suggestions The results of the study confirmed the inelasticity of electricity demand in proportion to the electricity price indicated by further studies in Iran and other countries. In addition, the results indicate that all the coefficients at the levels 5 and 10 % are significant. The results also show that the pricing policy cannot be influential in controlling the electricity demand. Therefore, we should take actions to invest more and to increase the electricity production. On the other hand, we need to implement non-pricing policies such as using energy-saver lamps, informing people on how to use the electricity in an efficient way, and manufacturing products with low energy consumption (energy label: A) to reduce the increasing trend in energy consumption for homes. Another effective way for economizing electricity consumption is exerting various electricity prices and tariffs in terms of season, region, and consumption peak hours. For example, we can encourage the consumers to consume less in the peak hours using multi-tariffs electricity meters.
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