An Empirical Analysis Of Residential Electricity Demand

Published Date: 02 Nov 2017

Abstract

This research examines the relationship between the UK residential electricity demand and its determinants such as electricity prices, real disposable income, population and average temperature. These variables were found to be co-integrated and the estimated long-run price, income, population and temperature were -0.067, 0.394, 1.337 and -0.085 respectively. Also, the estimated short-run price, income, population and temperature were -0.081, 0.848, 1.645 and -0.060 respectively Furthermore, the estimated Error correction coefficient confirmed the existence of a stable long-run relationship between the residential electricity consumption and its determinants and the estimated speed of adjustment is 0.346 which suggest that about 35 % of shocks to the long-run equilibrium is restored after one year.

INTRODUCTION

Different energy sources and specifically electricity supplies are necessities for fuelling the economy and keeping households warm. Therefore, energy policy choices have a broad and long-term influence on the structure of the existing and future energy system, as well as rate of future economic growth (Madlener et al, 2011). Estimated residential electricity elasticity provide the stakeholders in the energy sector vital information as to the sensitivity of energy consumers with respect to variations or changes in the key determinates of electricity (e.g. electricity prices, disposable income, population and temperature).

Energy economists and researchers are therefore interested in estimating both short-run and long-run electricity demand elasticity which is useful for planning and applying strategic energy policies (Silk and Joutz 1997). Econometric studies still appear to be at the centre of most of the applied research with respect to empirical analysis of dynamics of energy consumption. Notably, new econometric techniques (e.g. autoregressive distributive lag (ARDL) model and various panel estimation techniques) have been progressively utilised by researchers. Therefore, policy makers and investors rely on correct estimates of the responsiveness of energy demand to changes in determinate of energy consumption, especially at the residential level.

Hence, an empirical study on the dynamics of residential electricity market is important to understand how the market responds to changes in economic environments. Consequently, this study seeks to provide the policy-makers with a possible regulatory framework in planning appropriate electricity-related policies, and to provide the industry investors in the sector the correct estimate of how energy consumers respond to changes in electricity price, level of their disposable income. Also, this study will evaluates the effects of population growth and unpredictable British weather condition on electricity consumption.

LITERATURE REVIEW

According to Silk and Joutz (1997) and Madlener et al (2011) modelling the linkage between energy consumption, the level of economic activities offers an essential evaluation of energy policies to achieve the double objectives of safer environment and accelerated economic growth, thereby minimising a possible trade-off between pro-environmental friendly energy usage and economic growth. Madlener et al (2011) documents four casual relationships between energy consumption and economic output. These linkages include unidirectional relationship causality running from energy consumption to economic growth; unidirectional causal relationship from economic growth to energy consumption; bidirectional causal relationship where economic growth and energy consumption reinforce each other; and absence of causal relationship between energy consumption and economic performance.

Silk and Joutz (1997) applied Johansen co-integration technique and error correction model to estimate both short run and long-run of the United States residential electricity demand. The study found a long-run relationship between electricity consumption, its prices and real disposable income and reported price and income elasticities of residential electricity demand to be -0.48 and 0.52 respectively. Also, Silk and Joutz (1997) reported the short-run price and income elasticity of US residential electricity demand to be -0.62 and 0.32 respectively.

Filippini (2011) examined the residential demand elasticity of 22 cities in Switzerland using panel data approach. The study modelled the peak and off-peak residential electricity demand functions to estimate prices, income and cross-price elasticity for the Switzerland residential electricity sub-sector. Filippini (2011) found that the peak period long-run own price elasticity to between -1.60 and -2.26; and off-peak long-run own price elasticity to between -1.27 and -1.65. Also, the study found that an increase in the peak period price of electricity has a larger effect on the level of electricity consumption than an increase in the off-peak period electricity prices.

METHODOLOGY AND SOURCES OF DATA

Following the influential study by Engle and Granger (1987), there has become common for researchers to utilise co-integration analysis for time series analysis. Madlener et al (2011) emphasised that the data generating processes (DGPs) of most of the economic series follow a one order of integration process, I(1) or even higher than I(1). Hence, regression estimation with I(1) variables in levels may lead to wrong inferences or spurious results.

As an alternative, deriving the first differences of the variable can be used to overcome this challenge but results in the loss of long-run information available in levels. (Engle and Granger, 1987) postulated that this problem can be addressed by the use of co-integration through the identification of the linear combinations non-stationary time series. The established co-integration is then interpreted as the evidence of long-run equilibrium relationships between the set of variables analysed. For example, if two time series such residential electricity consumption and its prices are co-integrated by a common vector, the use a normal VAR-approach will be inappropriate rather an error-correction model will be applied to account for this relationship and to estimate the correct results.

Therefore, using the residential electricity consumption, let (electricity demand) and (electricity prices) and assuming that the quality of electricity consumption depends on the price level then this relationship can be expressed as:

. Note that if is I(0), then there will be a linear combination between electricity consumption and its prices price level such thatwill be stationary.

Furthermore, Johansen (1988, 1995) proposed alternative (ML) estimation technique for co-integration. According this approach, If two or more non-stationary time series follow a common long run path, a co-integration can be applied to test if their linear combination stationary or not. Contrary to the single-equation techniques, Johansen’s framework does not assume priori that there exists a unique co-integrating vector between the variables. Also, Johansen’s framework allows for the efficient estimation of both long-run and short-run relationships. Consequently, Gonzalo (1994) applies simulation tests and finds evidence in support of superior finite sample properties of the maximum likelihood estimator developed by Johansen when compared to other four co-integration analysis techniques that are generally used.

It is therefore important to note that while most previous empirical studies on the analysis of energy demand and other economic studies have attempted to address the spurious regression problem after the introduction co-integration analysis, Madlener et al (2011) opine that the problems associated with the time series estimation are not fully resolved. Madlener et al (2011) states that the conventional unit root and co-integration tests performed on time series framework are generally problematic and suffer from usual weakness of very low power and size.

AUTOREGRESSIVE DISTRIBUTED LAG (ARDL) BOUNDS TESTING APPROACH TO CO-INTEGRATION

A dominant alternative way of addressing short-comings associated conventional time series regression analysis is the autoregressive distributed lag (ARDL) bounds testing method to co-integration. This technique, which was developed by Pesaran and Shin (1999) and Pesaran et al. (2001), has been widely used in time series analysis and particularly in estimating energy demand elasticity given the peculiar properties of energy variables Madlener et al (2011)

The major advantage of the autoregressive distributed lag (ARDL) bounds testing co-integration framework is that usual evidence as regards the order of integration of the series included in the time series analysis as a precondition for estimation the true parameters is not necessary and can be circumvented. Rather, the existence of a long-run relationship between variables included in the analysis is tested using bounds lower and upper critical values. The bounds lower and upper critical results from the presence I(0) variables which represent the lower bound, and I(1) variables for the upper bound included in the analysis.

MODEL SPECIFICATION

To analyse the UK’s residential electricity demand, we follow the general specification in the energy literature and assume that the UK’s residential electricity consumption is a function of electricity prices, real disposable income, population and the weather condition.

(1)

Expressing the equation (1) in logarithmic form and adding an error term gives the econometric specification of the long-run UK’s residential electricity demand function:

(2)

Where

= UK’s residential electricity consumption

= electricity prices

= population

= real disposable income

= average annual temperature

The first step in applying the bounds testing methodology is to estimate an unrestricted error-correction model (ECM) equation below which can be estimated using OLS.

(3)

Where represents are the long-run coefficients,are the short-run coefficients and is the error term. The second step in applying the bounds testing methodology is test an F-test on the joint hypothesis that the long-run coefficients of the lagged level in the right hand of the equation (3) are jointly equal to zero. The null hypothesis is tested against the alternative hypothesis which states that at least one long-run coefficient is different from zero.

Pesaran and Pesaran (2009, 2001) provide critical values for the bounds testing. As stated earlier, these Critical values are determined by the number of regressors and the inclusion of a constant. Pesaran and Pesaran (2009, 2001) provides two sets of critical values which represent the lower and the upper bound 1%, 5% and 10%significance levels respectively. The lower bound of the critical values assume that the included series are I(0). On the other hand, the upper bound critical values assumes that the series are I(1). Consequently, both the lower and upper bound critical values takes into account the two possible combinations of orders of integration for each series. The decision rule is to reject the null hypothesis of no co-integration between the variables if the calculated F-statistic lies above the upper bound. On the contrary, if the calculated F-statistic lies below the lower bound, then the null hypothesis of no co-integration is not rejected. Nevertheless, if the calculated F-statistic lies in-between the upper and lower bounds, then result co-integration test is considered inconclusive Pesaran and Pesaran (2009, 2001).

The third step in applying the bounds testing methodology follows the identification of co-integration relationship though the bounds F-test. If co-integration relationship is established, we proceed with the selection of the optimal ARDL lags of Equation (3) using Akaike Information Criterion (AIC) and the Schwarz Bayesian Criterion (SBC). Also, the post-estimation test of serial correlation is performed on the residual to test absence of serial correlation.

The specification of the model is:

(4)

Where are the optimal lag lengths of ,, and respectively, are the long-run coefficientsand is an error term.

Finally, short-run coefficients are estimated through the error correction representation of as in equation (4). Thus, error correction representation is specified as follows:

(5)

Where is the error correction term which the residual from t Equation (4), and is the error correction coefficient which represents the speed of adjustment from shocks to long-run equilibrium, that is the percentage annual adjustment after a deviation from the long-run equilibrium.

DATA SOURCES

Energy Consumption in the UK (ECUK) Domestic data tables 2012 Update titled: the overall drivers of energy consumption 1970 to 2011 UK’s provides datasets for residential electricity consumption, electricity prices, real disposable income, population and the weather condition. These datasets are downloaded from the department of energy and climate change.

DISCUSSION OF RESULTS AND FINDINGS

Unit Root Tests

Pesaran (1997) and Pesaran et al (2001) show that the application of Autoregressive Distributive Lag (ARDL) bounds test framework remains valid and consistence even when the combination I(0) and I(1) including I(2) series are included in the estimation. However, Pesaran et al (2001) argue that the presence of I(2) variables will make the computed F-statistics of ARDL bounds test framework inefficient. Consequently, to examine the unit root properties of the variables included in this study, the Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) unit root tests have been applied and the results are reported in the table 1 below:

variable

ADF Unit Root Test

PP Unit Root Test

Order of

integration

Level

First-Differences

Level

First-Differences

Electricity consumption

-2.253

-3.251**

-2.164

-3.412**

I(1)

Prices

-0.068

-2.769*

-0.522

-2.731*

I(1)

Income

-0.026

-2.510**

-1.006

-2.970**

I(1)

Population

-0.155

-2.586**

0.460

-2.679**

I(1)

Temperature

-4.605***

-6.929***

-4.606***

-7.761***

I(0)

table 1: Unit Root Tests for Log Level and First-Difference Form

*** Statistical significance at 1% level; ** Statistical significance at 5% level; * Statistical significance at 10% level.

The result of the Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) unit root tests presented in the above table show that while electricity consumption, electricity prices, real disposable income, population variables are all integrated in order of one i.e. I(1), the unit root tests show that temperature variables are stationary in level i.e. I(0). This evidence I(0) and I(1) series according Pesaran and Shin (1999) and Pesaran et al (2001) validates the application Autoregressive distributed lag (ARDL) bounds testing co-integration framework instead of usual Johansen co-integration framework.

The estimated Long-Run and Short-Run coefficients (Elasticity)

Tables 3 and 4 below shows the estimated long-run and short-run elasticity of residential demand for electricity in the UK

TABLE 3: Estimated Long Run Elasticity

Regressors

Coefficient

Standard Errors

p-value

constant

13.685**

5.241

0.021

Electricity prices

-0.067**

0.025

0.020

Population

1.337**

0.574

0.035

Disposable income

0.394***

0.117

0.004

Average temperature

-0.085***

0.023

0.003

F( 4, 17) = 139.44

Adj R-squared = 0.9635

*** Statistical significance at 1% level; ** Statistical significance at 5% level; * Statistical significance at 10% level

TABLE 4: Short-run Elasticity

Regressors

Coefficients

Standard Errors

p-value

∆ electricity prices

-0.081**

0.032

0.025

∆population

1.645***

2.703

0.007

∆income

0.848**

0.329

0.023

∆Temperature

-0.060***

0.021

0.005

ECM(-1)

- 0.346***

0.361

0.003

constant

0.013

0.018

0.474

Misspecification = F(3, 11) = 0.22 ; prob> F = 0.8773

Breusch-Pagan (1) = 0.01; prob> = 0.9237

Serial Correlation (1) = 2.399; prob> = 0.1214

*** Statistical significance at 1% level; ** Statistical significance at 5% level; * Statistical significance at 10% level

The results from table 3 and 4, show that the long-run and short-run price elasticity are -0.067 and -0.081 respectively and statistically significant. These results show that the effect of an increase in the prices of electricity on household electricity consumption is larger in the short-run than in the long-run. On the contrary, the results show that population is positively related to level of residential electricity consumption. This means that as the number of people living in the UK increases, more electricity will be consumed by the households. The estimated long-run and short-run population elasticities are 1.337 and 1.645 respectively.

Furthermore, the results show that the real disposable income is a significant determinant of residential electricity consumption. The estimated long-run and short-run income elasticities are 0.394 and 0.848 respectively and are statistically significant. These results suggest that as the disposable income increases, households tend to spend more and increase their electricity consumption. On the other hand, temperature is negative and statistically significant. This suggests that as the average annual temperature rises, less electricity will be consumed by the households in the UK. The estimated long-run and short-run temperature elasticities are -0.085 and -0.060 respectively.

Finally, the estimated Error correction coefficient from the short run residential electricity demand model is -0.346 which represents the speed of adjustment and suggest that about 35 % of deviation from the long-run equilibrium residential electricity function will be corrected after one year. Also, diagnostic tests show absence serial autocorrelation, misspecification and heteroscedasticity.

SUMMARY AND CONCLUSIONS

This study analysed the UK residential electricity demand function for the sample period of 1990 to 2010. The results show that while the real disposable income and population are positively related to the level of residential electricity consumption, the prices of electricity and temperature are negatively related to residential electricity consumption. These variables were found to be co-integrated and the estimated long-run price, income, population and temperature were -0.067, 0.394, 1.337 and -0.085 respectively. Also, the estimated short-run price, income, population and temperature were -0.081, 0.848, 1.645 and -0.060 respectively. Furthermore, Error correction coefficient validates the existence of a stable long-run relationship between the residential electricity demand and its determinants. In addition, the estimated speed of adjustment of 0.346 suggests that about 35% of shocks to long-run equilibrium are corrected each year.

REFRENCES

Engle, R. and C.W.J. Granger (1987) Co-integration and error-correction: representation, estimation and testing, Econometrica 55, 2, 251-276.

Filippini, M. (2011). Short- and long-run time-of-use price elasticities in Swiss residential electricity demand. Energy Policy, 39, 5811-5817.

Johansen, S. (1988). Statistical analysis of cointegrating vectors. Journal of Economic Dynamics and Control, 12, 231–254.

Johansen, S. (1994). The role of the constant and linear terms in cointegration analysis of non-stationary variables. Econometric Reviews 13, 2, 205–229.

Madlener, R., Bernstein, R. &Gonzalez (2011). Econometric Estimation of Energy Demand Elasticities. E.ON Energy Research Centre Series Volume 3, Issue 8

NARAYAN, P. K., SMYTH, R. & PRASAD, A. (2007) Electricity consumption in G7 countries: panel cointegration analysis of residential demand elasticities. Energy Policy, 35, 4485-4494.

SILK, J. I. & JOUTZ, F. L. (1997). Short and long-run elasticities in US residential electricity demand: a co-integration approach. Energy Economics, 19, 493-513.

Pesaran, M. H., Shin, Y. and Smith, R. J. (2001) Bounds testing approaches to the analysis of level relationships, Journal of Applied Econometrics, 16,289–326.

Datasets

year

electricity

price

population

income

temperature

1990

8066

3.718

57237.5

580002

7.61

1991

8436

3.825

57438.7

591251

6.09

1992

8555

4.061

57584.5

607296

6.11

1993

8639

4.264

57713.9

625622

6.15

1994

8721

4.150

57862.1

634365

7.21

1995

8790

4.007

58024.8

650903

6.88

1996

9243.97

3.916

58164.4

670766

5.69

1997

8981.51

3.687

58314.2

698050

7.28

1998

9407.57

3.667

58474.9

716921

7.50

1999

9484.78

3.623

58684.4

738354

7.16

2000

9616.68

3.469

58886.1

774295

7.17

2001

9917.20

3.135

59113.5

816437

6.65

2002

10319.38

2.983

59318.8

838455

7.67

2003

10576.16

2.868

59552.2

863663

6.61

2004

10679.32

3.126

59841.9

872029

7.01

2005

10809.21

4.237

60235.5

887942

7.10

2006

10722.61

5.507

60584.3

901557

6.85

2007

10582.63

5.449

60985.7

912787

7.29

2008

10300.95

6.836

61398.2

915095

6.39

2009

10192.67

7.270

61792

929792

6.28

2010

10216.69

6.512

62262

927798

4.33

2011

9594.61

6.922

62736

916596

7.47

-

Stata outputs

. reg ldemand L2.ldemand L.lprice lpop lincome ltemp

Source | SS df MS Number of obs = 20

-------------+------------------------------ F( 5, 14) = 173.09

Model | .117049408 5 .023409882 Prob > F = 0.0000

Residual | .001893414 14 .000135244 R-squared = 0.9841

-------------+------------------------------ Adj R-squared = 0.9784

Total | .118942822 19 .006260149 Root MSE = .01163

------------------------------------------------------------------------------

ldemand | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

ldemand |

L2. | .5573651 .1237896 4.50 0.000 .2918628 .8228674

|

lprice |

L1. | -.0666358 .0253826 -2.63 0.020 -.1210761 -.0121954

|

lpop | 1.33712 .5740562 -2.33 0.035 .1058918 2.568348

lincome | .3938723 .1165061 3.38 0.004 .1439916 .643753

ltemp | -.0848643 .0237481 -3.57 0.003 -.135799 -.0339296

_cons | 13.68598 5.241226 2.61 0.021 2.444664 24.92729

------------------------------------------------------------------------------

. reg ddemand L.ddemand L.dprice dpop dincome dtemp L.ect

Source | SS df MS Number of obs = 20

-------------+------------------------------ F( 6, 13) = 10.84

Model | .011490489 6 .001915082 Prob > F = 0.0002

Residual | .002295958 13 .000176612 R-squared = 0.8335

-------------+------------------------------ Adj R-squared = 0.7566

Total | .013786447 19 .000725602 Root MSE = .01329

------------------------------------------------------------------------------

ddemand | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

ddemand |

L1. | -.4274198 .1657667 -2.58 0.023 -.785537 -.0693027

|

dprice |

L1. | -.0811002 .031966 -2.54 0.025 -.1501584 -.0120419

|

dpop | 3.927586 2.703156 -1.45 0.007 1.767399 l.912228

dincome | .8488943 .3286227 2.58 0.023 .1389482 1.55884

dtemp | -.0603993 .0180435 -3.35 0.005 -.0993799 -.0214188

ect |

L1.| -0.346262 .3612592 3.73 .0003 .1258086 2.126714

_cons | .0130919 .0177636 0.74 0.474 -.0252841 .0514679

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