Arabian Journal of Business and Management Review (Oman Chapter)

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1 Arabian J Bus Manag Review (Oman Chapter) DOI: / An Open Access Journal Vol. 6 (1), 017 Research Article Arabian Journal of Business and Management Review (Oman Chapter) Homepage: Arabian Group of of Journals ESTIMATION OF THE ELECTRICITY CONSUMPTION FUNCTION CASE OF THE TUNISIAN REGIONS Akram Belhadj Mohamed Faculty of Economics and Management of Mahdia, Tunisia Corresponding Akram781@gmail.com Mgadmi NIDHAL Faculty of Law, Economics and Management of Jendouba, Tunisia nidhalmgadmi@gmail.com Abstract The purpose of this study is to estimate the electricy demand from the residential sector in Tunisia. We use the Condional Demand Analysis (DCA) developed by Party and Party (1980) as the basic methodological framework. The DCA's approach is to disaggregate the total electricy consumption of the sampled households into as exhaustive a list as possible of electrical uses, while linking these characteristics to the characteristics of households and their housing that can influence demand for electricy. We empirically validate the total consumption of electricy for twenty Tunisian regions during a study period from by the static and dynamic panel technique. Keywords: Condional Demand Analysis, demand for electricy, Tunisian regions. Introduction The energy sources available in Tunisia are very limed. In this context, electricy is the most widely used form of energy in the commercial and industrial sectors. At the residential level, electricy accounts for two thirds of energy consumption at this level. The Tunisian Electricy and Gas Company (STEG) is the main supplier of electricy in Tunisia and is essential to have the most accurate estimates of future electricy consumption. The construction of power plants requires several years of work and significant investments. Knowing and being able to meet energy needs becomes val in a long-term strategy. The consequences, if there is a gap at this level, are significant: major power outages and load shedding that may occur. Similarly, short-term solutions for electricy supply can be more polluting and costly. It is therefore crucial to be able to predict future demand for electricy and to know the variables influencing. Electricy demand comes mainly from three sectors: commercial, industrial and residential. Our study focuses exclusively on the latter. The purpose of this study is to estimate the electricy demand from the residential sector in Tunisia. We use the Condional Demand Analysis (DCA) developed by Party and Party (1980) as the basic methodological framework. The DCA's approach is to disaggregate the total electricy consumption of the sampled households into as exhaustive a list as possible of electrical uses, while linking these characteristics to the characteristics of households and their housing that can influence demand for electricy. This article has two parts. In Part I, we will summarize the main previous work that has dealt wh the function of electricy consumption. In the second part, we empirically validate the total consumption of electricy for twenty Tunisian regions during a study period from by the static and dynamic panel technique. 49

2 Review of the lerature Arabian Journal of Business and Management Review (Oman Chapter) Disaggregating total electricy demand into different electricy-consuming uses is a prolific source of information. The purpose of these un consumption estimates is to develop forecasting tools. These estimates of consumption per use make possible to observe the behavior of households wh respect to energy consumption. This is an essential input for any simulation of energy efficiency policy implementation or for future electricy sales forecasts. Different approaches have been used to predict electricy demand. Macroeconomic approaches have been attempted: regressing the electricy demand of the population of a terrory on various aggregate variables such as: real income, the number of appliances using electricy, the market price of energy..etc. In order to obtain precise un consumptions per use, estimates based on engineering or direct measurement techniques were used. However, although precise engineering techniques do not allow a link between the consumption of electricy from the use analyzed and the characteristics of households and their dwelling. Wh respect to direct measurement techniques, although the association of measured consumption wh the characteristics defining the sampled households is possible, their major disadvantages are their exorbant cost. Microeconomic, low-cost approaches to associate energy consumption wh the characteristics influencing energy consumption have therefore been developed such as the Party and Party DCA (1980). This approach seeks to explain the total electricy consumption of a household as a linear function of electrical equipment, in interaction wh certain exogenous characteristics of households. The DCA may be expressed in general terms as follows: E = N i0 M j 0 bij ( VjAi) N: is the number of electrical uses considered and M: is the number of exogenous variables characterizing households and their homes that have an impact on electricy consumption. A i : is an indicator variable that equals 1 if household has device i and A i = 0 otherwise. V j is the j th exogenous variable characterizing the household or s dwelling, and b ij: is the associated parameter the interaction between A i and V j. Finally, E represents the total consumption of electricy in the household and : is the error term of the equation. In the study of Party and Party (1980), the estimated uses i are: central air condioner, electric water heater, electric dryer, freezer, refrigerator wh or whout frost, black and whe television and color television, dishwasher, as well as a constant for undefined uses, A 0. For the characteristics influencing the consumption of electricy, V j, we find variables such as: the number of people, the income and the area of the house. The Party and Party regression model (1980) assumed the independence between the error term of the equation, and the explanatory variables, notably the usages, A i, an essential hypothesis to obtain estimates of unbiased coefficients. We also retain this hypothesis throughout our study to the effect that the uses, A i, are exogenous. The condional demand analysis thus bridges the gaps in the types of estimation discussed above and, in addion, the DCA is applicable at a very low cost. Our main reference in terms of comparison of results is the work done by the researchers of the National Instute of Scientific Research (INRS) in Quebec, although they used a statistical approach in some points different from ours. The study, produced by C. Jacques and M. Perron (005) of INRS, uses condional demand analysis as a methodology. Moreover, their estimates are also made on the basis of the annual consumption data provided by Hydro-Québec. C. Jacques and M. Perron (005) used the following linear function for their regression, which is a simple mathematical transformation of the above equation developed by Party and Party (1980). It is only the interpretation of the estimated parameters that diverges slightly: E N E N M Ai bij ( Vj Vij )* Ai i i0 i0 j1 50

3 The dependent variable E, the annual electricy consumption of households, is regressed according to the variables in brackets. The coefficient Ei thus expresses the average electricy consumption of the appliance i and bij is the average impact of the socio-economic or technical variable j on the electricy consumption of the appliance i. In addion, should be noted that C. Jacques and M. Perron produce their estimates of consumption by type of dwelling, single-family and multi-dwelling, and by age group of residences. The differences between their study and ours are a more in-depth statistical analysis on our part as well as the time interval covered by the study. C. Jacques and M. Perron use the 1994 and 1999 data produced by Hydro-Québec, while we also include the 1989 survey. Their estimates of un consumptions are nonetheless an excellent basis for comparison. We also use Hydro-Québec's data for the Quebec residential sector, as there are no major differences in the composion of the data. Moreover, no deviation of temperature and behavior can occur. This can sometimes make the estimates difficult to compare when studies are carried out in another region. C. Jacques and M. Perron (005) used the stepwise regression procedure to estimate the parameters of the equation above. This approach may lead to an overestimation of the significance of the parameter estimates because the choice of the relevant explanatory variables is made on the basis of which the exogenous variables most strongly correlated wh the dependent variable are conserved. In addion, the stepwise correction method is invalidated by heterosedasticy. This method of estimation is not used in economic studies where a structural approach is favored. C. Jacques and M. Perron (005) proposed an analysis that relies more on variables of an economic nature as explanatory factors for electricy consumption. In addion, the choice of explanatory variables for electricy demand will be partly based on a priori considerations and their relevance will be corroborated by statistical tests of significance. Currently, Hydro-Québec uses the results produced by INRS-ENERGY AND MATERIALS. Although their results of un consumption are an excellent basis for comparison, we propose to carry out a more detailed statistical analysis which makes more use of economic considerations. In the next section, we present the statistical model that we developed based on the model of the Party and Party DCA (1980). The condional demand analysis is a regression method which aims to disaggregate the total consumption of electricy of the sampled households in all the consumption related to the electrical equipment that they possess. Households have a derived demand for electricy that is related to the services provided by the various electrical appliances, be heating, lighting or any other comfort service. The derived character of electricy demand in fact makes possible to associate the demand of the households wh the electrical appliances that they possess while taking into consideration the characteristics defining the households and their housing which can influence their consumption. In fact, if the energy consumption of the uses was known, we could regress these un consumptions on various explanatory variables. Thus, demand parameters for each use would be estimated. In this line of thought, the DCA would present self in s mathematical form as follows: E i = f i (V) + e ; i = 1,...,N Where Ei, the dependent variable is the electricy consumption of use i, fi is the electricy demand function for use i, V is the vector of explanatory variables and e is the error term of the utily, equation. If fi is linear, the equation below can be rewrten: M E i= j M bij * V j + e = b i0 + j bij * V j + e, i = 1,..., N. 0 1 Assume that the vector V has M + 1 components wh V0 = 1, and the bij are the M + 1 parameters of the i th function of the demand. While we do not know the consumption, Ei (i = 1,..., N), the DCA methodology allows to estimate the parameters of the equation above. 51

4 The un consumption Ei is unknown and the total consumption of household electricy is the only known variable. Simply put, one can conceive that the total consumption of electricy is equal to the sum of the un consumptions: N E = E 0 + i 1 Ei + e Where E is the total consumption of household electricy and the Ei (i = 1,..., N) represent the un consumption of uses. E 0 is the consumption of electricy from undefined uses, such as appliances wh excessive penetration rates such as refrigerators, stoves, lighting, or wh relatively low consumption, such as a radio, a dryer, a video recorder. The total energy consumption of the uses is represented by a condional demand function of whether or not the apparatus is in use. We thus define dichotomous variables, Ai, representing each of the defined uses and taking the value 1 for the households owning the appliance i and 0 otherwise. So : E i = f i (V) * A i + e ; E = N i 0 j0 M i = 1,..., N bij( VjAi) + e. The above equation can be estimated by the least squares method. Since regressors are the variables characterizing households and their dwellings, Vj and the variables indicating the uses, Ai. Bij is the estimated parameter associated wh the interaction between Ai and Vj. However, the relevance of the results obtained, the estimates of the bij, parameters, depends to a large extent on the methodological framework used, but also, to a greater extent, on the qualy of the data wh which we work, hence the importance of starting Statistical analysis by in-depth processing of data used: Empirical validation Our database is extracted from the World Bank, the International Monetary Fund, and the Central Bank of Tunisia. This database is the subject of an in-depth study of the residential demand for electricy in Tunisia. This demand is evaluated over time and through economic and climatic factors. We will treat the electricy demand approximated by the amount of electricy consumed by residential customers for each Tunisian region. We will study this consumption of electricy in Tunisia during a study period from 000 to 014 for a sample of 0 Tunisian regions namely Tunis Tunis, Zaghouan, Bizerte, Nabeul, Siliana, Béja, Jendouba, Monastir, Mahdia, Kef, Kairouan, Sfax, Kebili, Tataouine, Medina, Gabes, Kasserine, Sidi Bouzid, Gafsa and Touzeur. To study the effect of electricy demand on STEG's profabily in Tunisia, we will refer to a non-linear model that links the endogenous total electricy consumption (CTE) variable to the number of subscribers (NB ); Income by region (RR); The average price (PM); The heating day degree (DCH) and the degree of cooling (DR). This nonlinear model is wrten as follows: CTE A i NB PM RR DR DCH Exp( ) Wh Exp: matches the exponential The estimation of this model requires in the first integrated step the Log-Log specification in order to linearize this model. Log CTE LogA i LogNB LogPM Log RR LogDR Log DCH We will use the posion, dispersion and shape indicators to analyze the qualy of f, symmetry, flatness and normaly of the different components of the electricy consumption function during the 15 years for the twenty Tunisian regions. The table 1 (appendices) corresponds to the descriptive statistics for these different components. The standard deviations are very small, which means that there is a good linear f for these different components. The total consumption of electricy, the number of subscribers and the income per region follow a normal distance since the 5

5 statistical values of Jarque and Berra are below the crical value of Chi-square wh two degrees of freedom. On the other hand, the other components do not follow a normal law because there are problems of asymmetry and flattening for these components. We will analyze the dependence relations of these different components from the Variance-Covariance matrix (appendices) that shows the dependencies of these variables. The dependency relations are posive for the endogenous variable of the total consumption of electricy and the various explanatory variables, ie the increase in electricy consumption is explained by the increase in the numbers of subscribers, Average price, revenue by region and heating-cooling days. On the other hand, the subscriber numbers exert a negative influence on the heating-cooling degree of the day. Also, the average price has a negative effect on the degree of cooling day and a posive impact on the degree of heating day. We will identify the presence or absence of multicolourary problems from the matrix of total correlations. The matrix (table 3 in appendices) shows the coefficients of the total correlations for these different components of the total electricy consumption function in Tunisia. Using this matrix, we can conclude that there is no multicolary problem for the various explanatory variables of the model of total electricy consumption in Tunisia. We will try to specify this model from the homogeney-heterogeney test, the table 4 (appendices) corresponds to this test. We use the natural logarhm operator to linearize this model which links the total consumption of electricy according to the explanatory variables for 15 years for a sample of twenty Tunisian regions. We note that from this table above, all the coefficients of reactions of this model are identical for the twenty Tunisian regions and during the 15 years. On the other hand, the constants are heterogeneous for this sample. To do this, we model the function of Tunisian electricy consumption by a statistical panel wh individual effects and we will use the generalized least squares (GLS) methods to estimate this function. The table 5 (appendices) shows these estimation methods for this function. Appropriate techniques for estimating the function of electricy consumption yield expected and significant results. But, the interpretation of these results is above all based on an arbration test of Hausman (1978). The table 6 (appendices) corresponds to the Hausman test (1978) The Hausman test (1978) indicates that the individual effects are fixed since Hausman's (1987) statistic is greater than the tabulated Khi-two value at five degrees of freedom. Hence, the constants of the twenty Tunisian regions do not vary over individuals and time. We use the results of the estimation by the Whin procedure as a good interpretation of the static relation which describes the total consumption of electricy as a function of the explanatory variables. All, the explanatory variables exert posive and significant effects in the accumulation of the quanty of electricy for the twenty Tunisian regions during the period We will use the dynamic panel technique to estimate the cumulative quanty of Tunisian electricy according to the explanatory variables. The dynamic model of electricy consumption in Tunisia takes the following linear form: Log CTE LogA i LogCTE 1 LogNB LogPM Log RR LogDR Log DCH The lerature for the estimation of dynamic models on panel data provides a series of techniques, most notably the method of Anderson and Hsiao (198) and Arellano and Bond (1991). Although wh the first method we arrive at a convergent estimator, this technique does not explo all the condions on the moments and does not take the structure into account in terms of error. Therefore, in the framework of this study, we will use the method of Arellano and Bond (1991) which is more efficient. The latter is based on the use of instrumentation to explo the information contained in the first differences that are introduced into our theoretical model to be estimated. If we add the consumed quanty of the delayed electricy, the theoretical model can be wrten as follows: Log Log CTE i LogCTE 1 LogNB LogPM Log RR LogDR DCH e t The estimator is done in two steps; It is assumed in the first place that the error terms are independent and homoscedastic between the individual and temporal dimension. In a second step, the estimation of Arellano and Bond 53

6 (1991) takes residues from the first step to estimate the variance-covariance matrix and to release the previous hypotheses infinely. This two-step approach allows for the consideration of heteroskedasticy between regions, the autocorrelation of error terms, and simultaney and measurement errors bias (Kremp et al 1999). The consistency of Arellano and Bond's GMM estimator (1991) is based on the assumption that there is no second order autocorrelation in the errors of the first-difference equation and that the instruments are valid. They suggested the two tests where the rejection of the null hypothesis confirms the specification of our model: a direct test of the autocorrelation of the second-order residues and a Hansen (1987) test on the over-identification of equations. The table 7 (appendices) corresponds to the estimate of the function of electricy consumption over 15 years for the 0 Tunisian regions by the GMM technique of Arrellano and Bond (1991). The first observation concerning the estimation of the dynamic panel model of electricy consumption in Tunisia is that the coefficient of the delayed endogenous variable of this consumption takes a posive and significant sign from the method of generalized moments to a single one And two-step Arrelano-Bond (1991). Also, the explanatory variables have posive and significant signs. But, the estimation of the two steps yields results as the only step. These results confirm wh the work of Arrelano-Bond (1991). Sargan's statistic is statistically significant at the 5% risk threshold. Hence, the instruments are effective because we accept the hypothesis of over-identification of Sargan and Hansen where the instruments are over-identified. The Ljung-Box test and the m statistic validates the absence of a second-order autocorrelation problem in the function of electricy consumption in Tunisia in the first difference. Conclusion In this article, we studied empirically the total consumption of electricy during a study period ranging from on annual frequencies for a sample of the twenty Tunisian regions which are: Tunis cy, Zaghouan, Bizerte, Nabeul, Siliana, Beja, Jendouba, Monastir, Mahdia, Kef, Kairouan, Sfax, Kebili, Tataouine, Medina, Gabes, Kasserine, Sidi Bouzid, Gafsa, Touzeur. We have referred to the main previous work that has dealt wh the function of electricy consumption and have identified the different approaches to this function. We extracted a data base from the Central Bank of Tunisia, the World Bank and the International Monetary Funds. We studied the asymmetry, f and normaly of the various components of electricy demand from statistical indicators: Posion, Dispersion and Shape. We have given the different dependence relations between these different components from the Variance-Covariance matrix and we validated the absence of a multicolenary problem from the matrix of the coefficients of the total correlations. We have specified the basic model by a panel wh individual effects from homogeney-heterogeney statistics. We used the Whin and GLS procedures to estimate the endogenous variable total consumption of electricy according to the explanatory variables. We verified the nature of the fixed individual effects by the Hausem arbration test (1978) and we used the GMM method of Arelano and Bond (1991) in single step and double-step to estimate the dynamic relation Of electricy consumption in Tunisia. References Arellano, M. and Bond, S. (1991), Some Tests of Specification for Panel Data, Review of Economic Studies, Vol 58, p Anderson, T. W. and Hsiao, C. (198), Formulation and Estimation of Dynamic Models Using Panel Data, Journal of Econometrics, Vol 18, p Box, G. E. P and Pierce, D. A, (1970). Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models, Journal of the American Statistical Association,Vol 65, p Hydro-Quebec, (006), rapports périodiques de G. Lafrance et collaborateurs sur les modèles de prévision de demande, période Hansen, L. P. (198), Large Sample Properties of Generalized Method of Moments Estimators, Econometrica, 50, p Hausman, J. A. (1978), Specification Tests in Econometrics, Econometrica, Vol 46, p

7 Parti, M. and Parti, M. (1980), The Total and Appliance Specific Condional Demand Analysis for Electricy in the Household Sector, The Bell Journal of Economics, Vol 11. Sargan, J. D. (1958), The Estimation of Economic Relationships Using Instrumental Variables, Econometrica, Vol 6, p Kremp, C., Berger, U., Hoffmann, P., Keuer, D. and Sonnemann, G.R. (1999), Seasonal variation of middle latudes wind fields of the mesopause region - A comparison between observation and model calculation, Geophysical Research Letters, Vol 6, issn:

8 Appendices Table n 1 : Descriptive statistics CTE NB PM RR DR DCH Average Médian Maximum Minimum Standard deviations Skewness Kurtosis JB Significance Table : Variance-Covariance matrix CTE NB PM RR DR DCH CTE NB PM RR DR DCH Tablea 4 : Homogeney / Heterogeney tests Homogeney of coefficients Homogeney of constants Log( CTE ) 163.5(0.000) 0.75 (0.914) The value between paranthesis corresponds to the statistical significance of Hausman (1978) Table n 5 : Appropriate techniques for estimating the function of Tunisian electricy Estimate Whin Estimate GLS Coefficients Significance Coefficients Significance Log(NB ) Log(PM ) Log(RR ) Log(DR ) Log(DCH ) Stat-Hausman Table 6 : Hausman Test (1978) Log (CTE ) 5 = 9.4(0.0935) 56

9 Table 7 : Estimation of the electricy consumption by the GMM method of Arrellano and Bond (1991) Two step One step Variables The coefficients Variables The coefficients Constant Constant Log(CTE -1) ** Log(CTE -1) Log(NB ) * Log(NB ) Log(PM ) ** Log(PM ) Log(RR ) ** Log(RR ) Log(DR ) *** Log(DR ) Log(DCH ) * Log(DCH ) Over-identification test Sargan 9 = 16,346 (0,005) Sagan 9 = 18,761(0,041) Test of absence of autocorrelation of errors in the difference equation m m LB = Q = 5.650(0,13) LB = Q = 9.33(0,153) 57