Econometric Estimation of Energy Demand Elasticities

Transcription

1 E.ON Energy Research Center Series Econometric Estimation of Energy Demand Elasticities Reinhard Madlener, Ronald Bernstein, Miguel Ángel Alva González Volume 3, Issue 8

2 Table of Contents Executive Summary Introduction Goals of the project Positioning of the project within the E.ON ERC strategy Theoretical framework Disaggregate sectoral approach Industrial electricity demand Residential electricity demand Residential natural gas demand Interfuel substitution Literature overview on empirical econometric research Energy demand elasticities Industrial electricity demand Residential electricity demand Residential natural gas demand Causality in the energy/growth nexus Interfuel substitution Econometric methodologies used Unit root tests Unit root tests based on time series data Unit root tests based on panel data Approaches to cointegration analysis Johansen Maximum Likelihood Panel cointegration ARDL bounds testing approach Granger causality testing Translog model Empirical analysis Industrial electricity demand on the subsectoral level in Germany Data Unit root tests VAR specification Cointegration rank tests VECM estimation (long-run elasticities) Granger causality Impulse response functions Short-run elasticities Residential electricity demand in OECD countries Data Panel unit root tests Panel cointegration tests Long- and short-run elasticities Panel Granger causality testing Residential natural gas demand in OECD countries Data Bounds test to cointegration Long-run relationships and short-run dynamics Constancy of cointegration space Interfuel substitution in major European countries Data Translog estimations Conclusions Literature Attachments List of Figures List of Tables Publications generated by the project Short CV of scientists involved in the project Project timeline Activities within the scope of the project i

3 Executive Summary In this study we aim at shedding light on the responsiveness of energy demand to measures of economic activity and energy price. Furthermore, we also aim at analyzing the causal relationship between energy use and economic activity. The methodological focus of the study lies in the application of econometric methods based on time series and panel data. As most economic time series contain stochastic trends, the application of simple regression techniques will likely lead to spurious results. Hence, the application of cointegration analysis, which takes the non-stationarity of the data explicitly into account, is required. The concept of cointegration was introduced by the seminal paper of Engle and Granger (1987). Since then, a number of different approaches to cointegration have been introduced in the econometrics literature. We apply three of the most common state-of-the-art techniques, which all have their own merits: (1) the maximum likelihood system approach (Johansen, 1988 and 1995), (2) the fully modified OLS (FMOLS) and dynamic OLS (DOLS) group-means panel estimation framework (Pedroni, 1999 and 2004), and (3) the autoregressive distributed lag (ARDL) bounds testing procedure (Pesaran and Shin, 1999; Pesaran et al. 2001). A further focus of this study is the use of data at the lowest level of aggregation as possible, which stands in contrast to most similar studies in the energy demand literature. The reason for this approach is that analyzing data aggregated over widely heterogeneous sectors will most likely result in crude inference concerning economic relationships and consumer behavior. To this end, our aim is to reap the benefits of additional information otherwise blurred through aggregation, by analyzing sectoral/subsectoral demand functions for a single energy carrier. More specifically, in this study, we focus on industrial electricity demand, residential electricity demand and residential natural gas demand. For many developed countries, industry data is even available on a subsectoral level, which allows to further reduce the heterogeneity of the consumer groups analyzed. The report is organized as follows. Section 1 gives an introduction on the goals and on the content of the project. Section 2 provides the theoretical framework for the empirical analysis, while Section 3 gives an overview of the relevant empirical literature. Section 4 explains the different econometric methods used in the analysis. Section 5 describes the data used, the application of the estimation methods, and the results. Section 6 concludes. In the first part of the empirical analysis (Section 5.1), we use the Johansen maximum likelihood system approach to estimate industrial electricity demand elasticities at the subsectoral level. This enables us to reap the benefits of lower heterogeneity within the electricity-consuming sectors investigated and of retaining additional information otherwise blurred by aggregation. The annual data set used covers eight subsectors of the German economy for the period 1970 to By employing a cointegrated VAR model specification and accounting for structural breaks we find cointegration relationships for five of the eight subsectors studied. The long-run elasticities range between 0.70 and 1.90 for economic activity and between 0.52 and zero for the price of electricity. The short-run elasticities are estimated by single-equation error correction modeling and found to be between 0.17 to 1.02 for economic activity and 0.57 to zero for electricity price. Granger-causality tests indicate that, in the long term, causality runs from both economic activity and electricity price to electricity consumption, while Granger-causality from electricity price and electricity consumption to economic activity is detected in only two subsectors. Electricity price is found to be Granger-caused neither in the long nor the short run. Finally, an impulse response analysis yields plausible results with regard to the demand adjustment to a price shock, confirming the usefulness of the approach adopted. In the second part (Section 5.2), we estimate residential electricity demand elasticities and conduct an analysis of the causal relationship between electricity demand, disposable income and electricity price for a group of several OECD member countries. More specifically, we apply panel cointegration and Granger causality testing to a data set consisting of eighteen countries in the cross-sectional dimension and the years 1981 to 2008 in the time domain. Our results for the whole panel indicate a near unity income elasticity and an inelastic price elasticity of approximately 0.4 in the long run. These results are robust with regard to the estimation methods employed (i.e. group-means panel FMOLS and DOLS, respectively). In the short run, our estimates from an ECM indicate an income 1

4 elasticity of 0.2 and a price elasticity of approximately 0.1. Moreover, our tests on Granger causality provide an indication for a bidirectional causal relationship between electricity consumption and economic growth. Hence, our findings are in favor of the feedback hypothesis. In the third part (Section 5.3), we analyze residential natural gas demand for twelve OECD countries using available time series data from 1980 to We estimate long-run demand elasticities with regard to real disposable income and real residential natural gas price using the autoregressive distributed lag (ARDL) bounds testing procedure. By employing an error correction framework we also obtain estimates for the speeds of adjustment to long-run equilibrium and short-run elasticities for the single countries. The effect of weather conditions on natural gas demand in a given year is accounted for by including heating degree days as a control variable. On average, the long-run elasticities are 0.94 with regard to income, 0.51 with regard to price, and 1.35 with regard to heating degree days. The short-run dynamics assessed by estimation of the error correction models indicate an average adjustment coefficient of 0.58, a short-run income elasticity of 0.45, a short-run price elasticity of 0.24, and a short-run elasticity with regard to heating degree days of Hence, on average, the short-run elasticities have approximately half the magnitude of their long-run counterparts. In the fourth part (Section 5.4), we supplement the research with the inclusion of an analysis of interfuel substitution by using a translog model specification. In particular, we estimate to what extent there is substitution among different kinds of energy inputs (e.g., electricity, gas, oil) in the economy of five major European countries (i.e., Germany, France, Italy, Spain, and the UK). To this end, we apply a cost share model specification of energy consumption for four fuels (where data on coal were lacking three fuels), obtaining a set of own-price and cross-price elasticity estimates for the aggregate economy as well as the industrial and the residential household sector. The models are estimated both with and without a deterministic time trend as a proxy for technical change and other influences otherwise not picked up by the model specification, found to be statistically significant (and thus relevant to be included) in almost all cases. While many of the estimated coefficients are statistically significant and have the expected sign, the great range of results and lack of consistent patterns of results (across sectors, fuels and countries) makes it difficult to come up with specific recommendations for policy-makers. In this respect, we find the results obtained from the cointegration analysis as more robust and useful. Overall, regardless of the sector or energy type considered, our results imply that the steering effect of tax-induced price increases on energy demand has a very limited potential for energy conservation, and hence a reduction of GHG emissions. Furthermore, our findings suggest that reductions in electricity consumption are associated with a trade-off concerning economic growth in the residential sector, as well as some subsectors of the manufacturing industry. 2

5 1 Introduction Energy-related policy decisions have far-reaching and long-term consequences for the structure of the prevailing energy system. Hence also the awareness of the mechanisms of the energy markets is an important issue. In order to enable a more environmentally and socially benign use of energy in the future, and to provide guidance for policy-makers in designing appropriate policies, the accurate prediction of how energy consumers react to changes in price, income and other explanatory variables is paramount. Elasticity estimates provide some information as to how sensitive consumer behavior is with respect to changes in important explanatory variables (e.g. energy price, income, energy-using capital stock). In the field of energy use, it is a major challenge for applied energy economists/ econometricians and modelers to determine energy demand elasticities that are useful for policy design and strategic decision-making of utilities, technology manufacturers, and other relevant stakeholders. Furthermore, the assessment of the causal relationship between energy use and economic activity is valuable for an appraisal of potentially conflicting policy objectives, such as the trade-off between energy conservation and economic growth. There are four alternative economic hypotheses regarding the causal mechanisms underlying the energy consumption economic growth nexus, which are currently heavily under debate in the energy economics literature (for a useful survey see Payne, 2010): the conservation hypothesis, the growth hypothesis, the feedback hypothesis and the neutrality hypothesis. While the conservation hypothesis implies causality running from economic growth to energy consumption, the growth hypothesis implies the opposite causal relationship. The feedback hypothesis combines the latter hypotheses, by claiming an interdependent causal relationship between both variables. Finally, the neutrality hypothesis states that both variables are only of little importance in determining each other. Econometric work still seems to dominate the applied research done in quantitative analysis of energy demand. In recent years, importantly, new econometric techniques (e.g. panel data econometrics, cointegration analysis) have become more and more popular among researchers and analysts alike, and increasingly applied, while at the same time interest in the estimation of energy demand elasticities and changes thereof seems to have diminished. However, both policy-makers and decision-makers in industry alike, and energy modelers providing model-based insights, rely on reliable estimates of the sensitivity of energy demand in reaction to changes in important variables shaping energy demand. Reliable econometric estimates of energy demand elasticities are rare, and research interest seems to have waned in recent years, despite an increasing stock of data and the acknowledgement that a better understanding of energy consumer behavior is crucial for decision support in the energy domain. This is all the more surprising in view of dynamic structural change in the energy markets, especially in the electricity markets, and the availability of improved time series, cross-sectional, and micro data as well as econometric modeling techniques (such as cointegration analysis and panel data econometrics). The main aims of the proposed research project are at least threefold: (1) to describe and apply the state-of-the-art in using econometric techniques for estimating elasticities of energy demand; (2) to estimate sectoral and aggregate elasticities of energy demand in selected European countries for own- and cross-prices, income, temperature, and other explanatory variables; and (3) to compare and contrast the empirical results obtained from different model specifications, estimation techniques and data samples used with the existing literature. The results will provide new insights into the sensitivity of different classes of energy consumers with regard to changes in important explanatory variables. Furthermore, they will also shed new light on the robustness of the econometric estimates if different methods are employed. 3

6 1.1 Goals of the project The main goal of this research project is to discuss the state-of-the-art of estimating energy demand elasticities, and to estimate elasticities of energy demand for different sectors of selected European economies, based on state-of-the-art econometric estimation techniques. The following objectives are to be accomplished: Overview of the state-of-the-art of the literature on econometric studies of energy demand, and in particular the estimation of elasticities of demand for energy relative to a selection of influencing variables of interest (price, income, other). Collection and detailed descriptive analysis of the data available for the empirical study (annual, quarterly and monthly, if possible). Exploration and statistical testing of a set of different model specifications (e.g. translog and error correction) and econometric estimation techniques, and systematic comparison and interpretation of the results gained from the different model specifications. Selection of the best (most promising) models and results and testing for robustness and possible model misspecification. Systematic compilation of and reflection on the results obtained for the different sectors and time periods studied. Formulation of a Final Report. 1.2 Positioning of the project within the E.ON ERC strategy This project helps to improve the understanding of energy demand responsiveness in different sectors of the economy of selected OECD countries with regard to changes in price, income and weather, as well as the understanding of causality of the relationship between economic activity and energy use. With regard to capacity building at the E.ON ERC, the project helps to establish and improve both theoretical and applied competence in state-of-the-art time series and panel econometrics analysis. The results obtained are useful inputs to various kinds of energy models used within the E.ON ERC and by external modelers globally. Finally, the results are helpful for energy policy design aiming at influencing energy demand patterns by price-based incentives (subsidies or taxes). 2 Theoretical framework 2.1 Disaggregate sectoral approach Energy demand modeling on the basis of historical time-series data has traditionally been conducted for a specific country, at an aggregate or disaggregate level and in two dimensions. One dimension concerns the type of energy (i.e. mainly electricity, natural gas or gasoline), while the other dimension concerns different types of major end-use sectors: industry, commerce and public services, residential, and transportation. At one extreme, there is the analysis on the basis of data aggregated over all energy carriers and sectors (i.e. at the economy-wide level), whereas at the other extreme there is the analysis for only one energy carrier for one sector or subsector of the economy. The analysis of data aggregated over widely heterogeneous sectors will most likely result in crude inference concerning economic relationships and consumer behavior. In this respect, we share the view of Pesaran et al. (1998, p.46), viz. that it is important for a valid econometric demand analysis to be aimed at as homogenous a grouping of consumers as is feasible. This implies that studies on energy demand should use data at the lowest level of aggregation as possible. 1 To this end, our aim in the present study is to reap the benefits of additional information otherwise blurred through aggregation, by 1 Implying that aggregation in general is aimed at stepwise compiling entities with similar characteristics and, hence, also similar consumption behavior and technologies. 4

7 analyzing (sub-)sectoral demand functions for a single energy carrier. More specifically, in the following, we focus on industrial electricity demand, residential electricity demand and residential natural gas demand. For many developed countries, data for industry is even available on a subsectoral level, which allows us to reduce the heterogeneity of the consumer groups analyzed still further. 2.2 Industrial electricity demand A generic long-run electricity demand relationship for the industrial sectors of an economy can be characterized by the general function E f V, P, X, A, t t t t t (1) where electricity consumption (E t ) is contemporaneously dependent on the level of real economic activity (V t ), real electricity price (P t ), other endogenous or exogenous variables (X t ) (which may include, for example, the real price of an electricity substitute and/or weather variables), and exogenous factors (A t ), such as a sector-specific coefficient for autonomous technical change, energysaving technological progress or shifts/changes in the structure of industrial production. The latter may comprise structural changes due to substitution of labor by electricity-using capital and the offshoring of labor-intensive production processes to other countries. In contrast to energy-saving technological progress, both changes tend to increase the electricity intensity of the respective national sectors. These factors affect the relationships between the other variables and can be indirectly accounted for by the inclusion of deterministic terms. Various econometric studies have found that other energy inputs are generally poor substitutes for electricity in industrial processes (for a survey, see Barker et al., 1995). Thus, we refrain from controlling for interfuel substitution by including prices of other energy carriers. Moreover, the inclusion of heating and cooling degree day variables, which were available to us only from 1975 onwards, would have considerably reduced the number of degrees of freedom in our analysis. 2 Specifically, for the empirical analysis we chose the simple standard constant elasticity (Cobb-Douglas type) functional form exp v p E, t C0 dt Vt P t (2) where A t = C 0 exp(dt) is the deterministic term, C 0 is a constant, dt is a linear time trend and β v and β p are the constant demand elasticities with regard to economic activity and electricity price, respectively. As stated by Amarawickrama and Hunt (2008), this standard log-linear specification, apart from the obvious advantages, such as its simplicity, its straightforward interpretation and the limited data requirements, according to Pesaran et al. (1998) outperforms more complex models. 2.3 Residential electricity demand The long-run relationship between residential electricity demand and its determinants can be characterized by the general function t t t t E f Y, P, X. (3) Eq. (3) states that residential electricity consumption per capita (E t ) is a function of real (disposable) income per capita (Y t ) and real residential electricity price (P t ). Previous studies on residential electricity demand have included further control variables (X t ), as for example the real price of an 2 Other studies have also found that weather variables tend to be insignificant in industrial energy demand functions, especially in electricity demand functions (see Kamerschen and Porter, 2004). 5

8 electricity substitute (e.g., Narayan et al., 2007), heating and cooling degree days (e.g., Zachariadis and Pashourtidou, 2007), urbanization (e.g., Holtedahl and Joutz, 2004), and capital variables (e.g., Silk and Joutz, 1997). Following the principle of Ockham s Razor (see Ariew, 1976), we choose a parsimonious specification, which only includes real disposable income per capita and real residential electricity price as determinants of electricity demand. Furthermore, as the following analysis comprises a panel of various countries, problems with the availability of data on additional variables would have brought further restrictions to the data set with regard to the cross-sections and/or the time periods studied. 3 Finally, having less parameters to estimate has the advantage of attaining more degrees of freedom in the estimation of the core explanatory variables coefficients. More specifically, the demand model upon which our econometric analysis is based, takes the following standard constant elasticity functional form: y p t 0 t t, E C Y P (4) where C 0 is a country-specific drift term, and β y and β p are the long-run elasticities to be estimated with regard to income and electricity price, respectively. A higher income is expected to increase electricity demand on account of higher economic activity, whereas a higher electricity price is naturally expected to decrease electricity demand. Moreover, the price elasticity is expected to be inelastic, as in general electricity is characterized by a lack of substitutability. 2.4 Residential natural gas demand Similarly to the residential electricity demand function from the last section, natural gas demand can generally be considered to be a function of several determinants, such as t t t t G f Y, P, X, (5) where G t is residential natural gas consumption per capita, Y t is real net disposable income, P t is real residential natural gas price and X t stands for further control variables, all at time t. As most of the natural gas in the residential sector is used for heating purposes 4, a variable which controls for the temperature is included as well (heating degree days, HDD). More specifically, for the long-run natural gas demand relationship in the residential sector we chose the following constant elasticity functional form: 3 G t Y P HDD (6) 2 4 t 0exp 1 t t t, where HDD t are heating degree days and the βs are the coefficients to be estimated. Following other studies, we initially also considered the price of electricity as a substitute for natural gas. But as the estimates of the respective cross-price elasticities were not significant, we omitted these in order to gain degrees of freedom. 2.5 Interfuel substitution Assuming that production is characterized by a production function, Y = f(x), the solution to the problem of minimizing the cost of producing a specified output, given a set of factor prices, leads to the cost-minimizing set of factor demands x = x(y, p). The total cost of production is then given by the cost function, which can then be used as a starting point for interfuel substitution modeling. 3 Also, not all variables, such as cooling degree days or the price of natural gas, are likely to have the same relevance (or, more specifically, similar explanatory power) for all the countries considered. 4 A minor share of natural gas consumption is attributable to cooking. 6

9 The use of a cost function rather than a production function for estimating production parameters has certain advantages. First, having prices as independent variables, the inversion of the matrix of estimates is not necessary (i.e., less complexity is involved). Second, all estimation equations are linear (in logarithms, for the translog case) and, third, since there is usually little multicollinearity among factor prices, multicollinearity is a problem that does not arise in a cost function. In particular, the use of a transcendental logarithmic (translog) function can provide accurate global approximations of many cost frontiers used in econometric analysis (Christensen et al., 1973). Thus, differentiating the translog frontier while holding the necessary conditions for equilibrium constant, we obtain the factor cost shares for each kind of energy input i. The derivation is as follows. We start from a cost minimization problem n i i 1 2 n (7) min C X P s.t. Y f X, X,..., X ; i 1,2,..., n. i1 where C is production cost, X i is input of fuel i, and P i is the real price of fuel input i. The minimum cost function is specified as * C g Y, P1,..., Pn (8) or in natural logarithms as * ln C f ln Y,ln P1,...,ln P n. (9) Using a logarithmic Taylor series expansion (to the second term) on (9), we obtain the twice differentiable analytic cost function: 1 C v v Y v P P P P Y. (10) * ln 0 Y ln iln i i, jln iln j i, Y ln iln i 2 i j i Equation (10) can be directly estimated, or estimated in its first derivatives (by applying Shephard s Lemma), as factor shares (i.e., cost shares that sum up to unity), that is: S v P lny (11) * ln C 1 i i i, jln j i, Y ln Pi 2 j Thus, partial elasticities of substitution (among fuels) are defined as: i i 2 i 1 C i, j j, i xixj Pi Pj n PX. (12) The γ i,j parameters are related to elasticities of substitution and of factor demand shares as follows: (13) i, j i, j 1 SS i j Finally, the own-price elasticities and cross-price elasticities of input demand are defined as: 7

10 E S, S 1,and i j SS j j E (14) ii, i i ii, 2 i, j Si SiSj 3 Literature overview on empirical econometric research 3.1 Energy demand elasticities The econometric estimation of energy demand elasticities has a long tradition, going back as far as the early 1950s. Among the first studies are Houthakker (1951), Fisher and Kaysen (1962), Halvorsen (1975) and Pindyck (1979). Similarly, the related literature strand aiming at determining the causal relationship in the energy-growth nexus was sparked by the early work of Kraft and Kraft (1978), and has received considerable interest especially since the turn of the century. However, it was only with the introduction of cointegration 5 analysis, which was triggered by the seminal paper of Engle and Granger (1987), that the problem of spurious regressions 6 was starting to be adequately dealt with in econometric applications Industrial electricity demand Despite the crucial relevance of sound elasticity estimates in energy modeling used for policy advice, scholarly literature on the econometric estimation of energy demand elasticities in industry is surprisingly scarce, and this is even more so with regard to electricity. Table 1 summarizes recent studies in which electricity demand elasticities of economic activity and/or electricity price in industry are estimated (Beenstock et al., 1999; Bose and Shukla, 1999; Kamerschen and Porter, 2004; Polemis, 2007). These studies differ with regard to the model specification, the econometric method used and time span covered, the data frequency, and the country analyzed. Beenstock et al. (1999) use dynamic regression and cointegration techniques to analyze electricity demand in the household and industry sector in Israel. For the industrial sector they estimate long-run elasticities of 0.99 to 1.12 with regard to economic activity and 0.31 to 0.44 with regard to electricity price, depending on the estimation method applied. Using time series data for nine years from 19 states in India, Bose and Shukla (1999) estimate sectoral elasticities including industry (split into small/medium and large industries) by employing a pooled regression approach. The estimated elasticities of economic activity and price are 0.49 and 0.04 (the latter not significant), respectively, for the small- and medium-sized industries, and 1.06 and 0.45 for the large industries. Kamerschen and Porter (2004) employ a simultaneous equation approach for estimating price elasticities of electricity demand by the U.S. industry. 7 Depending on the specification their estimates vary between 0.34 and Polemis (2007) uses a multivariate cointegration technique (the Johansen maximum likelihood approach) to estimate aggregate oil and electricity demand functions for the Greek industry. His estimates for longrun elasticities regarding economic activity and price are 0.85 and 0.85, while in the short-run they amount to 0.61 and 0.35, respectively. The only energy demand study known to us that uses disaggregated industrial data at the two-digit level of the NACE taxonomy is Agnolucci (2009). In contrast to our study however, he focuses on aggregate energy in the British and German industry. Moreover, the analysis is based on a panel data approach, as the time series estimates mostly failed to show intuitive results. This presumably is due to the short time spans covered by the data. Finally, although information from disaggregated data is used in the estimation, the panel approach does not deliver subsector-specific estimates of energy demand elasticities. 5 If a linear combination of two or more non-stationary stochastic processes exists, which itself is stationary, the processes are said to be cointegrated. Tests on cointegration are introduced in Section 4. 6 A regression, which reveals a statistically significant relationship not due to a causal relationship is said to be spurious. 7 Kamerschen & Porter (2004) also consider a partial-adjustment approach, which, however, had to be dropped due to counterintuitive estimates. 8

11 Table 1 Industrial electricity demand studies and elasticity estimates Study Country Method Data Elasticity estimates Econ. activity Price Beenstock et. al. (1999)* Israel Cointegration Time series (quarterly), 1975q21994q4 L: 0.99 to 1.12 L: 0.31 to 0.44 Bose & Shukla (1999)* India Pooled regression Panel data (annual), 1985/861993/ to to 0.45 Kamerschen & Porter (2004)* USA Simultaneous equations Time series (annual), to0.55 Polemis (2007)** Greece Cointegration Time series (annual), L: 0.85 S: 0.61 L: 0.85 S: 0.35 Notes: * also estimate demand for other sectors. ** also estimates an oil demand function separately. S and L denote estimates for the short and the long run, respectively Residential electricity demand Table 2 gives an overview of selected recent studies on residential electricity demand elasticities, most of which employ pure time series methods for single countries: 8 Athukorala and Wilson (2010) for Sri Lanka; Dergiadis and Tsoulfidis (2008) for the US; Halicioglu (2007) for Turkey; Holtedahl and Joutz (2004) for Taiwan; Hondroyiannis (2004) for Greece; Nakajima (2010) for Japan; Nakajima and Hamori (2010) for the US; Narayan and Smyth (2005) for Australia; Narayan et al. (2007) for the G7 countries; Zachariadis and Pashourtidou (2007) for Cyprus and Ziramba (2008) for South Africa. The long-run demand elasticities from these studies range between 0.25 and 1.57 with regard to income and between 0.14 and 1.56 with regard to own price. For the short run, the elasticity estimates range between 0.10 and 0.44 with regard to income and between 0.11 and 0.46 with regard to own price. Unlike the majority of the studies reported, Nakajima and Hamori (2010), Nakajima (2010) and Narayan et al. (2007) all use cointegration techniques that are based on panel data in their analyses. In order to attain a cross-sectional dimension, the former two studies make use of available data on geographical regions within Japan and the US, respectively. The latter study is closest to ours with regard to the countries 9 analyzed and the econometric approach applied, but interestingly comes to different conclusions. Specifically, Narayan et al. (2007) analyze a panel consisting of the G7 countries as the cross-sectional dimension for the time period They employ both the ordinary least squares (OLS) and the dynamic OLS (DOLS) method (Stock and Watson, 1993; Kao and Chiang, 2000) to estimate the cointegration relationship between electricity demand, income, electricity price, and natural gas price. For the whole panel they estimate an inelastic income elasticity of 0.25 (0.31) and an elastic price elasticity of 1.56 (1.45) using DOLS (OLS). Consequently, they come to the conclusion that pricing policies aimed at reducing residential electricity consumption and hence GHG emissions are bound to be successful. 8 We only consider studies here that employ time-series or panel estimation techniques, that account for non-stationarity in the data generating process (DGP), and that were published after the year Our set of countries also includes the G7 countries, except for Canada, for which recent data on the residential electricity price were lacking. 9

12 Table 2 Residential electricity demand studies and elasticity estimates Study Country Method Data Elasticity estimates Income Price Athukorala & Wilson (2010) Sri Lanka Johansen / VECM Time series, (annual) L: 0.78 S: 0.32 L: 0.62 S: 0.16 Dergiades & Tsoulfidis (2008) US Bounds testing / ARDL Time series, (annual) L: 0.27 S: 0.10 L: 1.07 S: 0.39 Halicioglu (2007) Turkey Bounds testing / ARDL Time series, (annual) L: 0.49 to 0.70 S: 0.37 to 0.44 L: 0.52 to 0.63 S: 0.33 to 0.46 Holtedahl & Joutz (2004) Taiwan Johansen / VECM Time series, (annual) L: 1.04 to 1.57 S: 0.22 L: 0.15 S: 0.15 Hondroyiannis (2004) Greece Johansen / VECM Time series, (monthly) L: 1.56 S: 0.20 L: 0.41 Nakajima (2010) Japan Panel cointegration, DOLS Panel data, (annual), T N: = 1426 L: 0.60 to 0.65 L: 1.13 to 1.20 Nakajima & Hamori (2010) US Panel cointegration, DOLS Panel data, (quarterly), T N: = 1568 L: 0.38 to 0.85 L: 0.14 to 0.33 Narayan & Smyth (2005) Australia Bounds testing / ARDL Time series, (annual) L: 0.32 to 0.41 S: 0.01 to 0.04 L: 0.47 to 0.54 S: 0.26 to 0.27 Narayan et al. (2007) G7 Panel Cointegration, OLS & DOLS Panel data, (annual), T N: 26 7 = 182 L: 0.25 to 0.31 S: 0.19 L: 1.45 to 1.56 S: 0.11 Zachariadis & Pashourtidou (2007) Cyprus Johansen / VECM Time series, (annual) L: 1.18 L: 0.43 Ziramba (2008) South Africa Bounds testing / ARDL Time series, (annual) L: 0.31 to 0.87 S: 0.30 L: 0.01 to 0.04 S: 0.02 Notes: S and L denote estimates for the short and the long run, respectively. Elasticity estimates which are not statistically significantly different from zero on conventional levels are printed in italics. T: Number of time series observations; N: Number of cross-sections. DOLS: Dynamic OLS; ARDL: Autoregressive Distributed Lag Residential natural gas demand There are many studies on the econometric analysis of (residential) natural gas demand, but nearly all of these are from the 1960s to the 1980s (for a useful survey see Madlener, 1996). More recent studies, especially from the 2000s, are very rare, and none of them take the aforementioned problems related to non-stationarity in the data / spurious regressions into account. Table 3 provides an overview of recent studies known to us: Asche et al. (2008) analyze residential natural gas demand in 12 EU member countries, using panel data for the time period 1978 to Their shrinkage estimator reveals an income elasticity of 3.32 in the long run and 0.81 in the short run. For the price elasticity the estimates are 0.10 and 0.03 for the long run and the short run, respectively. Berkhout et al. (2004) use fixed effects to estimate residential natural gas demand elasticities in the Netherlands. The 10

13 estimates are (surprising) 0.27 and 0.19 (the latter not significant) for the long-run income and price elasticity, respectively. Using an error-components and seemingly unrelated regression (SUR) approach, Lin et al. (1987) estimate elasticities for the US based on panel data from 1960 to Their estimates for the income elasticities are 0.57 and 0.11 for the long run and the short run, respectively. For the price elasticity, their estimates are 1.22 for the long run and 0.15 for the short run. Using the shrinkage estimator, Joutz et al. (2008) estimate elasticities for the US based on panel data. Their of price elasticity estimates are 0.18 in the long run and 0.09 in the short run. Table 3 Residential natural gas demand studies Study Country Method Data Elasticity estimates Income Price Asche et al. (2008) 12 EU countries Shrinkage estimator* Panel data (annual), L: 3.32 S: 0.81 L: 0.10 S: 0.03 Berkhout et al. (2004) Netherlands Fixed effects Panel data (annual), L: 0.27 L: 0.19 Joutz et al. (2008) US Shrinkage estimator Panel data (monthly), 1980unclear L: 0.18 S: 0.09 Notes: S and L denote estimates for the short and the long run, respectively. * Asche et al. (2008) also use fixed effects, random effects and OLS estimators, but the results appear to be rather implausible. 3.2 Causality in the energy/growth nexus Table 4 displays the four studies that conduct Granger causality analyses between industrial or residential electricity consumption, economic activity and electricity price. Table 4 Results from causality analyses on residential electricity demand in the literature Study Country Data Direction of causality Long-run Short-run Dergiades & Tsoulfidis (2008) R US Time series, (annual) Y, P E P Y Halicioglu (2007) R Turkey Time series, (annual) Y, P E Y, P E Polemis (2007) I Greece Time series, (annual) Y, P E E, Y P Zachariadis & Pashourtidou (2007) R Cyprus Time series, (annual) Y, P E E, P Y E Y Notes: R : Residential sector; I : Industrial sector; Y: Economic activity; P: Electricity price; E: Electricity consumption; denotes the direction of causality. For the industrial sector, Polemis (2007) finds unidirectional long-run causality from economic activity and electricity price to electricity consumption, while in the short run he finds causality running from economic activity and income to electricity price. Hence, empirical evidence for the industrial sector so far is in favor of the conservation hypothesis in the long run. 11

14 For the residential sector, Dergiades and Tsoulfidis (2008) and Halicioglu (2007) both find unidirectional long-run causality from income and price to electricity consumption. For the short run, the former find causality from electricity price to income, while the latter finds causality from income and price to electricity consumption. 10 Zachariadis and Pashourtidou (2007) find evidence for a longrun causal relationship, running from income and price to electricity consumption, and from electricity consumption and price to income. For the short run, they only find causality running from electricity consumption to income. Hence, so far there is empirical evidence for the conservation as well as the feedback hypothesis concerning the causal relationship between residential electricity demand and real income. 3.3 Interfuel substitution For the case of energy demand with different kinds of fuel inputs (e.g., coal, gas, electricity) we use an approach that is based on production theory, where energy is the output of several factors (i.e., fuels). Such an approach fits into the context of a flexible functional form that is often used in econometrics to obtain elasticities (unrestricted ones, i.e., all elasticities of factor substitution do not necessarily add up to one), which are functions of the second derivatives of production, cost or utility functions. Commonly, the most popular flexible functional forms are the transcendental logarithmic (translog) and logit cost share models (e.g. Jones, 1995; Urga and Walter, 2003). Here we focus on the translog model specification. Since the 1970s, many authors have used a cost function rather than a production function for estimating production parameters. More complex model structures (where, e.g., electricity expenditure in each time period considered is determined according to separate utility functions) have been proposed recently but most of which present very sophisticated empirical specifications whose application is beyond the scope of this study. The work of Christensen et al. (1973) paved the way for the use of translog production possibility frontiers in energy demand studies. There, the authors set the theoretical basis for further econometric studies where the translog frontiers provide global approximations to the input and output relations. Along this avenue, Berndt and Wood (1975) explicitly investigated cross-substitution between energy and non-energy inputs by employing a translog cost function (i.e., a KLEM model) to investigate elasticities in US manufacturing (for the period ), and in particular how the energy input does substitute and complement with other inputs (e.g., labor and capital). Griffin and Gregory (1976) explored the generality of those results and applied the same methodology with a pooled international time series data set (time period ) for the manufacturing sector of nine industrialized countries. Pindyck (1979) conducted further research on the determination of input substitution and, more specifically, also dealt with interfuel substitution, i.e., he divided expenditures on energy into expenditures on oil, gas, coal, and electricity, respectively, and studied the industrial demand of ten countries. Such studies were the first ones to explore the possibilities of the translog method and triggered a lively debate about appropriate model specifications. Bohi and Zimmerman (1984) surveyed a number of econometric studies of energy demand behavior and conclude that (at that time) investigations of commercial and industrial energy use are very much constrained by the lack of detailed information on how energy is used within these sectors. During the 1970s the oil price shocks led to considerable increases in energy prices which spurred research in this field due to the increased policy relevance of energy elasticities. Hesse and Tarkka (1986) focused their research on the impact of such disturbances and separated the analysis for 9 Western European countries into two periods: and Kim and Labys (1988) applied the translog approach for interfactor and interfuel substitutiton in the Korean industrial sector (by disaggregating it into manufacturing and non-manufacturing sectors). Ibrahim and Hurst (1990) analyzed energy demand and in particular oil demand in (thirteen) developing countries, in particular, oil demand, during the 1970s and early 1980s. 10 Dergiades and Tsoulfidis (2008) also consider other variables, such as oil price and cooling and heating degree days, for which we do not report the results here. 12

15 Harris et al. (1993) continued the estimation of demand and substitution elasticities for the UK economy (disaggregated into 19 sectors), but in comparison with previous studies, extended the period of time studied to Taheri (1994) did an analysis taking into account the marked price increases of the 1970s and investigates substitution among fuels such as coal, gas and electricity during that period, by identifying inter- and intra-industry variations of industrial fuel use in the US. Also for the case of the US, Jones (1995) analyzed interfuel substitution by contrasting the translog model with a dynamic linear logit model (using data for ), where the latter provided superior global properties, i.e., a direct, unbiased estimate of the rate of dynamic adjustment. Filippini (1994), estimated electricity demand by time-of-use with a share equation approach, thus using a decomposition of the cost function, in order to be able to compute the elasticities of substitution in a simpler way. In the tradition at that time, i.e. to use (mostly geographically) aggregated data, Ryan et al. (1996) examined residential energy demand in a single province of Canada in order to better be able to observe the asymmetric price response of energy demand; specifically they allowed for interfuel substitution and used annual data for Henley and Peirson (1998) investigated consumer responses conditional on temperature levels, specifiying a translog model of residential electricity demand and modeling price and temperature interactively. Concerning comparisons between models, Zarnikau (2003) compared linear, log-linear and translog functional forms against non-parametric ones; his results, for cross-sectional household-level data for the US, suggested that the parametric forms may not be sufficiently flexible to provide valid results in certain applications. Urga and Walters (2003) contrasted dynamic formulations of the translog and the logit cost share model and confirmed a poor performance of the former, concluding that this one cannot be explained only by a mis-specification of the model or the inclusion of nonenergy fuel s price-unresponsiveness. Recently, with pooled data from several countries, Roy et al. (2006) estimated long-run substitution and own-price elasticities for the paper and the iron and steel sector, and aggregate manufacturing industries (i.e., no interfuel substitution), and reported a wide variation across countries and industries. Another recent study of interfuel substitution using (static and dynamic versions of the) translog and logit cost share models is Madlener (2004), with a focus on Switzerland. The price elasticities and elasticities of fuel substitution for the private and industrial sector from that study are reported in Table 5 as an illustration and comparison with our results. Table 5 Price-elasticities and elasticities of substitution for Switzerland, private and industrial sector Input Private sector ( ) Industrial sector ( ) Price elasticities Oil 0.02 (0.55) 0.43** (5.17) Electricity 0.08* (2.54) 0.12** (3.46) Gas 0.61** (2.58) 0.43** (4.64) Elasticities of substitution OilElectricity 0.01 (1.00) 0.45** (5.09) OilGas 0.01 (0.47) 0.02 (0.74) ElectricityOil 0.02 (1.00) 0.16** (5.09) ElectricityGas 0.10** (2.87) 0.04** (6.30) GasOil 0.03 (0.47) 0.05 (0.74) GasElectricity 0.58** (2.87) 0.38** (6.30) Notes: t-statistics in parentheses; bold font for those elasticities statistically significant at the 5% (*) and 10% (**) level, respectively. 4 Econometric methodologies used Ever since the seminal paper by Engle and Granger (1987), cointegration analysis has increasingly become the favored methodological approach for analyzing time series data containing stochastic 13

16 trends. If the data generating processes (DGPs) underlying the time series are integrated of order one, I(1) (which is the case for most economic variables), or higher, usual regression analysis can lead to spurious results. Instead of taking first differences of the data, which was the common prior solution but leads to a loss of long-run information, this problem can be tackled by identifying possibly existing stationary linear combinations of two or more non-stationary time series. Such stationary linear combinations indicate common stochastic trends (i.e. cointegration), which can be interpreted as longrun equilibrium relationships between the variables considered and, therefore, according to the Granger representation theorem (Engle and Granger, 1987), can be characterized by being generated through an error correction mechanism. A methodology for cointegration analysis that has received considerable attention is the maximum likelihood (ML) system estimation and testing procedure developed by Johansen (1988, 1995). In contrast to single-equation methods, the Johansen approach does not impose the assumption of a unique cointegrating vector a priori and efficiently estimates the short-run dynamics simultaneously along with the long-run relationship. Moreover, restrictions to the cointegration space can be applied and tested for. Furthermore, Johansen et al. (2000) provide an extension for incorporating structural breaks in the cointegrating vectors. In a simulation study, Gonzalo (1994) finds superior finite sample properties of the Johansen ML estimator when compared to four other commonly used estimation methods in cointegration analysis, even when the dynamics are not known and the errors are non- Gaussian. This approach is explained in more detail in Section and applied to industrial electricity demand on a subsectoral level in Section 5.1. Most previous studies on the estimation of energy demand elasticities are based on time series data. Since the introduction of cointegration analysis, the spurious regression problem has been accounted for in most of these studies. However, traditional unit root and cointegration tests in a pure time series context are known to suffer from the problem of very low power and size. Hence, increasing the number of observations by including a cross-sectional dimension helps to reduce this problem. The added cross-sections can be interpreted as repeated draws from the same distribution that increase power and hence permit more reliable statistical inference. Amongst others, Pedroni (1999, 2004) has developed an estimation and testing framework for cointegration analysis based on panel data. This approach is explained in more detail in Section and applied to residential electricity demand in Section 5.2. An alternative way of circumventing the problem associated with a very low power of unit root tests is the autoregressive distributed lag (ARDL) bounds testing approach to cointegration. This method, which was introduced by Pesaran and Shin (1999) and Pesaran et al. (2001), has received considerable attention over the past years. The advantage of this approach is that information regarding the order of integration of the variables included in the analysis is not necessarily needed. Hence, the pretesting for unit roots, which is required for other cointegration approaches, can be omitted. Rather, the significance of a long-run relationship is tested using critical value bounds, which are determined by the two extreme cases that all variables are I(0) (the lower bound) and that all variables are I(1) (the upper bound). This approach is explained in more detail in Section and applied to residential natural gas demand in Section Unit root tests Before turning to the single cointegration approaches in more detail, this section briefly outlines the methods used for checking the unit root properties of the variables included in the analysis. This is necessary as an order of integration of at least one, I(1), is a prerequisite for including them in most cointegration tests Unit root tests based on time series data It is well known that the standard ADF (Augmented-Dickey-Fuller) and PP (Phillips-Perron) tests suffer from a considerable loss of power in cases where the DGP underlying a series is a near-unit root (trend-)stationary process. Furthermore, the existence of structural breaks, if not accounted for, 14

17 distorts unit root test results (see Perron, 1989). Therefore, we apply more recent efficient unit root tests, which to a certain extent overcome the deficiencies of the traditional unit root tests: the ERS (Elliott-Rothenberg-Stock, see Elliott et al., 1996) test for non-breaking series and the LLS (Lanne- Lütkepohl-Saikkonen, see Saikkonen and Lütkepohl, 2002; and Lanne et al., 2002) test for variables containing structural breaks, both of which have good power properties compared to alternative tests. The ERS test is a modification of the ADF test in that the series under consideration is detrended by using a GLS (Generalized-Least-Squares) regression before the actual unit root test is conducted. The LLS test works in a similar manner, but also takes into account a level shift in the deterministic term. In a Monte Carlo simulation study, Lanne and Lütkepohl (2002) show that their LLS test enables remarkable gains in size and power and performs best in comparison to a number of other unit root tests that incorporate level shifts at some known points in time Unit root tests based on panel data Recently a number of panel unit root tests have been developed by various authors. Amongst the most common ones are the LLC (Levin et al., 2002), the UB (Breitung, 2000), the IPS (Im et al., 2003), the ADF-Fisher (Maddala and Wu, 1999), and the PP-Fisher (Maddala and Wu, 1999). All the mentioned tests are based on the following AR(1) panel regression model: x x X u i = 1, 2,, N; t = 1, 2,, T, (15) it, i it, 1 i it, it,, where δ i are the autoregressive parameters, X i,t represents exogenous variables and/or fixed effects and cross-section-specific time trends and u i,t are stationary error terms. In the case that δ i < 1, x i is referred to be weakly trend-stationary. In contrast, if δ i = 1, x i is considered to be a unit root process. The five aforementioned tests can be divided into two different groups with respect to the assumptions about the δ i. On the one hand, the LLC test and the UB test assume that all crosssections have a common unit root, i.e. δ i = δ for all i. On the other hand, the IPS test, the ADF-Fisher test and the PP-Fisher test all assume that the δ i can be heterogeneous across the cross-sections. Due to space limitations we refer the reader to the original articles for further details on these tests. In the case where the test results for a variable in levels indicate a rejection of the null hypothesis, whereas the test results for the same variable in first differences does not reject the null at conventional significance levels, this variable is assumed to be integrated of order one, denoted I(1). 4.2 Approaches to cointegration analysis Johansen Maximum Likelihood For estimating the industrial electricity demand function outlined in Section 2.2, we apply the Johansen ML approach. Taking the natural logarithm of Eq. (2) and adding a stochastic error term yields the linear double-log specification of our econometric model for the long-run electricity demand function e c dt v p t 0 v t p t t, (16) where e t = ln(e t ), v t = ln(v t ), p t = ln(p t ), c 0 is a constant, dt is a deterministic time trend and ε t is the error term. β v and β p are the constant elasticities of economic activity and price, respectively, with regard to electricity demand. The Johansen ML system approach is briefly outlined as follows: As the basic DGP, consider the unrestricted three-variable vector autoregression model of order p, VAR(p), defined as Y T S I A Y U, (17) t t t t j t j t j 1 p 15

18 where Y t is a (3 x 1)-dimensional vector containing the endogenous I(1) variables, Y t = [e t, v t, p t ], the A j are (3 x 3)-dimensional parameter matrices, and U t is a three-dimensional Gaussian white-noise process representing the error terms. The deterministics are a constant (δ), a linear trend (T t ), a shift dummy (S t ), and impulse dummies (I t ). The vectors Φ and Ξ and the matrix Θ contain the corresponding parameters. Eq. (17) can be rewritten as a vector error correction model of order (p 1), VECM(p 1), specified as p1 t t1 j t j t t j1 Y Y Y I U, (18) where Π = (I A 1 A p ) and Γ j = (A j A p ) for j = 1, 2,, (p 1). If the variables in Y t are indeed cointegrated, Π has reduced rank, rk(π) = r, and can be decomposed into Π = αβ. Here β spans the space of r cointegrating vectors, so that β Y t-1 represents up to (k 1) cointegration relationships, whereas α contains the corresponding adjustment coefficients. 11 Using the trace test provided by Johansen (1994, 1995) and Johansen et al. (2000), respectively, depending on whether structural breaks are incorporated or not, it is then possible to determine how many r (k 1) distinct eigenvalues (λ i ) exist that are significantly different from zero, and hence how many cointegrating relationships are present in β. The likelihood ratio trace statistic (λ Trace ) is given by Trace k ir1 T ln 1 ˆ i, (19) where k is the number of endogenous variables and T is the number of observations. The null hypothesis is the existence of at most r cointegrating relations (0 r k) against the alternative of (r + 1) cointegrating relations. If the null hypothesis is rejected on the first level (i.e. r = 0), but accepted on the second level (i.e. r 1), we can conclude that there exists only one cointegrating vector, which leads to the following most general specification of the VECM(p 1): 12 et 0, e 1, e e p 1 t j e, t vt 0, v 1, v et 1 vvt 1 ppt 1 Dt 1 j vtj It v, t, (20) j1 p t 0, p 1. p p t j p, t where the term in squared brackets is the error correction term (ECT t-1 ). The deterministic term (D t ) in the most general case is D t = c + d 1 t + d 2 s. The restricted constant (c) is always included, the linear time trend (t) is included whenever significant, and the shift dummy (s) is included only when a structural break occurs in one of the series. I t is a vector of impulse dummies and Θ is a matrix containing the corresponding parameters. The Γ j are the (p 1) coefficient matrices for the lagged differences of the three endogenous variables. Following Lütkepohl and Krätzig (2004, pp ), we include a shift dummy for the time of any break date τ (tau) and further intervention dummies for τ, τ + i,, τ + (m 1), where m is equal to the lag length of the corresponding VAR (m = p). Estimation of Eq. (20) yields the estimates of the long-run equilibrium demand relationship, i.e. the estimated cointegrating vector, which equals zero in the long-run equilibrium ECT e ˆ v ˆ p Dˆ, (21) t t v t p t t where ECT t stands for the error correction term, which represents the deviation from the long-run equilibrium in any period t. In order to attain the short-run elasticities we can then proceed by 11 Note that in the software package JMulTi 4.24, which we use in cases where shift dummies are included in the cointegrating vector (otherwise we use EViews 6), the constant is restricted to the cointegrating vector. 12 Note that this specification is sufficient, since in all cases where we did find a long-run relationship, our inference has always led to a model with one cointegrating vector only. 16

19 estimating a standard single-equation error correction model (ECM) based on the long-run relationship obtained from estimation of Eq. (20): l m n (22) e ECT e v p, t 0 t1 e, i ti1 v, i ti p, i ti t i0 i0 i0 where γ 0 is a constant, α is the loading coefficient, γ e,i, γ v,i and γ p,i are the short-run parameters and ε t is a white-noise error term. By deleting insignificant coefficients, a parsimonious specification of the short-run dynamic equation can be searched for. An additional advantage of a cointegrated VAR setting is the possibility of further analysis on the dynamics of the examined relationship. Hence, before estimating the short-run elasticities in the single-equation ECM framework, we employ tests on Granger-causality and examine the impulse response functions Panel cointegration For the residential electricity demand relationship described in Section 2.3, we examine the possibility of using the panel cointegration approach by Pedroni (1999, 2004). Taking natural logarithms of Eq. (4) and adding an error term and the cross-sectional dimension (i > 1) yields the econometric specification of our long-run residential electricity demand function: e c y p i = 1, 2,, N; t = 1, 2,, T, (23) it, i yi, it, pi, it, it,, where e i,t = ln(e i,t ), y i,t = ln(y i,t ), p i,t = ln(p i,t ), c i are country-specific fixed effects and ε i,t are the error terms, which are interpreted as deviations from long-run equilibria. The country-specific slope coefficients β y,i and β p,i are the long-run elasticities to be estimated with regard to income and electricity price, respectively. Hence, this specification allows for the cointegrating vectors to vary across the single countries of our panel. Pedroni (1999, 2004) extends the cointegration testing approach of Engle and Granger (1987), which is based on examining the stationarity properties of the residuals from a regression using I(1) variables, to a panel data setting. Following this approach, Eq. (23) is estimated by OLS, and the residuals obtained, ˆi, t, are used for the following auxiliary autoregression for every i: n i (24) ˆ ˆ ˆ w, i, t i i, t1 i, t i, tj i, t j1 Where the ρ i are autoregressive parameters, n i are the lag lengths in the augmented case, and w i are stationary error terms. Under the null hypothesis of no cointegration, the ˆi, t should be found to be I(1). This is the case if H : 1, i 1,..., N 0 i is not rejected. For each of the seven statistics provided by Pedroni (1999, 2004) this is the null hypothesis. Concerning the alternative hypothesis, the tests can be divided into two classes. For the so-called (within-dimension) panel statistics tests (i.e. the Panel-v, the Panel-PP-ρ, the Panel-PP-t and the Panel-ADF-t test) the alternative hypothesis is H : 1, i 1,..., N, 1 i whereas for the so-called (between-dimension) group statistics tests (i.e. the Group-PP-ρ, the Group- PP-t and the Group-ADF-t test) the alternative hypothesis is 17

20 1 H : 1, i 1,..., N. i Hence, the group statistics tests are less restrictive in the sense that they allow for heterogeneity across countries. Given that the panel cointegration tests indicate a significant cointegration relationship, we apply the fully modified OLS (FMOLS) and the dynamic OLS (DOLS) group-means panel estimators proposed by Pedroni (2000, 2001) for estimating the long-run demand relationship characterized by Eq. (4). Both estimators allow for standard normal inference through incorporating corrections for endogeneity bias and serial correlation. 13 While the FMOLS estimator employs a semi-parametric correction using y i,t, p i,t and ˆi, t, the DOLS estimator employs a parametric approach by augmenting Eq. (23) with lead and lag dynamics of y i,t and p i,t as follows: li e y p y p it, i yi, it, pi, it, yil,, it, l pil,, it, l it, lli lli li (25) where l i is the lead and lag length, μ i is the country-specific fixed effect and υ i,t is the error term. The group-means FMOLS and DOLS panel estimates for the slope coefficients, ˆ FMOLS G and their corresponding t-statistics, t ˆ FMOLS G and t ˆ DOLS G, are calculated as follows: ˆ t N m ˆm Gy, yi, N i1 and ˆ DOLS, G 1 (26) N ˆm 1, ˆm Gy t yi, ˆ t (27) N i1 1 (28) N m ˆm G, p p, i N i1 N ˆm 1, ˆm G p t p, i (29) N i1 where the superscript m is a place holder denoting either the FMOLS or the DOLS estimation method; ˆy, i and ˆp, i are the country-specific estimates of income and price elasticity, respectively. Considering both the FMOLS and the DOLS panel approach has the advantage of being able to provide some evidence on the robustness of our results with regard to the estimation method. In order to estimate the short-run elasticities and the speed of adjustment to long-run equilibrium, the residuals from the cointegrating regressions, which resemble the deviation from long-run equilibrium in any given period t, are used as error correction terms (ECT) in country-specific and panel error correction models (ECM). The latter takes on the form e ECT y p (30) m m m m m m it, 0, i i it, 1 yi, it, pi, it, it,, where m denotes the estimation method (FMOLS or DOLS), γ 0,i is a country-specific constant, α i is the speed of adjustment coefficient, ECT i is the aforementioned error correction term lagged by one period, γ y,i and γ p,i are the short-run income and price elasticities, respectively, and ν i,t the error terms. Note that in order to ensure an error correction mechanism via adjustments of electricity consumption, α i has to be negative. 13 Harris and Sollis (2003) provide an excellent exposition on this topic. 18