فرم تابعی و کشش تقاضای انرژی کل: یک روش پانل غیرپارامتریک برای 17 کشور عضو سازمان همکاری و توسعه

This paper studies whether the commonly used linear parametric model for estimating aggregate energy demand is the correct functional specification for the data generating process. Parametric and nonparametric econometric approaches to analyzing aggregate energy demand data for 17 OECD countries are used. The results from the nonparametric correct model specification test for the parametric model rejects the linear, log-linear and translog specifications. The nonparametric results indicate that the effect of the income variable is nonlinear, while that of the price variable is linear but not constant. The nonparametric estimates for the price variable is relatively low, approximately − 0.2.

There has been an increased awareness and interest on the impact of human activities on the world's climate in recent years, especially through emission of greenhouse gases. A lot of focus in the discussions of curbing climate change has been on issues related to energy use and clean production. For example, there has been an intense debate among energy policy analysts on how policies can promote efficient energy use, less dependence on fossil fuels, and how these have contributed to reduce emissions of greenhouse gases. The central point in this discussion concerns the behavioral response among households and firms to various policy reforms. That is, how do households and firms change their energy consumption as a result of changes in, for instance energy taxes and/or incomes? In order to answer such questions, which are a prerequisite for designing an efficient policy, knowledge about behavioral response is needed. In other words, we need knowledge about price and income elasticities. Most of the elasticities that are used come from econometric models of energy demand. A look at the literature on energy demand reveals that there exist numerous econometric models, of different types, starting with simple static models to more general dynamic ones. It is interesting to note that most of these models are linear or log-linear models. However, whether the assumed functional form is appropriate or not for the underlying energy demand data generating process (DGP) is usually not tested for. Hence the conclusions drawn must be viewed as conditional on the assumption that energy demand is linear. Aggregate Energy demand studies can be found in the following surveys; Hartman (1979), Bohi (1981), Bohi and Zimmerman (1984), Dahl (2005) as well as Atkinson and Manning (1995). The consequences of a mis-specified model on the parameter estimates cannot be over emphasized, as it leads to bias and inconsistent estimates. To the best of our knowledge, only two studies exist that study the choice of functional form for energy demand models, Zarnikau (2003) and Xiao et al. (2007). Zarnikau (2003) focuses on electricity demand at the household level for the USA. He studied three functional forms for household electricity demand (linear, log-linear and trans-log) and uses a nonparametric specification test developed by Härdle and Manmen (1993) and Zheng (1996) to test the parametric models. The test results from his study reject each of the three functional forms as the correct specification for the household electricity demand (regressors used are price of electricity, price of natural gas, income and heating degree days). Xiao et al. (2007) on the other hand adopted a Bayesian model selection criterion (that of the Deviance information criterion (DIC)) proposed by Spiegehalter et al. (2002) and applied it to the same data set as in Zarnikau (2003). The result from their study indicates that the AIDS1 and trans-log models are superior to the log-linear model, which in turn is better than the linear model. However, none of these studies makes extensions to panels nor uses aggregate data on energy demand using fully nonparametric modeling that allows for all possible nonlinearities and interactions among the regressors, while controlling for boundary bias at the same time. There is thus a scope for further investigations into the correct functional forms in estimating energy demand with aggregate data. Further, Zarnikau (2003) and Xiao et al. (2007) did not consider cointegration relationships between the dependent variable and the regressors and hence implicitly assume a long run relationship to exist without testing for it. In this paper we will test for cointegration in panels, using the Westerlund (2007) error-correction approach. Getting the correct functional form is a very difficult task to do, since economic theory does not provide a guide regarding the correct functional specification. In this paper we therefore model energy demand more flexibly by applying a fully nonparametric approach. Particularly the local linear kernel estimator is used in estimating energy demand for 17 OECD countries from 1960 to 2006. Modeling energy demand in a fully nonparametric sense will avoid the issue of functional mis-specification since we do not restrict the functional form a priori. The main objective of this paper is thus to assess the commonly used log-linear functional form for energy demand models (our focus here is on long run energy demand model) which is the appropriate functional form for such models. We applied the panel error correction model to study if there is cointegration between energy demand, real price of energy, real income per capita and the effect of climate. This paper is organised as follows: Section 2 deals with the literature review for the study; Section 3 is the modeling of aggregate energy demand for 17 OECD countries. The data and the econometric analysis are presented in 4 and 5 concludes the paper with a summary of the findings and some proposals for future research.

In this paper we applied a nonparametric approach to investigate whether the log-linear functional form usually assumed in the empirical literature in estimating aggregate energy demand models is appropriate. To do this we used a panel data on aggregate energy consumption in 17 OECD countries. The log-linear parametric model could not pass the nonparametric correct model specification test. Since the test itself does not give any guidance concerning what parametric specification is to be chosen. One possible option is to use a less restrictive modeling approach, such as the nonparametric approach, which provides an excellent option in this regard. The results from the nonparametric estimation indicate a non log-linear relationship between income and consumption, but with a log-linear relationship between the price of energy and energy consumption. Furthermore, it turns out that the coefficient of determination is higher in the non-parametric than in the log-linear parametric model. The estimates for the price variable from the nonparametric estimation appear to be log-linear but vary over time; the price elasticity is − 0.18 at low price levels and decreases only slightly (increases in absolute terms) to − 0.19 at higher price levels. The income elasticity on the other hand is fluctuating relatively much with respect to the income level, although the trend is decreasing in the sense that the income elasticity falls as income rises. In a nutshell we can say that for a panel of developed countries the simple log-linear functional specification appears to be an incorrect functional form to use for aggregate energy demand modeling, more so with respect to the income variable. The log-linear parametric model performed badly in capturing the price elasticity when the benchmark is the estimates from the more flexible nonparametric model. For the income elasticity, the log-linear parametric specification performed almost equally as poorly, if not worse, using the nonparametric estimates as the benchmark. An alternative linear and translog specification also fails the functional specification test, which implies that both the linear and the translog specification are also inappropriate. It will be very interesting to investigate this on individual country basis using time series data, but the nonparametric approach is data driven and therefore requires a long time series data, which we do not have at the moment. An alternative may therefore be to apply a semi-parametric approach, where we assume a log-linear parametric relation between energy consumption, price and other important covariates, while we model the income variable nonparametrically. As regards to policy implications, the results from the nonparametric model shows that the response of energy consumption to price changes is relatively low, compared to the values usually used in energy policy discussions, which are based on results from parametric models. One implication is that the potential policy impact on energy consumption from, say, an energy tax may be exaggerated. Furthermore, since the response to income seems to vary across income levels with both a trend and a fluctuation around the trend it should be clear that this may have serious consequences on the success of energy policy. Again, we may very well over- or underestimate the effect of policy, especially the long run effects depending on what assumptions we make concerning economic growth. Finally, it is important to treat the results here with caution because the nonparametric approach is also prone to most of the problems associated with the parametric model, except that of functional misspecification.