Economy-wide Estimates of Rebound Effects: Evidence from Panel Data.

• Author: Adetutu, Morakinyo O.

1. INTRODUCTION

   There appears to be a consensus within the energy policy community about the contributions of energy efficiency improvements towards reducing global energy consumption and greenhouse emissions. Protagonists of energy efficiency improvement often highlight its non-costly nature, arguing that the resulting decrease in energy use may not require higher energy prices or result in slower economic growth. However, a strand of literature starting with the early works of Brookes (1979) and Khazzoom (1980) argues that the underlying assumption that energy efficiency improvements yield proportionate reduction in energy consumption is misleading. This view was recently elucidated by Saunders (2013) who argued that over time, rebound effects (RE) could potentially result in the partial or total erosion of energy savings arising from improved energy efficiency. (1)

   Since its inception, the RE literature has grown significantly, but controversies remain about its magnitude, mechanisms and the most appropriate approach to measuring it. Clearly, the debate has been more intense regarding macroeconomic RE since it approximates the net effect of different mechanisms that are complex and interdependent, and whose effects may vary over time and across efficiency sources. This possibly explains the scarcity of macroeconomic RE studies. (2) Moreover, the few economy-wide studies use different empirical and theoretical approaches, with most of them covering different time periods. As expected, given the differences in methodological approaches and data sets, these studies are non-comparable. In particular, Dimitropoulos (2007) showed that the use of diverse models/methodologies and the lack of a widely accepted rigorous theoretical framework have contributed immensely to the controversies surrounding RE.

   Understanding the nature and estimating economy-wide RE is vitally important for a number of reasons. First, the key issues associated with RE, especially global climate change, require top-down analyses of different economies over long time frames, which microeconomic or bottom-up analysis may be inappropriate to handle. This is because effective climate change policies require multilateral co-operation and co-ordination among different countries, thus, there is need for a comparative and consistent measurement of RE across different countries. (3) However, the available pool of studies (4) is inadequate in the context of the broad, extensive and systematic cross-country analysis required to tackle climate change. Secondly, this analysis is crucial given the important role that energy efficiency plays in the derivation of future energy forecasts and in the formulation of wider energy policy measures. Possibly, due to the dearth of reliable and consistent estimates of RE, most of these forecasts and policy measures hardly account for RE, implying that such forecasts might have underestimated future energy consumption, if RE is significant or large. Thirdly, a broad and extensive cross-country analysis of RE, such as this one undertaken here, is crucial to the evolution of more useful debate on RE.

   As far as is known, no multi-country study of macroeconomic RE across several countries has been undertaken to provide greater clarity on the RE debate using a sound technique and consistent dataset. This is an important gap in literature given that RE arising from aggregate consumption and production by households and firms are likely to be of great significance and implication (Kydes, 1999).

   In this paper, our objective is to provide estimates of aggregate RE for a panel of 55 countries over the period 1980 to 2010 using a two-stage procedure. First, we estimate energy efficiency using Stochastic Frontier Analysis (SFA). Secondly, by employing a dynamic panel framework, and using the efficiency scores from the SFA model, we estimate short-run and long-run RE. To give an insight into our main empirical findings, we find significant RE magnitudes across sampled countries, especially non-OECD countries. However, an encouraging sign is the declining RE magnitudes for some countries over the sample period which possibly indicates the potential for energy efficiency in the future.

   The remainder of the paper proceeds as follows. Section 2 presents the modelling approach. Specifically, we present a two-stage estimation approach including the parametric SFA approach for estimating energy efficiency, and a generalized method of moments (GMM) model for estimating short-run and long-run RE. In section 3, the dataset is described in detail. Section 4 presents the empirical results from both models and the resulting rebound effects. We offer our concluding remarks and recommendations in Section 5.

2. MODELLING AND THEORETICAL APPROACH

   Our aim is to estimate RE within a macroeconomic production function by accounting for the increase in energy use arising from energy efficiency gain. This efficiency saving is expected to impact energy consumption, resulting in energy conservation which is defined as:

   [[eta].sup.E] = [dln E/d Ef] (1)

   where E is energy consumption and Ef represents energy efficiency. [[eta].sup.E] is also referred to as efficiency elasticity of energy demand, which allows us to derive RE:

   R = 1 + [[eta].sup.E] (2)

   Intuitively, RE represents the size or percentage of the energy efficiency savings that is lost such that if energy consumption E falls by 40% due to a 40% increase in energy efficiency, then [[eta].sup.E] = -1 and R = 0. In the same vein, if a 100% increase in energy efficiency yields only a 40% fall in energy consumption, then R = 0.6. Given these discussions above, it is easy to see that five rebound conditions are possible (Saunders, 2000; Wei, 2010):

   * R > 1or [[eta].sup.E] > 0: 'Backfire' occurs as energy consumption increases due to improvements in energy efficiency;

   * R =1 or [[eta].sup.E] = 0: Full rebound as energy demand remains unchanged in the face of energy efficiency gains;

   * 0

   * R = 0 or [[eta].sup.E] = - 1: Zero rebound implies a one-to-one or unit relationship between energy consumption and efficiency improvements;

   * R

   Now we turn to the multi-stage approach to estimating RE. The key objective is the econometric estimation of the efficiency elasticity [[eta].sup.E] and we proceed as follows.

   Stage One: Energy Efficiency Estimation

   Our starting point is the estimation of energy efficiency (Ef) using the stochastic frontier analysis (SFA) (Aigner et al., 1977 and Meeusen and van den Broeck, 1977). The SFA allows for a composed error term which contains a one-sided error term to measure inefficiency in addition to the traditional two-sided error term which captures random noise. A number of studies have estimated efficiency in aggregate energy consumption. One of such is Filippini and Hunt (2011) who demonstrated the need for an econometric estimation of efficiency when estimating aggregate energy efficiency for 29 OECD countries using an energy demand SFA. The parametric estimation of energy efficiency using SFA is underscored by criticisms and inappropriateness of using energy intensity as a proxy for energy efficiency (see Filippini and Hunt, 2011; Saunders, 2013). More recently, Filippini and Hunt (2012) also estimated energy efficiency in residential energy demand for a panel data of 48 U.S states using an input requirement function (IRF).

   Although we employ the SFA, this study differs from the studies mentioned above by estimating a production technology using an input distance function (IDF) (5), rather than an IRF. With an IRF, the objective is to radially contract energy use in an input vector for a given level of output, conditional on energy prices and other exogenous factors. By implication, other factor inputs are implicitly assumed to be fixed; hence studies relying on an IRF have arguably estimated short-run energy efficiency. However, an IDF seeks to radially contract energy and the other factor inputs in the input vector for a given level of output. This approach is consistent with long term energy efficiency estimation since in reality one would expect efficiency gains to alter relative/effective prices of factor inputs, resulting in factor substitution as firms adjust input combinations to take advantage of energy efficiency improvements.

   Our proposed production technology can be represented by the input requirement set I(y) which represents the set of Kinputs x[member of][R.sup.+] which can produce a set of R outputs y[member of][R.sup.+] i.e. I(y)={x[member of][R.sup.+] : x can produce y}. We can obtain an input distance function equation (see Kumbhakar and Lovell (2003):[D.sub.I](y', x', t) which takes a value of 1 if a country is efficient (i.e. on the frontier) but is greater than 1 when a country is inefficient [D.sub.I][greater than or equal to] 1, so that:

   ln [D.sub.I](y,x,t)-u = 0 (3)

   where u [greater than or equal to]0. This input distance function is non-increasing in outputs, non-decreasing and homogeneous of degree 1 in inputs. By adopting a translog functional form in conjunction with the elements, i = 1,..., N; t = 1,..., T, and applying the linear homogeneity property, equation 3 can be written in panel data context: (6)

   -ln [X.sub.Kit] [approximately equal to] TL[(y,x/[X.sub.K],t).sub.it] + [v.sub.it] - [u.sub.it] (4)

   where TL[(y,x/[X.sub.K],t).sub.it] represents the technology as the translog approximation to the log of the distance function; while [v.sub.it] is the traditional symmetric error term representing sampling, specification and measurement errors, while [u.sub.it] represents the non-negative inefficiency component of the composed error term.

   The energy efficiency of each country in each period is then estimated as the conditional expectation of the one-sided error term, exp(u), given the composed error, v- u so that the energy inefficiency of each country i in period t is given by:

   [TE.sub.it] = E [exp(-...