A general equilibrium model of macroeconomic rebound effect: A broader view

doi:10.1016/j.eneco.2021.105232

Energy Economics

Volume 98, June 2021, 105232

https://doi.org/10.1016/j.eneco.2021.105232 Get rights and content

Highlights

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The more price-inelastic is the energy supply, the more likely is the full rebound.
•
A model with a single energy service does not allow negative rebound effects.
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In the simplest models, the long-run rebound effect is greater than the short-run.
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In neutral technical change, homogeneous production function leads to backfire.
•
Backfire is a concern when energy use is polluting and energy intensity is high.

Abstract

Economists recognize that energy efficiency improvements generate behavioral responses that reduce potential energy savings (rebound effect) and may even increase energy consumption (backfire). Much work has been done to explain rebound economics. Nevertheless, many of the important issues still do not have a clear answer, that is, under which circumstances the rebound is more powerful or weaker and whether the long-run effect is greater or less than the short-run effect. Furthermore, it is still unclear in which situations backfire is definitely a problem. In order to answer these questions, the article expands the Wei (2010) general equilibrium model, including any number of energy services and non-energy inputs and endogenizing the output price. Furthermore, in order to analyze the effects of a neutral technical change on energy consumption, a parameter of non-energy inputs productivity is also included. The analysis corrects some results presented in Wei (2010) and provides several new findings. Regarding the energy-augmenting technical change, the main findings are the importance of the energy supply and the use of more than one energy service in the model for the rebound size. Moreover, in the simplest models, the long-run rebound effect is greater than the short-run effect. Regarding the neutral technical change, it is highlighted that the use of homogeneous production functions generates backfire. Moreover, we find that backfire is definitely a problem in terms of welfare only in situations where energy consumption is based on highly polluting energies and where output is highly energy-intensive.

Introduction

Energy efficiency improvements are often seen as an important tool for reducing energy consumption. However, economists have long recognized that energy efficiency improvements generate behavioral responses that reduce potential energy savings (rebound effect) and may even increase energy consumption (backfire). The emerge of the rebound effect literature can be traced back to Jevons (1865). Jevons (1865) noted that England's coal consumption increased considerably after energy efficiency improvements in the steam engine, rather than decreasing as expected. The modern era of rebound economics was initiated by Khazzoom (1980) and Brookes, 2000, Brookes, 1990, Brookes, 1978, who also defended the backfire hypothesis. Saunders (1992) was one of the first authors to use the Neoclassical Growth theory to explain rebound economics, arguing that economic theory allows backfire in some cases.

Since then, much work has been done to explain rebound economics. Simply put, we can divide the theoretical literature on the rebound effect into macroeconomic rebound models and microeconomic rebound models (Gillingham et al., 2016). Macroeconomic rebound models are derived through the Neoclassical Growth theory or Neoclassical Production theory, such as Saunders, 2008, Saunders, 2000a, Saunders, 1992, Howarth (1997), Wei, 2010, Wei, 2007, Sorrell (2014), Zhang and Lawell (2017), Brockway et al. (2017), and Lemoine (2020). Microeconomic rebound models are derived through Neoclassical Consumer theory, such as Borenstein (2015), Ghosh and Blackhurst (2014), Chan and Gillingham (2015), and Sorrell and Dimitropoulos (2008). This article focuses exclusively on the macroeconomic rebound effect.

Since the beginning of the rebound theory, there has been a debate about its magnitude (Dimitropoulos, 2007). Several literature reviews have been carried out and they all argue that there are the most diverse empirical results, ranging from negative rebound effects (super-conservation) to backfire (Chakravarty et al., 2013; Gillingham et al., 2016; Jenkins et al., 2011; Maxwell et al., 2011; Sorrell, 2007; Stern, 2020; van den Bergh, 2011). Turner (2013) argues that one of the reasons for this is the lack of solid understanding of the theoretical foundations of the wide range of mechanisms that govern the rebound effect.¹ Turner (2013) further argues that the identification of these mechanisms is surely as, if not more, important than developing empirical studies. As we will show in this paper, the assumptions about the model and, consequently, about the rebound mechanisms that are included in it, can change the rebound size.

The main issue would be to identify under which circumstances energy efficiency gains would lead to backfire. Empirical evidence shows that the rebound effect is particularly large when the energy efficiency gains are accompanied by improvements in the productivity of non-energy inputs (neutral technical change), tending to generate backfire (Saunders, 2015; Saunders, 2013; Saunders, 2005; Saunders, 1992). As Sorrell (2009, 2007) points out, rebound effects may be particularly large when energy efficiency improvements are associated with general-purpose technologies, which have potential for use in a wide variety of products and processes and have strong complementarities with existing or potential new technologies. Sorrell (2009, 2007) also argue that this energy efficiency improvement was used by Jevons and Brookes, that is, repetitively steam engines and electric motors, in order to support the backfire hypothesis. In fact, the neutral technical change, also known as the innovation rebound effect (Gillingham et al., 2016), is the rationale behind many of the backfire claims in the literature (Gillingham et al., 2016; Jenkins et al., 2011; Sorrell, 2009; Sorrell, 2007). However, the conditions under which the innovation effect results in backfire are not yet clear.

In addition, there has been extensive discussion of the need to mitigate the rebound effect (Font Vivanco et al., 2016; Freire-González, 2020; Freire-González and Puig-Ventosa, 2015; Maxwell et al., 2011; Ouyang et al., 2010; van den Bergh, 2011). This perspective is based on the fact that energy consumption contributes heavily to several of the most important environmental problems, especially climate change. That is, energy consumption is seen as a strong generator of external costs, which in turn decreases welfare. Nevertheless, several authors have described why such a perspective may be mistaken, since energy efficiency gains can increase economic output and so welfare (Hanley et al., 2009; Saunders, 1992; Saunders and Tsao, 2012; Tsao et al., 2010; Wei and Liu, 2017). Therefore, looking at it exclusively from the perspective of welfare, backfire may not be a concern. As far as we know, no study has aimed to analyze the innovation rebound effect from a perspective of welfare economics.²

The literature has also been debated whether the short-run rebound would be greater or less than the long-run rebound. Some empirical works find that the long-run effect is greater than the short-run effect, such as Small and Van Dender (2007), Odeck and Johansen (2016), Wang et al. (2016), Yang et al. (2019), and Belaïd et al. (2018). Some theoretical works corroborate these findings, such as Saunders (2008) and Wei (2007). However, other empirical works, such as Allan et al. (2007), Turner (2009), Saunders (2013), Lu et al. (2017), Adetutu et al. (2016), and Yan et al. (2019), found that short-run effect can be greater than long-run effect, which seems to contradict previous theoretical studies. In this sense, Wei (2010) develops a theoretical model where the short-run effect can be both greater and lesser than the long-run effect. However, as will be shown in this article, the comparison between the long-run and short-run effects made by Wei (2010) only allows the long-run rebound to be greater than the short-run rebound. Thus, the conditions under which the long-run rebound effect is greater or less than the short-run effect are not yet clear.

Therefore, many of the important theoretical issues on the macroeconomic rebound effect still do not have a clear answer. One of the main reasons for this is that the existing theoretical models have a limited capacity to explain the mechanisms that govern macroeconomic rebound. First, because most macroeconomic rebound models focus exclusively on direct rebound effect (Brockway et al., 2017; Saunders, 2008; Saunders, 2000a; Saunders, 1992; Sorrell, 2014; Zhang and Lawell, 2017). That is, the models are generally partial equilibrium models, being composed of single energy service and with all exogenous prices. Only a few theoretical works incorporate some indirect rebound effects, such as the general equilibrium models developed by Wei (2010, 2007) and Lemoine (2020). Furthermore, according to Stern (2020), most empirical studies using econometric methods are partial equilibrium approaches (e.g., Adetutu et al. (2016) and Yan et al. (2019)) that do not include all the mechanisms that can influence the rebound effect.

Second, because most of the macroeconomic rebound models incorporate only a single representative energy service (no work that using more than one energy service to explain the economics of the macroeconomic rebound effect was found³). However, as we will see in this article, the use of a single energy service limits the rebound size, that is, in this case, super-conservation is not allowed.

Third, most of the macroeconomic rebound models use specific production functions, such as Leontief, Cobb-Douglas, Constant Elasticity of Substitution (CES), and many others (Brockway et al., 2017; Lemoine, 2020; Saunders, 2008; Saunders, 2000a; Sorrell, 2014; Wei, 2007; Zhang and Lawell, 2017). In addition, as highlighted by Broberg et al. (2015), in general, empirical studies using computable general equilibrium models employ CES production function or one of their special cases (Allan et al., 2007; Hanley et al., 2009; Lu et al., 2017). Nevertheless, one of the main contributions of Saunders' work (Saunders, 2008; Saunders, 2000a, Saunders, 2000b) was to show that the specification of the production function considerably influences the rebound size. One of the few works to use generic production functions is Wei (2010). However, this author bases his analysis on the functions of marginal product of inputs, rather than on the functions of inputs demand and of output supply, which makes it difficult to draw some important conclusions.

Therefore, the objective of the article is to propose a macroeconomic rebound effect model that allows identifying:

•
the theoretical mechanisms that govern the rebound effect;
•
under what circumstances the long-term rebound effect is greater or less than the short-term rebound effect.
•
under what circumstances the rebound is more powerful or weaker;
•
in which situations the backfire is a concern in terms of welfare.

For this, this article expands the general equilibrium model developed by Wei (2010), including any number of energy services and non-energy inputs and endogenizing the output price. Furthermore, in order to analyze (in a simplified way) the innovation rebound effect, a parameter of non-energy inputs productivity is also included. However, in order to facilitate the understanding of the rebound concept, we will describe the macroeconomic rebound effect through generics demand and supply functions (i.e., generic functional forms), and not through the functions of marginal product of inputs as in Wei (2010).

The paper is structured as follows. Section 2 presents the energy–energy services relationship. Section 3 expands the general equilibrium model developed by Wei (2010). Section 4 defines the rebound effect. Section 5 shows the macroeconomic rebound effect from energy-augmenting technical change (called the reallocation rebound effect). Section 6 shows in a simplified way the innovation rebound effect. Section 7 provides cautions and limitations related to the analysis. Section 8 draws conclusions. Furthermore, five appendices give a detailed description of the model and the in-depth proof of some important results.

Section snippets

Energy services

Consumers do not demand energy per se, but rather the services generated by this energy, called energy services.⁴

The model

Let a representative firm that produces a global output (Y) using m non-energy inputs (q_i) and n energy inputs (E_i), which are associated with n energy services (S_i): $Y = f (\vec{τq}, \vec{εE})$ , where f(.) is the production function,⁶ $\vec{τq}$ represents the vector [τ₁q₁, …, τ_m q_m], τ_i is the productivity of

Rebound effect definition

First, it should be noted that, in this section, we will deal only with the long-run effect, since the short-run effect is analogous (in Appendix A and Appendix B the short-run effect is developed). In addition, as the rebound effect is generally defined through elasticities, then we will denote ${\dot{η}}_{j} (i) = \frac{di}{dj} \frac{j}{i}$ and $η_{j} (i) = \frac{\partial i}{\partial j} \frac{j}{i}$ as the elasticity of the function “i” with respect to the variable “j”.

The rebound effect is the difference between the actual energy savings (AES) and the potential energy

Reallocation rebound effect

Decomposing the effects of eq. (8) ( ${\dot{η}}_{ε_{i}} (S_{j})$ ), we find the long-run rebound effect (see Appendix A): $R_{ε_{i}} = - σ_{i} η_{P_{S_{i}}} (S_{i}) - \sum_{j \neq i} σ_{j} η_{P_{S_{i}}} (S_{j}) + \sum_{j = 1}^{n} \sum_{x = 1}^{n} σ_{j} η_{P_{S_{x}}} (S_{j}) {\dot{η}}_{ε_{i}} (P_{E}) + \sum_{h = 1}^{m} \sum_{j = 1}^{n} σ_{j} η_{P_{Q_{h}}} (S_{j}) {\dot{η}}_{ε_{i}} (P_{q_{h}}) + \sum_{j = 1}^{n} σ_{j} η_{P_{Y}} (S_{j}) {\dot{η}}_{ε_{i}} (P_{Y})$

Where R_{ε_i}(S_i) = − σ_iη_{P_{S_i}}(S_i) is the direct effect, $R_{ε_{i}} (S_{j}) = - \sum_{j \neq i} σ_{j} η_{P_{S_{i}}} (S_{j})$ is the cross-price effect, $R_{ε_{i}} (P_{E_{j}}) = \sum_{j = 1}^{n} \sum_{x = 1}^{n} σ_{j} η_{P_{S_{x}}} (S_{j}) {\dot{η}}_{ε_{i}} (P_{E})$ is the energy price effect, $R_{ε_{i}} (P_{q_{h}}) = \sum_{h = 1}^{m} \sum_{j = 1}^{n} σ_{j} η_{P_{Q_{h}}} (S_{j}) {\dot{η}}_{ε_{i}} (P_{q_{h}})$ is the input price effect and $R_{ε_{i}} (P_{Y}) = \sum_{j = 1}^{n} σ_{j} η_{P_{Y}} (S_{j}) {\dot{η}}_{ε_{i}} (P_{Y})$ is the output price effect. All rebound effects, other

The backfire hypothesis

Since the innovation effect is the rationale behind many of the backfire claims in the literature (Gillingham et al., 2016; Jenkins et al., 2011; Sorrell, 2009; Sorrell, 2007), it is important to determine under what circumstances this effect results in backfire. In order to reduce complexity, we will use the simplest model to analyze the innovation rebound effect. It is noteworthy that this model has been used in most works that examine the innovation effect (Saunders, 2015; Saunders, 2013;

Cautions and limitations

Several cautions and limitations were already exposed in Wei (2010), such as the use of perfect competition hypotheses and the static comparison between market equilibriums. However, since our model does not incorporate all the economic mechanisms that govern the rebound effect, some caveats are still needed.

First, we assume a global economy or a closed economy. However, Koesler et al. (2016) find that the rebound effect on a global scale is less than the rebound effect of the economy in which

Conclusion

In expanding Wei's (2010) general equilibrium model, this article has attempted to contribute to broadening the theoretical foundation of macroeconomic rebound effects. The article raised several new findings and corrects some results presented in Wei (2010). These findings can serve to assist the intuitive understanding of results generated from empirical studies.

The article demonstrated several theoretical mechanisms that govern the rebound effect (i.e., direct effect, cross-price effect,

Acknowledgments

This research was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance code 001. We would like to thank Gustavo Alves Soares, Luciano Dias Losekann, and Mauricio Silva De Carvalho for enriching suggestions and comments for the research. We would also like to thank the anonymous reviewers for their comments, which helped to improve this article. Of course, responsibility for errors and omissions remains with the authors.

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A general equilibrium model of macroeconomic rebound effect: A broader view

Highlights

Abstract

Introduction

Section snippets

Energy services

The model

Rebound effect definition

Reallocation rebound effect

The backfire hypothesis

Cautions and limitations

Conclusion

Acknowledgments

Energy Econ. Model. Indust. Energy Consump.

Energy Policy

Energy Policy

Energy Policy

Energy Policy

Energy Policy

Curr. Opin. Environ. Sustain. Energy Syst.

Energy Policy

Energy Res. Soc. Sci.

Energy Policy

J. Public Econ.

Ecol. Econ.

Energy Policy Energy Efficiency Policies Strat. Regular Pape.

Ecol. Econ.

Energy Econ.

Eur. Econ. Rev.

Energy Econ.

Transp. Res. A Policy Pract.

Energy Policy

J. Clean. Prod.

Energy Policy

Energy Policy

Energy Econ.

Technol. Forecast. Soc. Chang.

Energy Policy

Ecol. Econ.

Energy Policy

Energy Econ.

Renew. Sust. Energ. Rev.

Energy Policy