Residential and Industrial Energy Efficiency Improvements: A Dynamic General Equilibrium Analysis of the Rebound Effect.

• Author: Kahouli, Sondes

1. INTRODUCTION

   While the rebound effect due to energy efficiency improvement (EEI) has been extensively studied, empirically and theoretically, in both manufacturing and residential sectors, all or almost all these works, to the best of our knowledge, dealt with rebound effect in each sector separately. Nevertheless, energy efficiency improvements in one sector could spill-over into the second sector, affecting the rebound effect on sectoral energy consumption and on global energy consumption. The purpose of the paper is to fill the gap by building a theoretical model in order to investigate the channels through which energy efficiency improvements in industrial sectors could affect energy consumption in the residential sector, and vice-versa, both in the short- and long-term. It also focuses on the impact of nesting structure as well as the size of elasticities of substitution of production and utility functions on the magnitude and the transitional dynamic of rebound effect.

   There is a large body of theoretical and empirical literature dealing with energy efficiency and rebound effects that are expected to happen. In general, energy efficiency refers to the amount of output that can be produced with a given input of energy. It is usually measured as the amount of energy output for a given energy input and listed as a percentage between 0% and 100%. (1)

   In many cases, improvements in energy efficiency result in energy savings that are lower than expected. Sometimes, it can even induce an increase in energy consumption. This phenomenon is called the rebound effect or Jevons' paradox (Jevons, 1865). It appears when consumers do not simply replace an old product with a more efficient one which fulfills the same function, but upgrade to a larger product and often involves supplementary energy consumption that offsets part of the energy savings. So far, the rebound effect has been mainly associated with energy use and the question of how energy efficiency improvements affect energy consumption. Khazzoom (1980, 1987) and Brookes (1990) proposed a precise definition of the rebound effect, which can easily be applied to resource use in general. According to this definition, if technological progress makes equipment more energy efficient, less energy is needed to produce the same amount of product or service. However, the amount of product or service does not usually stay the same. As the equipment becomes more energy efficient, the cost per unit of product or service that is produced with this equipment falls which, in turn, increases the demand for the product or the service. Since the 1980s, several empirical studies have confirmed the existence of rebound effect with respect to, both, residential and firms' energy demand. The economic literature recognizes the existence of rebound effect but disagrees about its magnitude.

   The definition of the rebound effect encompasses different mechanisms that may reduce energy savings derived from the improvements in energy efficiency (Greene et al., 1999; Sorrell and Dimitropoulos, 2008; Orea et al., 2015). Through the three typologies of rebound effects as identified in the economic literature, i.e. direct, indirect and economy-wide rebound effect, this definition distinguishes a microeconomic and macroeconomic views of such phenomenon.

   The direct rebound effect represents a pure price effect. It refers to the fact that improved energy efficiency for a particular energy service (2) will decrease the effective price of that service and should, therefore, lead to an increase in its consumption (Khazzoom, 1980). This will tend to offset the reduction in energy consumption provided by the efficiency improvement. For consumers, the direct effect of a price decrease may be decomposed into a substitution effect and an income effect. In addition to this direct rebound effect, an indirect one can also occur. In fact, the lower effective price of the energy service may lead to an increase in the demand for other goods, services. It also may lead to economic growth since it may induce an increase in factors of production that require energy for their provision. The size of the indirect effect for a consumer is dependent on the share of the consumer's total income spent on energy services. For firms in a given sector, indirect effect results from both the increased demand for non-energy inputs to their production process as a result of increased demand for production, and the effect of the lower cost of one sector's output on production costs of other sectors. The structural changes in the economy due to the variation of prices of goods and services subsequent to the improvement of energy efficiency represents the economy-wide rebound effect (cf. Appendix B.1). It means that a fall in the real price of energy services may reduce the price of intermediate and final goods throughout the economy, leading to a series of price and quantity adjustments, with energy-intensive goods and sectors likely to gain at the expense of less energy-intensive ones

   There is a large body of literature estimating the size of the rebound effect in residential and industrial sectors (Dubin et al., 1986; Frondel et al., 2008; Greene et al., 1999; Klein, 1987, 1988; Nadel, 1993; Schwarz and Taylor, 1995; West, 2004; Greening et al., 2000; Sorrell and Dimitropoulos, 2008; Sorrell et al., 2009; Van den, 2011; Zhou et al., 2018). (3) Usually formal theoretical analyses of rebound effects focuses on partial equilibrium settings that hold some prices fixed. These studies assume that there are no changes in prices or nominal incomes following the efficiency improvement, and that the impacts are limited to the direct market for household energy use. This approach gives a partial equilibrium figure which is generally known as the direct rebound effect. Some researches like for example Dufournaud et al. (1994) considered full general equilibrium economy-wide rebound effects from increased energy efficiency in the household sector. It examines the impacts of increasing efficiency in domestic wood stoves. Druckman et al. (2011), Freire-Gonzalez (2011) and Thomas and Azevedo (2013a,b) use a fixed price input-output model to study indirect rebound effects resulting from household income variation induced by energy efficiency improvements and spent on nonenergy commodities. A few other studies consider changes in energy use in production, as well as household consumption but are still studying the issue based on a partial equilibrium approach as it fails to incorporate endogenous prices, incomes or factor supply effects. As a consequence, there is a need to consider general equilibrium models in order to study consequences of energy efficiency and the associated rebound effect in a more comprehensive context.

   Indeed, for a long time Jevons (1865) has been especially worried about general equilibrium channels. More recently, his concerns have been reinforced by insights from computable general equilibrium models suggesting a potential for strong rebound effects through economy-wide or alternatively indirect channels (Allan et al., 2009). In this context, many have called for theoretical research to illuminate these channels (Dimitropoulos, 2007; Turner, 2009; Borenstein, 2015). Therefore, there has been extensive investigation of the economy-wide rebound effects resulting from energy efficiency improvements in production using a computable general equilibrium (CGE) modelling approach (cf. Appendix A.1 and Brockway et al. (2021)). However, very few studies have attempted to measure the economy-wide impacts of energy efficiency improvements in the household sector (Lecca et al., 2014). More interestingly, there are also very few studies about rebound effect which consider interactions between production and consumption sectors. For instance, Lemoine (2020) developed an analytically general equilibrium framework to study the implications of improved energy efficiency (4) but he did not take into account feedbacks between production and consumption sectors.

   This paper is intended to fill the gaps by building a general equilibrium framework where we allow for interaction between residential and industrial sectors in order to study consequences of energy efficiency improvement, in particular, the magnitude and the short- and long-run transitional dynamic of the rebound effect. We consider a variety of possible feedbacks affecting energy use in, both, residential (household) and production (industry) sectors. In particular, we focus on bi-directional energy spillover effects expected to spread in the residential and industrial sectors and we look at channels through which these spillovers operate. We mainly highlight the role played by labor and income channels. We quantify the rebound effect through numerical simulation after calibrating our model on the U.S. economy.

   In this framework, we also investigate how important is the choice of, both, the nested structure of functions, i.e. production function for firms and utility function for households, as well as the size of the elasticity of substitution. Regarding the size of the elasticity of substitution in the production function, we consider the elasticity of substitution between capital/labor, and energy and between capital and labor. As for the utility function, we study the impact of a variation in the inter-temporal elasticity of substitution and in the elasticity of substitution between consumption and energy. Such choices are particularly important for analyzing the magnitude and the short- and long-run transitional dynamics of rebound effect through its impact on the demand for energy and other inputs. Indeed, by studying possible nesting structures for the constant elasticity of substitution, Van der Werf (2008)) argues that the size of elasticities in the production function is a crucial parameter for climate policy modeling. This may also apply for energy...