An empirical analysis of the welfare implications of the direct rebound effect

Improving the energy efficiency of an energy service, such as lighting, cooling, or driving, makes the service cheaper, normally leading consumers to demand more of it. This additional demand is known as the direct rebound effect. Rebound is often perceived negatively because it usually eliminates some of the expected energy savings. To determine if the direct rebound effect is welfare reducing, we undertake a cost-benefit analysis that compares the consumer surplus gained from direct rebound to the associated increase in negative externalities. Focusing on driving, the results reveal that the direct rebound effect is welfare reducing in most cases, as the consumer surplus gains were smaller than the increase in external costs. These external costs include greenhouse gas emissions, air pollution, congestion, and accidents. Finally, we show that overlooking the costs and benefits of the direct rebound effect can lead to a misleading cost-benefit evaluation of energy efficiency, particularly when rebound effects are large.


Introduction
Energy is consumed to provide an energy service, such as lighting, cooling, or driving, while capital equipment is used to convert the energy into an energy service. A passenger car, for example, is used to convert gasoline into driving or vehicle kilometers traveled (VKT). Similarly, a light bulb is used to convert electricity into lighting.
When the energy efficiency of capital equipment improves, economic agents tend to adjust their behavior by consuming more of the energy service. This behavioral response, which reduces the expected energy savings from improved energy efficiency, is known as the rebound effect. Economic agents will normally alter their behavior when energy efficiency improves because the relative price of the energy service decreases. This change in relative prices leads to a change in demand. The price of the energy service is often called an Bimplicit price^because it is not directly seen by consumers. For example, a consumer may see the price of electricity on their bill, but it would not show the implicit price of lighting or air conditioning. The implicit price of an energy service depends on both the price of energy and the efficiency of the capital equipment (in addition to other factors). The implicit price of driving a car, for example, depends on the price of gasoline and the energy efficiency of the vehicle. Just as a fall in the price of gasoline would result in a fall in the implicit price of driving, a more energy efficient car will also make it cheaper to drive. This normally leads to increased VKT, giving rise to the rebound effect. 1 Although the rebound effect is the economically expected outcome of improved energy efficiency, as noted by Jevons (1865) more than a century ago, many studies have discussed the need to mitigate rebound (for example, Herring and Roy 2007;Ouyang et al. 2010;Gloger 2011;Maxwell et al. 2011;van den Bergh 2011;Otto et al. 2014;Brown and Wang 2017). Rebound is often perceived as a negative phenomenon that works against the intended objectives of energy efficiency: namely to reduce energy consumption and greenhouse gas (GHG) emissions.
However, a few studies have noted that the rebound effect may be welfare enhancing (Hobbs 1991;Borenstein 2015;Chan and Gillingham 2015). Chan and Gillingham (2015) developed a theoretical microeconomic framework for studying the welfare implications of rebound. They showed that in the absence of externalities, the rebound effect is always welfare enhancing. With externalities, however, the welfare implications depend on which is bigger: the benefit from additional consumption of the energy service or the cost associated with that additional consumption.
Measuring the welfare implications of rebound is critical because it affects the welfare implications of energy efficiency policymaking. An energy efficiency improvement that has larger benefits than costs (in other words, welfare enhancing) may turn out to be welfare reducing after accounting for the rebound effect. Many economic evaluations of energy efficiency, however, have been done through a narrow lens that focuses only on the upfront capital costs and the monetary benefits from reduced energy consumption (Clinch and Healy 2001). Such an incomplete approach to evaluating energy efficiency overlooks the costs and benefits of rebound, which, as we will demonstrate, can lead to a misleading evaluation of energy efficiency.
This study is, to the best of our knowledge, the first to quantify the benefits and costs of the direct rebound effect for a large number of countries and consider the welfare implications. Our empirical analysis initially focuses on driving as the energy service due to several factors. First, road transport accounts for a large share of final energy consumption in most economies around the world (IEA 2016a). Second, many governments have successfully implemented energy efficiency policies in this sector. According to the IEA (2016b), 74% of the global road transport sector is covered by energy efficiency policies, mostly in the form of fuel economy standards. 2 Third, estimating the rebound effect from more energy efficient passenger cars is relatively straightforward since many countries rely on a single source of fuel (gasoline in most countries) to power their vehicles. This is described by Hunt and Ryan (2014) and Chan and Gillingham (2015) as 'single-energy singleservice.' Estimating the rebound effect becomes more complicated when there are multiple sources of energy and multiple services involved, such as the case of electricity, which provides lighting, heating, and air conditioning, in addition to many other services.

Literature review
More than a century ago, Jevons (1865) conjectured that an improvement in energy efficiency would not necessarily lead to reduced energy use. However, little attention was given to this effect until many years later following a paper published by Khazzoom (1980), which suggested that energy efficiency standards may not lead to significant energy savings because of the increased demand for the energy service. Dublin et al. (1986) stated that Benergy-efficient appliances reduce the marginal price of the services they deliver,^and that this results in Benergy savings that are smaller than those engineering techniques generally project^(p. 310). Furthermore, Frey and Labay (1988) showed there was a consistent shortfall between forecasted and actual energy savings following an energy retrofit. They referred to this phenomenon as the take-back effect and suggested that the shortfall may be as large as 35%. Henly et al. (1988) discussed the rebound effect and described it as Bentirely consistent with economic behavior^(p. 164). Brookes (1990Brookes ( , 1992Brookes ( , 1993 discussed the fallacies associated with energy efficiency because of the rebound effect, focusing on claims that energy efficiency represented a fifth fuel. Researchers now classify the rebound effect into different types: direct, indirect, and economy-wide rebound. The different types of rebound effects are best illustrated through an example. Consider a consumer that upgrades to a more efficient passenger car. The relatively lower price of driving due to the more efficient car will likely spur the owner to drive more, resulting in higher fuel consumption. This is the direct rebound effect. The relatively lower price of driving will also free up some of that consumer's income, which can be spent on other goods and services. Given that other goods and services generally require energy to be produced, an increase in their consumption will stimulate greater energy consumption in other areas of the economy. This is the indirect rebound effect. The direct and indirect rebound effects can alter the prices and consumption patterns of goods and services across the economy, together giving rise to an economy-wide rebound effect. Greene (1992) was one of the first to measure the direct rebound effect from light-duty vehicle efficiency improvements in the USA. He estimated its size to be between 5 and 15% using price elasticities. Other seminal articles that measured the size of the direct rebound effect include Berkhout et al. (2000) for the Netherlands, Greening et al. (2000) for the USA, and Roy (2000) for India. All these studies relied on the use of energy price elasticities as proxies for measuring the size of the direct rebound effect.
It has become common to measure the direct rebound effect using energy price elasticities. Arguably, the most widely used definition states that the direct rebound effect is equal to the negative of the energy price elasticity (Sorrell and Dimitropoulos 2008). With this definition in hand, any estimated energy demand model that provides an estimate for the energy price elasticity would also implicitly provide an estimate for the direct rebound effect.
Other studies have used a general equilibrium approach instead to measure rebound (direct, indirect, and economy-wide). Dufournaud et al. (1994) were the first to model the rebound effect using an applied general equilibrium model, focusing on the rebound effect from energy efficient wood burning stoves in the Sudan. Subsequently, Grepperud and Rasmussen (2004) used a general equilibrium model to explore the size of the rebound effect in different sectors of Norway's national economy. General equilibrium methods have since been used in subsequent studies to measure economy-wide rebound effects, such as Liang et al. (2009) for China, Allan et al. (2009 for the UK, and Wei (2010) for the world economy. In addition to general equilibrium methods, bottom-up models have also been used by researchers to estimate economy-wide rebound effects, such as Barker et al. (2007) for the UK and Barker et al. (2009) for the world economy.
Questions on the size of the rebound effect have received significant attention from researchers in the energy economics literature. However, as noted by Azevedo (2014), the Bwelfare changes resulting from rebound have also largely been ignored^(p. 393). In a recent paper, Chan and Gillingham (2015) were the first to explore rebound's welfare implications. In their study, they presented a theoretical framework of how the direct rebound effect may influence energy efficiency's welfare implications. We build on their work by empirically estimating the costs and benefits of the direct rebound effect in 100 countries. This is done by calibrating demand curves for driving (that is, VKT) and combining them with external cost data on a country-by-country basis to conduct the welfare analysis.

Methodology
This study employs a partial equilibrium approach to measure the costs and benefits of the direct rebound effect for 100 countries. Our analysis does not consider the indirect or economy-wide rebound effects, which would likely require a calibrated computable general equilibrium model (or possibly a detailed bottom-up model) for each of the 100 countries, which is far beyond the scope of a single paper. Our partial equilibrium approach allows us to extend the analysis to 100 countries and is sufficient for modeling the direct rebound effect.
Our partial equilibrium analysis rests on calibrated demand curves for driving. The demand curves are used to estimate both the consumer surplus gained and the external costs exacerbated by the direct rebound effect. The benefits (the consumer surplus gains) are then compared to the costs (the exacerbated externalities) to determine whether the direct rebound effect is welfare enhancing.
We assume a 10% improvement in energy efficiency in the analysis that follows. However, it is worth noting that the size of the improvement (whether 5, 10, or 30%) does not alter the welfare outcomes significantly. For very large improvements in energy efficiency, however, the methods used in this paper become less useful as the constant elasticity functions may not adequately capture how consumers would respond.
Estimating the direct rebound effect using elasticities Our treatment begins with a general framework that links energy demand to energy service demand. As shown by Sorrell and Dimitropoulos (2008), If we consider driving as the energy service, S would be the demand for driving (measured in kilometers), η the average efficiency of gasoline vehicles (measured in kilometers per liter), and E the demand for gasoline (measured in liters).
Using the framework presented by Sorrell and Dimitropoulos (2008), the implicit price of driving (P S ) can be expressed as a function of the price of gasoline (P E ) and the level of energy efficiency (η). 3 Given the empirical nature of this study, we follow the approach used by Davis (2017), where he assumed that gasoline demand takes the form of a constant elasticity function. Davis (2017) calibrated the gasoline demand function for each country using price and demand data, and assumed a constant gasoline price elasticity of − 0.6. He then used the calibrated demand curves to estimate the deadweight loss and externalities associated with subsidies. In this paper, we employ the same functional form but use it to estimate the changes in surplus and externalities associated with the direct rebound effect. We also measure the welfare outcomes across a range of price elasticities instead of a single fixed elasticity.
Following the approach in Davis (2017), we define the following demand curve for gasoline: where A is a scale parameter and α the elasticity of gasoline demand with respect to its price.
We also define a constant elasticity demand curve for driving: where K is another scale parameter and β the elasticity of driving with respect to its implicit price. This functional form allows an improvement in the energy efficiency of passenger cars to manifest as a pure price effect (Greening et al. 2000).
According to Sorrell (2009), the direct rebound effect is often defined to be the elasticity of the energy service with respect to energy efficiency. Denoting the elasticity of a with respect to b by ε a, b , the direct rebound effect is therefore given by ε S, η . Using the constant elasticity function, we can show that: With our constant elasticity function, the direct rebound effect is equal to the negative of the elasticity of driving with respect to its implicit price (ε S;η ¼ −ε S;P S ¼ −β).
These elasticity relationships have already been demonstrated more generally by Sorrell and Dimitropoulos (2008), Hunt and Ryan (2014), and Chan and Gillingham (2015). Furthermore, they demonstrated that in a single-energy single-service case, the elasticity of driving with respect to energy efficiency would be equal to the negative of the energy price elasticity: In the single-energy single-service case, if the price elasticity of gasoline demand were estimated to be α = − 0.2, then the direct rebound effect would be ε S, η = 0.2. This implies that 20% of the expected energy savings would be lost due to the direct rebound effect. In fact, the direct rebound effect is usually expressed in terms of percentages. Thus, ε S, η = 0.2 would be interpreted as a direct rebound effect of 20%.
The energy price elasticity is not always a perfect proxy for measuring the direct rebound effect. It becomes a biased estimator when multiple energy sources and services are involved. Hunt and Ryan (2014) and Chan and Gillingham (2015) have proven that the direct rebound effect is equal to the negative of the energy price elasticity only in the single-energy single-service case. In the multipleenergy multiple-services case, different elasticity relationships emerge as demonstrated by Chan and Gillingham (2015): This relationship shows that the elasticity of the demand for driving with respect to its implicit price (ε S;P S ) reflects the size of the direct rebound effect even in the case of multiple-energy multiple-services. For this reason, the welfare results are presented for a range of elasticities, from ε S;P S ¼ −0:1 to ε S;P S ¼ −0:9, to account for cases where the gasoline price elasticity does not provide us with an indication of the size of the direct rebound effect.
In countries such as Saudi Arabia where almost all passenger cars are gasoline-based (IEA 2016a), the price elasticity of gasoline demand will provide a reliable estimate of the direct rebound effect. This is the same in India, where the primary fuel used by two-wheelers is gasoline. For such countries, the use of the energy price elasticity is suitable for estimating the direct rebound effect, as noted by Menon (2017) in the case of India. However, in countries such as France where consumers purchase both gasoline and diesel vehicles, the estimates will be less accurate. However, according to ExxonMobil (2016), gasoline is the primary fuel used in light-duty vehicles in most countries, and therefore the use of energy price elasticities for measuring the direct rebound effect is suitable in most cases.

Estimating the benefits of energy efficiency and rebound
When the energy efficiency of passenger cars improves, the implicit price of driving falls. The demand function for driving can then be used to predict the consumer surplus gained from this price decrease: The prices P S, B and P S, A reflect the implicit prices of driving before and after the improvement, respectively, while B CS denotes the total consumer surplus gained from improved energy efficiency. The total gain can be broken down into two smaller areas, as illustrated in Fig. 1. The first area B MS reflects the monetary savings from improved energy efficiency, holding the demand for driving fixed. It can be calculated as follows: where S 0 denotes the initial demand for driving before the energy efficiency improvement. On the other hand, S R denotes the demand for driving after the direct rebound effect occurs. The second area B R reflects the consumer surplus gained from additional driving. This can be calculated as follows: There is also a third benefit from improved energy efficiency. Since gasoline consumption is associated with external costs such as air pollution and GHG emissions (Parry et al. 2014), any reduction in gasoline consumption will lead to a reduction in these externalities. The benefit from reducing these external costs can be calculated by multiplying the fall in gasoline consumption (measured in liters) by the externalities of air pollution and GHG emissions (measured in US$ per liter), which are denoted by δ E and obtained from the IMF (2016).
B EC denotes the total benefit from lower external costs, E 0 the gasoline consumption before the energy efficiency improvement, and E NR the gasoline consumption after the improvement, assuming no rebound, which is estimated as follows: To summarize, the total benefit from improved energy efficiency includes the benefit from monetary savings, the benefit due to the consumer surplus gained from additional driving, and the benefit from reduced external costs, as shown by the following equation: Estimating the costs of energy efficiency and rebound Although energy efficiency delivers multiple benefits, there are also multiple costs that need to be accounted for. There is first the capital cost of an energy efficiency improvement. This can include the cost of the initial purchase, depreciation, and vehicle registration. In this paper, we assume that the capital cost is zero. We therefore conduct a welfare analysis of a costless, exogenous energy efficiency improvement-a common assumption in rebound studies. The goal of this assumption is to turn the focus towards an often overlooked cost: the cost of the direct rebound effect. The cost of the direct rebound effect can be broken down into two segments. The first segment is due to the energy-related external costs that arise from the additional consumption of gasoline above a scenario in which there was no rebound. This cost can be calculated by multiplying the additional consumption by the externalities of air pollution and GHG emissions.
C E denotes the total energy-related cost of the direct rebound effect, while E R denotes the demand for gasoline following rebound, which can be estimated through the following equations: The second segment is due to the external costs that arise from the increase in VKT. The direct rebound effect implies that consumers are driving more, leading to greater congestion and accidents. We can estimate this cost by multiplying the additional driving by the externalities of congestion and accidents (measured in US$ per kilometer), which are denoted by δ S . As mentioned previously, δ E and δ S are obtained from the IMF (2016). where C S denotes the total service-related cost of the direct rebound effect. Thus, the total cost of the direct rebound effect (C R ) is equal to the energy-related external costs plus the service-related external costs.
Given that the upfront capital costs are assumed zero (C c = 0), the total cost of an energy efficiency improvement (C EE ) is therefore equal to the total cost of the direct rebound effect.
Estimating the welfare implications of energy efficiency and rebound The welfare implications of energy efficiency and rebound are governed by the relative sizes of the benefits and costs. For the direct rebound effect, the welfare implications are determined as follows: The direct rebound effect is therefore welfare enhancing when its benefit-to-cost ratio (BCR R ) is greater than one, that is, when the consumer surplus from additional driving outweighs the associated external costs.
Similarly, the welfare implications of an energy efficiency improvement with zero upfront capital costs are determined as follows: An efficiency improvement is therefore welfare enhancing when its benefit-to-cost ratio (BCR EE ) is greater than one.

Welfare implications when prices deviate from private cost
If gasoline were sold at private cost, there would be no need to account for the impact on the government. However, gasoline is taxed by some governments and subsidized by others. Deviations in the price of gasoline from private cost can therefore affect government spending/revenues and consequently the welfare results.
As noted by Borenstein (2015), the savings that a consumer gains from improved energy efficiency may be different from the economy-wide savings because of non-marginal-cost pricing. 4 For example, if the private cost of a liter of gasoline were $2, but the consumer only pays $1, then the consumer will only gain $1 for each liter of gasoline saved. However, the economy-wide monetary savings would be $2 since the government, which was subsidizing the gasoline, would also gain $1.
We account for the impact of improved energy efficiency on the government, assuming no rebound initially, as follows: where G NR denotes the gain or loss to the government from energy efficiency under a zero rebound scenario, P E * the international price of a liter of gasoline, which is obtained from Platts (2016), and P E the domestic Bprice at the pump^, obtained from the World Bank (2016). We account for the impact of the direct rebound effect on the government (G R ), through the following equation: To include the government in the welfare analysis of rebound, the absolute value of the variable G R is added to either the benefits (when G R is positive) or costs (when G R is negative) in Eq. (20).
We account for the net impact of the energy efficiency improvement (including rebound) on the government as follows: To include the government in the welfare analysis of energy efficiency, the absolute value of the variable G EE is added to either the benefits or costs in Eq. (21), depending on its sign.
Appendix 1 provides an example of how these methods are combined, using data specific to Saudi Arabia.

Data
All data are collected for the year 2010. The choice of study year was largely determined by the external cost data, which were estimated by the IMF (2016) for 2010. These external costs have likely changed in recent years for most countries, but to the best of our knowledge, there are no estimates for external costs on a country-bycountry basis more recent than 2010. The external cost data are arguably the most important input to our welfare analysis, and are directly taken from the IMF's (2016) database on 'Getting Energy Prices Right'. The IMF (2016) data originate from a study by Parry et al. (2014) that estimated the external costs of air pollution, GHG emissions, congestion, and accidents associated with driving on a country-by-country basis for the year 2010. We refer to air pollution and GHG emissions as energy-related external costs, while we refer to congestion and accidents as service-related external costs.
Determining whether a cost is internal or external can be tricky. For both congestion and accidents, there are internal and external components to each. An internal cost is one that consumers account for when making decisions regarding driving, while they do not account for the external costs that are ultimately borne by others. In the case of accidents, Parry et al. (2014) viewed the damage that drivers pose to pedestrians and cyclists as an external cost. On the other hand, they viewed the cost of injury to occupants in single-vehicle collisions as internal, because drivers consider such risks when deciding how much to drive. For multi-vehicle collisions, Parry et al. (2014) appeared to treat 25% of the damages as external. In the case of congestion, Parry et al. (2014) estimated the external cost by first calculating the total congestion cost to all passengers. Dividing the total cost by the traffic volume produces the average congestion cost per kilometer, which Parry et al. (2014) assumed is internal. On the other hand, differentiating the total cost with respect to the traffic volume produces the marginal congestion cost per kilometer. This marginal cost is made up of the average cost plus an additional term, which captures the cost to passengers of other vehicles, which is not taken into account by the driver (they only account for the cost to themselves, which is captured by the average cost). The additional term is therefore assumed by Parry et al. (2014) to be the external cost of congestion. More detailed information on the methods and assumptions behind the external cost data used in this paper can be found in Parry et al. (2014).
Gasoline demand data were collected from the IEA's (2016a) World Energy Statistics. Gasoline prices at the pump were from the World Bank (2016). Fuel economies, which were needed to convert the demand for gasoline into demand for driving, were also obtained from the IMF (2016). It should be noted, however, that the fuel economies in the IMF (2016) database were estimated on a region-by-region basis due to data limitations.
Finally, four different spot prices were used to measure the gasoline subsidy/tax in each country: For Middle Eastern countries, the average 2010 'free on board' spot price of 95-octane gasoline at Jebel Ali port (Platts 2016); for Asian countries, the 2010 gasoline spot price at Singapore port (Platts 2016); for European and African countries, the 2010 Eurobob gasoline spot price at Rotterdam port (Platts 2016); for North and South American countries, an average of the 2010 New York Harbor and U.S. Gulf Coast Conventional Gasoline spot prices (Reuters 2016).

Results and discussion
Energy efficiency is often thought to be welfare enhancing so long as the monetary savings from improved energy efficiency are greater than the capital costs. However, as we have discussed, such thinking overlooks other important benefits and costs, mainly the impact of the rebound effect. In this paper, we quantify the benefits and costs of the direct rebound effect and demonstrate its welfare implications. We begin with the welfare results from the simplest case: a free energy efficiency improvement and zero rebound.
The welfare implications of a free energy efficiency improvement Given that the upfront capital cost of a free energy efficiency improvement is, by definition, zero, and that we assume zero rebound, the total cost of the improvement is therefore zero. As a result, such an improvement will always have larger benefits than costs and be welfare enhancing. The benefits stem from both the cash savings that consumers are rewarded with because of reduced gasoline demand and the associated reduction in gasoline-related external costs. The demand curve for driving in this simple case is perfectly price inelastic, so that the fall in the implicit price of driving due to improved efficiency does not stimulate any additional demand for driving. As a result, VKT remains fixed and there are no changes in the service-related external costs.
The welfare implications of the direct rebound effect The direct rebound effect was found to be welfare reducing in most countries, as shown in Table 1, in which the welfare results are presented across a range of elasticities. The elasticities in question are the elasticities of the demand for driving with respect to its implicit price (ε S;P S ), which reflect the size of the direct rebound effect. For example, an elasticity of ε S;P S ¼ −0:3 reflects a direct rebound effect of 30%. For countries where driving can be described as single-energy single-service, this elasticity is also equal to the gasoline price elasticity (ε E;P E ). The results marked by * in Tables 1 and 2 reflect the welfare results for ε S;P S ¼ ε E;P E , where the gasoline price elasticities were obtained from Dahl (2012). However, for some countries, the gasoline price elasticity may not accurately capture the direct rebound effect because of the existence of multiple fuels for driving, and therefore ε S;P S ≠ε E;P E . The welfare results are thus presented for a range of elasticities, from ε S;P S ¼ −0:1 to ε S;P S ¼ −0:9, or in other words, for direct rebounds effects of 10 to 90%.
The welfare results in Table 1 suggest that regardless of the size of the direct rebound effect, the welfare implications remain largely unchanged (minor decreases in the benefit-to-cost ratio at larger elasticities are not visible in Table 1). Most countries were found to have welfare reducing direct rebound effects following a 10% improvement in energy efficiency. Furthermore, the direct rebound effect was found to be considerably more welfare reducing in countries that had some combination of low gasoline prices and medium to high external costs. Low gasoline prices imply that the consumer surplus gained from the same percentage improvement in energy efficiency is lower than it could have been at higher prices (see Fig. 2). Thus, when energy efficiency improves in a country with low fuel prices, the additional fall in the price of driving because of improved efficiency provides little benefit to consumers since driving is already very cheap. High external costs also play an important role. Unlike the external cost of GHG emissions, which is the same for all countries, the external costs of congestion and accidents vary markedly. On the one hand, the cost of congestion estimated by Parry et al. (2014) depended on both how much time is wasted in traffic and the monetary value of that time, which in turn is a function of income. The higher the income level in a country, the higher the cost of congestion. On the other hand, the cost of accidents they estimated depended on both income and road safety levels. In summary, countries with low gasoline prices, medium to high congestion costs, and/or medium to high accident costs were found to have the worst (that is, with the smallest benefit-to-cost ratio) direct rebound effects.
Is the direct rebound effect welfare reducing more often than not, even for improvements in the energy efficiency of other energy services? An improvement in the efficiency of lighting or cooling for example would give rise to a rebound effect that generates external costs in air pollution and GHG emissions only (although there may be other minor external costs). We can roughly approximate the potential welfare implications of such an improvement by setting the external costs of congestion and accidents to zero and then reestimating the benefit-to-cost ratio of the direct rebound effect from the previous analysis (see Appendix 2 for more details). The results reveal welfare enhancing direct rebound effects in most cases when the external costs of congestion and accidents are set to zero, suggesting that direct rebound may be welfare enhancing for other energy services.
There may be benefits associated with the direct rebound effect that have not been captured in our analysis. These benefits may be thought of as external or social benefits, in analogy to the external costs that are considered in this paper. External benefits would reflect welfare gains that are not captured by consumer surplus (Schwartz 2005). For example, the lower cost of driving due to improved efficiency may allow a person to drive greater distances each day, potentially providing access to better job opportunities in farther areas. These opportunities may then contribute to greater productivity in the economy. Such external benefits are difficult to estimate, but it is clear that they would improve rebound's welfare outcomes. Further studies on these external benefits, however, are needed before they could be incorporated into studies such as this one. Nevertheless, capturing these benefits will improve the welfare outcomes for the direct rebound effect. Therefore, the benefit-to-cost ratios presented in Table 1 may be thought of as lower bound estimates. Table 1 The benefit-to-cost ratio of the direct rebound effect following a 10% improvement in the energy efficiency of passenger cars. The * denotes the welfare results obtained using Dahl's (2012) elasticities

Country
Total external cost Gasoline price Benefit-to-cost ratio of rebound (B R ) for a range of elasticities (ε s;PS )    The overall welfare implications of a free energy efficiency improvement With our estimates of the benefits and costs of the direct rebound effect in hand, we are now able to assess the overall welfare implications of a costless, exogenous energy efficiency improvement, where the term 'overall' denotes that the direct rebound effect is accounted for.
As previously demonstrated, a free energy efficiency improvement will always be welfare enhancing with zero rebound. But what happens when rebound occurs? Table 2 presents the overall welfare implications of a free 10% improvement in the energy efficiency of passenger cars, accounting for the costs and benefits of the direct rebound effect. The welfare results demonstrate that in most cases, a free energy efficiency improvement will continue to be welfare enhancing, even when accounting for the negative impact on welfare due to the direct rebound effect. There are however a few countries where a free energy efficiency improvement becomes welfare reducing because of the direct rebound effect. This occurs because these countries had direct rebound effects that were welfare reducing to a degree that overturned the welfare enhancement initially generated by the energy efficiency improvement. As discussed previously, the countries that exhibited the worst direct rebound effects shared characteristics such as low gasoline prices, medium to high congestion costs, and/or medium to high accident costs.
The elasticities play an important role in determining the welfare outcomes of energy efficiency. In general, higher elasticities reduce the net benefits of energy efficiency for two reasons: First, they imply larger direct rebound effects, which in turn have a bigger impact on energy efficiency. Second, at higher elasticities, all benefits that stem from energy savings decrease as the rebound effect grows, turning negative for rebound effects beyond 100%. Table 2 shows that at an elasticity of − 0.1 (that is, at a direct rebound effect of 10%), a free energy efficiency improvement is welfare enhancing in all 100 countries. At 10%, the direct rebound effect is too small to have any significant impact. Moving to an elasticity of − 0.3, a free energy efficiency improvement becomes welfare reducing in Singapore  Table 2 The benefit-to-cost ratio of a free 10% improvement in the energy efficiency of passenger cars, accounting for the direct rebound effect. The * denotes the welfare results obtained using Dahl's (2012) . 2 The consumer surplus gained from additional driving (B R ) at high and low prices following the same fixed percentage improvement in energy efficiency Energy Efficiency (2019Efficiency ( ) 12:1987Efficiency ( -2010 factors play a role. Both Iran and Venezuela enjoyed the lowest gasoline prices and had Bmedium^accident and congestion costs. At an elasticity of − 0.6, the group of countries in which a free energy efficiency improvement was found to be welfare reducing grows to 16. At an elasticity of − 0.9 (that is, at a direct rebound effect of 90%), a free energy efficiency improvement was found to be welfare reducing in every country with Bvery high external costs^, which includes Japan, South Korea, Luxembourg, Singapore, Switzerland, Belgium, Denmark, Norway, and Turkey, in addition to a number of other countries.
In summary, the more price elastic the demand for driving, the larger the direct rebound effect. The larger the direct rebound effect, the more significant its impact on the cost-benefit evaluation of energy efficiency. When direct rebound effects are large, countries with very low gasoline prices and/or high external costs will likely find a free energy efficiency improvement in passenger cars to be welfare reducing.
How would the results change if the upfront capital costs of an energy efficiency improvement were accounted for? For countries where a free energy efficiency improvement was found to be welfare reducing, the welfare outcomes would not change. For example, at a direct rebound effect of 30%, an energy efficiency improvement in passenger cars would be welfare reducing in Singapore and Denmark (see Table 2). If we included the capital costs, then the welfare reduction would be even greater. However, the assessment that the improvement is welfare reducing in both countries does not change by accounting for the capital costs-it simply makes the improvement more welfare reducing. On the other hand, for countries where a free energy efficiency improvement is welfare enhancing, accounting for the capital costs may potentially overturn the result. If the benefit-to-cost ratio is only slightly greater that one, then it is very likely that accounting for the upfront costs, even if small, would overturn the result and produce a welfare reduction (that is, a benefit-to-cost ratio less than one).
On a final note, when there is an upfront cost to the energy efficiency improvement, the boost to income from improved energy efficiency becomes smaller, as discussed by Borenstein (2015). As a result, the income effect that contributes to rebound becomes weaker, leading to smaller rebound effects.

Conclusion
This paper is, to the best of our knowledge, the first to conduct a global empirical welfare analysis of the direct rebound effect. It also demonstrates empirically the extent of the impact that the direct rebound effect can have on the welfare outcomes of energy efficiency.
Our results reveal the direct rebound effect in driving to be welfare reducing in most countries. Because of high externalities, the costs of rebound are often found to exceed the benefits. Furthermore, we found that the direct rebound effect is generally worse (that is, more welfare reducing) in countries with some combination of low gasoline prices and medium to high congestion and accident costs.
The results carry important implications for energy efficiency policymaking given that most evaluations of energy efficiency do not account for the costs and benefits of rebound, which can produce a misleading picture of energy efficiency. In fact, in countries with the most welfare reducing direct rebound effects, we demonstrate that even a free energy efficiency improvement in passenger cars can become welfare reducing when accounting for rebound.
Our work has three key messages for policymakers. First, it highlights the importance of accounting for the rebound effect, which can have a considerable impact on cost-benefit analyses of energy efficiency policies. Policymakers should therefore be skeptical about any assessments of energy efficiency that do not include the costs and benefits of rebound.
Second, energy efficiency policies such as fuel economy standards are less likely to be welfare enhancing when the external costs of congestion and accidents are high, because rebound effects lead to higher levels of congestion and accidents. Energy efficiency policies for passenger cars may thus find greater success when combined with complementary policies that can mitigate congestion and reduce road accidents, such as better public transport to reduce congestion and speed enforcement cameras to reduce accidents (Tang 2017).
The third key message is that the rebound effect is not always welfare reducing, as some studies have suggested. The direct rebound effect from more efficient cars was found to be welfare enhancing in some cases. Furthermore, the direct rebound effect in other energy services (such as lighting and cooling) where total external costs are smaller appears likely to be welfare enhancing. More work in this area could help change the negative perceptions that the rebound effect holds in energy policy discussions. Moreover, if energy prices were increased (through taxes for example) such that all negative externalities are incorporated into the price, then any subsequent rebound effects would always be welfare enhancing, as noted by Azevedo (2014). By getting energy prices right, policymakers would not need to worry about rebound since it would only improve social welfare.
Ultimately, the primary goal of energy efficiency is to maximize welfare rather minimize energy consumption, and the rebound effect may help support that goal. The results presented in this paper could help inform the Bheated^debate around energy efficiency, which revolves around a number of key questions including the rebound effect (Brown and Wang 2017).
There remains huge scope for empirical research on the area of rebound and social welfare. The analysis presented in this paper focused on consumers and the government. We effectively assumed a market structure of perfect competition such that producer surplus falls to zero. Furthermore, the analysis did not consider the welfare implications of the indirect and economy-wide rebound effects. Future work could account for these factors, providing an even more complete picture of the welfare implications of energy efficiency and rebound. Future work could also examine rebound in other energy services, such as heating, cooling, and lighting. Future work would also benefit from the provision of more recent estimates for the external costs of energy consumption on a country-by-country basis, which is often the limiting factor in such studies. This will allow researchers to conduct cost-benefit analyses with more recent data, delivering insights that are more relevant and practical to policymakers. cents per kilometer. We can then calculate the total surplus gained by consumers because of this 10% improvement: Thus, the consumer surplus gained from the direct rebound effect would have been about half a percent of the total gain in consumer surplus. This is not surprising given that the elasticity in this example was small. For larger elasticities, the portion of consumer surplus gained from rebound rises considerably.
The final benefit of improved energy efficiency stems from the reduction in external costs through reduced gasoline demand, assuming no rebound. The IMF (2016) data shows that the external costs of GHG emissions and air pollution associated with each liter of gasoline consumption in Saudi Arabia were 8.3 and 2.5 cents per liter, respectively (δ E = 10.8 cents per liter). Assuming no rebound, a 10% improvement in energy efficiency would have reduced gasoline demand in Saudi Arabia to 24;165;966;000 1þ10% ð Þ ¼ 21; 969; 060; 000 liters. Thus, In summary, a 10% improvement in the energy efficiency of gasoline-based cars in Saudi Arabia would have yielded a total benefit of: The gasoline consumption associated with this new level of driving is obtained as follows: According to the IMF (2016), the external costs of air pollution and GHG emissions are δ E = 10.8. The increase in energy-related external costs can thus be calculated as follows: According to the IMF (2016), the external costs of congestion and accidents associated with each kilometer of driving in Saudi Arabia were 4.9 and 6.6 cents per kilometer (δ S = 11.5 cents per kilometer). The increase in service-related external costs can thus be calculated as follows: The total cost associated with the direct rebound effect is the sum of the energy-and service-related external costs: Assuming zero capital costs, the total cost of the improvement is equal to the total cost of the direct rebound effect: ðA:13Þ At this point, we can produce preliminary estimates of the benefit-to-cost ratio for both the direct rebound effect and the energy efficiency improvement. But these estimates would not account for the impact on the government, which may subsidize or tax gasoline. In the case of Saudi Arabia, an energy efficiency improvement will lead to a net gain for the government so long as the direct rebound effect is less than 100%, since any fall in gasoline consumption will lead to a fall in the implicit subsidy for gasoline. According to Platts (2016), the average international market price for gasoline at Jebel Ali port in 2010 was 54.1 cents per liter, compared to a domestic price of 16.0. Therefore, the total gain to the government because of the 10% energy efficiency improvement was: It is possible to isolate the part of this gain that is purely due to the direct rebound effect. In the case of Saudi Arabia, the direct rebound effect causes a loss to the government as it increases gasoline consumption above a scenario in which there was no rebound. This loss can be calculated as follows: The minus sign indicates that the rebound effect leads to a loss for the government.

Benefit-to-cost ratios
With all the necessary components calculated, we can proceed to estimating the benefit-to-cost ratio for the direct rebound effect, Given that the direct rebound effect leads to a cost for the government, G R is placed in the denominator of Eq. (A.16).
In the case of the energy efficiency improvement, Given that energy efficiency leads to a net gain for the government, G EE is placed in the numerator of Eq. (A.17). Thus, the benefit-to-cost ratio reveals that the benefits of a free energy efficiency improvement are considerably larger than the costs, even when accounting for the negative welfare reduction caused by the direct rebound effect.

Appendix 2
The potential welfare implications of the direct rebound effect in other energy services An improvement in the efficiency of lighting or cooling for example would give rise to a rebound effect that generates external costs in air pollution and GHG emissions only (there may be some other minor external costs). We can roughly approximate the potential welfare implications of such an improvement by setting the external costs of congestion and accidents to zero and then re-estimating the benefit-to-cost ratio of the direct rebound effect.
In the case of driving, most of the cost associated with the direct rebound effect is due to congestion and accidents. According to Parry et al. (2014), the average external cost of air pollution and GHG emissions together was 10.7 US cents per liter, while the average external cost of congestion and accidents amounted to 43.5 US cents per liter (both averages taken across all 100 countries for 2010). Service-related externalities thus accounted for over 80% of the total cost of the direct rebound effect in driving. Table 3 The benefit-to-cost ratio of the direct rebound effect following a 10% energy efficiency improvement, assuming zero servicerelated external costs

Countries
Gasoline price Benefit-to-cost ratio of rebound (B R ) for a range of elasticities (  Benin High 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5  Table 3 presents the welfare results from an analysis of the direct rebound where congestion and accident external costs are set to zero. This leaves behind only the air pollution and GHG emissions costs in the analysis. Of course, the external costs associated with air pollution and GHG emissions from burning a liter of gasoline in a car differ from the external costs associated with burning natural gas or coal to produce electricity. Nevertheless, we maintain the same fuel-related external costs just to show rough, indicative results of what the welfare outcomes might be for other energy services. Table 3 reveals welfare enhancing direct rebound effects in most cases, given that the costs associated with direct rebound are considerably lower than before. This suggests that there may be a need to review the conventional wisdom that rebound is a negative phenomenon that requires mitigation. In fact, such welfare enhancing rebound effects may help improve the welfare outcomes of energy efficiency when accounted for, thus making energy efficiency more attractive to policymakers.
On a final note, we must emphasize that these results are suggestive. To accurately quantify the welfare implications of the direct rebound effect in energy services such as cooling and lighting, a different empirical framework would be needed. First, a demand curve for each energy service would need to be estimated and calibrated. Second, the external costs associated with the energy service would need to be estimated for each country. Nevertheless, the results in Table 3