Energy Efficiency (2022) 15:47 https://doi.org/10.1007/s12053-022-10048-7 ORIGINAL ARTICLE Do household energy services affect each other directly? The direct rebound effect of household electricity consumption in Spain Martín Bordón‑Lesme · Jaume Freire‑González · Emilio Padilla Rosa © The Author(s) 2022 Abstract We estimate the magnitude of the direct (Sorrell, 2007) or as Fell (2017, p. 137) stated: “Energy rebound effect (DRE) of households’ electricity services are those functions performed using energy consumption in Spain, through an econometric esti- which are means to obtain or facilitate desired end ser- mation method of panel data. The results indicate a vices or states.” An example of an energy service would DRE between 26 and 35% in the short run and around be “transportation”. The improvements in energy effi- 36% in the long run. Moreover, we find a significant ciency, due to innovation and technical change, decrease influence of other energy sources that appear to be the effective cost of an energy service as it requires less complementary to electricity consumption according energy to provide the same energy service, which leads to our estimation. Hence, our results suggest that an to energy savings. However, as shown by empirical evi- improvement in the energy efficiency of an energy dence, this decrease in the cost of the energy service service may affect its own energy consumption as causes behavioral responses from consumers, causing well as the energy consumption of other energy ser- what is known in the literature as the direct rebound vices. This would entail a new source of DRE. effect (DRE). Hence, the DRE can be defined as the consumer behavioral responses, following a reduction Keywords Direct rebound effect · Complementary in the cost of energy services, due to an improvement of energy sources · Energy efficiency · Households’ energy efficiency. This partially or fully reduces the ini- electricity consumption · Panel data tially expected energy savings, or in some cases, could even increase the energy consumption. The purpose of this article is twofold. First, we Introduction obtain empirical evidence of the DRE for all the energy services that require electricity for their provision in Energy services can be understood as useful work or Spanish households. useful outputs obtained by energy conversion devices Second, the main contribution of this article is the consideration of alternative energy sources in the estima- M. Bordón‑Lesme (*) · J. Freire‑González · tion of the DRE for the energy source of electricity for E. Padilla Rosa Spanish households. Using recent data, this paper deliv- Department of Applied Economics, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain ers an estimated magnitude of the DRE in the consump- e-mail: martinadolfo.bordon@autonoma.cat tion of electricity of Spanish households providing short- run and long-run estimates. The results of this research J. Freire‑González will contribute to the empirical literature concerning Institute for Economic Analysis (CSIC) and Barcelona School of Economics, 08193 Bellaterra, Spain the DRE in a developed country of the energy services Vol.: (0123456789) 13 47 Page 2 of 21 Energy Efficiency (2022) 15:47 provided by electricity in households. We will provide additional measures to tackle the rebound effect, up to date evidence for the case of the residential sec- such as energy taxation or tradable permits (Freire- tor in Spain since Freire-González (2010) employed González & Puig-Ventosa, 2014; van den Bergh, a similar estimation method to ours for the DRE of 2011) or if social welfare is a priority (as efficiency household electricity consumption in Catalonia. improvements in energy services would reduce its There is also recent empirical evidence of the effective cost) rather than saving energy (Sorrell, rebound effect for Spain by Cansino et al. (2022), 2018). who estimate the direct, the indirect, and the econ- To put our analysis into context, we show next omy-wide rebound effect for 14 productive sectors, to some empirical evidence of the DRE. We focus on estimate the DRE they also employed an economet- the DRE estimation through econometric techniques ric estimation method. They found a positive DRE for for a collection of energy services supplied by elec- the 14 productive sectors. tricity and natural gas in households. The empirical Other recent empirical evidence related to the evidence that we review next does not consider alter- rebound effect for Spain is done by Cansino et al. native energy sources for the estimation of DRE of (2019) and Román-Collado and Colinet (2018), the energy source studied, with the only exception whereas Román-Collado and Colinet Carmona (2021) of Freire-González (2010). Nevertheless, his coeffi- focused on the Spanish region of Andalusia. They cient of the alternative energy source variable was not used a Logarithmic Mean Divisia Index I (LMDI-I) significant. Thus, by considering alternative energy decomposition model to test how energy efficiency sources that have significance in the estimation of affects energy consumption in different economic sec- the DRE of an energy source considered, our article tors in Spain. Cansino et al. (2019) found that there are would contribute to bridging the gap in the literature energy consumption savings after energy efficiency regarding this issue. improvements. Román-Collado and Colinet (2018) Under certain assumptions, the estimation of the highlighted the relevance of focusing on Spanish own-price elasticity of domestic energy demand household energy consumption, as it became the most would reveal the DRE. In this approach, the estima- relevant energy consumption change in Spain with a tion is based upon an overall improvement in energy 25.1% increase from 2000 to 2013. Román-Collado efficiency of energy services used by households and Colinet Carmona (2021) found that, to achieve (Sorrell, 2007). Hence, the DRE refers to all energy Spain’s energy consumption targets, the energy con- services run by energy source considered. sumption of Andalusia should reach the average Span- Table 1 summarizes some empirical evidence of ish energy consumption. The main additional contri- the direct rebound for household electricity and gas bution of this article is the consideration of alternative consumption. One of the first studies to analyze the energy sources in the estimation of the DRE for the DRE of a collection of energy services was Freire- energy source of electricity for Spanish households. González (2010) for the case of Catalonia (Spain). As different economic variables tend to change He used panel data from the period 1991–2003 with over time, it is expected that the magnitude of the a sample size of 43 Catalan municipalities. He found rebound effect varies through the years (Sorrell, 2007, that the short-run and long-run elasticities were 35% 2018). Henceforth, this research will not only con- and 49% respectively. Several subsequent studies tribute to the DRE literature, but it will also provide have analyzed the DRE for electricity consumption updated and useful information to policymakers. An in households using the same econometric approach additional contribution of our paper is that we test the to estimate the short-run and long-run elasticities. impact of the prices of other energy sources, which The results of these studies for residential electricity may be substitutes or complementary goods. If we consumption are in line with the theory suggesting find that household energy services affect each other that the DRE is expected to be greater in developing directly, this would involve a new source of DRE, regions (Sorrell, 2007), since the DREs estimated for which could open a new research line. China, Tunisia, and Pakistan (Alvi et al., 2018; Labidi The study of the rebound effect is essential for & Abdessalem, 2018; Wang et al., 2014; Zhang & policymakers whether they want to maximize energy Peng, 2017) were higher than those estimated for Cat- and climate policy effectiveness by incorporating alonia (Spain) and Beijing (China) (Freire-González, Vol:. (1234567890) 13 Energy Efficiency (2022) 15:47 Page 3 of 21 47 Table 1  Econometric estimates of direct rebound of all energy services in households that use electricity or gas Author/year Country Energy source Short run Long run Data Estimation Price coefficient technique of other energy sources Freire- Catalonia Electricity 35% 49% Panel: Fixed effects Price of natural González (Spain) 1991–2002 and error gas, not sig- (2010) Sample size: 43 correction nificant model Wang et al. China Electricity 72% 74% Panel: Fixed effects Not included in (2014) 1996–2010 and error the model Sample size: 30 correction model Wang et al. Beijing (China) Electricity 16% 40% Time series: Fixed effects Not included in (2016) 1990–2013 and error the model correction model Zhang and China Electricity 72% on aver- Panel: 14 years Linear panel Not included in Peng (2017) age, 68% (2000–2013) model and the model low-income and 29 panel thresh- regime, 55% provinces of old model high income China regime Alvi et al. Pakistan Electricity 42.9% 69.5% Panel: Fixed effects Not included in (2018) 1973–2016 and error the model Sample size: correction not specified model Labidi and Tunisia Electricity 81.7% Panel: 1995, Fixed effect Not included in Abdessalem 2000, 2005, the model (2018) and 2010 Sample size: 21 Belaïd et al. France Natural gas 60% 63% Time series: OLS and Not included in (2018) 1983–2014 ARDL the model Source: own elaboration 2010; Wang et al., 2016). Beijing is not only the income variable such as household disposable income capital of China, but also the second richest city of or GDP, and the climatic variables such as heating the country in per capita disposable income (Wang and cooling degree days. et al., 2016). Another recent measure of the DRE for domestic energy services was conducted by Belaïd et al. (2018). They found short-run and long-run Methodology and data DREs of 60% and 63%, respectively, for all energy services supplied by residential gas in France. The Methodological developments on the estimation of size of both effects may seem large for a developed the direct rebound country considering the economic literature on the DRE. However, these results should be taken with This subsection details the theoretical and meth- caution, since they used average data for the whole odological developments for the estimation of the country, which may not capture the heterogeneity DRE using econometric approaches. We follow the among French regions. Table 1 indicates the findings theoretical developments made by Berkhout et al. of these studies. (2000), Sorrell (2007), and Sorrell and Dimitropoulos The most common control variables used by the (2008). There is a consensus in the economic litera- studies shown in Table 1 are the price of the energy ture regarding the measurement of the DRE through source considered (electricity or natural gas), an the efficiency elasticity of the demand for useful work Vol.: (0123456789) 13 47 Page 4 of 21 Energy Efficiency (2022) 15:47 (Berkhout et al., 2000). This is the primary definition exogeneity: energy prices (PE) are exogenous, so they of the DRE: do not affect energy efficiency (Sorrell, 2007). Under these assumptions, the DRE can be expressed as: 𝜂𝜀 (E) = 𝜂𝜀 (S) − 1 (1) 𝜂𝜀 (E) = −𝜂Ps (S) − 1 (2) where ηε(E) is the efficiency elasticity of the demand for energy and ηε(S) is the efficiency elasticity of the where the energy cost elasticity for useful work demand for useful work. One definition of useful (𝜂Ps (S)) can be used as a proxy for the efficiency elas- work or useful output is what consumers required in ticity of useful work. It is expected that 𝜂Ps (S) ≤ 0 if terms of an end-use service (Patterson, 1996). For useful work is a normal good (Sorrell & Dimitropou- example, a useful work measure of transportation los, 2008). service from private car ownership can be the calcu- It is also possible to arrive at another definition lation of passenger kilometers. This calculation can for the DRE, through the estimation ) of the own-price come from the product of the number of cars, the elasticity of energy demand 𝜂PE (E) . ( mean driving distance per car per year, and the aver- age number of passengers carried per year (Sorrell & 𝜂𝜀 (E) = −𝜂PE (E) − 1 (3) Dimitropoulos, 2008). The additional assumption required for this defini- From this theoretical development, the different tion (besides symmetry and exogeneity) is that energy results found in the literature are the following: efficiency does not change with the level of energy (i) A zero DRE, when the efficiency elasticity use (Sorrell & Dimitropoulos, 2008). To deal with of the demand for useful work equals to zero endogeneity (energy efficiency affects energy costs (ηε(S) = 0). Hence, the efficiency elasticity of and energy costs affect energy efficiency), empirical the demand for energy (ηε(E)) is equal to minus estimates can be addressed analyzing cointegration one. This would imply that final energy savings relationships between the variables (Freire-González, are proportional to the efficiency improvement. 2010). Since periods of rising prices may induce (ii) A positive DRE, when the efficiency elasticity improvements in efficiency, to avoid overestimating of the demand for useful work is between 0 and the size of the effect, empirical estimates must be 1 (0 < ηε(S) < 1) and, therefore, the efficiency based upon periods of stability or decrease of energy elasticity of the demand for energy is between prices (Sorrell, 2007; Sorrell et al., 2009; Sorrell & 0 and −1 (−1 < ηε(E) < 0) (Sorrell & Dimitro- Dimitropoulos, 2008). poulos, 2008). This implies energy savings that We estimate the DRE through Eq. 3. Given the are less than proportional to the improvement assumptions explained above, we use the own-price in energy efficiency. This is the most common elasticity of electricity demand as a proxy for the outcome in the literature. efficiency elasticity of the demand for useful work of (iii) A positive DRE, causing an increase in energy electricity (Eq. 1). Sorrell (2007) clarified that Eq. 1 consumption, when the demand for useful work requires energy efficiency data for the energy service is elastic (ηε(S) > 1) and (ηε(E) > 0). Thus, an considered, and for this type of data generally there improvement in energy efficiency increases is limited variation in energy efficiency providing energy consumption (what is known as back- results with large variance. On the other hand, Eq. 3 fire) (Saunders, 1992). only requires data on energy prices, usually more available than data on energy efficiency, which pro- Under certain assumptions, the DRE can be meas- vides a greater variation in the independent variable ured indirectly, without data on energy improvements, (Sorrell, 2007). through price elasticities (Sorrell, 2007; Sorrell & Most of the empirical evidence briefly reviewed in Dimitropoulos, 2007, 2008). First, symmetry: for a the “Introduction” section suggests that the DRE is normal good, it is expected that rational consumers lower than 100%, implying that there will be energy will respond in the same way to a decrease in energy savings after an improvement in efficiency. However, prices as they do to an improvement in energy effi- it is important to point out that these estimates only ciency (and vice versa) (Sorrell et al., 2009). Second, measure the DRE without considering the indirect Vol:. (1234567890) 13 Energy Efficiency (2022) 15:47 Page 5 of 21 47 rebound effect, when both the direct and indirect An additional issue to be considered in the esti- rebound effect can be linked through a re-spending mation of the DRE is that different energy sources framework (Freire-González, 2011), leading to differ- may be complementary or substitutes. Therefore, ent rebounds at microeconomic level. In this frame- the price of other energy sources may be influencing work, low estimations of the DRE give rise to the the demand of a particular energy source and so, it possibility that the indirect rebound effect reaches a should be taken into account in the estimation of the wider range of values; likewise, high estimations of DRE. The only previous study that included the price the DRE entail less potential fluctuation of the indi- of another energy source was Freire-González (2010), rect rebound effect (Freire-González, 2017a). Given though he did not find it to be significant. We propose this relationship between both effects, it is not possi- to include it in the model to obtain a more accurate ble to confirm whether the direct and indirect rebound estimation of the DRE. Moreover, in case of being effect is greater or lower than 100% when only the significant, it would open a new line of research, as DRE is measured. Freire-González (2017b) found it would involve evidence that there is an additional direct and indirect rebound effects greater than 100% source of rebound to the ones usually considered in of energy efficiency in households in Cyprus, Poland, the literature. Belgium, Bulgaria, Lithuania, Sweden, Denmark, and Finland by using a combination of econometric Data estimations of energy demand functions, re-spending modeling, and generalized input–output of energy We obtained annual data from 2007 to 2016 for the modeling. 52 provinces of Spain for all the variables described. A comprehensive way to jointly estimate the direct We obtained the price of domestic electricity and nat- and indirect rebound is through the Almost Ideal ural gas from the Eurostat (2016).1 These prices do Demand System (AIDS) (Deaton & Muellbauer, not vary between provinces, but they do over time. 1980). These models, however, require a lot of infor- We gathered the information about heating oil prices mation on consumption, expenditures, prices, and from the Eurostat (2016).2 We could not find data for other variables from a basket of goods and services renewable energy prices, which is mainly biomass. which is often not available. Chitnis and Sorrell According to IDAE (Instituto para la Diversificación (2015) estimated a direct and indirect rebound effect y ahorro de la Energía), the renewable energy sources of 48% for electricity efficiency improvements in UK used by Spanish households are the following: bio- households through an AIDS, and using the same mass (96.6%), solar thermal (0.03%), and geothermal methodology, Lin and Liu (2013) found a direct and (0.002%). In this sense, Vinterbäck and Porsö (2011, indirect rebound effect of 165.22% (backfire) in Chi- p. 9) stated that for Spain: “There is no official infor- nese households. mation or statistics about prices of wood pellets and The existing literature suggests that the magnitude briquettes. There are several independent organiza- of the DRE lies between 30 and 50% (Sorrell et al., tions related to the wood sector (e.g. Confemadera, 2009). As energy efficiency data is usually unavail- Cismadera, Cesefor) that handle internal data about able, most studies rely either on the elasticity of prices, but these statistics are not available for all demand for energy services with respect to the price stakeholders but only for organization members and of energy or on the elasticity of demand for energy people registered on the webpage.” with respect to the price of energy to estimate the We assigned the price of electricity and natural gas DRE (Sorrell, 2007; Sorrell et al., 2009). Under the considering their price categories. The price catego- assumptions explained above, both approaches are ries of each Spanish energy carrier (electricity and accepted in the DRE literature (Freire-González, natural gas) are shown in Appendix Table 6 and 7. In 2017b; Sorrell & Dimitropoulos, 2007). Regard- ing the term of the effects, Sorrel stated: “Rebound effects may be larger or smaller over the long-run as 1 a greater range of behavioral responses become avail- http://​appsso.​euros​t at.​ec.​europa.​eu/​nui/​show.​do?​datas​et=​ nrg_​pc_​204&​lang=​en able” (Sorrell, 2018; p. 14). 2 https://​ec.​europa.​eu/​energy/​en/​data-​analy​sis/​weekly-​oil-​bulle​ tin Vol.: (0123456789) 13 47 Page 6 of 21 Energy Efficiency (2022) 15:47 the case of electricity consumption, we can find prov- the DRE for each energy service is disguised into inces that fell into two categories (Band DB and DC) our results. It would also be desirable to enlarge the along the 10 years, such as Álava, Burgos, and Can- panel data by collecting data at the municipality level. tabria. On the other hand, there are provinces whose However, the cost of collecting this specific type of price category remained the same during the 10 years, data for Spain might exceed its benefits since differ- such as Barcelona and Madrid (Band DC), and Ávila ent types of data used in different types of economet- and Cáceres (Band DB). This feature is also present ric estimation methods give an estimated magnitude in natural gas consumption. We captured this price of the DRE of around 30%, for a developed country variability for both energy sources (electricity and (Sorrell & Dimitropoulos, 2007). Thus, given the pre- natural gas) considering the average household con- sent data availability, our results provide useful and sumption per province per year to be the dependent robust information, especially regarding the direct variable in the estimates. Heating oil is charged at the influence that arises between households’ energy same price regardless of the amount used. services. Given data availability issues, the household dis- posable income of each Spanish region, which was Econometric models estimated obtained from the National Institute of Statistics (INE, 2016),3 is used as a proxy for the household This subsection shows the econometric models esti- disposable income per province. Nevertheless, we mated to measure the DRE. Following the proposal transformed all the monetary variables to constant of Freire-González (2010), the estimation of the DRE 2016 prices by accounting for the inflation in each was performed by obtaining the price and income province. elasticities using a double-logarithmic functional We collected data on the minimum and maximum form for the demand of electricity consumption in daily temperature of each province from the State households. A general household electricity demand Meteorological Agency of Spain (AEMET, 2016).4 model for Spain can be specified as follows: The base temperature chosen to calculate the heat- ( ) ing and the cooling degree days are 21°C and 22°C ln Eit ∕hhit = 𝛼 + 𝛽1 ln PEit + 𝛽2 ln PXit + 𝛽3 ln Yit respectively; Appendix Table 8 shows the formula ( ) +𝛽4 ln CDDit + 𝛽5 ln HDDit + 𝛽6 ln Eit−1 ∕hhit−1 used. Nevertheless, there is no consensus regarding (4) the suitable values of the “threshold” or base tem- where Eit/hhit is the aggregate electricity consumption perature to define the comfort zone (Blázquez et al., divided by the number of households subscribed in 2013). In this sense, the base temperature for heating period t, in province i; PEit is the price of electricity in degree days was defined following the values cho- period t, in province i; PXit is the price of other energy sen by Freire-González (2010) for his estimation of sources needed in Spanish households in period t, in the DRE for Catalonia; and the cooling degree days province i, such as natural gas (G) and heating oil base temperature was defined following the Spanish (HO); Yit is the households’ disposable income in Technical System Operator (REE, 1998). Data on period t, in province i; CDDit and HDDit are the cool- electricity consumption (the dependent variable in ing and heating degree days in period t, in province i, the estimates) and subscribers was obtained from the respectively; and Eit − 1/hhit − 1 is the average electric- Ministerio de Industria, Comercio y Turismo (2016).5 ity consumption in period t − 1, in province i; which The data collection process could be improved by captures the long-run effects. collecting the specific price charged for each energy We expect a negative sign in the coefficient accom- service. We estimate the DRE for a collection of panying the price of electricity, that is, an increase in energy services that require electricity; therefore, electricity prices would reduce the electricity consump- tion. The relationship between electricity consump- 3 Instituto Nacional de Estadistica. (Spanish Statistical Office), tion and the price of other energy sources seems more www.​ine.​es/ complex. To identify whether electricity and the other 4 Agencia Estatal de Meteorología (AEMET). Sede Cataluña, energy sources are substitutes or complementary goods, from aemet.es/es/portada we can focus on the energy services provided from each 5 https://​energ​ia.​gob.​es/​balan​ces/​Publi​cacio​nes/ Vol:. (1234567890) 13 Energy Efficiency (2022) 15:47 Page 7 of 21 47 energy carrier. Considering the period 2010–2015, elec- consumption (Abel, 1990; Romero-Jordán et al., tricity is the major energy source in providing lighting 2014). Given these relationships and the models used and energy for appliances. This energy service amounts in previous studies concerning the direct rebound for approximately 74% of the total electricity consump- estimation in households, we presume that all rel- tion in Spanish households (IDAE, 2015). For space evant variables have been accurately included in the cooling services, electricity is the main energy source model. with a 99% share (IDAE, 2015). Therefore, families do not have many possibilities of substituting the energy Two‑step error correction model sources for these energy services. As regards space heat- ing, which is the energy service with the greatest share In the long run, households’ energy demand can be of energy consumption in Spanish households, electric- adjusted completely to changes in prices and income ity has a share of 7% (IDAE, 2015), biomass, natural within the unit period, which is 1 year in our model gas, and heating oil being the most important energy (Sorrell & Dimitropoulos, 2007). On the contrary, in sources. If we combined the energy services of space the short run, households’ energy demand has fewer heating, water heating, and cooking, electricity amounts adjustment possibilities. Therefore, to estimate both for 14% of the total energy consumption for those energy short-run and long-run price elasticities in household services (IDAE, 2015) (see Appendix Fig. 1 and Table 9 electricity consumption, an error correction model for further information). Nevertheless, most families just (ECM) (Granger, 1981) is used to calculate the DRE have one type of installation to provide each of these (Alvi et al., 2018; Freire-González, 2010). An ECM energy services and, therefore, there are not many pos- is an econometric model that deals with the cointe- sibilities for substituting the energy sources providing gration of variables to obtain both short-run and them. Households need not only electricity to satisfy long-run estimators, and solve spurious relationships their demand for energy services, but they also require between them (Greene, 2003). For residential elec- other energy sources, such as natural gas and heating tricity demand, we can expect that households would oil. Therefore, when we estimate the DRE of a collec- respond not only to current values of independent tion of energy services provided by electricity, we could variables but also to past values. As this effect might expect a negative (complementary) relationship between persist over time, an ECM with lagged variables the other energy sources used in households and the is an appropriate model to deal with these potential residential electricity consumption. That is, an increase endogeneity issues providing consistent estimations in the price of the other energy sources would tend to (Greene, 2003). In this case, the ECM is performed reduce the consumption of electricity. in two steps. First, a fixed effects model is estimated Households’ disposable income is expected to following this specification: have a positive relation with electricity demand, as ( ) ln Eit ∕hhit = 𝛼 + 𝜇i + 𝛽1 ln PEit + 𝛽2 ln PXit + 𝛽3 ln Yit we consider that electricity is a normal good. Degree (5) days measure the duration and intensity of warm or +𝛽4 ln CDDit + 𝛽5 ln HDDit + uit cold temperatures, along different periods. They are where α represents the common fixed effect or con- computed using a base temperature that should ade- stant; μi are the individual fixed effects. The fixed quately separate the cold and heat branches of the effects model has been estimated using a general- demand–temperature relationship (Pardo et al., 2002). ized least squares (GLS) method, correcting potential Concerning the weather variables, a wider tempera- heteroskedasticity and autocorrelation problems by ture range is expected to have a positive influence using cross-sectional weights. This model provides on electricity consumption (Romero-Jordán et al., long-run elasticities. Second, the predicted residuals 2014), that is, the colder (warmer) the temperatures from estimating Eq. 5 have been saved and used as are from the base temperature, the greater is the use exogenous variable in a regression containing differ- of heating (cooling) devices run by electricity. In this enced endogenous and exogenous variables plus the sense, HDD and CDD are expected to have a posi- lagged error term (ϑuit − 1), which is a specification of tive relationship with electricity demand. Regarding an ECM. The ECM model is specified as follows: the lagged electricity consumption, a positive sign is expected, due to existing inertia in electricity Vol.: (0123456789) 13 47 Page 8 of 21 Energy Efficiency (2022) 15:47 Table 2  Pedroni residual cointegration test Table 4  Redundant fixed effects tests Statistic Prob. Weighted Prob. Test cross-sectional fixed effects statistic Effects test Statistic d.f. p-value Panel v-statistic −4.473 1.000 −4.633 1.000 Cross-sectional F 49.126 (51.462) 0.000 Panel rho-statistic 9.151 1.000 8.746 1.000 Cross-sectional fixed effects test equation Panel PP-statistic −15.135 0.000 −14.542 0.000 Variable Coefficient Std. error t-statistic p-value Panel ADF-statistic NA NA NA NA C −2.303 0.410 −5.611 0.000 Alternative hypothesis: individual AR coefs. (between-dimension) ln PEit −0.811 0.056 −14.388 0.000 Statistic Prob. ln PGit 0.064 0.033 1.938 0.053 Group rho-statistic 11.627 1.000 ln PHOit −0.331 0.051 −6.401 0.000 Group PP-statistic −27.688 0.000 lnCDDit 0.159 0.011 13.978 0.000 Group ADF-statistic NA NA lnHDDit −0.219 0.019 −11.424 0.000 lnYit 0.405 0.040 10.097 0.000 Table 3  Hausman test null hypothesis of no correlation between the unique errors and the regressors. Likewise, Table 4 shows Correlated random effects—Hausman test that the first step equation of the ECM suggests that Test cross-sectional random effects cross-sectional effects are significant. Moreover, the cross-sectional fixed effects test equation is relevant Test summary Chi-Sq. statistic Chi-Sq. d.f. Prob. for all the variables. Cross-sectional 66.046 6 0.000 random System generalized method of moments ( ) Δln Eit ∕hhit =∝ +𝛿1 ΔlnPEit + 𝛿2 ΔlnPXit As previously stated, we expect a significant influ- (6) ence from past values of the explanatory variables on +𝛿3 ΔlnYit + 𝛿4 Δ ln CDDit + 𝛿5 ΔlnHDDit ( ) the current values of the dependent variable. To deal +𝛿Δ6 ln Eit−1 ∕hhit−1 + 𝜗it uit−1 + 𝜀it with this dynamic relationship, we can also estimate the model through a dynamic generalized method of moments (GMM) panel estimator. This estima- A significant and negative coefficient accompany- tor is consistent and unbiased if we assume that the ing the error correction term (ϑituit − 1) would imply unobserved heterogeneity (μi) is fixed (Wintoki et al., that the system corrects its previous period disequi- 2012). librium. Expected values of the error correction term To deal with potential endogeneity issues, the are between 0 and −1. Table 2 shows that three of the dynamic GMM estimators instrument current val- eight statistics reject the null hypothesis of no coin- ues of explanatory variables with their lagged val- tegration, suggesting the existence of cointegration. ues (Wintoki et al., 2012). According to Rood- The ECM has also been estimated assuming cross- man (2009b), the dynamic GMM panel estimators, sectional heteroskedasticity, that is, with a GLS speci- whether using difference or system GMM, are fication. In both steps, the ECM has been estimated designed for situations when the time span (T) ana- with the common coefficients to all provinces; the lyzed is relatively small with respect to the cross fixed effect of each province is displayed in Appendix sections (N). Relating the econometric method to Table 10. our data generating process, we can see that the indi- The Hausman test confirms that there are differ- viduals (52) are relatively large compared to the time ences between the random and the fixed effects esti- frame (10). mators (Table 3). Hence, the fixed effects estimator We base our estimation on the system GMM esti- is more suitable than the random effects to estimate mator (Arellano & Bond, 1991; Arellano & Bover, the two-step ECM because Table 3 output rejects the 1995; Blundell & Bond, 1998; Holtz-Eakin et al., Vol:. (1234567890) 13 Energy Efficiency (2022) 15:47 Page 9 of 21 47 1988). This approach also addresses fixed effects, variable and the system GMM produces two (Arel- heteroskedasticity, and autocorrelation (Roodman, lano & Bover, 1995; Blundell & Bond, 1998; Rood- 2009a). man, 2009b). Arellano and Bover (1995), Blundell The dynamic model is specified as follows (Arel- and Bond (1998), and Roodman (2009b) also demon- lano & Bover, 1995; Baltagi, 2008; Blundell & Bond, strated a weak instrumentation of difference GMM, 1998; Roodman, 2009a). See Roodman (2009a) for especially if the variables are close to a random walk, further details regarding the difference and system system GMM being the favored alternative. Sys- GMM: tem GMM augments difference GMM by estimating simultaneously in differences and levels (Roodman, yit = 𝛼yi,t−1 + 𝛽xit� + 𝜀it 2009b). ( ) 𝜀it( = )𝜇i + 𝜐(it ) (7) The system GMM estimator instruments the equa- E 𝜇i = E 𝜐it = E 𝜇i 𝜐it = 0 tion in levels with first-differenced variables in a The two orthogonal conditions of the disturbance “system” of equations that includes both equations in term are the fixed effects (μi) and the idiosyncratic levels and differences (Wintoki et al., 2012): shocks (υit) (Roodman, 2009b). For these conditions [ yit ] [ yit−p ] [ x́ it ] to be valid, the instruments must provide an exoge- Δyit =𝛼+𝜅 Δyit−p +𝛽 Δx́ it + 𝜈it (9) nous source of variation on the explanatory variables. For example, past values of the explanatory variables Blundell and Bond (1998) contributed to the have no direct effect on the current dependent vari- method by eliminating the fixed effect not through able (electricity consumption per province) and only instrumenting differences with levels but instrument- affect it through its effect on current values of the ing levels with differences (Roodman, 2009b). The explanatory variables (Wintoki et al., 2012). assumption required for the system GMM is that To remove the fixed effects (μi) from Eq. 7, Arel- changes in any instrumenting variable (w) are uncor- lano and Bond’s (1991) estimator subtracts the pre- related with the fixed effects E(∆witμi) = 0 (Roodman, vious observation from the contemporaneous one 2009b). which is known as “difference GMM”: In the design of the instrument matrix, we assume the climatic variable cooling degree days to be strictly Δyit = 𝛼Δyi,t−1 + Δxit� 𝛽 + Δ𝜈 it (8) exogenous. For the appropriate instruments for Nevertheless, the weakness of this estimator is that predetermined variables, we use the lagged dependent it increases data loss (due to the first difference trans- variable, the price of electricity, and the natural formation) especially in unbalanced panels (Rood- gas price, with a lag limit of 2, and longer for the man, 2009a). There is also a potential endogenous transformed equation, and lag 2 for the equation in issue, as the yi, t − 1 term in ∆yi, t − 1 = yi, t − 1 − yi, t − 2 is levels (Roodman, 2009a). correlated with νi, t − 1 in ∆νit = νit − νi, t − 1. Addition- ally, predetermined variables in x´ could also add another endogeneity problem, as they might also be Results correlated with νi, t − 1 (Roodman, 2009b). Arellano and Bover (1995) presented an alternative In this section, we show the obtained results, the transformation of Eq. 7, by using forward orthogonal first three columns of Table 5 provide the results of deviations. They proposed to subtract the average this article, and the latter two are the correspond- of all future available observations. For each (T − 1) ing robustness checks for the estimation method of observation, they subtract the mean of the remaining the third column, which is the system GMM. The future observations available in the sample, instead coefficients highlighted in bold font are the coeffi- of subtracting the previous observation from the con- cients of the variables of interest in this article. As temporaneous one (Roodman, 2009a). Thus, only the we can see in Table 5, the sign and significance of last observation is kept out of the computation. For the alternative energy sources (natural gas and heat- example, in a panel data of (T = 3), the difference ing oil) indicate a complementary relationship with GMM produces one instrument per instrumenting electricity consumption. Vol.: (0123456789) 13 47 Page 10 of 21 Energy Efficiency (2022) 15:47 Table 5  Empirical estimates of the residential electricity demand in Spain Dependent variable: ln(Eit/hhit) ECM System GMM Pooled OLS Fixed effects Long run Short run (∆ln) α −1.923*** −0.001 −0.578*** −0.574*** −0.785* 0.000 0.618 0.000 0.000 0.047 (0.498) (0.003) (0.134) (0.139) (0.386) ln PEit −0.358*** −0.348*** −0.261*** −0.378*** −0.418*** 0.000 0.000 0.000 0.000 0.000 (0.039) (0.045) (0.049) (0.068) (0.088) ln PGit −0.142*** −0.129*** −0.079** −0.016 −0.132** 0.000 0.000 0.008 0.494 0.001 (0.016) (0.015) (0.028) (0.024) (0.037) ln PHOit −0.104** −0.121** 0.013 0.006 (0.042) (0.044) lnCDDit 0.061** 0.062*** 0.048** 0.030** 0.080* 0.001 0.000 0.004 0.009 0.030 (0.018) (0.013) (0.015) (0.011) (0.036) lnHDDit 0.067* 0.034 (0.031) lnYit 0.111* 0.042 (0.055) ∆ ln(Eit − 1/hhit − 1) 0.092* 0.596*** 0.716*** 0.177** 0.044 0.000 0.000 0.001 (0.046) (0.099) (0.059) (0.050) uit − 1 −0.790*** 0.000 (0.061) R-squared 0.945 0.560 0.758 0.560 Prob (F-statistic) 0.000 0.000 0.000 0.000 0.000 Durbin-Watson stat. 1.470 2.048 Number of instruments 48 Number of groups 52 52 52 52 AR(1) test (p − value) 0.012 AR(2) test (p − value) 0.642 Hansen test of over-identification (p − value) 0.183 Diff-in-Hansen tests of exogeneity (p − value) 0.766 IV (lnCDD) Hansen test excluding group 0.157 We use asterisks alongside each coefficient to denote its significance: *p < 0.05, **p < 0.01, ***p < 0.001 As explained above, we also estimate the param- 2009a). The p-values are below each coefficient. The eters for the relevant variables of the system GMM standard errors are in parentheses below each p-value. through pooled OLS and fixed effects. These estima- Regarding the ECM model, the long-run coef- tions will give us the suitable range of values of the ficients of electricity price, natural gas price, and lagged dependent variable (Bond, 2002; Roodman, cooling degree days have a significance level of Vol:. (1234567890) 13 Energy Efficiency (2022) 15:47 Page 11 of 21 47 1%. Alternatively, the coefficients of the price of 5% in the long run and no significance of the variable heating oil, the heating degree days, and the house- in the short run. holds’ disposable income have a significance level of Regarding the system GMM estimates, we also 5%. The sign of the coefficients is as expected, that found a significance level of 1% for the coefficients is, an increase in the price of electricity would reduce of electricity price, natural gas price, and cooling its consumption. In the same way, an increase in the degree days, and all these three coefficients have the price of heating oil and natural gas would reduce expected sign. The results of these estimates heighten residential electricity consumption. This seems to the potential complementary relationship between corroborate that there is a complementary relation- different energy sources when providing the collec- ship between these energy sources in providing the tion of energy services needed by households, espe- collection of energy services needed in households. cially for electricity and natural gas. The sign and Blázquez et al. (2013) also found a significant and significance of the lagged dependent variable confirm negative coefficient for the gas variable in their analy- the dynamic setting of our model. sis of residential electricity demand in Spain, consid- The lagged dependent variable coefficient seems a ering the period 2000 to 2008 and 47 Spanish prov- good estimate of the parameter; a useful check of it, inces. They considered the number of gas consumers when estimating through difference or system GMM, divided by the number of houses to use the gas pen- is to estimate the specified model through OLS and etration rate as a proxy for the gas price. fixed effects. The first estimation will give us the upper Climatic variables show a positive relationship bound limit and the latter the lower bound one (Bond, with electricity consumption, that is, we could expect 2002; Roodman, 2009a). The coefficient of the lagged a greater use of heating and cooling devices run by dependent variable of the system GMM estimate fell electricity, as the weather gets cooler or hotter with into this range of values (0.716 > 0.596 > 0.177). respect to the base temperature. The income vari- The Hansen test failed to reject the null hypothesis able suggests that electricity consumption is a normal of joint validity of the instruments. Additionally, for good, meaning that, the higher a household’s dispos- this specific test, the conventional threshold of 0.05 able income gets, the higher the electricity consump- and 0.10 when deciding whether a coefficient is sig- tion is. nificant or not should not be the only criterion. We Regarding the statistics values of the long-run should also treat with caution if the p-value is greater ECM, the weighted Durbin-Watson Statistic esti- than 0.25 (Roodman, 2009b). The problem of too mated below 1.5 strongly indicates a positive first- many instruments is that this impairs the efficiency order serial correlation. of this test. This can overfit the endogenous vari- Regarding the second step of the ECM, which pro- ables and not succeed in taking out their endogenous vides the short-run elasticities, the significance of component (Roodman, 2009a). In this sense, Rood- the error correction term confirms that the series are man (2009b, p. 142) stated that: “The conventional cointegrated. thresholds (0.05 and 0.10) are liberal when trying to The significance level of 5% of the lagged depend- rule out correlation between instruments and the error ent variable indicates that the electricity consumption term.” The Hansen test reported from our estimations in period t − 1 has a positive effect on the electricity is below 0.25. Furthermore, as regards this issue, a consumption in period t. Moreover, the value of the minimally arbitrary rule of thumb found in the litera- error correction term (uit − 1) indicates that the sys- ture is that the number of instruments should be less tem corrects its previous disequilibrium at a speed of than the number of groups (Roodman, 2009a), which 79%. In the short run, we found no significance of the is the case in our estimates (48 < 52). HDDit coefficient, nor the income variable. The difference-in-Hansen of 0.766 also failed It is important to recall that the income variable is to reject the null hypothesis of joint validity of all at the regional level and not at the province level; this instruments; this statistic tests the validity of addi- data issue might explain the significance level of just tional moment restrictions necessary for system Vol.: (0123456789) 13 47 Page 12 of 21 Energy Efficiency (2022) 15:47 GMM (Heid et al., 2012). The cooling degree days elasticity of energy demand can be the proxy of the is a valid strictly exogenous instrument given its DRE (Sorrell, 2007). In the same sense, the varia- reported Hansen test. tion in the associated pollutant emissions in Spain By construction, a first-order autocorrelation is might be greater when prices change than when expected, which is confirmed by the reported p-value other variables change. of the AR(1), which rejects the null hypothesis of no Appendix Table 11 shows the robustness checks first-order serial correlation. Furthermore, there is no of the two econometric approaches we used. For evidence of a significant second-order serial correla- the ECM approach, we specified a model using tion AR(2), as the null hypothesis was not rejected. only the variables which have a significance level This presumes a proper specification of the system of 0.1% in the original model and so we drop the GMM (Heid et al., 2012). parameters of heating oil price, heating degree We use robust standard errors for the system days, and income. GMM, and we also use the one-step system GMM For the system GMM approach, we specified a results as we did not see major efficiency gains fixed effect model without lags as instruments and from the two steps. The p-value of the F-statistic without the lagged dependent variable. We also of the five estimates rejects the null hypothesis that specified another system GMM without the lagged all slope coefficients are equal to zero. Hence, the dependent variable to arrange a new set of instru- estimated coefficients (excluding the constant) are ments. We use the same lag limits as the original jointly significant in explaining the household elec- model. tricity consumption in Spain. Considering the variable of interest, which is The estimated results suggest a direct rebound the own-price elasticity of electricity demand, between 26 and 35% in the short run and 36% in the the resulting magnitudes from these models, with long run for all energy services supplied by electricity different specifications, are in the range of val- in households. That is, an overall costless exogenous ues shown in the literature between 30 and 50% (Gillingham et al., 2016) increase in electricity effi- (Freire-González, 2017b). Nevertheless, the alter- ciency potentially entailing savings of 10 megawatts native econometric models presented in Appen- hour (Mwh) per year in electricity consumption would dix Table 11 could overestimate the magnitude of be reduced by between 26 and 35% in the short run and our variable of interest because they estimate the 36% in the long run. This would decrease final electric- econometric model without controlling some vari- ity savings to between 7.4 and 6.5 Mwh per year in the ables of the original model. short run and 6.4 Mwh per year in the long run. According to the literature, the estimation of the Our findings are in line with previous studies DRE through the own-price elasticity of energy concerning the DRE in households’ electricity con- demand could overestimate its magnitude (Sorrell, sumption, with a slightly higher DRE in the long 2007). For most conversion devices, it is necessary run than in the short run. Our estimated DRE in to purchase new equipment to improve energy effi- Spanish households falls within the expected range ciency. Hence, if higher capital costs from more in relation to the literature concerning this issue, efficient conversion devices are not considered, around 30%, indicating electricity savings after the the DRE could be overestimated to some extent. improvement in efficiency, as long as only the DRE However, if the government promotes energy effi- is considered. Price elasticities are greater than ciency through subsidies, in order to make energy- income elasticities and weather variables’ elastici- efficient devices cheaper than the inefficient ones, ties are smaller than the former two. Taking into the DRE may be underestimated (Sorrell, 2007; consideration the findings of this article, which are Sorrell & Dimitropoulos, 2008). in line with the results of Freire-González (2010) Regarding the symmetry assumption, Schimek for Catalonia, one can expect a greater response (1996) found approximately equal magnitudes when from households to price changes than to changes estimating the DRE through the elasticity of the in income or weather variables in Spain. This fact demand for travel with respect to fuel ( efficiency (ηε(S)) highlights the relevance of improvements in effi- and with respect to fuel prices 𝜂PE (E) (Sorrell & ) ciency to obtain energy savings, since the own-price Dimitropoulos, 2007). The energy service considered Vol:. (1234567890) 13 Energy Efficiency (2022) 15:47 Page 13 of 21 47 in their study was transportation. In contrast, Whea- service. However, in this study, we provide empirical ton (1982) found a significant larger magnitude of the evidence that the prices of natural gas and heating oil DRE when estimating it with respect to fuel prices may have a direct influence on electricity consumption. than with respect to fuel efficiency (Sorrell & Dimitro- The direct relationships between household energy poulos, 2007). One possible explanation of this could services that we found open the study of a new source be that energy prices are more salient for consumers for the DRE, which will help to assess its magnitude than energy efficiency. Hence, the symmetry assump- (Greening et al., 2000). If there are no measures to tion, when estimating the DRE with respect to elec- tackle the DRE in Spain, our results indicate that elec- tricity prices, could give an upper bound magnitude. tricity savings would be diminished. Concerning the exogeneity assumption, it should not Another contribution of this paper is that it is the be a source of bias since the period analyzed is based first empirical analysis of this type for Spain because upon a period of stability in energy prices. other research done for Spain focus on the economy- wide rebound effect (Duarte et al., 2018; Freire- González, 2020; Guerra & Sancho, 2010). Using Conclusions recent data from all the provinces of Spain, a time frame of 10 years, and controlling the weather vari- The purpose of this article is twofold. First, we ables by using information on all provinces’ weather obtain empirical evidence of the DRE for all energy stations, we found a positive DRE with energy sav- services that require electricity for their provision ings. We also provide the individual short-run and in Spanish households. Second, the main contribu- long-run fixed effects of each Spanish province. Hence, tion of this article is the consideration of alterna- our results provide useful information to policymak- tive energy sources in the estimation of the DRE for ers at different levels. Since we estimated the DRE of the energy source of electricity for Spanish house- a collection of energy services, the magnitude of the holds. To do so, we add to the econometric estima- DRE of each of them is disguised (Sorrell & Dimi- tion method the price of alternative energy sources. tropoulos, 2007). Our results are more relevant for We have found significant coefficients for the prices the energy services of lighting and energy for appli- of the alternative energy sources, that is, natural ances, as they dominate the consumption of electricity. gas and heating oil have an influence on electricity Given the goals assumed by Spain in the EU context as consumption in the case of Spain. Improvements regards energy efficiency and greenhouse gas emission in energy efficiency in energy services that require mitigation, Spanish policymakers should incorporate natural gas or heating oil would increase the DRE additional measures to tackle all sources of DRE to for electricity given its complementary relationship. increase the effectiveness of the measures to produce This is the main contribution of this article because, electricity savings and reduce the associated pollutant as explained in Table 1, previous estimations of the emissions (Freire-González & Puig-Ventosa, 2014). DRE do not consider alternative energy sources, with the only exception of Freire-González (2010), who Funding Open Access Funding provided by Universitat Autonoma de Barcelona. found no significant coefficient for the variable of the alternative energy source for the case of Catalonia. Open Access This article is licensed under a Creative Com- This newness in the estimation of the DRE opens mons Attribution 4.0 International License, which permits up a new line of research, by means of exploring the use, sharing, adaptation, distribution and reproduction in any relationship between different sources of energy in the medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Crea- study of the different rebound effect channels, either tive Commons licence, and indicate if changes were made. The direct, indirect, or economy-wide. In this sense, Hunt images or other third party material in this article are included and Ryan (2014) developed a theoretical and empirical in the article’s Creative Commons licence, unless indicated illustration of three household’s energy sources, such otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your as electricity, natural gas, and oil products. Neverthe- intended use is not permitted by statutory regulation or exceeds less, they assumed as an indirect rebound effect the the permitted use, you will need to obtain permission directly changes in the demand for energy services that result from the copyright holder. To view a copy of this licence, visit from an increase in the efficiency of a different energy http://​creat​iveco​mmons.​org/​licen​ses/​by/4.​0/. Vol.: (0123456789) 13 47 Page 14 of 21 Energy Efficiency (2022) 15:47 Appendix 1 Energy carrier price categories Appendix 2 Calculation method of the climatic variables Table 6 Table 7 Table 8 Table 6  Electricity price categories Table 8  Calculation of heating and cooling degree days Band Annual consumption Condition Heating degree days formula Tmin > Tbase HDD = 0 DA Consumption < 1000 kWh (Tmax + Tmin)/2 > Tbase HDD = (Tbase − Tmin)/4 DB 1000 kWh < consumption < 2500 kWh Tmax ≥ Tbase HDD = (Tbase − Tmin)/2 − (Tmax − Tbase)/4 DC 2500 kWh < consumption < 5000 kWh Tmax < Tbase HDD = Tbase − (Tmax + Tmin)/2 DD 5000 kWh < consumption < Condition Cooling degree days formula 15,000 kWh Tmax < Tbase CDD = 0 DE Consumption > 15,000 kWh (Tmax + Tmin)/2 < ­Tbase CDD = (Tmax − Tbase)/4 Tmin ≤ Tbase CDD = (Tmax − Tbase)/2 − Source: own elaboration based on Eurostat (2016) (Tbase − Tmin)/4 http://​appsso.​euros​tat.​ec.​europa.​eu/​nui/​show.​do?​datas​et=​nrg_​ Tmin > Tbase CDD = (Tmax + Tmin)/2 − Tbase pc_​204&​lang=​en Source: https://​www.​degre​edays.​net/​calcu​lation Table 7  Natural gas price categories Band Annual consumption D1 Consumption < 20 GJ D2 20 GJ < consumption < 200 GJ D3 Consumption > 200 GJ Source: own elaboration based on Eurostat (2016) http://​appsso.​euros​tat.​ec.​europa.​eu/​nui/​show.​do?​datas​et=​nrg_​ pc_​204&​lang=​en Vol:. (1234567890) 13 Energy Efficiency (2022) 15:47 Page 15 of 21 47 Appendix 3 Data on final energy consumption of Spanish households Fig. 1 Table 9 Fig. 1  Sources of energy for final energy consump- tion in Spanish households (Ktep) (2010-2015). Source: IDAE (2015) Vol.: (0123456789) 13 47 Page 16 of 21 Energy Efficiency (2022) 15:47 Table 9  Final energy consumption by uses of residential sector (Ktep). Period 2010–2015 Energy source Space heating Space cooling Water heating Cooking Lighting and TOTAL appliances 2015 Electricity 444 141 450 560 4431 6025 Heat 0 0 0 0 0 0 Gas 1398 0 1291 329 0 3017 Solid fuels 72 0 6 11 0 89 Petroleum products 2174 0 625 187 0 2985 LPG 393 0 465 187 0 1045 Other kerosene 0 0 0 0 0 0 Diesel oil 1781 0 160 0 0 1941 Renewable energy 2460 2 259 27 0 2749 Solar thermal 16 0 205 0 0 221 Biomass 2439 0 52 27 0 2517 Geothermal 5 2 3 0 0 11 TOTAL 6548 143 2631 1113 4431 14,865 2014 Electricity 448 142 454 565 4472 6081 Heat 0 0 0 0 0 0 Gas 1433 0 1324 337 0 3094 Solid fuels 75 0 6 11 0 92 Petroleum products 1876 0 607 191 0 2674 LPG 401 0 474 191 0 1066 Other kerosene 0 0 0 0 0 0 Diesel oil 1476 0 133 0 0 1608 Renewable energy 2479 2 243 27 0 2751 Solar thermal 15 0 188 0 0 203 Biomass 2459 0 52 27 0 2537 Geothermal 5 2 3 0 0 11 TOTAL 6311 144 2634 1131 4472 14,691 2013 Electricity 450 143 456 568 4494 6111 Heat 0 0 0 0 0 0 Gas 1479 0 1366 348 0 3193 Solid fuels 77 0 6 11 0 95 Petroleum products 1858 0 636 204 0 2698 LPG 429 0 507 204 0 1140 Other kerosene 0 0 0 0 0 0 Diesel oil 1429 0 128 0 0 1558 Renewable energy 2462 2 231 27 0 2722 Solar thermal 14 0 176 0 0 190 Biomass 2443 0 52 27 0 2521 Geothermal 5 2 3 0 0 10 TOTAL 6327 145 2695 1158 4494 14,819 2012 Electricity 476 151 482 600 4749 6458 Heat 0 0 0 0 0 0 Vol:. (1234567890) 13 Energy Efficiency (2022) 15:47 Page 17 of 21 47 Table 9  (continued) Energy source Space heating Space cooling Water heating Cooking Lighting and TOTAL appliances Gas 1625 0 1501 382 0 3509 Solid fuels 89 0 7 13 0 110 Petroleum products 1784 0 653 214 0 2651 LPG 451 0 533 214 0 1198 Other kerosene 0 0 0 0 0 0 Diesel oil 1333 0 120 0 0 1453 Renewable energy 2452 2 220 26 0 2700 Solar thermal 13 0 165 0 0 178 Biomass 2434 0 51 26 0 2512 Geothermal 5 2 3 0 0 10 TOTAL 6426 153 2863 1236 4749 15,428 2011 Electricity 482 153 489 608 4814 6545 Heat 0 0 0 0 0 0 Gas 1580 0 1460 372 0 3411 Solid fuels 100 0 8 15 0 122 Petroleum products 1913 0 677 220 0 2809 LPG 462 0 546 220 0 1228 Other kerosene 0 0 0 0 0 0 Diesel oil 1451 0 130 0 0 1581 Renewable energy 2413 2 206 26 0 2647 Solar thermal 12 0 152 0 0 164 Biomass 2396 0 51 26 0 2473 Geothermal 5 2 3 0 0 10 TOTAL 6488 155 2839 1240 4814 15,535 2010 Electricity 479 152 486 605 4786 6508 Heat 0 0 0 0 0 0 Gas 1972 0 1821 464 0 4257 Solid fuels 141 0 11 21 0 173 Petroleum products 2238 0 771 248 0 3257 LPG 521 0 617 248 0 1386 Other kerosene 0 0 0 0 0 0 Diesel oil 1717 0 154 0 0 1871 Renewable energy 2403 2 186 26 0 2617 Solar thermal 11 0 133 0 0 144 Biomass 2388 0 51 26 0 2464 Geothermal 5 2 3 0 0 9 TOTAL 7233 154 3275 1363 4786 16,812 Source: IDAE (2015) Vol.: (0123456789) 13 47 Page 18 of 21 Energy Efficiency (2022) 15:47 Appendix 4. Fixed effects of each Spanish province Table 10  (continued) Provinces Long-run Fixed Short-run Fixed Table 10 effect (μi) effect (μi) Table 10  Cross-sectional fixed effects 41. Tenerife 0.170 −0.011 42. Salamanca −0.198 −0.007 Provinces Long-run Fixed Short-run Fixed effect (μi) effect (μi) 43. Segovia −0.093 0.005 44. Sevilla 0.262 −0.004 1. Alava −0.070 0.008 45. Soria −0.317 0.011 2. Albacete 0.002 −0.000 46. Tarragona −0.036 0.001 3. Alicante 0.030 −0.014 47. Teruel −0.200 −0.008 4. Almeria 0.029 −0.003 48. Toledo 0.132 −0.008 5. Avila −0.412 −0.018 49. Valencia 0.073 −0.006 6. Badajoz −0.034 0.002 50. Valladolid −0.058 0.005 7. Barcelona 0.116 0.010 51. Zamora −0.289 −0.009 8. Bizkaia 0.027 0.001 52. Zaragoza 0.014 −0.000 9. Burgos −0.084 0.036 10. Caceres −0.151 −0.014 Source: own elaboration 11. Cadiz 0.081 −0.010 12. Cantabria −0.008 0.010 13. Castellon −0.009 0.006 14. Ceuta 0.140 0.015 15. Ciudad Real 0.060 −0.001 16. Cordoba 0.227 0.006 17. Coruna A 0.083 −0.006 18. Cuenca −0.178 −0.007 19. Gipuzkoa 0.045 0.008 20. Girona 0.006 0.004 21. Granada 0.014 −0.011 22. Guadalajara 0.003 0.013 23. Huelva 0.001 0.006 24. Huesca −0.075 −0.000 25. Baleares 0.380 0.002 26. Jaen 0.150 0.001 27. La Rioja −0.143 0.002 28. Las Palmas 0.297 −0.009 29. Leon −0.187 0.007 30. Lleida 0.079 0.011 31. Lugo −0.079 0.008 32. Madrid 0.120 −0.004 33. Malaga 0.188 −0.007 34. Melilla 0.092 −0.010 35. Murcia 0.206 0.001 36. Navarra −0.001 −0.002 37. Ourense −0.208 −0.002 38. Palencia −0.245 0.011 39. Pontevedra 0.094 −0.001 40. Asturias −0.050 −0.016 Vol:. (1234567890) 13 Energy Efficiency (2022) 15:47 Page 19 of 21 47 Appendix 5. Robustness checks Table 11 Table 11  Robustness checks Dependent variable:ln ECM ECM System GMM System GMM Fixed effects (Eit/hhit) (OM) Long run Short run (∆ln) Long run (OM) Short run (∆ln) (OM) α −0.520** 0.003 −1.923*** −0.001 −0.937*** −0.578*** −0.520** 0.001 0.091 0.000 0.618 0.000 0.000 0.001 (0.162) (0.002) (0.498) (0.003) (0.241) (0.134) (0.162) ln PEit −0.408*** −0.409*** −0.358*** −0.348*** −0.567*** −0.261*** −0.408*** 0.000 0.000 0.000 0.000 0.000 0.000 0.000 (0.033) (0.036) (0.039) (0.045) (0.065) (0.049) (0.033) ln PGit −0.159*** −0.137*** −0.142*** −0.129*** −0.049 −0.079** −0.159 0.000 0.000 0.000 0.000 0.358 0.008 0.000 0.015 (0.014) (0.016) (0.015) (0.053) (0.028) (0.015) ln PHOit Without Without −0.104** −0.121** 0.013 0.006 (0.042) (0.044) lnCDDit 0.063*** 0.061*** 0.061** 0.062*** 0.120*** 0.048** 0.063 0.000 0.000 0.001 0.000 0.000 0.004 0.000 0.0169 (0.012) (0.018) (0.013) (0.240) (0.015) (0.016) lnHDDit Without Without 0.067* 0.034 (0.031) lnYit Without Without 0.111* 0.042 (0.055) ∆ ln(Eit − 1/hhit − 1) 0.132** 0.092* Without 0.596*** Without 0.001 0.044 0.000 (0.041) (0.046) (0.099) uit − 1 −0.813*** −0.790*** 0.000 0.000 (0.058) (0.061) R-squared 0.945 0.559 0.945 0.560 0.945 Prob (F-statistic) 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Durbin-Watson stat. 1.445 2.062 1.470 2.048 1.445 Number of instruments 34 48 Without Number of groups 52 52 52 52 52 52 52 AR(1) test (p − value) 0.037 0.012 AR(2) test (p − value) 0.103 0.642 Hansen test of 0.059 0.183 over-identification (p − value) Diff-in-Hansen tests of 0.543 0.766 exogeneity (p − value) IV (lnCDD) Hansen test 0.056 0.157 excluding group Source: own elaboration (OM) stands for original model We use stars alongside each coefficient to denote its significance: *p < 0.05, **p < 0.01, ***p < 0.001 Vol.: (0123456789) 13 47 Page 20 of 21 Energy Efficiency (2022) 15:47 References Fell, M. 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The rebound effect: An assessment of the evidence for economy-wide energy savings from improved Publisher’s note Springer Nature remains neutral with regard energy efficiency. In Report by the Sussex Energy Group to jurisdictional claims in published maps and institutional for the UK Energy Research Centre. UK Energy Research affiliations. Group. Vol.: (0123456789) 13