Exploring the direct rebound effects for residential electricity demand in urban environments: evidence from Nice

In this paper, we use the term spatial dependence as a synonym for spatial autocorrelation, and spatial heterogeneity as a synonym for spatial nonstationarity.

This mainly relies upon the assumption in behavioral theory for which different socioeconomic characteristics of households and different psychological traits are responsible for heterogeneous energy behaviors (see Dorner 2019).

For a detailed survey, see Carmona and Coulon 2013.

The quality and type of the electricity grid result to be of foremost importance in affecting the nodal prices of the transmission system; indeed, nodal prices impact the provider’s cost of electricity provision, and hence, ultimately, the price related to the contracted electricity power charged on consumers. As a result, energy providers can charge different prices for the contracted electricity power in different areas endowed with their own transmission network specificities (Sarfati et al. 2019; Richard 2007).

The efficiency elasticity of energy services can be expressed as the proportionate change in energy services consumption over the proportionate change in energy efficiency; i.e., \(\eta _{\epsilon }(S) = \frac{\partial {S}}{S}/\frac{\partial {\epsilon }}{\epsilon }\) = \(\frac{\partial {S}}{\partial {\epsilon }}\cdot \frac{\epsilon }{S}\); plugging into this expression Eq. 2 yields \(\eta _{\epsilon }(S)\) = 1 + \(\frac{\partial {E}}{\partial {\epsilon }}\cdot \frac{\epsilon }{E}\), which can be further simplified into Eq. 3.

In the literature, the inclusion of the gas price in model specifications exploring rebounds in electricity consumption is generally dictated by two main reasons. First, gas might serve as a substitute commodity by households with respect to other energy sources such as electricity or coal (Kulmer and Seebauer 2019; Ye et al. 2018; Chitnis and Sorrell 2015); accordingly, the non-inclusion of the gas price component in the model specification could potentially lead to omitted variable bias (Sorrell and Dimitropoulos 2008; Narayan et al. 2007), especially in those scenarios where the share of households utilizing alternative energy sources to electricity is consistent (Schwarz et al. yyy). Second, gas might be used by households as a complementary commodity for energy services to satisfy peaks in electricity(/alternative energy sources) demand (Chaudry et al. 2014; Duraiappah Anantha et al. 2003). In the city of Nice, natural gas remains virtually the only alternative to electricity usage as a substitute (rather than complementary) commodity, although its use remains negligible (IRIS 2019b, c). Specifically, the vast majority of buildings is endowed with (purely) electrical systems, whereas gas systems are only found in fewer old buildings across the city (and mainly localized in the central and central-east districts of Nice (IRIS 2019b)). In our model specification, the substitution effect of the gas price has to be intended as the opportunity cost for gas usage following increases in the electricity price (Golombek et al. 2013).

The composition of the electricity price in the city of Nice mirrors that of other French cities and is based on a two-part tariff system; a variable part (which is based on the regulated price per kWh of electricity consumed), and a fixed part based on the level of contracted power.

Specifically, EPCs provide the annual level of energy intensity in kilowatt-hours per square meter of useful living area (\(kWh/m^2a\)) D that would be required to provide 100% energy services (S) in a particular building given its thermal characteristics. This amount of energy is subsequently mapped to a rating system ranging on a scale from A to G, denoting, respectively, the highest and lowest levels of residential building energy efficiency (see, Collins and Curtis 2018). The computation for the average level of energy dwelling efficiency in each district is computed as: \(\epsilon _{i} = \frac{\sum _{n \in \Gamma (i)}^{N} {D_{n}}^{-1}}{N}\), with \(D_{n}\) representing the level of energy intensity in building n located in district i, and \(\Gamma (i)\) the set of all N residential buildings in district i.

Compared to the average of the other districts of Nice, the districts of the eco-valley denote substantial positive differences in terms of energy-related characteristics (respectively: 8.746 MWh versus 3.421 MWh for electricity demand, 153.452 €/kWh versus 166.655 €/kWh for the electricity price, 84.2 kWh/\(m^{2}\)a versus 147.06 kWh/\(m^{2}\)a for energy intensity, and 74.302€/kWh versus 78.202 €/kWh for the gas price). At the same time, they are not characterized by remarkable variation in socio-demographic attributes of households, with the exception for the income and residential density variables (35234.341 € versus 23020.260 € for average household income, 0.0029 residents/\(m^{2}\) versus 0.0092 residents/\(m^{2}\) for residential density, 74.943 \(m^{2}\) versus 62.061 \(m^{2}\) for average house surface, 68.43% versus 71.49% for the total share of individual heating systems, and 94.16% versus 90.35% for the total share of apartment buildings).

Despite its simplicity, the OLS estimation does not consider joint dependence of some or all of the covariates. In the presence of joint dependence, the usage of instrumental variables techniques represents a more feasible alternative in order to derive unbiased coefficient estimates. Generally speaking, the issue of joint dependence mainly refers to whether energy efficiency can be expressed as a function of energy prices, and this usually differs depending on the type of energy service considered (Small and Dender 2005). Nonetheless, in the case of domestic electricity consumption, energy efficiency can be usually considered as an exogenous component, following from Khazzoom’s original focus on the effect of mandatory energy efficiency standards for household appliances (see Sorrell and Dimitropoulos 2008).

Specifically, four different types of local spatial autocorrelation in residential energy demand emerge among districts; High–High (first quadrant): when districts displaying high residential electricity consumption levels neighbor on districts displaying similar high levels of residential electricity consumption; Low–Low (third quadrant): when districts displaying low residential electricity consumption levels neighbor on districts displaying similar low levels of residential electricity consumption; High–Low (second quadrant): when districts displaying high residential electricity consumption levels neighbor on districts displaying low levels of residential electricity consumption; and Low–High (fourth quadrant): when districts displaying low residential electricity consumption levels neighbor on districts displaying high levels of residential electricity consumption. High–High and Low–Low levels entail the presence of positive spatial autocorrelation, whereas High–Low and Low–High negative spatial autocorrelation.

The magnitude of the rebound effect is inversely related to the coefficient estimates for energy efficiency, being the latter an inverse measure for energy intensity (Belaid et al. 2020).

For each figure related to the coefficient estimates of determinants, we report in Fig. 4 the corresponding local levels of significance. The latter were derived following Mennis’s approach (Mennis 2006) for the computation of the local t values resulting from a spatially varying-coefficient model.

In this regard, successful educational campaigns would require, in addition to installing smart meters and smart monitors, to also educate households about how to read their electricity bills (Attour et al. 2020; Loi and Ng 2018).

In this regard, our result confirms recent findings in the literature (see Navamuel et al. 2018), for which urban areas with higher levels of sprawling houses tend to denote higher levels of domestic energy demand due to a larger share of detached residential buildings. Particularly, the latter tend to be generally more energy intensive than medium-density building units, due to factors such as savings in shared walls, economies of scale, surface area-to-volume ratio (Heinonen and Junnila 2014; Rickwood et al. 2008; Norman et al. 2006).

The availability of more disaggregated (i.e., household-level) data for the districts of the Nice eco-valley would provide a more in-depth understanding of the determinants of the direct rebound effect. In this regard, household-level information on important drivers such as housing typology and income, for instance, might help to disentangle household sensitivity to energy prices for similar typologies of building units across heterogeneous income groups.

In broad terms, appliance standards mainly affect consumers that would otherwise have acquired appliances less efficient than the minimum standards. Such consumers are likely to be relatively insensitive to changes in operating costs but sensitive to changes in the purchase price of appliances.

In our study, however, season-related issues might be partially mitigated by the fact that the average temperatures in Nice do not register excessive variations throughout the years. This is due to the Mediterranean climate of the French Riviera, characterized by mild winters and dry summers.