Cooling demand in integrated assessment models: a methodological review

The relationship between the energy system and the economy can be modeled: (i) in a partial equilibrium (PE) fashion, with models representing only the energy or building sector; (ii) considering the general equilibrium (GE) interactions and representing the interaction between the energy sector and all other sectors.

PE models provide the ex-ante climate-induced potential impacts prior to any adjustment induced by market interactions with energy supply and the rest of the economy through price changes. These shocks are instead accounted for in a GE modeling framework. Of the 15 studies considered in this review, 5 rely exclusively on a PE approach, generally an energy sector or an energy demand model. Four studies have coupled a PE model with a GE model (Labriet et al 2015, Hasegawa et al 2016, Park et al 2018, Clarke et al 2018 in the models TIAM-WORLD, AIM/GCE, GCAM, respectively), three studies (Eboli et al 2010, Francesco Bosello et al 2012, Roson and Van der Mensbrugghe 2012 in the models ICES-POLES and ENVISAGE, respectively) have used an exclusively GE model, and one study (Tol 2013 in the FUND model) has used an optimization model.

The energy sector can be modeled through: (i) process-based, bottom-up simulations, in which engineering bottom-up models are applied to simulate the energy performance of building archetypes, and to forecast specific end uses or top-down simulations; (ii) top–down models which do not articulate end-use services, but rely on aggregate national statistics and macroeconomic drivers to obtain empirically reduced-form responses of energy demand. GE approaches generally use projections from top-down simulation as inputs or shocks to exogenously perturbate the final energy demand in the CGE model. Bottom-up simulations can be further divided in relation to the type of model used to study heating and cooling energy demand: energy system models and energy demand models. Energy system models cover both demand and supply and are a comprehensive representation of the energy sector. The energy system models enable a technology-rich, bottom-up analysis of the global energy system. Energy demand models rely on aggregate end-use energy functions describing the relationships between energy demand and underlying socio-economic factors, with different geographical scopes, end-uses and carriers. Most studies rely on multi-model frameworks that couple a GE model or an integrated assessment framework with a more detailed energy or building sector bottom-up model. Eboli et al( 2010) and Francesco Bosello et al( 2012) for instance couple the top-down recursive-dynamic computable GE model (ICES), used for the assessment of the macro-economic impacts of climate change with the bottom-up POLES model. Specifically, shocks from the POLES energy system model are used to calibrate the intensive margin in ICES. Labriet et al( 2015) couple the GE GEMINI-E3 with the bottom-up, energy TIAM-WORLD system model. The adoption of the economy-wide GEMINI-E3 model makes it possible to examine the overall macroeconomic implications of the changes in energy demand for heating and cooling due to climate change. Hasegawa et al( 2016) and Park et al( 2018) conduct a GE framework analysis by combining a dynamic CGE model (AIM/CGE) with the AIM/End-use model, a bottom-up, energy system model (Fujimori et al 2012).

3.3.1. Intensive and extensive margins

The literature identifies two separate mechanisms through which climate shocks are transmitted to energy demand (Auffhammer and Mansur 2014, Wing and Lanzi 2014): short-term demand responses to weather (henceforth 'intensive margin') and long-term demand responses driven by an increase in the penetration of air conditioner appliances (henceforth 'extensive margin'). The short-term intensive margin transmission of weather conditions to energy demand characterizes both cooling and heating services in a similar way. Yet, long-term adjustments due to appliance penetration have usually been considered explicitly only for cooling services, on the assumption that saturation of heating appliances has already occurred across the world. While extensive margin adjustments amplify demand for cooling services due to the utilization of newly acquired appliances, capital stock replacement of heating appliances, under the hypothesis that more efficient appliances will replace less efficient ones, would reduce the energy demand per unit of calorific output.

The approaches used to model the 'intensive margin' can be schematized in two different categories: (i) scaling factor; (ii) exogenous shift parameter. The 'scaling factor' approach involves including, in the energy demand function for the thermal adaptation service s in region r and with a time step of t( $EDCC_{t,r}^{\,s}$), a multiplicative term based on the level (equation (1a)) of the climate variable ($CLI{M_{t,r}}$) or its relative increase with respect to the baseline year ($CLI{M_{0,r}}$), equation (1b)):

$$\begin{equation}EDCC_{t,r}^{\,s} = CLIM_{t,r}^{\,s}{\text{ }}ED_{t,r}^{\,s}\end{equation} \tag{ 1a }$$

or

$$\begin{equation}EDCC_{t,r}^{\,s} = \frac{{CLIM_{t,r}^{\,s}}}{{CLIM_{0,r}^{\,s}}}{\text{ }}ED_{t,r}^{\,s}\end{equation} \tag{ 1b }$$

Where ED is the energy demand for the thermal adaptation service s( cooling or heating) without climate change and $EDCC{\text{ }}$is the energy demand for the thermal adaptation service under climate change.

The climate variables ($CLI{M_{t,r}}$) most commonly used to capture thermal stress are cooling degree days (CDDs) and heating degree days (HDDs). The CDDs (HDDs) are defined as the number of degrees above (below) the thermal comfort threshold, measured in terms of day count (ASHRAE 2017):

$$\begin{equation}CDD = \mathop \sum \limits_{i = 1}^n \left( {{T_d} - {T_b}} \right) + ;HDD = \mathop \sum \limits_{i = 1}^n \left( {{T_b} - {T_d}} \right) + {\text{ }}\end{equation} \tag{ 2 }$$

where '+' signifies only positive values that accumulate over n days in the chosen time period, ${T_d}$ the daily mean outdoor air temperature and ${T_b}{\text{ }}$the threshold temperature. All the studies are reviewed by adopting the scaling factor set ${T_b}$ to 18 °C, while few of them evaluate alternative thermal comfort thresholds (Hasegawa et al 2016, Park et al 2018).

In some cases, the scaling factor includes an empirically estimated parameter ${\text{ }}\beta$ that modulates the proportional variation in the climate indicator, either in a linear (equation (3a)) or an exponential fashion (equation (3b)):

$$\begin{equation}EDCC_{t,r}^{\,s} = {\beta _r}\frac{{CLIM_{t,r}^{\,s}}}{{CLIM_{0,r}^{\,s}}}{\text{ }}ED_{t,r}^{\,s}\end{equation} \tag{ 3a }$$

or

$$\begin{equation}{\text{ }}EDCC_{t,r}^{\,s} = {\left( {\frac{{CLIM_{t,r}^{\,s}}}{{CLIM_{0,r}^{\,s}}}} \right)^{{\beta _r}}}ED_{t,r}^{\,s}\end{equation} \tag{ 3b }$$

Equations (1a)–(1b) are the most commonly used approach that is found both in the engineering and end-use demand models—they add the scaling factor to the building energy consumption model (Labriet et al 2015, IEA 2018, Levesque et al 2018, Clarke et al 2018), and by energy system bottom-up analyses—they add the scaling factor to their stylized income–demand relationship (Isaac and van Vuuren (2009)), Mima and Criqui (2009), Hasegawa et al( 2016), Park et al( 2018). Equation (3a) is adopted by Tol (2013), while equation (3b) is adopted by Clarke et al( 2018).

The scaling factor method relies on the computation of CDDs and HDDs (equation (2)) from the historical and future mean air temperature. The increase in energy demand across different warming scenarios therefore will depend on two transmission mechanisms: (1) how mean temperature increases affect CDDs and HDDs; (2) how variations in the CDDs and HDDs affect the cooling and heating demand via the scaling factors (Equations 1 and 3). Therefore, if the relationship between mean temperature and degree days is non-linear (Mourshed 2012), the relationship between temperature and energy demand is also non-linear, even when models include a simple proportional factor between energy and degree days (equation(1a) and (1b)).

An empirical estimation of the non-linear transmission from temperature to degree days and energy demand is presented in figure 2. The estimated relationship is based on a pooled regression model between temperature, CDDs and HDDs (Panel a), computed with varying thresholds: 18 °C and 22 °C as for CDDs, 18 °C and 16 °C as for HDDs (equation (2)). Meteorological data is obtained from the NASA Earth Exchange Global Daily Downscaled Climate Projections (NEX-GDDP)⁵ dataset, for the years from 1986 to 2005. The left quadrants show the best fit (cubic) obtained from the regression model. A stylized relationship between the country-level, mid-century mean temperature shocks (temperature scale factor) and the shock on the CDDs and HDDs is assessed by computing the percentage variation of the mean future realization (mean of 2041–2060) with respect to the variables' historical level (mean of 1986–2005). The indicator corresponds to the shock of energy demand that models adopting the scaling factor would transmit on cooling and heating energy demand at the country-level. Results underscore that a given annual mean temperature percentage variation leads to a more-than proportional increase (decrease) in the CDDs (HDDs) percentage variation (as most observations fall above or below the bisector). Furthermore, the magnitude of the degree days' percentage variation associated to a given temperature shock increases sharply when the higher threshold for CDDs is adopted and in RCP 8.5, while the shock is more uniform across thresholds and climate scenarios as for HDDs.

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The 'exogenous shift parameters' approach varies key model parameters describing the efficiency of energy use and therefore, indirectly, of demand for energy, on the basis of parameters estimated empirically with historical data. This approach entails a different representation of the responses to weather shocks with respect to the 'scaling factor'. First, elasticities are differentiated by fuel type (typically oil, gas and electricity) rather than by end-user service. A fuel-specific coefficient provides a measure of the shock that compounds the contribution of different thermal adaptation services. Second, climate indicators used by empirical studies are more commonly mean temperature levels (De Cian et al 2013) or temperature bins (De Cian and Sue Wing 2019), rather than CDDs and HDDs. A V-shaped or a linear-spline response function of energy demand to climate (figure 3) makes it possible to associate the coefficients of low temperature levels or bins to heating requirements, while cooling needs are associated with the coefficients related to high temperature levels or bins.

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Within this approach, a climate change impact shock Ψ for each fuel f, country c, and future time period t is obtained by combining the estimated coefficients $\beta$ with exposure under historical ($\widetilde {CLIM}_{c,t}^{Hist}$) and future ($\widetilde {CLIM}_{c,t}^{Fut}$) climate (equation(4a)). The resulting shock is applied to energy demand without climate change (ED) to obtain demand with climate change ($EDCC$):

$$\begin{equation}{\Psi _{f,t,c}} = \left[ {\left\{ {\frac{{\exp \left( {\hat \beta _{f,c}^{CLIM}*\widetilde {CLIM}_{c,t}^{Fut}} \right)}}{{\exp \left( {\hat \beta _{f,c}^{CLIM}*\widetilde {CLIM}_{c,t}^{Hist}} \right)}}} \right\} - 1} \right]*100\end{equation} \tag{ 4a }$$

$$\begin{equation}EDC{C_{f,t,c}} = {\Psi _{f,{\text{ }}t,{\text{ }}c}}E{D_{f,t,c}}\end{equation} \tag{ 4b }$$

Computable GE (CGE) models (Eboli et al 2010, Francesco Bosello et al 2012, Roson and Van der Mensbrugghe 2012) have used climate-induced shocks on energy demand, such as those estimated by De Cian et al( 2013),⁶ De Cian and Sue Wing (2019), or by van Ruijven et al( 2019) to calibrate the exogenous shifts in their models. It is important to distinguish between the empirical studies estimating those shocks, which are top-down PE studies that do not take price adjustments into account, and the CGE modeling studies, which are top-down assessments that explicitly account for GE adjustments. The parameter of the response of thermal adaptation to temperature ($\hat \beta _{f,c}^{CLIM}$) can be estimated by using dynamic models (such as error correction models) that make it possible to identify long-term elasticities, combining the contributions of the intensive and extensive margins in a single parameter. In this manner, modeling studies using exogenous shifts calibrated on long-term elasticities implicitly account for the penetration of AC.

The extensive margin has been modeled through a market penetration model that explicitly estimates the market penetration of air-cooling appliances. Most studies (Isaac and van Vuuren 2009, Mima and Criqui 2009, Hasegawa et al 2016, Park et al 2018; Levesque et al 2018,⁷ Arnell et al 2019) rely on the two-stage penetration model by Mcneil and Letschert (2008, 2010) and Sailor and Pavlova (2003),⁸ in which Penetration (P) of air-cooling appliances is a function of two components: the Climate Maximum, CM( figure 4, panel a, left quadrant), which identifies the maximum share of AC adoption modulated by the climate conditions (measured by the CDDs) if no income constraint existed; and Availability, AV (figure 4, panel a, right quadrant), which identifies the share of the Climate Maximum which is actually achievable given the income level of the population (I). Penetration is defined as the product of these two components (figure 4, panel b).

A few studies rely on other approaches. IEA (2018) uses a 'stock model' approach. The modeling of penetration is based on the stock of cooling equipment that is necessary to meet the required energy service demand. Assumptions on average equipment lifetime are applied by using a Weibull distribution to determine the rate at which each equipment category diminishes over time. Annual sales volumes and corresponding energy performance assumptions are calculated with respect to remaining stock and energy service demand in a given year. Clarke et al( 2018) model the extensive margin as a unitless calibration coefficient, modulating the per capita energy service demand per unit of HDD/CDD and floorspace (a 'saturation parameter'). A narrow number of studies do not account for extensive margin developments (Tol 2013, Labriet et al 2015).

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3.3.2. Sectoral heterogeneity

Table 1 summarizes the resulting classification of the studies reviewed, based on the different modeling characteristics pertaining to the relationship between the economy and the energy system, its level of detail, breaking down the climate feedback of final use of energy into five overall model types. Type 1 models (bottom-up, PE models with a market penetration module for AC) have been adopted most frequently, followed by Type 3 (CGE coupled with a process-based representation of the energy sector and a market penetration module for AC) and Type 5 (top-down CGE simulation approaches deploying exogenous shifts) models. Type 2 models (top-down PE simulation approaches deploying exogenous shifts) have been adopted only by two studies, while Type 4 (CGE coupled with a process-based representation of the energy sector characterizing only the intensive margin) shows the contribution made by a single study. The comparison of consistent scenarios between Types 3 and 4 makes it possible to discern the effect of including the extensive margin in CGE. The comparison of consistent scenarios between Type 2 and Type 5 sheds light on the role of adaptive behaviors induced by changes in prices and interactions across markets.

Model results underscore that at the global level the increases in energy demand driven by higher cooling needs more than compensate for the decreases in energy demand due to lower heating needs. Figure 5 shows the distribution of the results obtained across different climate change scenarios (RCPs) for cooling services, heating services and combinations for all buildings and the residential sector only. Projections are reported for 2050 and 2100, in quantity (left quadrants) and in relative terms with respect to the demand in 2016 (right quadrants). The range in the projections expressed by the boxplots represents differences across models and socioeconomic scenarios (SSPs) in Panel a and Panel b, while differences across models and climate scenarios (RCPs) in Panel c. The projections point to an important increase in energy for thermal adaptation as the combination of cooling demand increases and heating demand decreases. The evidence of the increase (decrease) in cooling (heating) demand is consistent across warming scenarios and over time. Depending on the combination of service, sectors, and RCP scenarios, there are important differences in the magnitude of the projections. Uncertainty increases over time, especially in relation to cooling demand when commercial activities are also included. The boxplots show that the range of projection results is much wider for cooling demand than for heating demand and for total building demand than for residential demand. In the scenario assuming no variations in the climatic conditions, the median total demand for thermal adaptation increases up to 77 (85) EJ and by a factor of 1.30 (1.43) with respect to 2016 (59 EJ), in 2050 (2100). In the low warming scenarios, RCP 1.9 and RCP 2.6, the median total demand increases up to 92–96 (120–130) EJ and by a factor of 1.5–1.6 (2–2.2) in 2050 (2100). In the moderate warming scenario RCP 4.5 the median total demand increases up to 75 (115) EJ and by a factor of 1.26 (1.93) in 2050 (2100). In the high warming scenarios RCP 6 and RCP 8.5 the median total demand increases up to 73–97 (130–147) EJ and by a factor of 1.23–1.63 (2.2–2.47) in 2050 (2100). The heterogeneity across SSPs and IAM models is presented in Panel b. Median values of thermal energy demand exhibit moderate variability across SSPs especially for the residential sector and in the first half of the century. Differences across socio-economic scenarios are instead more evident in the building sector in 2100, for both cooling and heating demand. Overall, heterogeneity across scenarios is more marked when focusing on climate shocks of different magnitude (Panel a), than on socioeconomic scenarios (Panel b). This result points to the need for further investigation of the way in which different mechanisms of propagation between climate and energy demand can affect model projections.

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The additional contribution of climate-induced shock on energy demand for thermal adaptation is obtained by computing the difference between the projected demand in a given RCP scenario and its counterpart in the 'no climate change' scenario, sharing the same socio-economic assumptions (SSPs). This approach makes it possible to single out the climate transmission effect from the impact of socio-economic trends (Panel c). The studies included in Panel c correspond to the one included in Panels a and b, with the addition of the projections by van Ruijven et al( 2019). The latter are singled out (highlighted as an asterisk) and are not used to compute the distribution of the boxplots, to ease the comparison between Panel a and c, as this study only provides results in terms of the additional contribution due to climate change.

As for cooling, the climate change-induced median variations in energy demand for the building sector range from 4 EJ to 17 EJ (from 20 EJ to 84 EJ) in 2050 (2100), depending on the climate scenario. As for heating, the climate change-induced median variations in energy demand for the building sector range from −4 EJ to −11 EJ (from −4 EJ to −23 EJ) in 2050 (2100), depending on the climate scenario. Thermal adaptation in buildings is projected to require additional energy ranging from a median value of 0.01 EJ (16 EJ) under the RCP 1.9 and to 8.5 EJ (61 EJ) under the RCP 8.5 in 2050 (2100). Current energy usages amount to 52 EJ for heating and 7 EJ for cooling, for a total of 59 EJ, in buildings, and to 39 EJ for heating and 3 EJ cooling, for a total of 42 EJ, in the residential sector. Even in the low warming scenarios, RCP 1.9 and RCP 2.6, net final demand goes up by a median value of 16–22 EJ in 2100, though a net reduction cannot be excluded. The realization of a very low warming scenario, RCP 1.9, with respect to the RCP 2.6, would reduce the median net final demand by 3.7 EJ (6 EJ) in 2050 (2100), that is by 6% (10%) of net final demand in 2016. The commercial sector accounts for the largest share in the incremental contribution of climate change to energy demand, as specific projections of residential sectors show that the additional demand required ranges from −2 EJ to −0.5 EJ (from 1.4 EJ to 14 EJ) in 2050 (2100).

The relative importance of the climate change-induced variations in the energy demand for residential buildings, with respect to the no-climate change scenario, are amplified at the regional level (figure 6). All macro regions are characterized by a net increase of a building's energy demand for thermal adaptation, ranging from 0.5 to 7 EJ in 2050 and from 6 EJ to 23 EJ in 2100, depending on the region and the degree of warming. Sharp increases in median additional energy due to cooling requirements from 2050 to 2100 are projected for all regions, with a median addition in Asia, the Middle East and Africa (MAF) and OECD countries between 23 EJ and 28 EJ under the highest warming scenarios. As for the residential sector, the median additional energy due to cooling requirements in 2100 ranges from 1.9 EJ to 8.7 EJ in Asia, from 1.4 EJ to 9.1 EJ in MAF, from 0.3 EJ to 2.4 EJ in OECD countries, from 0.3 EJ to 1.7 EJ in Latin America (LAM) and from 0.02 to 0.3 in Russia (REF), depending on the RCP. In temperate regions, OECD and REF, sharp decreases in heating energy needs result in a median value of total additional energy requirements in 2100 which ranges from −1.1 to −3.6 in the former and −0.3 and −0.9 in the latter region, depending on the RCP. On the other hand, in Asia and MAF the total energy requirements range in 2100 from 0.5 to 4 EJ (an almost tenfold increase from RCP 1.9 to RCP 8.5) in the former region and from 1 EJ to 6 EJ in the latter. In LAM total additional demand goes from almost zero to 1 EJ. The additional energy demand projected in higher warming scenarios, with respect to the low warming scenarios, is greatly amplified from the second half of the century in both the residential and the commercial sector.

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Global and regional trends in heating and cooling demand are assessed with respect to the most common drivers modeled by IAMs: climate and GDP. Other key cooling and heating demand drivers, namely building characteristics (floor space, insulation properties), appliance characteristics (HVAC system type and efficiency) and behavioral aspects (thermal comfort thresholds, energy saving behaviors), could not be investigated in similar detail. The IAMs incorporating bottom-up technology rich modules (building or energy system models) or flexible end-use functions (energy demand models) account for such drivers by including building characteristics (generally floor space) and HVAC system efficiencies (generally the energy efficiency ratio, or EER). Usually, the positive correlation between floor space and GDP is used to model the evolution of this variable over time. Some studies simulate different behaviors of people towards the use of AC by varying the temperature thresholds used to compute CDDs and HDDs across SSPs (Hasegawa et al 2016, Levesque et al 2018, Park et al 2018). Even when building and behavioral characteristics are taken into account, the marginal contribution of such drivers is often hidden in model results and projections are presented in an aggregate way that does not permit a direct comparison between those different assumptions. Based on the results gathered, it was possible to elaborate only on the role of HVAC system efficiency by by relying on Isaac and van Vuuren (2009) and IEA (2018), which investigate the extent to which the energy efficiency of heating and cooling appliances influence space cooling energy needs. Table 2 summarizes the main assumptions and key results: higher appliance efficiency brings cooling energy demand down by 30% in 2050 (IEA 2018) and by 45% in 2100 (Isaac and van Vuuren 2009), while heating demand would be more than halved in 2100 (Isaac and van Vuuren 2009).

With respect to the economic implications, most CGE-based studies underscore that, since energy is only a small part of the overall macroeconomic inputs, climate-induced impacts on energy demand have little economic repercussion; such repercussions are mainly driven by impacts on the agricultural sector, sea level rise, health and tourism impacts. Figure 7 presents the results of the climate-related impact on GDP due to variations in energy demand for cooling and heating as a response to global warming. Substantial impacts are identified under the RCP 8.5 scenarios, with a median relative variation in GDP equal to −0.29%, with the lowest value reaching −1.9%. The projections based on the SSP 1 are characterized by a positive median GDP percentage change of relatively small magnitude,⁹ while a negative median GDP percentage change is found in the projections based on SSP 2 and SSP 3.

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While early studies generally found a very limited macroeconomic impact in terms of welfare change at the global level, a more recent analysis has identified a higher role of the energy demand with respect to the macroeconomic impacts of climate change. Francesco Bosello et al( 2012), Roson and Van der Mensbrugghe (2012) and Dellink et al( 2014), Labriet et al( 2015) find negligible impacts of changes in energy demand due to HDD and CDD variations. Tol (2013), using the FUND model, finds that the negative impact of the net increase in energy demand is quantified as a variation of −1.9% of GDP by 2100. In contrast to the previous studies, Hasegawa et al( 2016) and Park et al( 2018) include the incremental costs for investments in cooling technology on top of the welfare changes due to the variations in energy demand and find negative median impacts on GDP in 2100, ranging from −0.94% under the RCP 8.5 to −0.05% under the RCP 1.9.

At the regional level, these studies highlight the role of terms-of-trade as a driver of GDP changes. The economy will be negatively affected in fossil-fuel-exporting countries, as they experience a reduction in the demand for their exports due to the reduction in heating service, while fossil-fuel-importing countries will benefit from the decrease in heating expenses. In some cases, these welfare mechanisms are moderated by the rebound effects generated by the changing fuel prices, as shown by Labriet et al( 2015). The study is the only IAM-based assessment accounting for price-induced rebound effects on consumption. GE gas consumption for heating is higher than what is found in the PE. The price change deriving from the decrease in gas consumption for heating impacts the energy markets through rebound effects that, globally, result in a less sharp decrease in the demand for heating energy (the ex-post percentage decrease is 34.2%–38.3% higher than the initial projections, depending on the long-term temperature increase going from 1.6 °C to 5.7 °C).¹⁰

The few studies reporting the impact of thermal adaptation on global emissions with respect to the emissions in the no climate change scenario tend to find only marginal impacts. Labriet et al( 2015) quantify the total emissions from the increase in energy demand for buildings in 2100 to be 1.2 (2.5) Gt CO2/year under RCP 6 (RCP 8.5), while Isaac and van Vuuren (2009) find an increase related to residential energy demand of 1.17 Gt CO2/year under RCP 8.5. The feedback between the energy and climate systems due to changes in heating and cooling services at the global level should not be considered negligible even if the overall magnitude of the increase is low. Moreover, it is important to keep in mind that these two studies might underestimate the needs of energy for adaptation because the extensive margin is not modeled (Labriet et al 2015) or because the commercial sector is not included (Isaac and van Vuuren 2009).

Notwithstanding the robust general trends with respect to heating and cooling demand, model results show significant heterogeneity. Figure 8 presents a disaggregation of the incremental energy demand projected by different IAM categories (Types 1–5), for residential (left quadrant) and buildings (right quadrant). Only part of the groups identified provide projections in each combination of year (2050 and 2100), energy service (cooling, heating and combined) and sector (residential, buildings). Therefore, only the projections which make it possible to simultaneously compare the highest number of groups are included, namely the projections reporting the value of the incremental energy demand in 2050.

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The analysis of the projections reported in figure 8 suggests that models lacking extensive margin adjustments (Type 4) highly underestimate the additional cooling needs of the building sector, finding an overall reduction in energy demand. Instead, the requirements for heating are in line with other modeling approaches. This result points to the importance of including the extensive margin in the structure of IAMs energy demand. Other major modeling differences are ruled out, as Type 4 models differ from Type 3 models only as regards their representation of the extensive margin.

There is no univocal relationship between the results of projections and the modeling of the interactions between the economy and the energy system. Among the processed-based, bottom-up models, PE IAMs (Type 1) tend to project a median energy increment in line with the level projected by those GE IAMs adopting the same type of modeling of climate shock (Type 3). Scenarios from Type 1 models show a much smaller dispersion compared to Type 3. Type 1 models—bottom up models—might be more optimistic regarding the role of technological change and efficiency improvements compared to Type 3 models.

Among the top-down simulation models relying on exogenous shifts, PE IAMs (Type 5) tend to project a higher median increment than GE IAMs (Type 2) and a higher median reduction. Type 2 models do not include the important effect of prices, which are also related to the net trading position on the international market (terms of trade effect). Higher prices would induce a partial reduction in demand. Lower prices could induce a rebound effect, pushing further demand. GE effects also imply changes in the income available to households and in the cost structure of producers, which are further elements that can lead to differences between PE and GE effects.

The intensity of future global warming exacerbates the differences across model type results. For instance, in the projections of the total incremental demand of buildings (Panel a), under RCP 4.5 (RCP 8.5), the median total demand of Type 2 models is two times (five times) higher than the median demand of Type 3 models. This pattern is consistent across end uses and sectors, and suggests that the specific choice over the climate variable and the functional form of climate shock may affect the projections more sharply than other modeling aspects.

The differences across the projections of model types vary according to the specific sector and end use service. The gap between the projections is higher than for the cooling demand of the commercial sector (panel a) and for the heating demand of the residential sector (panel b). Top-down models based on sectoral-specific exogenous shift parameters project substantially higher increases in incremental commercial cooling demand. Energy demand for the residential sector projected by Type 2 top-down models (van Ruijven et al 2019) and by Type 3 models (GCAM by Clarke et al 2018 and AIM/CGE by, Park et al 2018) under the SSP 2 and RCP 8.5¹¹ is comparable (8 EJ in the former study and 9–10 EJ in the two latter studies), while it differs remarkably when the commercial sector is considered (114 EJ in the former study and 4–22 EJ in the two latter studies). Therefore, the adoption of transmission mechanisms of climate on energy demand allowing for the sectoral characterization of the shocks can be identified as a key driver of heterogeneous results.