# How to allocate mitigation efforts between home insulation, fuel switch and fuel decarbonization?
## Insights from the French residential sector

Célia Escribe, Lucas Vivier, Louis-Gaëtan Giraudet, Philippe Quirion

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Célia Escribe, Lucas Vivier, Louis-Gaëtan Giraudet, Philippe Quirion. How to allocate mitigation efforts between home insulation, fuel switch and fuel decarbonization? Insights from the French residential sector. Environmental Research Letters, 2024, 19 (5), pp.054018. 10.1088/1748-9326/ad3a7f.hal-04861252

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ENVIRONMENTAL RESEARCH
LETTERS

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LETTER

# How to allocate mitigation efforts between home insulation, fuel switch and fuel decarbonization? Insights from the French residential sector

Célia Escribe<fnref n="1" />,<fnref n="4" />,<fnref n="5" />,* ID, Lucas Vivier<fnref n="1" />,<fnref n="2" />,<fnref n="5" />,* ID, Louis-Gaëtan Giraudet<fnref n="1" />,<fnref n="2" /> ID and Philippe Quirion<fnref n="1" />,<fnref n="3" /> ID

E-mail: celia.escribe@polytechnique.edu and lucas.vivier@enpc.fr

**Keywords:** climate change mitigation, energy efficiency, residential buildings, integrated assessment, energy modeling, second-best policy

Supplementary material for this article is available online

Abstract

Reducing greenhouse gas emissions in residential buildings relies on three channels that are rarely assessed together—insulating homes, switching to low-carbon heating systems and decarbonizing heating fuels. Their combination results from an interplay between top-down planning of the energy system and decentralized policies for the residential sector—insulation subsidies in particular. In this paper, we examine how the design of insulation subsidies influences the allocation of efforts between these three channels. To do so, we use an innovative framework coupling a highly detailed model of residential energy demand with a highly detailed model of the energy system, both focused on France. We find that the most cost-effective effort allocation to reach carbon neutrality implies 19% emission reductions from home insulation, 36% from fuel switch and 45% from fuel decarbonization. This however requires perfectly targeted subsidies. In three alternative, arguably more realistic subsidy scenarios, we find that total system cost is increased by 11%–16%. Our results highlight the key role played by subsidy specifications in determining the trade-off between insulation and fuel switch, e.g. insulation investments doubles, and heat pump adoption is 19% lower, when subsidies are restricted to the most comprehensive measures. Finally, alternative assumptions regarding the availability of renewable energy sources—biogas in particular—imply stronger energy efficiency efforts.

1. Introduction

The building sector contributes significantly to energy consumption and greenhouse gas (GHG) emissions in temperate and high-income countries (Cabeza et al 2022, IEA 2023). Most of these contributions stem from residential space heating. To mitigate the associated GHG externality, three main actions can be pursued: (i) improving the energy performance of the building envelope, e.g. through home insulation; (ii) switching to low-carbon heating systems, e.g. through the adoption of heat pumps

and wood boilers; and (iii) decarbonizing heating
fuels, e.g. by investing in wind power, solar power or
renewable gas production (e.g. through methanation
or biogas). Mitigation strategies therefore result in a
trade-off between demand- and supply-side invest-
ments to abate GHG emissions while maintaining
energy balance at the hourly scale. In particular, the
strong seasonality in space heating demand drives
peak energy load, thus impacting the investments
needed in the energy sector (Maxim and Grubert
2023). These strategies also result from an inter-
play between centralized decisions about the energy

<footnote n="1">¹ Centre international de recherche sur l'environnement et le développement (CIRED), Nogent-sur-Marne, France</footnote>

<footnote n="2">² École des Ponts ParisTech, Champs-sur-Marne, France</footnote>

<footnote n="3">³ Centre national de la recherche scientifique (CNRS), Paris, France</footnote>

<footnote n="4">⁴ Centre de mathématiques appliquées de l'Ecole Polytechnique (CMAP), Palaiseau, France</footnote>

<footnote n="5">⁵ These authors contributed equally.</footnote>

<footnote>* Authors to whom any correspondence should be addressed.</footnote>
system and decentralized decisions from households
in the residential sector, which makes them challe-
ging to assess together.

From a policy perspective, the optimal effort
allocation between the three mitigation channels
would theoretically be guided by a carefully designed
carbon price—the textbook economic solution to the
GHG externality. In the residential sector, however,
investment barriers are at the source of the ‘energy
efficiency gap’ – i.e. suboptimal investment in energy
efficiency (Gerarden et al 2017). Chief among these
barriers are credit constraints keeping low-income
households in poorly insulated dwellings, where sig-
nificant adverse health effects have recently been
identified (Dervaux and Rochaix 2022). In this con-
text, a first-best policy aimed at maximizing social
welfare would combine a common carbon price with
individually tailored energy efficiency subsidies in
the residential sector (Allcott et al 2014, Chan and
Globus-Harris 2023). In practice, however, carbon
prices are rarely set at their socially optimal level, nor
do they cover all relevant sectors—if they are imple-
mented at all<fnref n="6" /> –, and subsidies cannot realistically be
individually tailored.

While using realistic energy efficiency subsidies
in the residential sector to jointly address the GHG
externality and the energy efficiency gap is considered
a second-best approach, there is significant flexibility
in the way they can be designed. The subsidy amount
can be proportional to the insulation performance,
or determined *ad valorem*, i.e. as a fixed proportion
of the product price. In addition, subsidies may be
uniform or targeted to more comprehensive meas-
ures. The combination of these features in turn affects
the allocation of efforts between home insulation,
fuel switch and fuel decarbonization in ‘second-best’
approaches.

Most related analyses, however, keep at least one
channel exogenous—e.g. home insulation and fuel
switch in energy system models (Brown et al 2018,
Shirizadeh and Quirion 2022), fuel decarboniza-
tion in building stock models (Giraudet et al 2021,
Mastrucci et al 2021, Berrill et al 2022, Cabeza et al
2022). This limitation may result in inconsistencies
between energy demand projections and the trans-
formations they imply in the supply system. A few
recent studies have made significant progress towards
endogenizing all three channels (Zeyen et al 2021,
Mandel et al 2023) for all EU. They however focus on
optimal investment and ignore distortions in house-
hold decision-making. Finally, mitigation strategies
have recently been investigated in the building sec-
tor using REMIND, a global integrated assessment
model (Levesque et al 2021), but its processes are too
coarse to capture the heterogeneity inherent in the

building sector and the detailed impact of demand-
side policies on the energy mix.

In this paper, we contribute to the integrated
assessment of mitigation strategies in the residen-
tial sector by assessing different effort allocations
under various subsidy designs. To do so, we develop
an integrated framework combining a detailed rep-
resentation of technology with advanced decision-
making processes. Specifically, we link Res-IRF, a
model of household energy demand (Vivier and
Giraudet 2024) and EOLES, a model of energy sup-
ply (Shirizadeh and Quirion 2021), both focusing on
France. The linkage is realized through joint optim-
ization in a dynamic recursive perspective. The dif-
ferent policy options are assessed by a social planner
seeking to minimize total system costs—including
investment, energy operation and health costs—while
achieving carbon neutrality by 2050. The added value
of our framework lies in providing a detailed, endo-
genous description of all three mitigation chan-
nels while relying on an optimization framework
fit for discussing first- and second-best approaches.
Specifically, we introduce four policy scenarios, each
including a shadow price of carbon in the energy sys-
tem alongside ad-valorem subsidies for heat pumps.
The differences among scenarios arise from the spe-
cification of home insulation subsidies. The first
scenario adopts a first-best approach, offering per-
fectly targeted subsidies for home insulation. In con-
trast, the subsequent three scenarios correspond to a
second-best approach, offering more realistic, albeit
coarser, subsidy specifications (see table 1).

In the ‘first-best’ approach where homeowners
are induced to invest in the insulation level that is
the most socially profitable for their dwelling, we find
that home insulation contributes 19% of emission
reductions, fuel switch 36% and fuel decarbonization
45%. Turning to alternative, arguably more realistic
subsidy designs in ‘second-best’ approaches, we find
that total system cost increases by 11% under pro-
portional subsidies, 14% under *ad valorem* subsidies
targeted at comprehensive actions and 16% under
uniform *ad valorem* subsidies. The increase in total
cost is paralleled by a greater role of fuel switch and
lesser role for insulation. As for the energy system, we
find that second-best scenarios imply a greater reli-
ance on peaking plants and solar PV than in first best.
Lastly, we assess the robustness of our results to fuel
decarbonization specifications and find the potential
of biogas to be the most sensitive assumption. Our
main policy conclusions are as follows: first, it is cru-
cial to engage all available channels for mitigation;
second, the specification of subsidy programs signi-
ficantly influences both the strategic approach and its
cost-effectiveness.

The remaining of the paper is organized as fol-
lows. Section 2 describes the method. Section 3
presents the results. Section 4 discusses them and
section 5 concludes.

<footnote n="6">⁶ For instance, in France, the government froze the ‘household’ carbon tax rate in response to the Yellow Vest protest movement (Douenne and Fabre 2022).</footnote>
<table><caption>**Table 1.** Summary of the interaction between decarbonization channels and policies.</caption><thead><tr><th rowspan="2">Channels</th><th>Supply-side: energy sector</th><th colspan="2">Demand-side: residential sector</th></tr><tr><th>Fuel decarbonization</th><th>Home insulation</th><th>Fuel switch</th></tr></thead><tbody><tr><td rowspan="2">First-best approach policies</td><td rowspan="2">Shadow price of carbon associated with the carbon neutrality constraint</td><td colspan="2">Residential carbon tax</td></tr><tr><td>Perfectly targeted subsidies</td><td>Ad valorem subsidies for heat-pumps</td></tr><tr><td rowspan="2">Second-best approach policies</td><td rowspan="2">Shadow price of carbon associated with the carbon neutrality constraint</td><td colspan="2">Residential carbon tax</td></tr><tr><td>Coarsely targeted subsidies</td><td>Ad valorem subsidies for heat-pumps</td></tr></tbody></table>

## 2. Methods

We take a whole-system approach coupling a demand-side model, Res-IRF, with a supply-side energy model, EOLES, both focusing on France.

### 2.1. Modelling parts

Res-IRF is a dynamic microsimulation model of energy demand for space heating in the French building stock (Vivier and Giraudet 2024). Developed with the goal of improving behavioral realism (Mundaca et al 2010), the model provides a rich description of insulation levels (for walls, roofs, floors and windows) and heating systems (heat pumps, electric heating, gas-, oil- and wood-fired boilers). It simulates the evolution of energy consumption through three endogenous processes—the construction and demolition of buildings, the renovation of existing dwellings through insulation and fuel switch, and adjustments in heating behaviour. Energy efficiency investments are made by households and influenced by key economic costs and benefits, namely investment and financing costs, energy bill savings, and subsidy amounts. When making these investments, households face various barriers, such as credit constraints (decreasing with income), landlords' inability to pass energy efficiency investment onto rents, decision frictions in collective housing, and hidden costs (e.g. the inconvenience of insulation works). The model also takes into account a wedge between predicted and realized energy consumption in order to capture the much-discussed energy performance gap (Christensen et al 2021). This wedge varies endogenously in response to energy efficiency improvements, energy prices and household income and captures the rebound effect in particular. The exercise presented here uses Version 4.0 of the model. Its main features and data are outlined in section A.1 of the supplementary material.

The EOLES model suite optimizes investment in and operation of the French energy system in order to meet a given energy demand (Shirizadeh and Quirion 2022). Total cost include annualized capital costs, maintenance costs and operating costs. The model relies on a detailed description of various technologies. Electricity can be generated by solar PV,

onshore and offshore wind, hydroelectricity, gas used in open cycle (OCGT) or combined cycle gas turbines (CCGT), and nuclear reactors. Hydrogen can be produced by water electrolysis. Gas can be fossil gas, biogas produced by methanization or pyrogazeification, or synthetic methane produced by methanaation. Energy can be stored in batteries and pumped-hydro storage stations, in the form of hydrogen in salt caverns or in the form of methane in gas reservoirs. Technology dispatch is specified with an hourly temporal resolution, capturing the weather dependence of supply and demand and the specific challenges related to flexibility options. Given the strong reliance on gas in the residential sector currently, the interaction between gas and electricity becomes critical. While Res-IRF focuses on residential energy demand, EOLES spans all end-use sectors electricity demand. We therefore need to feed the latter with exogenous assumptions regarding non-residential uses (i.e. commercial buildings, industry, transport and agriculture), which we borrow from the French transmission system operator latest projections (RTE (2022), central scenario). In particular, this exogenous demand includes space cooling demand, which is therefore not subject to endogenous rebound effects<fnref n="7" />. We consider France independently, excluding interaction with neighboring countries. Additional details can be found in the supplementary material A.2, and an exhaustive description of the model is available in Shirizadeh and Quirion (2021).

### 2.2. Coupling

Our approach to coupling Res-IRF and EOLES relies on a dynamic recursive optimization framework in which a social planner makes investments in the energy system while funding energy efficiency subsidy programs in the residential sector. Specifically, the social planner seeks to minimize the total system cost under a national carbon budget constraint. Two subsidy programs are considered, together supporting the most strongly encouraged energy efficiency measures in France—insulation of the building envelope and adoption of heat pumps. These programs add up to the carbon tax that is already in place in the

<footnote n="7">⁷ Reversible heat pumps are not included in the analysis.</footnote>
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French residential sector<fnref n="8" />. On top of this policy portfolio, a residual carbon price is endogenously determined as the shadow price of the carbon constraint.

The coupled modelling framework is illustrated in figure 1. The social planner's objective function is the annualized system cost, i.e. the sum of the annualized costs of the energy supply system, the annualized costs of heating and insulation investment, and the annualized health costs from poor insulation. Our inclusion of health costs in the social planner's objective function is motivated by recent evidence of high morbidity and mortality rates among low-income households living in the least energy efficient dwellings (Dervaux and Rochaix 2022)<fnref n="9" />. Within a given time step, a given set of subsidy parameters determines final energy demand for residential heating in the Res-IRF model. At the same time, the EOLES model is run to optimize capacity investment and dispatch while meeting total energy demand. The social planner therefore effectively sets the subsidy parameters so as to minimize total system cost under the carbon budget constraint. This optimization is particularly challenging from a computational perspective, since the objective function depends on the subsidy parameters in a nonlinear way. To cope

with this difficulty, we use a bayesian optimization framework relying on the Expected Improvement algorithm (Vazquez and Bect 2010). Further details can be found in section A.8 in the supplementary material.

The one-step optimization is then iterated over the entire time horizon, assuming a 5 year time step, from 2020 to 2050¹⁰. Note that our framework is myopic in that the social planner only considers one time step at a time. We argue this is fit for capturing short-sightedness in both the politicians' and stakeholders' behavior (Victoria et al 2020), resulting in slow capital accumulation in both the building stock and the energy mix. Electricity prices are endogenously determined through demand-supply equilibrium. Technically, electricity prices for a given period are computed as the levelized cost to meet endogenous demand from the previous period. The resulting prices are topped with exogenous taxes. The prices of other fuels (gas, oil, wood) are exogenous.

Building on ADEME (2022), we consider an emission target of 4 MtCO₂ in 2050 for the electricity and residential sectors, representing a 93% reduction compared to 2018 emissions, and we assume a convex decrease in emissions along the trajectory (as displayed in table S10 in the supplementary material). All investments costs are annualized with a 3.2% discount rate, which is the value recommended for public investment in France (Ni and Maurice 2021). We then compare all scenarios in terms of total system cost, defined as the sum of annualized costs

<footnote n="8">⁸ Initially scheduled to increase, the French carbon tax was frozen at €45/tCO₂ from 2020 to 2050 in response to the yellow vest movement.</footnote>

<footnote n="9">⁹ We thereby treat health costs as a pure externality, internalized by the social planner but not by households. One could argue that, since health is a private matter, failure to internalize it is rather akin to consumer irrationality. Notwithstanding, given the disproportionate prevalence of health costs among low-income households, we attribute them to credit constraints preventing their elimination through energy renovation—a legitimate market failure to correct.</footnote>

<footnote n="10">¹⁰ Res-IRF is run with the current policy scenario until 2025 and the first optimization period concerns the period 2025–2030.</footnote>
<table><caption>**Table 2.** Description of insulation policy scenarios and supply-side assumptions. All scenarios include *ad valorem* subsidies for heat pumps. Variants for supply-side assumptions are based on scenarios from ADEME (2022) (scenario S2) and RTE (2022).</caption><thead><tr><th>Scenario</th><th>Description</th></tr></thead><tbody><tr><td><strong>Insulation policy</strong></td><td></td></tr><tr><td>Optimal</td><td>The social planner designs an optimal subsidy for each household inducing them to invest in their more cost-effective option from a system perspective.</td></tr><tr><td>Uniform</td><td>All insulation measures are supported with the same <em>ad valorem</em> rate, to be determined. The <em>ad valorem</em> subsidy is restricted to the most comprehensive insulation measures-i.e. those permitting an upgrade by at least two energy performance certificate (EPC) ratings.</td></tr><tr><td>Comprehensive<br>Proportional</td><td>All insulation measures are supported by a subsidy, the amount of which is proportional to the expected energy savings. The policy variable to be determined is the euro amount per unit of saved energy.</td></tr><tr><td><strong>Variants with supply-side restrictions</strong></td><td></td></tr><tr><td>Biogas-</td><td>Biogas potential reduced by 28% compared to reference.</td></tr><tr><td>Renewables-</td><td>Potential for solar PV, onshore wind and offshore wind is reduced by 40%, 12% and 20% respectively compared to reference.</td></tr><tr><td>Nuclear-</td><td>Potential for newly built nuclear capacity is reduced by 50% compared to reference.</td></tr></tbody></table>

over the 2025–2050 period<fnref n="11" />. The health benefits from upgrading the least efficient dwellings are valued using newly published data for France (Dervaux and Rochaix 2022)<fnref n="12" />. We use the representative weather year 2006 as the basis for calculating renewable energy production and space heating demand (Pfenninger and Staffell 2016). It has been shown that 2006 is the best representative year for weather conditions (Shirizadeh et al 2022)<fnref n="13" />.

## 2.3. Scenarios

Subsidy specifications are the key control variables in the social planner's optimization problem alongside investment and dispatch in the energy system. We consider two types of subsidies—one for the adoption of heat pumps and one for insulation of the building envelope. As heat pumps emerge as the primary choice for transitioning to low-carbon heating fuels in the building sector (Fallahnejad et al 2024), we focus on a single *ad valorem* subsidy design, the rate of which is to be optimized.

In contrast, insulation investments offer a multitude of options. Hence, we explore diverse specifications for this subsidy design, presenting different scenarios that reflect different paradigms (refer to table 2). In a first-best, ‘optimal’ scenario, households behave as if they were facing no investment barrier and thus invest in the most socially profitable option.

In second-best scenarios, the barriers are taken into account and subsidies are implemented to overcome them, with a rate to be determined. In an effort to mimic the key programs implemented in France, we consider three subsidy regimes: a ‘uniform’ one, similar to the tax credit program that ran from 2005 to 2020; a ‘comprehensive’ one, similar to a scheme called ‘Habiter mieux sérénité’; and a ‘proportional’ one, similar to white certificate obligations (Giraudet et al 2021). By design, the ‘uniform’ subsidy is less targeted than the ‘comprehensive’ and the ‘proportional’ subsidies.

The endogenously-determined subsidy levels and the effort allocation they implement are sensitive to underlying assumptions regarding the potential for low-carbon energy sources—biogas (including methanization and pyrogazeification), solar, onshore and offshore wind and nuclear. As pointed out by public authorities, the magnitude of these potentials is highly uncertain (ADEME 2022, RTE 2022). To assess the robustness of our results to such uncertainty, we re-run our scenarios with more conservative assumptions regarding the potentials for biogas, renewables and nuclear power (table 2). The potentials for renewable energies (photovoltaics, onshore wind power, offshore wind power) and nuclear power in the reference scenario are given in the supplementary material.

## 2.4. Effect decomposition

In order to decompose the various channels of GHG emission reductions, we use an additive log mean division index model (Ang and Zhang 2000) specified as follows:

$$GHG = \text{Surface} \times \sum_{i} sh_{i} \times I_{i} \times HI_{i} \times C_{i}$$

where $sh_i$ is the share of heating system i in the building stock (%), $I_i$ is the specific energy consumption (kWh/m²) determined by the insulation

<footnote n="11">¹¹ Building on Hirth et al (2021)'s work with the EMMA model, we use a 0% rate of pure time preference to give equal weight to all years when adding up annualized costs over the whole time horizon.</footnote>

<footnote n="12">¹² €7500 for each upgraded dwelling occupied by a low-income household, which can be decomposed into €400 reduction in care costs, €1400 avoided morbidity cost and €5700 avoided mortality cost.</footnote>

<footnote n="13">¹³ Our study does not take into account the effects of climate change, as we assume a static climate throughout the study period. Climate change is expected to only slightly reduce space heating demand in France by 2050 (Elnagar et al 2023); this factor is outside the scope of our current study.</footnote>
<figure><img src="image_6.png" /><figcaption>**Figure 2.** Decomposition analysis of the main decarbonization channels for the first-best scenario ('optimal scenario') using LDMI method (section 2). The increase in heating intensity is due to the rebound effect. Home insulation accounts for 19% of total GHG emission reduction when accounting for rebound effects that stem from heating intensity.</figcaption></figure>

level and $C_i$ is the carbon content of the fuels used (gCO$_2$ kWh$^{-1}$). Next to these three channels of interest, we consider the contributions of total housing surface ($m^2$) and the varying intensity with which households heat their dwelling ($HI_i$, dimensionless)$^{14}$. Additional details about the methodology can be found in section A.4 in the supplementary material.

# 3. Results

## 3.1. First-best scenario

In the 'optimal' scenario, home insulation (net of rebound effect) accounts for 19% of total GHG emission reduction in 2050 compared to 2020, fuel switch for 36%, and fuel decarbonization for 45% (figure 2). In addition, energy consumption is reduced by 37% in 2050 compared to 2020, mainly through insulation (column 'Optimal' in table 3). This order of magnitude is consistent with that found in related assessments of the building sector, e.g. 21%–35% energy consumption reduction in Mandel et al (2023), 44–51% in Zeyen et al (2021) and 32% in Palzer and Henning (2014)$^{15}$.

Unconstrained by investment barriers in energy efficiency markets, the social planner targets

insulation efforts towards upgrading the least efficient dwellings, i.e. those with EPC ratings G and F. This approach significantly reduces energy bills, operational costs in the electricity sector and health costs. As a result, the count of F- and G-rated dwellings sharply decreases and 80% of dwellings are rated C or better in 2050 (figure S7 in the supplementary material).

By then, 25% of energy demand for space heating is met by electricity (table 3) and 15 million heat pumps have been installed, providing heating service to about 17% of dwellings. Annual electricity consumption remains relatively stable over time under the countervailing effects of insulation efforts and increased heat pump adoption. Overall, this first-best strategy requires approximately €150 billion investment in insulation (or €6 billion per year on average) and €77 billion investment in heat pumps (or €3 billion per year on average) (table 3).

In 2050, 77% of electricity generation is met by solar, wind, and hydro power. This order of magnitude is consistent with that found in related works, e.g. 92%–97% in Zeyen et al (2021) and 90% in Mandel et al (2023). Our somewhat lower figure can be attributed to the significant role played by nuclear in France, accounting for 20% of electricity generation in our assessment. As in Zeyen et al (2021), the available potential for biogas is fully utilized, providing 46 TWh through methanization and 19 TWh through pyrogasification. Synthetic methane (obtained from methanation) is employed to fulfill the remaining gas demand for space heating and peak-load power plants, while hydrogen (obtained

<footnote n="14">14 This heating intensity varies with energy efficiency improvements and energy prices in Res-IRF to reflect adaptation of households heating behavior.</footnote>

<footnote n="15">15 The latter two studies rely on coarser representations of the building stock, thus potentially overestimating the potential for cost-efficient insulation. They moreover have a broader regional scope, not limited to France.</footnote>
<figure><img src="image_7.png" /><figcaption>**Figure 3.** Difference in total annualized system costs over period 2025–2050 (Billion EUR) compared to the ‘optimal’ subsidy insulation scenario. Energy operational costs include all costs related to system operation (e.g. methanization variable cost, wood energy expenditures).</figcaption></figure>

from electrolysis) is exclusively used for peak-load plants. Overall, peak-load power plants (gas turbines, such as OCGT and CCGT, and hydrogen turbines H2-CCGT), contribute 2.4% of total electricity production. In 2050, 17 TWh of fossil gas are still used to meet total methane demand—including final gas demand from the residential sector and intermediary gas demand for peaking plants, which is low enough to stay within the 4 MtCO2 carbon budget of that year.

Figure 15 in the supplementary material displays the comprehensive breakdown of total system costs including the energy supply system cost.

## 3.2. Second-best alternatives

By design, the second-best scenarios entail a higher total system cost –11% to 16% higher than in first best, depending on the variants (figure 3 and table 3)<fnref n="16" />. This is due to the fact that, unlike second-best alternatives, the first-best scenario ignores energy efficiency barriers that differently affect heterogeneous households. For instance, while the first-best scenario will optimally select the most cost-effective insulation measure in a given dwelling, investment in that measure will be hindered in practice by credit constraints if the occupant is from the low-income group. This barrier could not be fully overcome by alternative subsidy designs. This results in a different effort allocation between first-best and second-best scenarios, with a larger role played by insulation in the first-best scenario (figure 4). In the first-best scenario, insulation alone achieves a 30% reduction in energy consumption, compared to the 6%–20% range observed in second-best designs. Consequently, in the first-best scenario, there is a lesser need for

additional capacities like peaking plants and batteries (–3 GW), as well as solar capacity (–30 GW) (figure 5). This adjustment substantially lowers the energy system’s annual costs by 0.7–1.5 billion euros per year.

The effort allocation between insulation, fuel switch and fuel decarbonization varies greatly across subsidy designs. Compared to ‘uniform’ subsidies, ‘comprehensive’ subsidies entail a €23 billion lower total system cost (or €0.9 billion per year on average), as illustrated in figure 3. Specifically, they involve twice as much investment in insulation (hence an extra €4.5 billion per year), less investment in both heat pump adoption (5 million fewer, hence a €3.7 billion less per year) and energy system (€0.5 billion less per year). This is achieved through endogenously-determined *ad valorem* subsidy rates of 50% to 75% for insulation and 0% to 60% for heat pumps over time horizon (figure S5 in the supplementary material). The ‘comprehensive’ and ‘proportional’ scenarios produce very similar results, save for more investment in insulation, and a slightly lower total system cost, in the former. Such a similarity by contrast highlights the poorer performance of the less well-targeted ‘uniform’ subsidy design, thereby revealing that energy performance is only poorly reflected in technology cost<fnref n="17" />.

Overall, our results highlight the key role played by subsidy specifications in determining the trade-off between insulation and fuel switch (figure 4). Subsidy specifications are more marginal in the energy system (which again supplies all end-use sectors), and concentrated on peak-load and solar capacity and production. The main result is a 6 GW lower peak-load

<footnote n="16">16 Preliminary tests established that the carbon budget could not be met without subsidies. All second-best scenarios therefore fare better than a ‘laissez-faire’ scenario.</footnote>

<footnote n="17">17 One can think of window replacement, for which households have a high willingness to pay, despite its ranking low in the energy performance merit order.</footnote>
<figure><img src="image_8.png" /><figcaption>**Figure 4.** Trade-offs between energy savings from home insulation and switch to heat pumps in 2050 across scenarios. Home insulation is reflected through energy demand savings compared to 2020, while heat pumps is reflected through stock evolution (in reference to 39 millions dwellings in 2050).</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Figure 5.** Comparison of electricity mix across different scenarios. All scenarios install maximal capacity of onshore and offshore capacity. First-best ('optimal') scenario needs less peaking plants and batteries (–3 GW), as well as solar capacity (–30 GW).</figcaption></figure>

capacity in the ‘comprehensive’ scenario than in the ‘uniform’ one (table 3).

The residual carbon values associated with the carbon constraint vary mildly across scenarios, within a range that is consistent with the value recommended by French authorities for public assessment (table S11 in supplementary material A.7).

Interestingly, our results continue to hold qualitatively when health costs are not included in the social planner's objective function, which establishes their robustness (figures S3 and S4 in supplementary material A.5).

**3.3. Variants with restricted supply-side assumptions**

As discussed in section 2.3, we assessed the robustness of our results to more conservative (yet plausible) assumptions regarding the potential for biogas, nuclear and renewables.

By design, all alternatives result in a higher total system cost compared to the reference assumptions. In general, more limited potentials for fuel decarbonization imply stronger energy efficiency efforts through home insulation or heat pump adoption. Figure 6 more specifically illustrates the trade-offs
<table><caption>**Table 3.** Summary of results. In the table, energy consumption refers to 2050. Values in billion euros are the sum of actual invested values between 2025 and 2050. In contrast, the metric Total system costs, used to compare scenarios (e.g in figure 3), refers to the average of annualized costs over time period 2025–2050. Comparison is done with the ‘optimal’ scenario.</caption><thead><tr><th></th><th>Unit</th><th>Uniform</th><th>Comprehensive</th><th>Proportional</th><th>Optimal</th></tr></thead><tbody><tr><td>Number of heat pumps</td><td>Million</td><td>21</td><td>17</td><td>15</td><td>15</td></tr><tr><td>Investments heat pumps</td><td>€Billion</td><td>181</td><td>88</td><td>84</td><td>77</td></tr><tr><td>Subsidies heat pumps</td><td>€Billion</td><td>141</td><td>29</td><td>12</td><td>NA</td></tr><tr><td>Investments insulation</td><td>€Billion</td><td>98</td><td>210</td><td>198</td><td>150</td></tr><tr><td>Subsidies insulation</td><td>€Billion</td><td>23</td><td>112</td><td>125</td><td>NA</td></tr><tr><td>Savings fuel switch</td><td>%</td><td>14</td><td>7</td><td>4</td><td>4</td></tr><tr><td>Savings insulation</td><td>%</td><td>6</td><td>17</td><td>20</td><td>30</td></tr><tr><td>Consumption electricity</td><td>TWh</td><td>63</td><td>53</td><td>52</td><td>47</td></tr><tr><td>inc. heat pumps</td><td>TWh</td><td>48</td><td>33</td><td>30</td><td>28</td></tr><tr><td>inc. direct electric</td><td>TWh</td><td>16</td><td>20</td><td>22</td><td>19</td></tr><tr><td>Consumption wood</td><td>TWh</td><td>60</td><td>56</td><td>57</td><td>55</td></tr><tr><td>Consumption district heating</td><td>TWh</td><td>24</td><td>22</td><td>21</td><td>18</td></tr><tr><td>Consumption oil</td><td>TWh</td><td>0</td><td>0</td><td>0</td><td>0</td></tr><tr><td>Consumption gas</td><td>TWh</td><td>52</td><td>63</td><td>66</td><td>65</td></tr><tr><td>Renewable capacity</td><td>GW</td><td>228</td><td>222</td><td>222</td><td>198</td></tr><tr><td>Peaking plants capacity</td><td>GW</td><td>54</td><td>48</td><td>48</td><td>51</td></tr><tr><td>Battery capacity</td><td>GW</td><td>8</td><td>8</td><td>8</td><td>2</td></tr><tr><td>Onshore/offshore production</td><td>TWh (%)</td><td>382 (52)</td><td>382 (53)</td><td>382 (53)</td><td>382 (54)</td></tr><tr><td>PV production</td><td>TWh (%)</td><td>147 (20)</td><td>140 (19)</td><td>140 (20)</td><td>106 (15)</td></tr><tr><td>Hydroelectricity production</td><td>TWh (%)</td><td>52 (7)</td><td>52 (7)</td><td>52 (7)</td><td>52 (7)</td></tr><tr><td>Peaking plants production</td><td>TWh (%)</td><td>22 (2.3)</td><td>17 (2.3)</td><td>15 (2.1)</td><td>17 (2.4)</td></tr><tr><td>Nuclear production</td><td>TWh (%)</td><td>124 (17)</td><td>122 (17)</td><td>121 (17)</td><td>140 (20)</td></tr><tr><td><strong>Total system costs</strong></td><td>€B/year (%)</td><td>47.3 (+16%)</td><td>46.4 (+14%)</td><td>45.4 (+11%)</td><td>40.7</td></tr></tbody></table>

between insulation and heat pump in all four scenarios, under alternative assumptions regarding fuel decarbonization potentials.

Clearly, the results are most sensitive to restrictions in the potential for biogas, which systematically and significantly increase heat pump adoption compared to the reference scenario. Their effect is more mixed on insulation—slightly positive in the ‘optimal’ and ‘uniform’ scenarios and slightly negative in the ‘comprehensive and proportional’ scenarios. In contrast, the impact of more conservative assumptions regarding nuclear and renewables is limited. Overall, in the ‘uniform’ scenario, restrictions on the energy system systematically imply more effort dedicated to home insulation, which was relatively little exploited under the reference supply-side assumptions due to a lack of targeting through the design.

## 4. Discussion

Our findings are consistent with those of a recent study by the French National Environmental and Energy Management Agency (ADEME 2022), which is the only integrated assessment of decarbonization in the French residential sector we are aware of. Specifically, our results align with their middle-of-the-road scenarios (S2 and S3), which anticipate a 48%–55% reduction in heating energy demand compared to 2020 and a 26% share of heating provided by electricity. Our results however differ from those

established at the global level, e.g. Levesque et al (2021) finding 81% of emissions reductions achieved through fuel decarbonization, against 45% in our assessment. This discrepancy is arguably due to the France’s already low-carbon electricity supply<fnref n="18" />, which leaves little room for more of this mitigation option. However, investments in the energy mix are still required to maintain such a low electricity carbon content, as many historic nuclear power plants will be decommissioned before 2050. It should be noted that our myopic approach may result in lower investment in long-lasting abatement technologies leading to some lock-in effects in the investment decision for home insulation, heating systems, and energy technologies. This may potentially lead to a lower role of insulation and fuel switching compared to a perfect foresight mitigation strategy.

One important added value of our framework is to compare first-best and second-best strategies in a detailed bottom-up modeling framework. This allows us to identify a 11% to 16% higher total-system cost under second-best policy, as illustrated in figure 3 and table 3. In contrast, related works tend to rely on a first-best approach, implicitly assuming the policy considered to be optimal (e.g. Zeyen et al (2021), Mandel et al (2023)). Our more comprehensive

<footnote n="18">¹⁸ For instance, electricity carbon content is 56 gCO2/kWh in France compared to 435 gCO2/kWh in Germany (Unnewehr et al 2022).</footnote>
<figure><img src="image_10.png" /><figcaption>**Figure 6.** Evolution of demand-side mitigation strategy depending on supply-side assumptions. x-axis corresponds to energy savings through home insulation in percentage of 2020 consumption, and y-axis corresponds to stock of heat pumps in million (in reference to 39 millions dwellings in 2050). Size of points on the figure corresponds to the total system costs.</figcaption></figure>

approach delivers a more cautionary message: granted, significant demand reductions can in theory be achieved in the residential sector, but only two thirds of it is attainable with realistic subsidy programs.

Our results point to the importance of targeting the most comprehensive insulation measures for increasing the cost-effectiveness of subsidy programs. In particular, we show that ambitious but non-targeted insulation subsidies lead to more expensive mitigation strategy. It should be added here that targeting is also crucial for fairness. Indeed, the least energy-efficient housing segments, where comprehensive measures make the most sense, are disproportionately occupied by low-income households, particularly exposed to health costs (Bourgeois et al 2021). Incidentally, our analysis illustrates the benefits from factoring in health costs in building sector assessments. Another step towards incorporating more co-benefits from energy efficiency would be to include reference values for enhanced energy security and reduced air pollution (Ürge Vorsatz et al 2014).

This is however contingent upon the availability of empirical estimates.

Lastly, our analysis emphasizes that uncertainty about supply-side assumptions matters tremendously for demand-side strategies, especially in relation to subsidy design. This is important to bear in mind, considering that the available potential for low-carbon energy sources is known to be highly uncertain (Krey et al 2019), in particular biogas potential (Pye et al 2015, Panos et al 2023). Similarly, the current installation rates of renewables like solar and onshore wind in Europe raise concerns about the ability to sustain the necessary installation pace.

## 5. Conclusion

Taking a whole-system demand-supply approach to the decarbonization of residential space heating, we show how a politically-constrained social planner can implement energy efficiency subsidies so as to mitigate the GHG externality while overcoming energy
efficiency barriers in the most cost-effective way. We
found that carbon neutrality can be achieved in res-
idential heating with fuel switch contributing 36%
of emission reductions, home insulation 19% and
fuel decarbonization 45%. These efforts involve the
installation of 15 million heat pumps and 34% energy
demand reduction by 2050. Compared to this first-
best benchmark, the total-system cost is 11% to 16%
higher under second-best subsidy scenarios. Targeted
subsidy designs place a greater emphasis on insula-
tion. Finally, our results are very sensitive to supply-
side assumptions, specifically a lower biogas potential
significantly increase heat pump adoption. Overall,
our findings show that it is crucial to engage all avail-
able channels for mitigation of the residential sector,
and that the specification of subsidy programs signi-
ficantly influences both the strategic approach and its
cost-effectiveness.

Data availability statement

The data that support the findings of this study
are openly available on the DOI of the models.
Simulation results are openly available at the follow-
ing DOI: https://doi.org/10.5281/zenodo.10409404.

The data that support the findings of this study
are openly available at the following DOI: https://doi.
org/10.5281/zenodo.10409266.

Acknowledgments

This research was supported by Agence Nationale
de la Recherche (ANR) project PREMOCLASSE
(Contrat ANR-19-CE22-0013-01). Lucas Viver
thanks Palladio Foundation for their funding and
support. Célia Escribe thanks ADEME and Chair
Stress Test, RISK Management and Financial Steering
of the Foundation Ecole Polytechnique for their fund-
ing and support. All authors thank Elizabeth Zeyen,
Thibault Briera, Valentin Moreau, Céline Guivarch
and Josselin Garnier for useful comments and sug-
gestions on previous versions of this paper. We would
also like to thank the participants of the EAERE 2023,
IAEE 2023 and FAERE 2023 conferences for their
feedback.

Code availability

Both models EOLES and Res-IRF 4.0 are open-
source. The code of the framework can be freely
accessed at the following URL/DOI: https://doi.org/
10.5281/zenodo.10409266. Res-IRF 4.0 code can be
freely accessed at the following URL/DOI: https://doi.
org/10.5281/zenodo.10409266.

CRediT authorship contribution
statement

**Célia Escribe**: Conceptualization, Methodology, Data curation, Software, Formal analysis, Investigation, Writing—original draft, Writing—review & editing.
**Lucas Vivier**: Conceptualization, Methodology, Data curation, Software, Formal analysis, Investigation, Writing—original draft, Writing—review & editing.
**Louis-Gaëtan Giraudet**: Conceptualization, Methodology, Funding acquisition, Writing—review & editing **Philippe Quirion**: Conceptualization, Methodology, Funding acquisition, Writing—review & editing

Conflict of interest

The authors declare that they have no known compet-
ing financial interests or personal relationships that
could have appeared to influence the work reported
in this paper.

ORCID iDs

Célia Escribe https://orcid.org/0009-0001-5866-8332

Lucas Vivier https://orcid.org/0009-0003-8779-8042

Louis-Gaëtan Giraudet https://orcid.org/0000-0003-4611-3564

Philippe Quirion https://orcid.org/0000-0003-4066-2984

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