Authors contributions

A.L, R.C.P and G.L designed the research. A.L performed the modelling. A.L wrote the manuscript with contributions from all authors.

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5.8 Supplementary Information 161

Supplementary Note 3. Calibration of the REMIND baseline scenario

The buildings module of REMIND does not represent all the necessary drivers and relations between variables that are important to project future energy demand in buildings. For instance, the regional heating and cooling degree days are not included in the model even though they are an important concept to derive varying demand for space cooling in hot and cool countries. Instead of relying on the limited capabilities of REMIND, conditioned by numerical constraints, we make use of the bottom-up model EDGE^1,2 for deriving useful energy and energy service demand projections for different energy services. We then calibrate REMIND baseline to these trajectories. The emphasis in the REMIND

buildings module is then set on the technological possibilities to reduce final energy demand (and useful energy demand via improved building shell) for the level of energy service prescribed by EDGE.

We calibrate REMIND in an iterative process by adjusting efficiency parameters of the energy demand functions in REMIND until the useful energy demand closely resembles the EDGE projections. Buildings’

energy demand in REMIND covers one minor sector in addition to the ones covered in EDGE¹ and therefore does not fully match the EDGE projections.

The energy demand functions in REMIND take the form of a (nested) CES function. Each level of the CES nest has the following form.

𝑉𝑉𝑜𝑜=�� 𝜉𝜉𝑖𝑖(𝜃𝜃_𝑖𝑖𝑉𝑉𝑖𝑖)^{𝜌𝜌𝑜𝑜}

(𝑜𝑜,𝑖𝑖)

�

𝜌𝜌1𝑜𝑜

(1)

Where 𝑉𝑉_𝑜𝑜 is the output, 𝑉𝑉_𝑖𝑖 one of the inputs, 𝜉𝜉_𝑖𝑖 the output share of 𝑉𝑉_𝑖𝑖, 𝜃𝜃_𝑖𝑖 an efficiency parameter,𝜌𝜌_𝑜𝑜 a parameter related to the elasticity of substitution 𝜎𝜎_𝑜𝑜.

𝜌𝜌𝑜𝑜= 1− 1

𝜎𝜎𝑜𝑜 (2)

At the lowest level of the nested CES function, the inputs 𝑉𝑉𝑖𝑖 represent energy carriers provided by the Energy System Module (ESM) of REMIND. The difficulty to produce these energy carriers is reflected in the energy prices derived from the ESM. The calibration consists in adapting the efficiency parameters 𝜉𝜉𝑖𝑖

and 𝜃𝜃𝑖𝑖 such that, for the energy prices provided by the ESM, exogenous demand quantities 𝑉𝑉� are 𝚤𝚤

optimal. These exogenous demand quantities are provided by the EDGE model.

The calibration has to fulfil two constraints. The first one is a technological constraint. According to the Euler’s rule, the output of a homogenous function of degree one equals the sum of inputs weighted by their derivatives. The second constraint is economic: the ratio of derivatives must equal the ratio of prices, which we here simplify by equalizing prices and derivatives. From this we can compute the intermediary products in the nested CES function from the exogenous demand pathways 𝑉𝑉� and from the 𝚤𝚤

exogenous prices 𝑝𝑝�𝚤𝚤, derived from the ESM (3).

1 While EDGE only accounts for residential and commercial energy demand, REMIND also covers energy demand which could not be attributed to residential, commercial, industrial, transportation or non-energy uses (ONONSPEC in the IEA Energy Balances). This energy demand category is however small compared to the two residential and commercial uses.

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𝑉𝑉𝑜𝑜= � 𝑝𝑝�𝑉𝑉𝚤𝚤�𝚤𝚤

(𝑜𝑜,𝑖𝑖) (3)

We then equalize the prices and the derivatives by adjusting 𝜉𝜉𝑖𝑖 and 𝜃𝜃𝑖𝑖. The couple (𝜉𝜉_𝑖𝑖,𝜃𝜃𝑖𝑖) =�^{𝑝𝑝���𝑉𝑉}_𝑉𝑉^{𝚤𝚤 𝑖𝑖}

𝑜𝑜 ,^𝑉𝑉_𝑉𝑉^𝑜𝑜

𝑖𝑖� solves the equality between the prices and the derivatives.

By adjusting the quantities 𝑉𝑉𝑜𝑜 (which become the inputs 𝑉𝑉𝑖𝑖 at the above level of the CES nest) iteratively over the levels of the CES nest, and the parameters 𝜉𝜉𝑖𝑖 and 𝜃𝜃𝑖𝑖, we ensure that the quantities 𝑉𝑉� at the 𝚤𝚤

bottom level of the CES nest are optimal for the 𝑝𝑝�𝚤𝚤 prices. At the top level of the CES nest, which combines labor, capital and energy services to produce GDP, we adjust the price of labor to make sure that the exogenous GDP trajectory is met while respecting equation (3).

However, the prices taken at first from the ESM may not correspond to the production of the EDGE quantities. To make sure that the prices from the ESM correspond to the exogenous energy demand quantities, we run REMIND with the efficiencies computed above and derive the new ESM prices from this run. We then compute new efficiencies based on the new prices and the EDGE projections, and run REMIND again. After several iterations, prices converge, so that the efficiencies computed do correspond to the EDGE projections and that the REMIND run yields the EDGE final energy projections.

Supplementary Note 4. Estimation of the elasticities of substitution

The central parameters in the representation of the trade-off between energy consumption and end-use capital investments are the elasticities of substitution. They determine how strongly the ratio between capital and energy will react to changes in prices. Here we explain the methodology we used to estimate the elasticities of substitution based on exogenous technological data.

Other studies have already used CES functions to model the trade-off between energy demand and end-use capital. This is for instance the case of the US-REGEN model from the Electric Power Research Institute ³. In order to estimate the elasticities of their model, they used dedicated simulations from an external model, CIMS, and computed the elasticities that best fitted the results from the CIMS

simulations. Another approach was taken by the AMIGA modelling team ⁴ in which they estimated the models’ elasticities of substitution directly with technological data. We adopt here a methodology close to that from Laitner and Hanson ⁴.

In a nutshell, we first derive technological cost curves from various data sources and aggregate them to the REMIND structure. We then fit the CES function to these technological curves by adjusting the elasticity of substitution.

5.8 Supplementary Information 163

Supplementary Figure 3: Estimation of the elasticity of substitution between space cooling energy consumption and investment costs in REMIND, for the European region. Dots are the various technological combinations available from the technological data, the yellow line represents the fitted CES isoquant, the black line stands for the price ratio between energy and capital in REMIND and the red dot corresponds to the initial mix of energy and capital in 2015 in REMIND.

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Supplementary Figure 4: Estimation of the elasticity of substitution between improved insulation and energy consumption for thermal comfort in REMIND, for the European region. Dots are the various technological combinations available from the technological data, the yellow line represents the fitted CES isoquant, the black line stands for the price ratio between energy and capital in REMIND and the red dot corresponds to the initial mix of energy and capital in 2015 in REMIND.

5.8 Supplementary Information 165

Supplementary Figure 5: Estimation of the elasticity of substitution between appliances and lighting energy consumption and investment costs in REMIND, for the European region. Dots are the various technological combinations available from the technological data, the yellow line represents the fitted CES isoquant, the black line stands for the price ratio between energy and capital in REMIND and the red dot corresponds to the initial mix of energy and capital in 2015 in REMIND.

Supplementary Note 4.1 Construction of the costs functions

A synthetic way of representing the various levels of efficiency available on markets is to show the plurality of combinations between energy consumption and capital costs attached to each product and which deliver the same level of energy service. In the economist’s lingo, such a representation is called an isoquant curve. In this section, our aim is to derive isoquants from technological data, which we could use for the estimation of the REMIND’s CES isoquants. Thereby, we can ensure that the opportunity space in which the model navigates is based on technological data.

Technological databases ^5–7, manufacturer websites and comparison websites (e.g.

http://www.topten.info) provide us with a wealth of information on costs and energy consumption of various technologies. In processing this data, we first operate a distinction between technologies which we consider substitutable (e.g. an incandescent lightbulb and a LED) and technologies which belong to a similar REMIND category but which are not substitutable (e.g. lightbulbs and dishwashers belong to the category Appliances and Lighting, but cannot be substituted for one another). For substitutable products, we include linear combinations of available products to populate the opportunity space (e.g.50% of incandescent lightbulbs and 50% of LEDs).

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Once we have designed curves for each category of substitutable products (lighting, dishwashers, windows, air conditioners, etc), we must combine these curves to recover isoquants for the broader category corresponding to REMIND’s variables (Appliances and Lighting, Space cooling, Space

Conditioning). We attach to each substitutable product a weight which stands for its proximate share in the energy consumption of the given category. Finally, because a CES isoquant is inconsistent with technological options which are both more expensive and less efficient than other options, we remove most of these products from the isoquant.

Supplementary Note 4.2 Estimation in the REMIND model

As in many if not all applied energy models, REMIND has to be calibrated to meet historical energy demand values. In addition, REMIND is calibrated in an iterative process to meet exogenous energy demand projections (Supplementary Note 1). The core tool for this calibration are the efficiency parameters of the buildings’ module. Practically, the efficiency parameters ξ and α in equation (4) are adjusted so that the model achieves the market equilibrium for the prescribed energy demand

projections. This leaves ρ, which is related to the elasticity of substitution (equation (2)), as the only free variable. We use this degree of freedom and set ρ to the value minimizing the distance between the REMIND CES isoquant and the isoquant that we derived from technological data (Figure 1).

𝑂𝑂𝑂𝑂𝑂𝑂= [𝜉𝜉1(𝛼𝛼₁𝐼𝐼𝑛𝑛1)^𝜌𝜌+𝜉𝜉2(𝛼𝛼₂𝐼𝐼𝑛𝑛2)^𝜌𝜌]^{𝜌𝜌1 (4)}

The elasticities of substitution are computed individually for each region. The ranges of values across regions are given in Table 1. They are most of the time below 1, which means that a 1% increase in the ratio between energy and capital prices will lead to a decrease in the ratio between energy and capital of less than 1% (and vice versa for elasticities above 1). The higher the elasticity of substitution is, the stronger the reaction to a price change is.

Importantly, the estimations are also influenced by the assumptions on the implicit discount rate which we do, as it translates into a higher capital price. As the price ratio defines the tangent to the isoquant and that the historical energy-capital combination is given, it means that the estimated elasticity of substitution will decrease in response to a higher assumption on implicit discount rate.

Variable Range of substitution elasticities

Insulation 0.66 - 1.33

Appliances and Lighting 0.32 - 0.56

Space cooling 0.32 - 0.46

Table 1: Ranges of elasticities of substitution derived from the estimation in the different regions. Regional differences arise from different starting points on the curve and different price ratios.

Supplementary Note 4.3 Evolution in the long run

The ease of substitution in the future will also depend on the future investments into research and development for energy efficient technologies. In REMIND, the substitution parameter is solely

estimated against currently available technologies and therefore underestimates the long-term effect of price changes as it precludes the influence of price-induced technological change. The induced

5.8 Supplementary Information 167

technological change as a response to prices (either shadow prices from regulations or real prices) has been inspected by environmental economists. The effect of prices on future technological development might be strong. Introducing induced technological change into the model is beyond the scope of the present study. In order to mimic the impact of induced technological change, we increase the elasticity of substitution over time. In the scenarios presented in the main text, the elasticities of substitution grow by 50% over their estimated value until 2050. Below, we tested the sensitivity of the model results to this assumption and designed three growth scenarios. ‘Low’ increases the elasticities of substitution by 30%,

‘Middle’ by 50% as in the main text, and ‘High’ doubles them. We find that the main results are qualitatively and quantitatively comparable across scenarios.

Supplementary Figure 6: Final energy demand projections at the global level for the aggregate buildings energy demand for three scenarios of growth in the elasticities of substitution

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Supplementary Figure 7: Final energy demand projections at the global level for end-uses for three scenarios of growth in the elasticities of substitution

Supplementary Note 5. The implicit discount rate

The majority of implicit discount rates estimates dates back to the eighties and nineties ^8–10. After that, it became clear that discount rates could not be the only explanation of interest to account for the energy efficiency gap. As Jaffe and Stavins ¹¹ noted, the implicit discount rate is a mere restatement of the energy efficiency gap. The attention therefore turned towards other explanations for the energy efficiency gap ¹², which could a priori lend support for non-price based efficiency policies. The attention lately embraced behavioural insights ¹³. But high individual discount rates, representing time

preferences, remain an important potential explanation for the efficiency gap ^14,15, though the role of discount rates as the expression of time preferences has been criticised ¹⁶.

Supplementary Note 6. Energy carrier choice

In REMIND, the demand for final energy carriers is split into two questions: what is the desired level of useful energy for each end-use, and what are the market shares of the conversion technologies and final

5.8 Supplementary Information 169

energy carriers. The first question concerns therefore the aggregate level of demand, and is treated with the calibration (see Supplementary Note 1). The second question addresses the shares of each energy carrier to fulfill the aggregate level of the demand.

For space cooling and appliances and lighting, we assume that the full demand is covered by electricity consumption. We thereby do not include other technological possibilities as district cooling, which could be interesting to investigate in future research.

For space heating and water heating/cooking, we use a multinomial logit function . The share of each conversion technology is given by Eq (5).

𝑆𝑆𝐻𝐻𝑡𝑡𝑡𝑡𝑡𝑡ℎ,𝑡𝑡𝑡𝑡,𝑡𝑡𝑒𝑒= exp�𝜆𝜆×𝐿𝐿𝐿𝐿𝑂𝑂𝐻𝐻𝑡𝑡𝑡𝑡𝑡𝑡ℎ,𝑡𝑡𝑡𝑡,𝑡𝑡𝑒𝑒+𝜇𝜇𝑡𝑡𝑡𝑡𝑡𝑡ℎ,𝑡𝑡𝑡𝑡,𝑡𝑡𝑒𝑒�

∑𝑡𝑡𝑡𝑡𝑡𝑡ℎ,𝑡𝑡𝑡𝑡,𝑡𝑡𝑒𝑒exp�𝜆𝜆×𝐿𝐿𝐿𝐿𝑂𝑂𝐻𝐻𝑡𝑡𝑡𝑡𝑡𝑡ℎ,𝑡𝑡𝑡𝑡,𝑡𝑡𝑒𝑒+𝜇𝜇𝑡𝑡𝑡𝑡𝑡𝑡ℎ,𝑡𝑡𝑡𝑡,𝑡𝑡𝑒𝑒�

(5)

𝐿𝐿𝐿𝐿𝑂𝑂𝐻𝐻=𝛼𝛼𝐼𝐼+𝑂𝑂𝑂𝑂+𝐹𝐹𝐿𝐿

𝐻𝐻 ⁽⁶⁾

𝛼𝛼= 𝑟𝑟𝑖𝑖

1−(1 +𝑟𝑟𝑖𝑖)−𝑙𝑙𝑖𝑖𝑙𝑙𝑡𝑡𝑡𝑡𝑖𝑖𝑙𝑙𝑡𝑡 (7)

𝐹𝐹𝐿𝐿 =�𝐹𝐹𝐸𝐸𝑝𝑝𝑝𝑝𝑖𝑖𝑡𝑡𝑡𝑡+𝐹𝐹𝐸𝐸𝑡𝑡𝑡𝑡𝑡𝑡− 𝐹𝐹𝐸𝐸𝑠𝑠𝑒𝑒𝑠𝑠𝑠𝑠𝑖𝑖𝑠𝑠+𝐼𝐼𝑛𝑛𝐼𝐼𝑜𝑜𝑛𝑛𝐼𝐼� ∗ �𝐻𝐻

𝜂𝜂 � ⁽⁸⁾

Parameter/index Explanation

α Capital recovery factor

ri Implicit discount rate

I Investment cost

OM Annual operation and maintenance cost

FC Annual fuel costs

H Energy (heat) produced annually

FEprice Energy carrier price

FEtax Energy carrier tax

FEsubsid Energy carrier subsidy

Inconv Income dependent inconvenience cost for specific fuels which are expected not to be used as income grows (traditional biomass, coal, and to a lower extent liquid and other solid energy carriers)

λ Price sensitivity parameter (negative)

SH Share in useful energy

tech Technology

ec Energy carrier

eu End-use (space heating or cooking and water heating)

μ Calibration parameter to match 2015 shares

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The energy carriers and conversion technologies considered cover traditional solids (traditional biomass and coal), modern biomass, natural gas, liquid fuels, district heating, electric resistance heating or electricity driven heat pumps.

We would like to underline the role of two important parameters in the model outcome concerning the energy carrier shares: the price sensitivity parameter and the calibration parameter. The price sensitivity parameter determines how large the reaction to price changes will be for the shares. Price changes occur in the baseline scenario, but are even more dramatic in case a carbon price is implemented. The price sensitivity is often interpreted as the market heterogeneity parameter. In case the absolute value of the parameter is low, the shares would be less sensitive to price changes, and the heterogeneity would be conserved. If the price sensitivity is high, we would observe a winner-takes-all situation where the cheapest technology would seize a large market share.

The second important parameter is the calibration parameter. The role of this parameter is to fill the gap between the predicted outcome from the multinomial logit, and the observed shares in historic periods.

Many factors could explain this gap: different political support for technologies across regions, different infrastructures, different preferences, difference in the model prices and the observed prices, etc. The size of the calibration parameter strongly depends on the price sensitivity parameter. If the latter is low, the calibration parameter will have to be important to offset the price effect. Thereby, the effect of future price changes would be relatively lower on the multinomial logit as the latter considers the sum of the technological cost and the calibration parameter. In case of a price sensitive parameter, the

adjustment to the prices must only be limited to change the shares, so the ratio between calibration parameters and prices would be low and changes in prices would have strong effects. Because we do not model all the aspects determining the observed shares of energy carriers, but only technological cost, we decided to reduce the calibration shares by 20% from 2015 to 2100. Thereby, the explanatory power of the prices, which are a result of the model unlike the calibration parameters, increases for periods farther away in the future. In particular, this allows “newcomer” technologies like heat pumps not to be penalized in the future by their current low penetration.

Unfortunately, it is difficult to find estimates for the price sensitivity parameter in the literature that would cover space heating, cooking and water heating, and that would have a similar structure as the modelled structure. Quite often in energy modelling, the choice on this parameter relies on expert judgement. A similar effort as in the transport sector¹⁷ would be necessary to improve modelling of fuel switching in buildings. We here use a price sensitivity parameter of -3.

In addition, in order to reflect the inertia of the system while conserving numerical simplicity, we apply the multinomial logit choice only to the addition of useful energy provision needed, after having depreciated the stock of technologies standing in the preceding period. In order to limit the numerical complexity of the model, we apply an economic discounting to the standing stock of technologies, with a yearly pro rata depreciation, as for the building stock, and not the technological vintaging which tracks which technology has been installed when and when it will be retire.

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Finally, in scenarios reducing the energy efficiency gap, the implicit discount rate also decreases for the choice of energy carriers, thus favoring capital intensive technologies like heat pumps over fuel intensive technologies.

Supplementary Note 7. Definition of end-use capital

The notion of end-use capital is not clearly defined in the literature, and diverging definitions yield substantial spreads in estimates of yearly investments¹⁸. The IEA for instance defines energy efficiency investment as the additional investment made for an energy efficient product over a standard product ¹⁹. Wilson and Grubler²⁰ criticise this definition as they consider it is not a comparable measure to the investment costs in the energy supply sector. For the technologies transforming energy from primary to final energy, the whole cost of the technology is taken into account, and not only the additional cost of a more efficient technology compared to a standard variant. They propose instead to consider either the full cost of the product (e.g. a refrigerator) or the cost of its energy transforming component (e.g. the compressor of a refrigerator). Depending upon the definition chosen, they find estimates diverging by

The notion of end-use capital is not clearly defined in the literature, and diverging definitions yield substantial spreads in estimates of yearly investments¹⁸. The IEA for instance defines energy efficiency investment as the additional investment made for an energy efficient product over a standard product ¹⁹. Wilson and Grubler²⁰ criticise this definition as they consider it is not a comparable measure to the investment costs in the energy supply sector. For the technologies transforming energy from primary to final energy, the whole cost of the technology is taken into account, and not only the additional cost of a more efficient technology compared to a standard variant. They propose instead to consider either the full cost of the product (e.g. a refrigerator) or the cost of its energy transforming component (e.g. the compressor of a refrigerator). Depending upon the definition chosen, they find estimates diverging by

Im Dokument Demand-side Mitigation Policies: The Role of the Buildings Sector (Seite 160-185)