A methodological framework for comparative assessments of equipment energy efficiency policy measures

Abstract

When government policy-makers propose new policies, they need to assess the costs and benefits of the proposed policy measures to compare them to existing and alternative policies and to rank them according to their effectiveness. In the case of equipment energy efficiency regulations, comparing the effects of a range of alternative policy measures requires evaluating their effects on consumers’ budgets, on national energy consumption and economics, and on the environment. A useful methodology to perform such policy analysis should represent in a single framework the characteristics of each policy measure and provide comparable results. This paper presents an integrated methodological framework for the prospective assessment of the energy, economic, and environmental impacts of a variety of equipment energy efficiency policy measures. The framework is a comparative assessment tool for energy efficiency policy measures that (a) relies on a common set of primary data and parameters; (b) follows a single functional approach to estimate the energy, economic, and emissions savings resulting from each assessed measure; and (c) summarizes results in a set of metrics to facilitate comparative assessments. It provides a general methodology useful for evaluating a broad range of policies to promote greater equipment energy efficiency and the capability to further compare the impacts of such market interventions. The paper concludes with a demonstration of the use of the framework to compare the estimated impacts of 12 policy measures focusing on increasing the energy efficiency of gas furnaces in the USA.

Appendices

Appendix 1: Calculating the result metrics for a policy measure

This appendix presents the methodology used by the framework to:

• Estimate the total lifetime consumption, costs, and emissions of all equipment shipped in a given year of the assessment period, either for the base-case or the policy measure-case scenario

• Calculate the cumulative values of these totals over the assessment period for either of these scenarios

• Calculate the metrics from the cumulative results evaluated for the base-case and the policy measure-case scenarios

A simplified version of these calculations is provided in “Appendix 2.”

Total lifetime values

Let dev _i (i = 1,…,N) represent the ith energy efficiency design option of the equipment targeted by an energy efficiency policy (energy efficiency of dev _i increases with i); t (t = 1,…,T) represent the sequence of years in a T-year assessment period⁴¹ and:

prc_i (t):

End-user price of a unit represented by dev _i shipped in t (the tth year of the assessment period)⁴²

inst_i (t):

Total installation costs of a unit represented by dev _i shipped in t ⁴³

mnt_i (t, j):

Maintenance costs in the jth year of operation of a unit represented by dev _i shipped in t ^{44 , 45}

rpr_i (t, j):

Repair costs in the jth year of operation of a unit represented by dev _i shipped in t ^{46 , 47}

energy_i,f (j):

Energy consumption of fuel f in the jth year of operation of a unit represented by dev _i ⁴⁸

water_i (j):

Water consumption in the jth year of operation of a unit represented by dev _i ⁴⁹

emission_i,g (j):

Emissions of pollutant g in the jth year of operation of a unit represented by dev _i ⁵⁰

shp_i (t):

Shipments forecast of the units represented by dev _i

The total lifetime energy and water consumption, emissions, and equipment and energy costs of units of all energy efficiency design options shipped in the tth year of the assessment period can be calculated from:

$$ {\text{Energy}}(t) = \sum\nolimits_i {\left( {{\text{sh}}{{\text{p}}_i}(t) \cdot \sum\nolimits_f {\sum\nolimits_{{j = 1,L{F_i}}} {\left( {{\text{energ}}{{\text{y}}_{{i,f}}}(j) \cdot {\text{pSur}}{{\text{v}}_i}(j)} \right)} } } \right)} $$

(10)

$$ {\text{Water}}(t) = \sum\nolimits_i {\left( {{\text{sh}}{{\text{p}}_i}(t) \cdot \sum\nolimits_{{j = 1,L{F_i}}} {\left( {{\text{wate}}{{\text{r}}_i}(j) \cdot {\text{pSur}}{{\text{v}}_i}(j)} \right)} } \right)} $$

(11)

$$ {\text{Emissio}}{{\text{n}}_g}(t) = \sum\nolimits_i {\left( {{\text{sh}}{{\text{p}}_i}(t) \cdot \sum\nolimits_{{j = 1,L{F_i}}} {\left( {{\text{emissio}}{{\text{n}}_{{i,g}}}(j) \cdot {\text{pSur}}{{\text{v}}_i}(j)} \right)} } \right)} $$

(12)

$$ {\text{qCost}}(t) = \sum\nolimits_i {\left( {{\text{sh}}{{\text{p}}_i}(t) \cdot \left( {{\text{pr}}{{\text{c}}_i}(t) + {\text{ins}}{{\text{t}}_i}(t) + {\text{mnt}}{{\text{L}}_i}(t) + {\text{rpr}}{{\text{L}}_i}(t) - v(t) + {\text{wEx}}{{\text{p}}_i}(t)} \right)} \right)} $$

(13)

⁵¹

$$ {\text{eCost}}(\text t) = \sum\nolimits_i {\left( {{\text{sh}}{{\text{p}}_i}(t) \cdot {\text{eEx}}{{\text{p}}_i}(t)} \right)} $$

(14)

and:

$$ {\text{mnt}}{{\text{L}}_i}(t) = \sum\nolimits_{{j = 1,{\text{L}}{{\text{F}}_i}}} {\left( {{\text{pSur}}{{\text{v}}_i}(j) \cdot {\text{mn}}{{\text{t}}_i}\left( {t,j} \right) \cdot {{\left( {1 + {\text{dRate}}} \right)}^{{1 - j}}}} \right)} $$

(15)

$$ {\text{rpr}}{{\text{L}}_i}(t) = \sum\nolimits_{{j = 1,{\text{L}}{{\text{F}}_i}}} {\left( {{\text{pSur}}{{\text{v}}_i}(j) \cdot {\text{rp}}{{\text{r}}_i}\left( {t,j} \right) \cdot {{\left( {1 + {\text{dRate}}} \right)}^{{1 - j}}}} \right)} $$

(16)

$$ {\text{wEx}}{{\text{p}}_i}(t) = \sum\nolimits_{{j = 1,{\text{L}}{{\text{F}}_i}}} {\left( {{\text{wate}}{{\text{r}}_i}(j){\text{pSur}}{{\text{v}}_i}(j) \cdot {\text{wPrice}}\left( {t + j - 1} \right) \cdot {{\left( {1 + {\text{dRate}}} \right)}^{{1 - j}}}} \right)} $$

(17)

$$ {\text{eEx}}{{\text{p}}_i}(t) = \sum\nolimits_f {\sum\nolimits_{{j = 1,{\text{L}}{{\text{F}}_i}}} {\left( {{\text{energ}}{{\text{y}}_{{i,f}}}(j) \cdot {\text{pSur}}{{\text{v}}_i}(j) \cdot {\text{fPric}}{{\text{e}}_f}\left( {t + j - 1} \right) \cdot {{\left( {1 + {\text{dRate}}} \right)}^{{1 - j}}}} \right)} } $$

(18)

where:

LF_i :

Maximum lifetime of a unit represented by dev _i ⁵²

pSurv_i (j):

Survival probability of a unit represented by dev _i on its jth year of operation⁵³

v (t):

Monetary incentive offered in t toward units at or above the target level

mntL_i (t):

Present value in t of the lifetime consumers’ expense with equipment maintenance for a unit shipped in t

rprL_i (t):

Present value in t of the lifetime consumers’ expense with equipment repair for a unit shipped in t

wExp_i (t):

Present value in t of the lifetime consumers’ expense with water for a unit shipped in t

wPrice (t′):

Water price in the t′th year of the assessment period

eExp_i (t):

Present value in t of the lifetime consumers’ expense with energy for a unit shipped in t

fPrice_f (t′):

Price of fuel f in the t′th year of the assessment period

dRate:

Social discount rate.

Cumulative totals over the assessment period

The cumulative (energy and water) consumption and emissions over the assessment period⁵⁴ and the present values of the total equipment and energy costs for the same period are given by:

$$ {\text{cumEnergy}} = \sum\nolimits_{\text t} {{\text{Energy}}(\text t)} $$

(22)

$$ {\text{cumWater}} = \sum\nolimits_{\text t} {{\text{Water}}(\text t)} $$

(23)

$$ {\text{cumEmissio}}{{\text{n}}_{\text g}} = \sum\nolimits_{\text t} {{\text{Emissio}}{{\text{n}}_{\text g}}(\text t)} $$

(24)

$$ {\text{pvEquip}} = \sum\nolimits_{{\text{t}}} {\left( {{\text{qCost}}({\text{t}})\cdot {{{\left( {{\text{1}} + {\text{dRate}}} \right)}}^{{{\text{1}} - {\text{t}}}}}} \right)} $$

(25)

$$ {\text{pvEnergy}} = \sum\nolimits_{\text t} {\left( {{\text{eCost}}(\text t) \cdot {{\left( {1 + {\text{dRate}}} \right)}^{{1 - t}}}} \right)} $$

(26)

Result metrics

Equations (22) to (26) should be evaluated for the base-case scenario and the policy measure-case scenario. These equations depend on Eqs. (10) to (14), where equipment costs and shipments are part of the calculation. These variables interact with each other and such interaction should be accounted for when evaluating Eqs. (22) to (26) for the base-case and the policy measure-case scenarios. Because a policy measure increases the shipments of higher-efficiency devices, the equipment costs of these devices are likely to be lower—and follow a different trend (see footnote 42)—in the policy measure-case than in the base-case scenario. Also, because equipment prices may affect shipments, when assuming non-zero price elasticity of demand or non-zero price elasticity of substitution in the shipments forecast for a policy measure-case scenario, the total shipments in the base case should be adjusted—for the sake of comparability—to be equivalent to the shipments in the policy measure-case scenario. Otherwise, the metrics calculated from Eqs. (22) to (26) will be distorted by these differences in shipments, even though these are the estimated effects of the policy measure. Alternatively, one can evaluate Eqs. (10) to (14) on a unitary basis, in which case the metrics calculated from Eqs. (22) to (26) will provide results at the (average) consumer level rather than as market totals (see footnote 5 in the main text for the meaning of totals).

Based on the results of Eqs. (22) to (26) for the base-case and the policy measure-case scenarios and on a potential direct rebound effect,⁵⁵ the assessment metrics for a policy measure pol is evaluated from the following equations:^{56 , 57}

$$ {\text{TE}}{{\text{S}}_{\text{pol}}} = {\left[ {\text{cumEnergy}} \right]_{\text{bc}}} - \left( {{{\left[ {\text{cumEnergy}} \right]}_{\text{pol}}} + \sum\nolimits_t {{\text{rbdEnergy}}(t)} } \right) $$

(27)

$$ {\text{TW}}{{\text{S}}_{\text{pol}}} = {\left[ {\text{cumWater}} \right]_{\text{bc}}} - \left( {{{\left[ {\text{cumWater}} \right]}_{\text{pol}}} + \sum\nolimits_t {{\text{rbdWater}}(t)} } \right) $$

(28)

$$ {\text{TE}}{{\text{R}}_{{{\text{pol}},g}}} = {\left[ {{\text{cumEmissio}}{{\text{n}}_g}} \right]_{\text{bc}}} - \left( {{{\left[ {{\text{cumEmissio}}{{\text{n}}_g}} \right]}_{\text{pol}}} + \sum\nolimits_t {{\text{rbdEmissio}}{{\text{n}}_g}(t)} } \right) $$

(29)

$$ {\text{cNP}}{{\text{V}}_{\text{pol}}} = {\left[ {\text{pvEquip}} \right]_{\text{bc}}} + {\left[ {\text{pvEnergy}} \right]_{\text{bc}}} - {\left[ {\text{pvEquip}} \right]_{\text{pol}}} - {\left[ {\text{pvEnergy}} \right]_{\text{pol}}} $$

(30)

$$ {\text{sNP}}{{\text{V}}_{\text{pol}}} = {\text{cNP}}{{\text{V}}_{\text{pol}}} - {v_{\text{pol}}} + \sum\nolimits_g {{\text{mEmissio}}{{\text{n}}_g} + {\text{sCos}}{{\text{t}}_{\text{pol}}}} $$

(31)

where:

$$ {\text{rbdEnergy}}(t) = \sum\nolimits_i {\left( {{{\left[ {{\text{sh}}{{\text{p}}_{{{i_r}}}}(t)} \right]}_{\text{pol}}} \cdot {\rho_{{{i_r}}}} \cdot \sum\nolimits_f {\sum\nolimits_{{j = 1,{\text{L}}{{\text{F}}_i}}} {\left( {{\text{energ}}{{\text{y}}_{{i,f}}}(j) \cdot {\text{pSur}}{{\text{v}}_i}(j)} \right)} } } \right)} $$

$$ {\text{rbdWater}}(t) = \sum\nolimits_i {\left( {{{\left[ {{\text{sh}}{{\text{p}}_{{{i_r}}}}(t)} \right]}_{\text{pol}}} \cdot {\rho_{{{i_r}}}} \cdot \sum\nolimits_{{j = 1,{\text{L}}{{\text{F}}_i}}} {\left( {{\text{wate}}{{\text{r}}_i}(j) \cdot {\text{pSur}}{{\text{v}}_i}(j)} \right)} } \right)} $$

$$ {\text{rbdEmissio}}{{\text{n}}_g}(t) = \sum\nolimits_i {\left( {{{\left[ {{\text{sh}}{{\text{p}}_{{{i_r}}}}(t)} \right]}_{\text{pol}}} \cdot {\rho_{{{i_r}}}} \cdot \sum\nolimits_{{j = 1,{\text{L}}{{\text{F}}_i}}} {\left( {{\text{emissio}}{{\text{n}}_{{i,g}}}(j) \cdot {\text{pSur}}{{\text{v}}_i}(j)} \right)} } \right)} $$

$$ {\text{mEmissio}}{{\text{n}}_g} = \sum\nolimits_t {\left( {\left( {{{\left[ {{\text{Emissio}}{{\text{n}}_g}(t)} \right]}_{\text{bc}}} - {{\left[ {{\text{Emissio}}{{\text{n}}_g}(t)} \right]}_{\text{pol}}} - {\text{rbdEmissio}}{{\text{n}}_g}(t)} \right) \cdot {\text{gPric}}{{\text{e}}_g}(t) \cdot {{\left( {1 + {\text{dRate}}} \right)}^{{1 - t}}}} \right)} $$

and:

rbdEnergy (t):

Energy consumption in t due to the direct rebound effect

rbdWater (t):

Water consumption in t due to the direct rebound effect

rbdEmission_g (t):

Emissions of pollutant g in t due to the direct rebound effect

v_pol :

Present value of all monetary incentives provided by the policy measure⁵⁸

mEmission_g :

Present value of the monetized annual emissions reduction of pollutant g provided by the policy measure

sCost_pol :

Present value of administrative costs incurred by the policy measure to economic agents in the supply chain of the targeted equipment

${\text{sh}}{{{\text{p}}}_{{{{{\text{i}}}_{{\text{r}}}}}}}({\text{t}})$ :

Shipments in the tth year of the assessment period of units represented by ${\text{de}}{{\text{v}}_{{{i_r}}}}$—the devices that contribute to the direct rebound effect in the policy measure-case scenario⁵⁹

${{\rho }_{{{{{\text{i}}}_{{\text{r}}}}}}}$ :

Percentage of additional energy service consumed by units represented by ${\text{de}}{{\text{v}}_{{{i_r}}}}$ due to the direct rebound effect

gPrice_g(t):

Market value of reducing one unit of emission of pollutant g in t

Appendix 2: Calculating the result metrics for a policy measure (simplified version)

In the following, we provide a simplified version of the methodology detailed in “Appendix 1.” This may be useful for situations where data needed to develop the exogenous forecasts are limited and/or where computational capability is limited. For example, such may be the case in some developing countries that may otherwise find the framework methodology quite useful. The simplifications assumed are:

• The targeted equipment operates on only one fuel and does not consume water

• All design options have the same effective useful life (EUL)⁶⁰

• End-user price and installation costs are combined in a single variable, as are annual maintenance and repair costs

• All equipment related costs, as well as annual energy consumption and emissions are constant both over the equipment lifetime and the assessment period

• Energy price is constant over the assessment period

• Any monetary incentive provided by a financial incentive policy measure is constant over the assessment period

• There is no direct rebound effect

• The social value of reducing the emissions of any pollutant is constant

• The policy measures do not result in additional administrative costs to economic agents in the supply chain of the targeted equipment

• Annual total shipments for the base-case and all policy measure-case scenarios are identical and differ only in their distribution across design options

Total lifetime values

Let dev _i (i = 1,…,N) represent the ith energy efficiency design option of the equipment targeted by an energy efficiency policy (energy efficiency of dev _i increases with i); t (t = 1,…,T) represent the sequence of years in a T-year assessment period⁶¹ and:

tic_i :

Total installed cost of a unit represented by dev _i

mr_i :

Annual maintenance and repair costs of a unit represented by dev _i

energy_i :

Annual energy consumption of a unit represented by dev _i

emission_i,g :

Annual emissions of pollutant g of a unit represented by dev _i

shp_i(t):

Shipments forecast of the units represented by dev _i

The total lifetime energy consumption, emissions, and equipment- and energy costs of units of all energy efficiency design options shipped in the tth year of the assessment period can be calculated from:

$$ {\text{Energy}}(\text t) = \sum\nolimits_i {\left( {{\text{sh}}{{\text{p}}_i}(t) \cdot {\text{energ}}{{\text{y}}_i}} \right) \cdot {\text{EUL}}} $$

(32)

$$ {\text{Emissio}}{{\text{n}}_g}(t) = \sum\nolimits_i {\left( {{\text{sh}}{{\text{p}}_i}(t) \cdot {\text{emissio}}{{\text{n}}_{{i,g}}}} \right) \cdot {\text{EUL}}} $$

(33)

$$ {\text{qCost}}(t) = \sum\nolimits_i {\left( {{\text{sh}}{{\text{p}}_i}(t) \cdot \left( {{\text{ti}}{{\text{c}}_i} + {\text{m}}{{\text{n}}_i} \cdot \sum\nolimits_{{j = 1,{\text{EUL}}}} {\left( {{{\left( {1 + {\text{dRate}}} \right)}^{{1 - j}}}} \right) - v} } \right)} \right)} $$

(34)

$$ {\text{eCost}}(t) = \sum\nolimits_i {\left( {{\text{sh}}{{\text{p}}_i}(t) \cdot {\text{energ}}{{\text{y}}_i} \cdot {\text{fPrice}}} \right) \cdot \sum\nolimits_{{j = 1,{\text{EUL}}}} {\left( {{{\left( {1 + {\text{dRate}}} \right)}^{{1 - j}}}} \right)} } $$

(35)

where:

EUL:

Estimated useful lifetime of any design option represented by dev _i

v:

Monetary incentive offered toward design options with energy efficiency equal or greater than the target level of the policy measure

fPrice:

Energy price

dRate:

Social discount rate

Cumulative totals over the assessment period

The cumulative energy consumption and emissions and the present values of the total equipment and energy costs over the assessment period are given by:

$$ {\text{cumEnergy}} = \sum\nolimits_{\text t} {\left( {{\text{Energy}}(\text t) \cdot {\sigma_e}(t)} \right)} $$

(36)

$$ {\text{cumEmissio}}{{\text{n}}_g} = \sum\nolimits_t {{\text{Emissio}}{{\text{n}}_g}(t) + \sum\nolimits_t {\left( {{\text{Energy}}(t) \cdot \left( {{\sigma_e}(t) - 1} \right) \cdot {\theta_{{e,g}}}(t)} \right)} } $$

(37)

$$ {\text{pvEquip}} = \sum\nolimits_{\text t} {\left( {{\text{qCost}}(\text t) \cdot {{\left( {1 + {\text{dRate}}} \right)}^{{1 - t}}}} \right)} $$

(38)

$$ {\text{pvEnergy}} = \sum\nolimits_{\text t} {\left( {{\text{eCost}}(\text t) \cdot {{\left( {1 + {\text{dRate}}} \right)}^{{1 - t}}}} \right)} $$

(39)

where:

σ _e(t):

Energy end-use-to-primary conversion factor $\left( {{\sigma_e}(t) \geqslant 1} \right)$ ⁶²

θ _e,g(t):

Emission factor of pollutant g in the energy supply chain.

Result metrics

Equations (36) to (39) should be evaluated for the base-case scenario and the policy measure-case scenario. Using solutions to these equations, the assessment metrics for a policy measure pol are evaluated from the following equations:

$$ {\text{TE}}{{\text{S}}_{\text{pol}}} = {\left[ {\text{cumEnergy}} \right]_{\text{bc}}} - {\left[ {\text{cumEnergy}} \right]_{\text{pol}}} $$

(40)

$$ {\text{TE}}{{\text{R}}_{{{\text{pol}},g}}} = {\left[ {{\text{cumEmissio}}{{\text{n}}_g}} \right]_{\text{bc}}} - {\left[ {{\text{cumEmissio}}{{\text{n}}_g}} \right]_{\text{pol}}} $$

(41)

$$ {\text{cNP}}{{\text{V}}_{\text{pol}}} = {\left[ {\text{pvEquip}} \right]_{\text{bc}}} + {\left[ {\text{pvEnergy}} \right]_{\text{bc}}} - {\left[ {\text{pvEquip}} \right]_{\text{pol}}} - {\left[ {\text{pvEnergy}} \right]_{\text{pol}}} $$

(42)

$$ {\text{sNP}}{{\text{V}}_{\text{pol}}} = {\text{cNP}}{{\text{V}}_{\text{pol}}} - {v_{\text{pol}}} + \mathop{\sum }\limits_{\text g} {\text{mEmissio}}{{\text{n}}_{\text g}} $$

(43)

where:

$$ {\text{mEmissio}}{{\text{n}}_g} = {\text{gPric}}{{\text{e}}_g} \cdot \sum\nolimits_t {\left( {\left( {{{\left[ {{\text{Emissio}}{{\text{n}}_g}(t)} \right]}_{\text{bc}}} - {{\left[ {{\text{Emissio}}{{\text{n}}_g}(t)} \right]}_{\text{pol}}}} \right) \cdot {{\left( {1 + {\text{dRate}}} \right)}^{{1 - t}}}} \right)} $$

and:

v_pol :

Present value of all monetary incentives provided by the policy measure⁶³

mEmission_g :

Present value of the monetized annual emissions reduction of pollutant g provided by the policy measure

Appendix 3: Estimating market penetration from financial incentives

This appendix details how to use the interpolated market penetration curves described by Blum et al. (2011, Appendix A) to estimate the increase in market penetration resulting from a monetary incentive according to the market barrier level and the benefit/cost ratio provided by the incentive. For a given pair of market barrier level and benefit/cost ratio (${\text{b}}_{\text{c}}^{{*}},{\text{b}}{{\text{c}}^{{*}}}$). the market implementation ${{imp}}\left( {{\text{b}}_{\text{c}}^{{*}},{\text{b}}{{\text{c}}^{{*}}}} \right)$ is given by:

$$ \begin{array}{*{20}{c}} {{\text{imp}}\left( {{\text{b}}_{{\text{c}}}^{*},{\text{b}}{{{\text{c}}}^{*}}} \right)} \\ { = \frac{{{{{\max }}_{{\text{c}}}}({\text{b}}_{{\text{c}}}^{*})}}{{\left( {{\text{1}} + \frac{{\text{1}}}{{{{{\text{r}}}_{{\text{c}}}}\left( {{\text{b}}_{{\text{c}}}^{*}} \right)\cdot {\text{b}}{{{\text{c}}}^{*}}}}} \right)\cdot ({\text{1}} + ({\text{mi}}{{{\text{d}}}_{{\text{c}}}}({\text{b}}_{{\text{c}}}^{*}\cdot {\text{b}}{{{\text{c}}}^{*}} - {\text{fi}}{{{\text{t}}}_{{\text{c}}}}\left( {{\text{b}}_{{\text{c}}}^{{\text{*}}}} \right)}}} \\ \end{array} $$

(44)

where r _c , fit _c , mid _c , and max _c are piecewise linear functions that interpolate these parameters between their corresponding values in the five reference curves developed by Rufo and Coito (2002).

Equation (44) provides an estimate of the market penetration of devices with a certain efficiency level according to the level of market barriers to their dissemination (b*) and their benefit/cost ratio to consumers (bc).⁶⁴ In the benefit/cost ratio, benefit refers to the energy cost savings that consumers will enjoy from using an energy-efficient device, and cost includes the likely greater purchase cost and possible differences⁶⁵ in installation and non-energy-related operational costs associated with the energy-efficient equipment. A financial incentive will reduce the higher costs of the more efficient technology and thus increase the benefit/cost ratios of models covered by the policy measure. With a greater benefit/cost ratio, the market penetration of those devices will increase. The dynamic increase in market penetration m(t) of models at the target level can be estimated from:

$$ m(t) = \lambda (t) \cdot \left( {{\text{imp}}\left( {{b^{*}},{\text{b}}{{\text{c}}_{\text{pol}}}(t)} \right) - {\text{imp}}\left( {{b^{*}},{\text{b}}{{\text{c}}_{\text{bc}}}(t)} \right)} \right) $$

(45)

where:

$$ \text{\text{b}}{{\text{c}}_{\text{pol}}}(t) = \frac{{{\text{incB}}(t)}}{{{\text{inc}}{{\text{C}}_{\text{pol}}}(t)}} = \frac{{{\text{incB}}(t)}}{{{\text{inc}}{{\text{C}}_{\text{bc}}}(t) - v(t)}} $$

(46)

$$ \text{\text{b}}{{\text{c}}_{\text{bc}}}(t) = \frac{{{\text{incB}}(t)}}{{{\text{inc}}{{\text{C}}_{\text{bc}}}(t)}} $$

(47)

$$ \text{\text{incB}}(t) = {\text{eCos}}{{\text{t}}_1}(t) - {\text{eCos}}{{\text{t}}_{{{i^{*}}}}}(t) $$

(48)

$$ \text{\text{inc}}{{\text{C}}_{\text{bc}}}(t) = {\text{qCos}}{{\text{t}}_{{{i^{{*}}}}}}(t) - {\text{qCos}}{{\text{t}}_1}(t) $$

(49)

and:

m(t):

Market penetration in the policy measure-case scenario of models at the target level shipped in t

λ(t):

Market penetration adjusting factor⁶⁶ ($0 < \lambda (t) \leqslant 1$)

b*:

Market barriers level, estimated such that$\text{\text{imp}}\left( {{b^{*}},{\text{b}}{{\text{c}}_{\text{bc}}}(t)} \right) = \frac{{{\text{sh}}{{\text{p}}_{{{\text{bc}},{i^{*}}}}}(t)}}{{\mathop{\sum }\nolimits_i {\text{sh}}{{\text{p}}_{{{\text{bc}},i}}}(t)}}$

bc_pol(t):

Benefit/cost ratio of dev _i* shipped in t in the policy measure-case scenario

bc_bc(t):

Benefit/cost ratio of dev _i* shipped in t in the base-case scenario

incB(t):

Incremental energy costs savings of dev _i* shipped in t

incC_bc(t):

Incremental equipment costs, in the base-case scenario, of dev _i* shipped in t

eCost_i(t):

Lifetime energy cost of dev _i shipped in t

qCost_i(t):

Lifetime equipment costs of dev _i shipped in t

Appendix 4: estimating market penetration from informational incentives

In the following, we detail how to use the interpolated market penetration curves proposed by Blum et al. (2011, Appendix A) to estimate the dynamic increase in market penetration resulting from information incentives. The estimate relies on the benefit/cost ratio provided by the design options targeted by the incentives and in the change in the market barriers level promoted by the measure. It also relies on historical data from earlier informational incentive programs focusing the targeted or any similar equipment. For each year y′ for which historical market penetration data are available, the relative change in market barrier level $b_{{{\text{w/wo}}}}^{\prime }\left( {{y^{\prime }}} \right)$ can be estimated using the ratio between the levels of market barriers with and without ⁶⁷ the earlier program:

$$ \text b_{{{\text{w/wo}}}}^{\prime }\left( {{y^{\prime }}} \right) = \frac{{b_{\text{w}}^{\prime }\left( {{y^{\prime }}} \right)}}{{b_{\text{wo}}^{\prime }\left( {{y^{\prime }}} \right)}} $$

(50)

⁶⁸where $\text b_{\text{wo}}^{\prime }\left( {{y^{\prime }}} \right)$ and $\text b_{\text{w}}^{\prime }\left( {{y^{\prime }}} \right)$ are such that:

$$ \text{\text{imp}}\left( {b_{\text{wo}}^{\prime }\left( {{y^{\prime }}} \right),{\text{b}}{{\text{c}}^{\prime }}\left( {{y^{\prime }}} \right)} \right) = \frac{{{\text{shp}}_{\text{wo}}^{\prime }\left( {{y^{\prime }}} \right)}}{{{\text{shp}}_{\text{tot}}^{\prime }\left( {{y^{\prime }}} \right)}} $$

(51)

$$ \text{\text{imp}}\left( {b_{\text{w}}^{\prime }\left( {{y^{\prime }}} \right),{\text{b}}{{\text{c}}^{\prime }}\left( {{y^{\prime }}} \right)} \right) = \frac{{{\text{shp}}_{\text{w}}^{\prime }\left( {{y^{\prime }}} \right)}}{{{\text{shp}}_{\text{tot}}^{\prime }\left( {{y^{\prime }}} \right)}} $$

(52)

and:

$\text b_{{{\text{w/wo}}}}^{\prime }\left( {{y^{\prime }}} \right)$ :

Relative change in the level of market barriers in year y′ due to the earlier program

$\text b_{\text{wo}}^{\prime }\left( {{y^{\prime }}} \right)$ :

Market barriers level in year y′ without the earlier program

$\text b_{\text{w}}^{\prime }\left( {{y^{\prime }}} \right)$ :

Market barriers level in year y′ with the earlier program in place

$\text{\text{b}}{{\text{c}}^{\prime }}\left( {{y^{\prime }}} \right)$ :

Benefit/cost ratio in year y′ of models covered by the earlier program⁶⁹

$\text{\text{shp}}_{\text{wo}}^{\prime }\left( {{y^{\prime }}} \right)$ :

Shipments in year y′ of models covered by the earlier program without the program

$\text{\text{shp}}_{\text{w}}^{\prime }\left( {{y^{\prime }}} \right)$ :

Shipments in year y′ of models covered by the earlier program with the program in place

$\text{\text{shp}}_{\text{tot}}^{\prime }\left( {{y^{\prime }}} \right)$ :

Total shipments in year y′ of units from the product classes covered by earlier program

The historical change in market barriers expressed by $b_{{{\text{w/wo}}}}^{\prime }\left( {{y^{\prime }}} \right)$ can be used to estimate a pattern in the market transformation that the policy measure under study is likely to promote. Let $M(t)$ be a function that transforms the historical market barrier changes stimulated by the earlier program into market barrier changes forecast for the policy measure under study. The increase in market penetration for the new policy measure can then be estimated from:

$$ m\prime (t) = {\text{imp}}\left( {{b_{\text{pol}}}(t),{\text{bc}}(t)} \right) - {\text{imp}}\left( {{b_{\text{bc}}}(t),{\text{bc}}(t)} \right) = {\text{imp}}\left( {{\cal M}(t) \cdot {b_{\text{bc}}}(t),{\text{bc}}(t)} \right) - {\text{imp}}\left( {{b_{\text{bc}}}(t),{\text{bc}}(t)} \right) $$

(53)

where:

m′(t):

Market penetration increase fostered by policy measure

bc(t):

Average benefit/cost ratio of models covered by policy measure and shipped in t

b_bc(t):

Base-case scenario market barriers level in t

b_pol(t):

Policy measure-case scenario market barriers level in t.