3 Mitigation overview and methodology

The Mitigation Module¹

World Bank

Paolo Agnolucci

Daniel Bastidas

Alexandra Campmas[^3_2]

Faustyna Gawryluk

Olivier Lelouch

Stephen Stretton[^3_3]

IMF

Simon Black

Victor Mylonas[^3_4]

Ian Parry

Nate Vernon

Karlygash Zhunussova

3.1 Executive Summary and Reviewer Guide

3.1.1 Introduction

The mitigation module lies at the heart of CPAT. It is based on a simplified reduced-form model of fuel consumption, with two alternative power sector models, one of which is a simplified structural technoeconomic power model.

The mitigation module’s goal is to predict energy use, energy prices, emissions, carbon tax revenues, economic costs, and GDP effects for a baseline and a policy scenario (carbon pricing, fuel taxes, energy efficiency policies, renewables subsidies, feebates, etc.), over the time horizon of CPAT (2019-2035).

To this end, the module is built around different inputs, including (1) energy balances and price inputs; (2) external forecasts (baseline international energy prices and macro indicators); (3) parameter inputs (elasticities, fiscal multipliers, etc.); (4) user-specified policy inputs (for example, the level and coverage of a carbon tax, exemptions and exemption phase-outs, and other inputs).

These inputs inform the calculation steps in which: (1) sectoral energy prices, including the effect of pricing policy, are determined; (2) fuel use in the buildings, transport, and industry are estimated; and (3) electricity production costs are calculated to feed the two power models, which then determine generation, investment, etc.

The module’s outputs include energy consumption by fuel type and sector, greenhouse gas emissions (CO₂ and other GHG such as methane), fiscal revenues and GDP effects, price changes, power generation, and power sector investment. The structure of the rest of this document is as follows:

Overview
- Introduction
- Summary of Mitigation Module
- Niche and Use Case
- Critical Policy Modelling Choices
- Data
- Testing and Validation
- Status of Upgrades since last time
- Caveats
- Notation
Prices and taxes;
Energy consumption (excluding power supply);
Power supply prices and models;
Emissions of CO2 and other GHG;
Fiscal Revenues;
Monetized welfare estimates;
Validation: including regression, comparison with other models, and hindcasting.
Appendices including:
1. Appendix A - Macro data of CPAT: Sources and codes;
2. Appendix B - Energy balances;
3. Appendix C - Prices and taxes methodology;
4. Appendix D - Examples of NDC calculations;
5. Appendix E - Parameter options in the mitigation module;
6. Appendix F – Notation in CPAT; and
7. Appendix G – Data sources.

3.1.2 Summary of Methodology

The mitigation module is a simplified reduced-form model of fuel consumption, deriving quantities under a baseline and a policy scenario broadly in line with more complex models (the IEA’s World Energy Model, Enerdata POLES – see 3.8.3 Model comparisons). The mitigation module’s goal is to predict energy use, energy prices, emissions, carbon tax revenues, economic costs, domestic environmental co-benefits, and GDP effects over the time horizon of CPAT (2018-2035) for a wide range of mitigation instruments (carbon pricing, fuel taxes, energy efficiency policies, renewables subsidies, feebates, etc.). The main drivers of the emissions projections are GDP growth (including GDP-per-capita and population), income elasticities, and rates of technological change. Fuel use responses to policies are driven principally by proportional changes in fuel prices caused by projected market dynamics and government policies (including carbon prices).

Figure 3‑1: Overview of the mitigation module

The mitigation module relies on several inputs and provides numerous outputs. The module is at the core of CPAT, as its results feed into other modules.

Figure 3‑2: Overview of the mitigation module’s inputs and outputs

The general approach to determining baseline fuel consumption and the response to a carbon tax or other policy is a simplified, reduced-form model based on income and price elasticities.² The changes in energy consumption from the base year are driven by energy prices (including the influence of mitigation policy) and real (total) GDP. Real GDP (which is the primary driver of the baseline) adjusts to changes in fiscal policy through multiplier effects (see the Chapter on Multipliers). Exogenous changes to efficiency and the price of renewable energy are also drivers of fuel use and composition.

The mitigation module comprises two power sector models and simple models for industry, transport, and buildings. The two power models, the ‘elasticity-based’ model and the hybrid techno-economic dynamic model (‘engineer model’) of the power sector with explicit capital stock use identical power demand elasticities and separately consider power generation’s costs by type. For ‘off-the-shelf’ usage of CPAT, we recommend an average of the two models. For more tailored work, we recommend using the engineer model.

The elasticity-based model requires only minor tailoring and checking. As a result, it makes no distinction between short-term and long-term behavior. It also fails to distinguish between dispatchable and non-dispatchable generation types. The engineer power model fills this gap by separating investments, retirement, and dispatch decisions. It includes countries’ generation capacities and makes it possible to investigate the radically different power systems compatible with high carbon prices. However, the model still cannot account for inflexibility, off-price policies, and local price variation (e.g., coal). Due to the constraints of Excel, it can only approximate the temporal match between electricity supply and demand.

The module’s outputs include energy consumption by fuel type and sector (i.e., buildings, transport, and industry). They are estimated based on a fundamental model structure described in an IMF paper.³ Energy use responds to energy prices and real GDP. Additional outputs include greenhouse gas (GHG) emissions (i.e., CO₂ and other GHG emissions such as leakage methane which represents small amounts of GHG gases), fiscal revenues and GDP effects, economic efficiency costs, price changes, power generation, and power sector investment.

To ensure that the model is correctly fitted, specific calibrations are undertaken for the observed years, i.e., 2019, 2020, and 2021 (and beyond if necessary and if data are available). In particular, due to the unprecedented global economic shock induced by Covid-19 and Ukraine invasion, energy prices may have behaved in an “anomalous” way, leading the model results to deviate from the observed data. This calibration ensures a proper starting trajectory for the model.

The rest of this section is intended to help reviewers navigate the Mitigation documentation by highlighting the tool’s key components, and the main conclusions resulting from the validation analysis of CPAT.

3.1.3 Niche & Use cases for CPAT

CPAT requires minimal training to be used effectively. Computer literacy, basic familiarity with Excel, and some understanding of economic and climate concepts. Flexibility is built-in for the more advanced user, to allow for different assumptions than those in the default assumption set and for choosing among various data inputs. Advanced users can also input their own data.

Although CPAT is powerful even on its own, it is still advisable to use it alongside other tools that may have a more granular representation, of say, technological detail, sectors, feedback mechanisms, trade linkages, behavioral responses, etc. CPAT is designed to be light on resource and skill needs, providing a rapid first-cut analysis when one seeks to test various carbon pricing designs.

The carbon tax is the most effective instrument for emissions reduction in CPAT. By default, its coverage spans the whole economy, but the user can also set this to select sectors. The ETS covers the whole economy by default with the option also to select coverage. A key assumption is that the ETS and carbon tax are equivalent in a frictionless market with full auctioning. While the ETS design lets the user select prices (rather than quantities), frictions imply that ETS is not as effective at reducing emissions as a carbon tax. The user can choose the initial carbon tax level, when to commence carbon pricing, the target carbon price, the year that the target level is achieved, and the sectoral coverage of the carbon tax.

Strengths and weaknesses of CPAT in relation to carbon pricing schemes:

Country’s needs	Yes/No	Remarks
Understanding which instrument (ETS or tax) to choose.	No	Like most other deterministic models, CPAT assumes that the ETS yields the same price as a carbon tax and does not currently consider offset markets.
Assessing the impacts of carbon price on the economy, employment, energy/fuel prices	Yes	CPAT provides an assessment of macroeconomic performance, energy consumption and price changes, emission reductions, distributional consequences, and co-benefits (health and traffic) of carbon pricing reform.
Different allowance allocation mechanisms	Partial	CPAT has an effectiveness and revenue parameter for ETSs.
With and without consideration of offsets	No	See above
Different carbon tax rates for different sectors	Yes	CPAT has a consistent carbon price that can be exempted by sector and/or fuel type. There is also an excise reform table that allows fuel and sector-specific pricing.
The potential distributional impacts of introducing a carbon price	Yes	This requires household expenditure survey data. If this data is not already available within CPAT, it must be entered to access the reform’s distributional consequences.
Understanding the potential “co-benefits” of introducing a carbon price.	Yes	Reduction in local pollutants and traffic co-benefits associated with carbon pricing reform are currently represented in the model.
Are all sectors represented in CPAT?	Yes	CPAT brackets the economy into 17 sectors.
Does CPAT account for pre-existing policies?	Yes	CPAT also allows the user to phase pre-existing subsidies, for instance, or exemptions if these have been added during instrument design.

3.1.4 Critical Policy and Modelling Choices

The reviewer should be aware of a few critical modeling choices.

First, the user has the option to as well as a carbon price to phase out fossil fuel subsidies. Those are shown on the top right of the main policy panel.

Figure 3‑3: Main Settings Panel

There is the option (default to on) to convert the carbon price into a GHG tax across all sectors (including LULUCF, Waste, etc.) See the red dash on the bottom left of the panel above.

The user can default to the Variable Renewable Energy maximum scale-up rate (See red arrow above). The default is ‘Country Specific,’ which gives and adds additional solar generation of 2% of the total power generated each year plus an extra 2% for wind (except for China which has 2.5% for solar and 2.5% for wind). The implications of these maximum scale-up rates are in the second panel below, bottom right.

Investment behavior in state-owned power sectors responds to the carbon tax as a shadow price of carbon for government investment, i.e., we assume state plans respond as well as the private sector.

Figure 3‑4: Power Setting Panel

Fourth, CPAT, by default, has two ad hoc adjustments: a Covid adjustment for 2021 and 2022 and a coal share adjustment. The engineer power model coal share adjustment is a country-specific value for some countries that adds an intangible cost to coal generation (representing regulations not captured in CPAT plus lack of flexibility relative to natural gas). That adjustment can be turned off in the power setting panel (around row 131). The setting is calibrated to current coal shares and long-term IEA projections.

3.1.5 Data choices in CPAT

3.1.5.1 Key data used

For more information, Appendix G, ‘Data sources,’ gives an overview of the data used in the mitigation module.

The main data sources are IEA data, various World Bank data sources, IIASA data for emissions, and Energy Prices and Energy projections are primarily from the IMF (from multiple processes).

3.1.5.2 Key parameters and choices

Sections of the Mitigation documentation detailing the key parameters and their methodology, if estimated:

Elasticities: 3.3.5 Income and Price Elasticities of Demand
Autonomous efficiency improvement: 3.3.5.6 Rates of technological change and exogenous rebound effects and 3.4.2.3 Power demand. Also, see caveats.
Renewable scale up rate: Section 3.4.2.4 ‘Power supply.’
CapEx: Section 3.4.4 ‘Power sector data sources and parameter choices.’

The following key parameters in CPAT rely on different data sources or assumptions:

Elasticities concerning prices and income are derived from Burke and Csereklyei (2016)⁴ using the relationship from Gertler and others (2016).⁵

The exogenous time trend or autonomous efficiency improvement is set based on IEA’s data and experts’ judgment. Values are different across sectors and fuels. See the caveats section.
Renewable scale up rates are set so that the user can choose a low, medium, high, or very high rate, corresponding to 1, 2, 3, and 4% of additional generation (as a proportion of total generation) per year, respectively. In addition, the CPAT dashboard provides transparency on country-specific scale-up historical rate, should the user decide to use a more specified rate as the one defined under the settings.

The engineer power model relies on forecast CapEx, subject to a learning rate methodology for renewable energies.

3.1.5.3 Key calibration exercises

Calibration exercises are presented under the corresponding section. In particular:

Overall energy use through Covid adjustment in 2020 and 2021: Section 3.3.4.4 ’Calibration of overall energy use through Covid adjustment in 2020 and 2021.’
Calibration in the engineer power model: Section 3.4.2.4 see sub-section ‘Calibration.’
Emissions: Section 3.5 ‘Emissions.’
Long-term storage is based on electrolyzes Section 3.4.2.5 see sub-section ‘Long-term storage.’

A calibration exercise is performed for some key variables to prevent the model from deviating from observed data (i.e., for 2019 to 2021) and ensure a proper starting trajectory, particularly in the context of Covid. Against this background, the following adjustments have been made:

Overall energy use through Covid adjustment in 2020 and 2021: Due to the unprecedented global economic shock induced by Covid-19, the energy consumption factor makes an ad hoc adjustment to the model and is calibrated using emissions outturn as the overall numeraire in 2020 and 2021.
Calibration in the engineer power model:
- Total electricity generation: A COVID adjustment factor can be used to calibrate total electricity generation. The latter, estimated by the model, is compared to observed data (IEA, 2020). It is worth mentioning that the default in CPAT does not account for this calibration, but this calibration can be turned on.
- Share of coal: The share of coal in electricity generation is calibrated to observed data in 2019 and 2020 (IEA, 2019 and 2020). The calibration uses an additional implicit price for coal – if necessary – to match the observed share of coal.
Emissions: In 2019, both $CO_{2}$ and $CH_{4}$ energy-related emissions are scaled to UNFCCC inventory emissions, meaning they are multiplied by a factor such that base-year emissions are equal in the model and the inventory.
Long-term storage is based on electrolysers: Given its interseasonal storage and geographic independence, we focus on the costs of electrolysers for storage. This storage cost is thus assumed as long-term storage and is measured with the interface (i.e., electrolysers) as the numeraire.

3.1.6 Testing and validation summary

The full validation analysis of the mitigation module is presented in Section 3.8 of the documentation.

The validation of the mitigation module is composed of several elements:

Analysis performed	Main conclusions
Elasticities estimations. As CPAT is mainly driven by elasticities with respect to prices and economic activity, an econometric analysis is carried out to compare the elasticities used in CPAT and those obtained from empirical analysis.	The empirical validation pointed out that the elasticities with respect to price and economic activity in CPAT tend to be in the same ballpark as those estimated here, with some exceptions related to road transport and the service sector.
Comparison of CPAT against other models.⁶ This analysis comprises comparisons between CPAT and Enerdata, IEA, and EPM models.	Overall, the comparison analysis shows comparable results between CPAT and other models with a few exceptions most likely linked to different components in fuel aggregation, divergent assumptions regarding nuclear, country-specific divergence (e.g., Russia), or Covid adjustment.
Ex-post studies. This section presents the literature’s estimates of the effectiveness of carbon pricing with respect to emissions and compares them to the CPAT results.	When looking into the range of CPAT’s estimates across all sectors, results are comparable with those of the literature. At the sector level, the power sector records the highest decrease in the long run, which is consistent with the literature.
Hindcasting. The hindcasting exercise aims at testing CPAT’s forecasts against observed data. It searches to evaluate the performance of the assumptions used when trying to reproduce historical information.	For the countries analyzed, CPAT generally fits the trend of observed data. There are some discrepancies and periods where gaps appear. However, for certain periods/countries, discrepancies of volatile magnitudes appear between CPAT projections and observed emissions. While this may result from implementing policies that were not modeled in the exercise, it can also result from discrepancies in price forecasting.
Parameter Sensitivity Analysis. The analysis explores the sensitivity of a set of selected parameters.	The sensitivity of the parameters to CPAT to CO2 emissions ranges from no effect to very sensitive when focusing on the relative changes (i.e., CO2 emissions reduction relative to the default parameter).

3.1.7 Status of upgrades since the last review

There have been many upgrades to CPAT since the last review, and the table below gives a partial list to give the reviewer an idea of the improvements. The version log in CPAT itself provides an exhaustive list.

Feature	Components	Status
Complete documentation	Full documentation, including but not limited to Biomass substitution; Power sector parameters; other mitigation features (e.g., NDCs)	Complete
Validate CPAT historically	Basic global validation of income elasticities	Complete
Validate CPAT historically	Panel data estimate of income elasticities and time trends	Complete
CPAT Shareability	Transform all non-shareable (proprietary) data into a shareable form	Complete
Single Time Period for Simplicity	CPAT, for a while, had short- and long-term components to the price elasticity. We eliminated these for now as the goal is not a short-term prediction but medium-term accuracy and simplicity	Complete
Update of power data	Full update and sourcing of power sector data (CapEx, variable and fixed OpEx, Efficiency, Lifetime, Capacity factor; Nuclear decommissioning, long-term waste storage, and fuel costs)	Complete
Testing across countries	Full testing across countries	Complete
Scheduled Retirement of Coal	Done based on global data set at the national level (data are taken from Power Plant Tracker)	Complete
Cost-Based Early Retirement	Implemented	Complete
PPAs	We implemented fossil PPA percentage for the ‘sclerotic’ power sector option when fossil fuel PPAs are present	Complete
Comparison with other models	Compare new and old power sector models to other power sector models	Done for EPM
Why the improvement?	Assess and discuss differences between the ‘old’ and ‘new’ model – i.e., why is new better	Partially implemented
Individual country masterplans.	The model now allows exogenous investment/capacity to be input in the manual Inputs tab	Complete

3.1.8 Caveats

There are some notable caveats/limitations to CPAT, given its largely reduced form approach and its mid-term (to 2035) horizon. Sections of this document could also complement this section by presenting the upgrades made to CPAT since the last review and outlining desired upgrades, known issues, and valuable analyses not completed.

3.1.8.1 Policy modeling

CPAT abstracts from the possibility of:

Designing complex policy packages, including a combination of instruments (e.g., ETS, carbon tax, and offsets) and accounting for mitigation actions in the baseline scenario (beyond those already captured in recently observed fuel use/price data and known carbon pricing mechanisms). However, policy combinations can be done sequentially — analyze one policy and use this outcome as the new baseline for the next policy, etc. In the same vein, CPAT does not account for international linkages across countries or emissions leakage, which prevents explicit analysis of the implications of border carbon adjustments which are receiving increased attention.
Differences in fuel price responsiveness may vary across countries with the structure of the energy system and regulations on energy prices or emission rates. Nonetheless, this latter default can be easily adjusted in individual country analysis. In addition, feedback from carbon pricing, like the impact of carbon pricing reform on commodity prices or interest rates which could be feedback to affect emission reductions, cannot be easily designed in an Excel-based tool.
Non-linear responses to significant policy changes, such as rapid adoption of carbon capture and storage (CCS) technologies (deployed in the power and industry sectors) or even direct air capture.
Upward sloping fuel supply curves and changes in international fuel prices that might result from simultaneous climate or energy price reform in large countries. CPAT is parameterized to behave like the mid-point of the broader modeling literature. Although many models account for these factors, no big difference is observed, given the relatively flat supply curves for coal.
Applying different coverage levels across sector groups. CPAT allows the user to select the sectors and fuels to be considered for policy implementation:
- For new policies, the coverage is binary, whether they are included or not.
- Whenever the user defines exemptions for fuels or sectors and determines a phaseout period for those exemptions, the coverage can be fractional during that period.
- For existing policies, instead, the coverage is mostly fractional, and it is currently computed as an average of the fuel demand covered across sector groups or fuel types.

3.1.8.2 Prices

When it comes to prices, CPAT does not model:

Upward sloping fuel supply curves and changes in international fuel prices that might result from simultaneous climate or energy price reform in large countries—parameter values are, however, chosen such that the results from the model are broadly consistent with those from far more detailed energy models that, to varying degrees, account for these sorts of factors (see Section 3.8.3).
Institutional setup driving prices. In CPAT, energy demand responds to prices in the private sector, although the institutional setup could, in some markets, prevent prices from determining supply and demand.

3.1.8.3 Emissions

The following limitations and constraints exist when computing the emissions:

In the current version of CPAT, international linkages across countries or emissions leakage are not factored in. This prevents explicit analysis (in the first public version) of the implications of border carbon adjustments which are receiving increased attention.
Energy related N2O emissions are calibrated on CO2 emissions preventing the independence of one from the other.
In the case of LULUCF CO2 emissions, a condition to model the sink activity can create an irreversible state of a positive sink (more absorptions than emissions). Even if the previous year’s emissions (the year before the base year) are negative, there is no possibility of returning to a negative sink.

3.1.8.4 Energy use (all energy sectors)

A first important caveat, common to all of our approaches, lies in the fact that the autonomous efficiency improvement and time trend of consumer preferences and technology are treated in the same way. In other words, it is implicitly assumed that the time trend of consumer preferences and technology is not varying. However, it can be subject to changes over time. For instance, technology can get more or less energy intensive as it changes.

3.1.8.5 Power sector

The two different power models in CPAT have different strengths and weaknesses. For ‘off-the-shelf’ use, we recommend using the average of the two models. We recommend the techno-economic (‘engineer’) power model specified with detailed modeling choices and input parameters for more tailored use.

The elasticity-based power model is responsive to relative price changes but not absolute prices. It does not explicitly model the capital stock, so it cannot distinguish between short-run capacity factor differences and long run capital stock changes. Thus, changes in generation for fixed capacity stock generation types may be too fast. It may also model unrealistic reductions in generation from renewables if their price were to increase relative to other options. Conversely, changes in generation for dispatchable types may be insufficiently responsive to price. The model could produce outcomes that are not physically realistic.

The techno-economic ‘engineer’ power model has the following caveats:

Investment behavior in state-owned power sectors responds to the carbon tax as a shadow price of carbon for government investment, i.e., we assume state plans respond as well as the private sector.
The power maximum retirement rate for coal is set to 80%.
Estimates of national capacity by generation type across time. Since no such dataset exists globally, CPAT’s current approach relies on its own estimates. Fossil capacity collected from the EIA is scaled using independently estimated shares.
In CPAT, the investment decision is not fully commercial but assumes a quasi-least cost approach to meeting aggregate energy demand (and power demand).
Fiscal expenditures of government investment in power are not accounted for. Such a feature is not implemented, partly because power investment is typically funded by customers even if financed by the government – so including it would raise consistency issues.
There could be a better assessment of flexibility (and ease of implementing VRE) based on the capacity reserve.
Losses associated with round-trip efficiency (i.e., the ratio between the power put in and the energy retrieved from storage) are currently not accounted for in the current model. Power storage consumes electricity and saves it to hand it then back to the grid. The higher the round-trip efficiency, the less energy is lost in the storage process.

3.1.8.6 Desirable upgrades, known issues, and useful analyses not completed: General

This section contains our assessment of upgrades that are desirable but were not able to be completed. We do not propose to do all these upgrades and seek the reviewer’s opinions if any of them are must-haves before releasing CPAT to the broader community.

Issue	Comment/Status
Emissions Factors from IIASA include process emissions and are then calibrated	The current approach to IIASA emissions factors (which, inappropriately, include process emissions) and then calibrating total emissions is unsatisfactory. Perhaps use detailed energy balances to determine weighted average CO2 Efs. Priority: low
A better methane model (and, more generally, better models outside the energy sectors) is needed	The IMF plans to upgrade the methane model.
Short and long-term elasticity distinctions not included	We now eliminated the distinction between the short and long run. However, we think this is important, particularly for residential power demand, which is inelastic in the short term. We intend to revisit this in 2.0.
Covid adjustment is ad hoc	The Covid adjustment for 2020 is unsatisfactory and may be partly a response to the lack of the short-term/long-term distinction (i.e., too high price elasticities in the short term). I am not sure we can improve it due to the asymmetric nature of the shock. However, it might be better to still go with differences from the outturn. It can be turned off.
Regulatory policy	The semantics of the shadow price of regulatory policy options and then the 70% effectiveness weighting is highly unclear
Time Trend is not backed by detailed research and only relates (notionally) to efficiency improvement rather than other components of the time trend	The current time trend includes energy efficiency (negative trend). Still, there are also positive trend components to the time trend (e.g., shifts in tastes toward SUVs) that may not be captured in the income elasticity. Could reestimate the model.
Income elasticity: how to get away from that? Is there a relationship with a CGE model, rather than using this, which can be crude?	It was not implemented. No plans to adjust this.
A closer connection to sectoral GVA forecasting might be desirable	To be discussed further.

3.1.8.7 Power Sector Models

CPAT does not aim to replace models like EPM; thus, we have limited the upgrades.

Comment	Status
Power supply feebates are implemented in the engineering model. Power efficiency feebates are in the elasticity model.	It would be better if both models would do both types of feebates.
The elasticity model could be phased out	Currently, we recommend the ‘average’ of two models. Could move to engineer model as a recommendation.
Land area-related physical limits	No change has been implemented – No current plans.
Interest rates not applied to the construction period	TBC
Part of the levelized cost is to do with the actual capacity factor (the fixed operation and maintenance), and this could drive retirement	No change has been implemented – No current plans.
Do not calculate the capacity reserve margin explicitly	No change has been implemented – No current plans.
Do not use residual Load curves or representative days, as they are viewed as too complex for Excel	No change has been implemented – No current plans.
We do not have resource curves; wind global wind costs are irrelevant. This is very significant for hydro, for example	For hydro and nuclear we recommend using exogenous scale up. These default to no investment before 2030 and only allow investment after this point if the generation type is already present
Calibrate storage requirements at a regional level	No change has been implemented – No current plans.
Explicitly estimate ‘k’ in the logit model (how sharply the sigmoidal function cuts out more expensive options)	No change has been implemented – No current plans.
Concerning State-Owned Enterprises (e.g., in Power Sector), we might want to make the investment/derisking decision explicit in these cases rather than relying on the carbon tax. That would reduce the effectiveness of a carbon tax but might be better communication of what MoFs need to do regarding the direction of SOEs.	Not currently implemented.

3.1.8.8 3.1.8.9 Remaining Known Bugs or Issues

A model as complex as CPAT has some ongoing issues. These are stated here and are, in most cases, minor.

Comment	Status
PPAs	PPAs only affect dispatch and so have limited effect in the long term. Probably not an issue, but it needs an investigation.
State-owned power markets; Investment decision	Currently, the investment decision is driven by the carbon price, representing a shadow price for investment appraisal. This needs to be flagged more strongly for regulated power markets either in the documentation or in CPAT, or an option to explicitly add/remove a shadow price for investment appraisal.
Bhutan and elasticity power model	Issue when in the elasticity model that the balances do not fully balance between energy consumption and energy supply and when exports or imports are substantial (e.g., in Bhutan).
Russia	Russia’s results need to be confirmed.
Small Countries	There are some issues with a few smaller economies. See the appendix showing the country list working. We do not intend to remediate all countries due to data limitations.

3.1.9 Notation and Acronyms

A table summarizing the Notation used is available in each modeling section. This section describes dimensions and acronyms.

3.1.9.1 Dimensions

CPAT exists across multiple dimensions. Each will be given the following index notation in the same order as described below.

Variable	Index
Scenario⁷	$o$
Country	$c$
UNFCCC emissions sector⁸	$u$
Sector grouping⁹	$g$
Sector	$s$
Fuel and generation type¹⁰	$f$
Pollutant	$p$
Year¹¹	$t$

That means that a typical variable might be defined as follows $x_{\text{ocsf},t}$ – with $x$ being specific to scenario, country, sector, fuel type, and time. Particular values for these general indices are indicated with capitals, for example, o=B for baseline.

The codes corresponding to elements of the dimensions (for example, fuel types and sectors) are also defined in tables in the appendices.

3.1.9.2 Institutions

EIA Energy Information Administration

IEA International Energy Agency

IIASA International Institute for Applied Systems Analysis

IMF International Monetary Fund

IRENA International Renewable Energy Agency

JRC Joint Research Centre (institution of the European Union)

NREL National Renewable Energy Laboratory

OECD Organisation for Economic Co-operation and Development

US EPA US Environmental Protection Agency

WBG World Bank Group

3.1.9.3 Abbreviations

CapEx Capital Expenditure

CCS Carbon Capture and Storage

CO2 Carbon Dioxide

CPAT Climate Policy Assessment Tool

EF Emissions Factor

ETS Emission Trading System

EV Electric Vehicle

ftr Fuel Transformation

GDP Growth Domestic Product

GHG Greenhouse Gas

HIC High Income Countries

HP filter Hodrick-Prescott filter

LCOE Levelized Cost of Electricity

LIC Low Income Countries

LMIC Lower Middle-Income Countries

LPG Liquefied Petroleum Gas

LULUCF Land-use, Land-use Change, and Forestry

MAC Marginal Abatement Cost

MT Multi Scenario Tool, a spreadsheet that allows multiple-country and -policies use of CPAT

NDC National Determined Contribution

OBR Output-Based Rebating

OpEx Operating and Maintenance Expenditure

PM Particulate Matter

PPA Power Purchase Agreement

PV Present Value

R&D Research & Development

SCC Social Cost of Carbon

SLCP Short-Lived Climate Pollutants

UMIC Upper Middle-Income Countries

UNFCCC United Nations Framework Convention on Climate Change

VAT Value-Added Tax

VKT Vehicle Kilometers Traveled

VRE Variable Renewable Energy

WACC Weighted Average Cost of Capital

3.1.9.4 Fuels

BIO Biomass

COA Coal

HYD Hydropower

NGA Natural Gas

NUC Nuclear

OIL Oil

REN Other Renewables

SOL Solar

WND Wind

3.1.9.5 Units

GJ Gigajoule

GWh Gigawatt Hour

ktoe Kilo Tonne of Oil Equivalent

kW Kilowatt

kWh Kilowatt Hour

kWy Kilowatt Year (=365*24 kWh)

MMBtu Million British Thermal Unit

MW Megawatt

MWh Megawatt Hour

MWy Megawatt Year (=365*24 MWh)

$\text{tC}O_{2}$ Ton of CO2 Equivalent

USD United States dollar

3.2 Fuel prices, taxes, and subsidies

3.2.1 Overview

At the time of writing, the base year for CPAT is 2019. The base year plus the next two years (2020 and 2021) are considered the ‘historical price years’ for CPAT. The algorithm for the historical price years and the future price years is different; we use historical price information in the historical price years and a forecast approach for the future price years.

Domestic price information for historical time periods comes from a dataset created by the IMF side of the joint WB-IMF team. We refer to this dataset as the ‘IMF dataset’. Information about this dataset is available from the IMF and is not part of this documentation. The user can supplement these data with specifically-sourced data (‘manual inputs’).

To forecast domestic prices forward, we also use projections of international fuel prices (for example, crude oil prices). These forecasts are created as an average of internationally recognized sources. The default is an average of IMF and WB projections, although other options are available if the user chooses. The user should however make sure that these sources are updated.

While the method used to build the data may change from the ‘historical price years’ to the years where fuel prices are forecasted, the identity to obtain retail prices $p_{\text{cgft}}$ (for a given country $c$, sectors grouping $g$ and fuel type $f$, during period $t$) remains the same: Retail prices equal the supply costs plus all relevant taxes. As for latter, the different hierarchies, coverage, exemptions, and types of tax, require additional disaggregations. For instance, value added taxes may be paid on top of other taxes and fees, so it will be convenient to express the retail price identity as:

$p_{\text{cgft}} = sp_{\text{cgft}} + \text{va}t_{\text{cgft}} + \text{tx}o_{\text{cgft}}$

where $\text{sp}$ stands for the supply cost (also referred to as the pre-tax price), $\text{vat}$ is the value added tax, and $\text{txo}$ stands for the excise and all other taxes. Furthermore, $\text{txo}$ acts as net additional taxes, as it corresponds to the addition of consumer subsidies $\text{cs}$, fixed or ad valorem taxes $\text{fao}$, any existing carbon price $\text{xcp}$, and any new carbon price $\text{ncp}$:

$\text{tx}o_{\text{cgft}} = cs_{\text{cgft}} + \text{fa}o_{\text{cgft}} + \text{xc}p_{\text{cgft}} + \text{nc}p_{\text{ocgft}}$

Note that the existing and new carbon prices may result from policies related either to carbon taxation or ETS permit prices, as it will be explained in upcoming sections.

The table below summarizes the process used to build the information for prices and subsidies for the base years and the forecasted period. Additional information on each element can be found in the upcoming sections.

Variable Code	Variable Name	Base years source	How Price is Projected
$\text{sp}$	Supply Price	IMF dataset	Scaled according to international prices
$\text{vat}$	VAT	IMF dataset	Scaled according to supply price
$\text{xcp}$	Existing Carbon Price	From State and Trends of Carbon Pricing (resulting from carbon taxes or ETS permits prices)	$Options$ Either a defined schedule of projections or base year carbon price plus defined growth rate
$\text{ncp}$	New Carbon Price	From dashboard	Calculated according to policy settings
$\text{fao}$	Fixed, Ad valorem and Other Taxes	Computed as a residual $\text{fao} = \text{txo} - \text{cs} - \text{xcp} - \text{ncp}$	$Options$ Kept fixed in time or scaled according to $\text{sp}$
$\text{txo}$	Excise and other taxes	IMF dataset	Addition of forecasted components
$p$	Retail Price	IMF dataset	Addition of forecasted components: $p = \text{sp} + \text{vat} + \text{fao} + \text{xcp} + \text{ncp}$

3.2.2 Notation

The table below presents the notations used in the section and the name of the variables to which they correspond. Note that the units are reported as input into CPAT, but further conversions are made to ensure that they match our calculations.

Notation	Variable	Unit
$p$	Retail price	US$/Gj
$P$	Aggregate retail price	US$/Gj
$\text{sp}$	Supply cost	US$/Gj
$\text{vat}$	Value added tax	US$/Gj
$\text{txo}$	Excise and all other taxes	US$/Gj
$\text{fao}$	Fixed, Ad valorem and Other Taxes	US$/Gj
$\text{cs}$	Consumer-side subsidy	US$/Gj
$\text{gp}$	Global fuel price	US$/bbl for oil, $/ton for coal and $/MMBtu for natural gas
$\phi_{\text{CS}}$	Phase-out factor for consumer-side subsidies
$\phi_{\text{PC}}$	Phase-out factor for price controls
$\text{pcc}$	Price control coefficient
$\text{Δgp}$	Difference between current and previous global prices
$\delta_{\frac{\text{CT}}{\text{ETS}}}$	Fix growth rate for existing carbon tax or existing ETS permit price
$\text{xct}$	Existing carbon taxes	US$/Gj
$\text{xetsp}$	Existing ETS permit prices	US$/Gj
$\text{xcp}$	Existing carbon price	US$/Gj
$\text{nct}$	New carbon tax	US$/Gj
$\text{netsp}$	New ETS price	US$/Gj
$\text{ncp}$	New carbon price	US$/Gj
$\text{NCT}$	National price per ton of $CO2$ under a carbon tax	US$/ton of CO2
$\text{NETSP}$	National price per ton of $CO2$ under an ETS	US$/ton of CO2
$\text{ef}$	Emission factors	$\text{tC}O_{2}e$/ktoe
$\varphi_{\frac{\text{NCT}}{\text{ETS}}}$	Sector-fuel coverage for the new policies (Carbon tax or ETS)	%
$F$	Use of fuel	ktoe

Fuel prices are different for each combination of fuel type $f$, country $c$ and ‘sector group’ $g$ (for prices meaning Residential, Industrial-including-Services, Transport and Power). Within the sector group, prices are equal – although more granular sectoral exemptions mean that prices in the sector can differ.

3.2.3 Base years: Sources of information

The IMF dataset on prices and subsidies includes data for supply costs, producer subsidies, VAT, excise and other taxes, consumer subsidies, and retail prices by country, sector group and fuel type. This dataset is, hence, at the core of the information for historical prices used in CPAT. Existing policies (carbon taxation or ETS permits) with information both in terms of carbon price levels as well as the fuel and sector coverage, complete the dataset for CPAT’s ‘historical price years’. A brief description of the price components used in CPAT is provided below:

Historical retail price: Included in the IMF data set. Rounding errors aside, it equals the sum of supply costs, VAT, and excise and other taxes.

Supply cost: Included in the IMF data set. It is calculated as a weighted average of domestic extraction costs and international prices plus transport costs, where the weights refer to the proportion of the components that are domestically produced or imported.

VAT: Included in the IMF data set. Computed as VAT collected over total sales (for a given fuel and sector), or as the result of applying a country or sector-specific VAT rate to the sales of a fuel to a sector.

Consumer Subsidy: Included in the IMF data set. Computed as total subsidy over total sales (for a given fuel and sector).

Producer Subsidy: Included in the IMF data set. Computed as total subsidy over total sales (for a given fuel).

Existing Carbon Price: Sourced from State and Trends of Carbon Pricing.

New Carbon Price: User-defined. It is typically zero in the base years.

Fixed ad valorem and other taxes: Balancing item, computed as a residual: $\text{fao} = \text{txo} - \text{cs} - \text{xcp} - \text{ncp}$.

3.2.4 Forecasted years: Construction of data on prices and taxes

Supply cost for a fuel type $f$ in a given country $c$ and sector grouping $g$ and during period $t$, is calculated using a coefficient of supply costs to base years (2017-2019) to the global prices in the same period, multiplied by the respective international fuel price in year $t$:

$sp_{\text{cgft}} = \frac{sp_{\text{cgf},t_{0}}}{gp_{f,t_{0}}}*gp_{\text{cft}}$

where $sp_{\text{cgf},t_{0}}$ denotes the average supply costs for country $c$, fuel $f$ in sector $g$ in base years $t_{0}$, $gp_{f,t_{0}}$ is the average global fuel price in base years, and $gp_{\text{cft}}$ is the global fuel price based on the chosen international energy price forecast in year $t$. As for the latter, note that information on global prices may be taken from different markets depending on the region or country.

In practice, the supply costs dependence on global prices may not be the same for a country that produces the fuel vs. one that imports it. Moreover, the supply cost can be affected by any existing producer-side subsidies, as well as by simulated policies where these would be phased out. The treatment of these advanced cases is presented in Appendix C - Prices And Taxes Methodology.

VAT payment equals the previous year’s VAT payment ratio to the supply cost multiplied by the current year’s supply cost:

$\text{va}t_{\text{cgft}} = \frac{\text{va}t_{\text{cgf},t - 1}}{sp_{\text{cgf},t - 1}}*sp_{\text{cgft}}$

NOTE: 1. Users are given the option to include $\text{txo}$ as part of the VAT base; 2. The residential and transport sectors may instead be computed by applying a nation-wide constant VAT rate to the VAT base ($\text{sp}$, here).

Consumer-side fossil fuel subsidy: Based on the fixed part of consumer subsidy per unit of energy, the new value is adapted to account for phasing-out of consumer side subsidies, and the phasing out of price controls, that create implicit subsidies.

$cs_{\text{cgft}} = cs_{cgf0}*\phi_{\text{CS},t} + \left( \text{pc}c_{\text{cf}} - 1 \right)*\left( \text{Δg}p_{\text{ft}}*\phi_{\text{PC},t} \right)$

where $\phi_{\text{CS}}$ is the phase-out factor for consumer-side subsidies, $\phi_{\text{PC}}$ is the phase-out factor for price controls, $\text{pc}c_{\text{cf}}$ is the price control coefficient and $\text{Δg}p_{\text{ft}}$ is the difference between current and previous global prices.

Fixed ad valorem and other taxes are projected based on last year’s information. There are two possible cases:

$o_{} = \left{

\[\begin{matrix} \frac{\text{Σfa}o_{\text{cgf},t_{0}}}{n_{t_{0}}} & \text{if\ fixed} \\ & \\ \frac{\text{fa}o_{\text{cgf},t - 1}}{sp_{\text{cgf},t - 1}}*sp_{\text{cgf},t} & \text{if\ ad\ valorem} \\ \end{matrix}\]

where $\frac{\text{Σfa}o_{\text{cgf},t_{0}}}{n_{t_{0}}}$ represents the average value of $\text{fao}$ during the base year.

Existing Carbon Price: Resulting for already implemented carbon taxes or ETS permits and their prices, it is assumed that these policies are complemented by any new measure selected by the user. Thus, the price is assumed to be equal to the latest available observation:

$\text{xc}p_{\text{cgft}} = \text{xc}p_{\text{cgf},t - 1} = \text{xc}t_{\text{cgf},t - 1}*\left( 1 + \delta_{\text{CT}} \right) + \text{xets}p_{\text{cgf},t - 1}*\left( 1 + \delta_{\text{ETS}} \right)$

with $\text{xc}t_{\text{cgf},t - 1}$ and $\text{xets}p_{\text{cgf},t - 1}$ representing the existing carbon taxes and ETS permit prices per energy unit, respectively. As part of the advanced options, CPAT allows the user to select a fix growth rate for each – the existing carbon tax and the existing ETS permit price. This is captured by the parameter $\delta$ in both cases.

New Carbon Price: It accounts for the price resulting from the implementation of new policies (carbon taxation or ETS permit prices). It can be decomposed as follows:

$\text{nc}p_{\text{cgft}} = \text{nc}t_{\text{cgft}} + \text{nets}p_{\text{cgft}} = \text{NC}T_{\text{ct}}*ef_{\text{cgf}}*\varphi_{\text{NCT},\text{cgft}} + \text{NETS}P_{\text{ct}}*ef_{\text{cgf}}*\varphi_{\text{NETS},\text{cgft}}$

where $\text{nc}t_{\text{cgft}}$ and $\text{nets}p_{\text{cgft}}$ stand for the new carbon tax per energy unit and the new ETS price per energy unit, respectively. In both cases, the value per energy unit is obtained based on the national price per ton of $CO2$ ($\text{NC}T_{\text{ct}}$ or $\text{NETS}P_{\text{ct}}$), and scaling it by the country-sector-fuel specific emission factors, $ef_{\text{cgf}}$, and the sector-fuel coverage for the new policies within the country in question ($\varphi_{\text{NCT},\text{cgft}}$ and $\varphi_{\text{NETS},\text{cgft}}$).

Among the options available, the user can select the sector or fuel that will be exempted from the policy implemented. This is already considered in the sector-fuel coverage $\varphi$. Moreover, such exemptions can be phased out according to user-defined parameters.

Note that both the existing and the new ETS permit prices per ton of CO2, $\text{XETS}P_{c,t}$ and $\text{NETS}P_{c,t}$ respectively, correspond to the adjusted values after the penalization. In other words, to the value comparable to the level of a carbon tax. For more information on this, refer to Appendix C - Prices And Taxes Methodology.

Excise and other taxes are computed as the sum of its forecasted components.

$\text{tx}o_{\text{cgf},t} = cs_{\text{cgf},t} + \text{fa}o_{\text{cgf},t} + \text{xc}p_{\text{cgf},t} + \text{nc}p_{\text{cgf},t}$

Retail price for fuel $f$ in sector $s$ in years $t$ is the sum of the supply price, VAT, and excise and other taxes.

$p_{o,\text{cgf},t} = sp_{\text{cgf},t} + \text{va}t_{\text{cgf},t} + \text{tx}o_{\text{cgf},t} = sp_{\text{cgf},t} + \text{va}t_{\text{cgf},t} + \left( cs_{\text{cgf},t} + \text{fa}o_{\text{cgf},t} + \text{xc}p_{\text{cgf},t} + \text{nc}p_{\text{cgf},t} \right)$

It should be noted that, while this relationship is true for all cases, for the baseline scenario the new carbon price component, included in $\text{txo}$, is null.

3.2.5 Price aggregation

For reporting purposes, it is convenient to have an aggregate price for each type of fuel within a country. This price, computed for each scenario, is obtained as a weighted average of the sector-specific retail prices, where the weights are given by the total use of fuel $f$ in country $c$:

$P_{\text{cf},t} = \sum_{g}^{}{\frac{F_{\text{cgf},t}}{\Sigma_{g}F_{\text{cgf},t}}*p_{\text{cgf},t}}$

where $P_{\text{cf},t}$ is the aggregate price for fuel $f$ in country $c$, $F_{\text{cgf},t}$ is the use of fuel $f$ in sector $g$ within country $c$, and $\Sigma_{g}F_{\text{cgf},t}$ is the aggregation of the fuel $f$ use across all sectors in that country.

3.3 Fuel Consumption

3.3.1 Overview

CPAT’s mitigation module is based on a fundamental model structure described in a recent IMF paper.¹² Energy use responds to energy prices and real GDP (total real GDP, not per capita GDP). The price elasticity includes a ‘usage’ response (e.g., how much each car is used) and an ‘energy efficiency’ (e.g., how fuel efficient the car is) component. The fuel equation estimate fuel consumption in the different sector groupings of CPAT.

In what follows, we present the equation form and then specific cases in which the equation might be slightly transformed or in which we factor in additional technologies in accordance with the sector under consideration, that is Transport, Buildings, Industry, Other Energy Use and Electricity.

3.3.2 Notation

The table below presents the notations used in the section and the name of the variables to which they correspond. Note that the units are reported as they were input into CPAT, but further conversions are made to ensure that they match our calculations.

Notation	Variable	Unit
$F$	Use of fuel	ktoe
$Y$	Total real GDP	US$
$p$	Retail price	US$/Gj
$\alpha$	Autonomous annual energy efficiency improvement	%
$\Psi$	Covid adjustment factor to energy demand	%
$\epsilon_{Y}$	Forward-looking real GDP-elasticity of fuel demand	%
$\epsilon_{U}$	Elasticity of usage of energy products and services	%
$\epsilon_{F}$	Efficiency price elasticity	%
$\epsilon_{\text{bio},f}$	Substitution elasticity between the most cooking fuel used and biomass	US$/Gj
$\text{Ef}f_{f}$	Natural gas, LPG and kerosene efficiency	%
$\text{Ef}f_{\text{bio}}$	Biomass efficiency	%

3.3.3 Fuel Consumption Dynamics

The fuel use for fuel type $f$ and sector $s$ can be related to the fuel use in the previous year as follows:

$\frac{F_{\text{ocsf},t}}{F_{\text{ocsf},t - 1}} = \left( \frac{1}{1 + \alpha_{\text{sf}}} \right)^{1 + \epsilon_{U,c\text{sf}}}\Psi_{\text{ct}}\left( \frac{Y_{c,t}}{Y_{c,t - 1}} \right)^{\epsilon_{Y,\text{csf}}}\left( \frac{p_{\text{ocsf},t}}{p_{\text{ocsf},t - 1}} \right)^{\epsilon_{U,\text{csf}}}\left( \frac{p_{\text{ocsf},t}}{p_{\text{ocsf},t - 1}} \right)^{\epsilon_{F,\text{csf}}\left( 1 + \epsilon_{U,\text{csf}} \right)}$

where the main components of the equation are $F$, the fuel usage in ktoe, $Y$, the total real GDP, the prices $p$ as presented in Section 3.2, $\alpha$, the autonomous annual energy efficiency improvement and, $\Psi$, a Covid adjustment factor to energy demand (see Section 3.3.4.4). Note that additional policies affecting the parameter $\alpha$ can be manually added.

Figure 36: Dashboard: Additional policy-induced efficiency gains by sector

Figure 3‑5: Dashboard: Additional policy-induced efficiency gains by sector

$\epsilon_{Y}$ denotes the forward-looking real GDP-elasticity of fuel demand for fuel $f$ in sector $g$. It thus translates a 1% increase in total real GDP into a fuel demand increase. CPAT does not distinguish between the elasticity for real-GDP-per-capita and the elasticity for population.

$\epsilon_{U}$, is the elasticity of usage of energy products and services (i.e. for a 1% increase in prices, how much will total usage be affected in the same year).

Finally, $\epsilon_{F}$ denotes the efficiency price elasticity.

For more information on the elasticities and the autonomous annual energy efficiency improvement, see Section 3.3.5. The latter is set to 0.5% or 1%, depending on the sector.

The terms of the energy use equation represent:

A GDP effect $\left( \frac{Y_{c,t}}{Y_{c,t - 1}} \right)^{\epsilon_{Y,\text{csf}}}$
A price effect on usage $\left( \frac{p_{\text{ocsf},t}}{p_{\text{ocsf},t - 1}} \right)^{\epsilon_{U,\text{csf}}}$
A price effect on energy efficiency, $\left( \frac{p_{\text{ocsf},t}}{p_{\text{ocsf},t - 1}} \right)^{\epsilon_{F,\text{csf}}\left( 1 + \epsilon_{U,\text{csf}} \right)}$

Both autonomous and price-driven efficiency components are subject to rebound effects by raising to the power of $\left( 1 + \epsilon_{U} \right)$, where $\epsilon_{U}$ is negative.

Note that the term effect on energy efficiency is affected by the shadow price¹³ in case non-pricing policy types are implemented, that is feebates and power feebates, energy efficiency regulations, vehicle fuel economy, residential and industrial efficiency regulations. In the equation, the shadow price only affects the efficiency margin and not the price effect since, for instance, an energy efficiency regulation does not aim to increase prices but increases the efficiency.

For simplicity, we assume that all the effects take place over the course of one year. In reality, some effects will take time, but CPAT abstracts from these effects. CPAT is more suited to anticipated and progressively phased policies over the medium term.

Energy use is aggregated into five main sector groupings: Transport, Buildings, Industry, Other Energy Use and Electricity demand.

3.3.4 Specific cases

Few specific cases slightly affect the energy use equation described above or the energy composition, that is:

The breakdown of biofuels and existence of jet fuel in the transport sectors;
Self-generated renewables in the building and industry sectors;
The substitution between biomass and LPG/kerosene/natural gas in the residential sector;
For the year 2020-21, energy use is calibrated with a Covid adjustment;
Fuel transformation; and
Other energy use sector.

3.3.4.1 Biofuels and jet fuel

In the transport sector, for road transport only, biomass is further broken down into Bioethanol, Biodiesel and Other Biofuels. In addition, domestic aviation jet fuel is a fuel type not seen in other sectors.

3.3.4.2 Self-generated renewables

When aggregating energy use at the sector level, power generated outside of the power sector, that is self-generated renewables, is also accounted for. The energy use equation is the same as the one presented above, and the price used is that of solar energy.

3.3.4.3 Biomass substitution in the residential sector

When aggregating energy used, an option to account for leakage into biomass in the residential sector is available.

Figure 37: Sectors disaggregation in CPAT

Figure 3‑6: Sectors disaggregation in CPAT

If this option is turned on, a percent change of the most used cooking fuel (i.e., natural gas, LPG or kerosene) is transferred to biomass. In other words, the relative price change in the most used cooking fuel results in a percentage change in its consumption; this variation change is substituted by biomass. The latter is composed of the substitution elasticity between the most cooking fuel used and biomass ($\epsilon_{\text{bio},f}$), but also accounts for the relative efficiency between the fuels considered, that is only natural gas, LPG and kerosene ($f = \text{nga},\text{lpg\ and\ ker}$) and biomass ($\text{Ef}f_{f}$ and $\text{Ef}f_{\text{bio}}$, respectively):

$\epsilon_{\text{bio},f}*\frac{\text{Ef}f_{\text{bio}}}{\text{Ef}f_{f}}$

The substitution elasticity between the most cooking fuel used and biomass, $\epsilon_{\text{bio},f}$, is 0.25 (see Section 3.3.5 for more information). The efficiency¹⁴ for each fuel is detailed in the table below:

Energy type	Efficiency
Natural gas	0.58
LPG	0.56
Kerosene	0.45
Biomass	0.20

The proportion of the natural gas transferred to biomass is thus dependent on the relative efficiency of representative stoves that are used. Therefore, for a 10% price change in, for instance, natural gas, 0.9% of natural gas consumption is shifted to biomass.

3.3.4.4 Calibration of overall energy use through Covid adjustment in 2020 and 2021

Due to the unprecedented global economic shock induced by the Covid-19, the energy consumption factor makes an ad hoc adjustment to the model and is calibrated using emissions outturn as the overall numeraire in 2020 and 2021.

This sets baseline 2020 emissions to equal estimates for most countries and applies a GDP-linked scalar adjustment for all other countries to match global emissions (difference in recent three-year average GDP growth vs. 2020 growth rate times 1.4). For 2021, emissions are set for very large emitters (US, China, India, EU) to a specific rebound vs. 2019 emissions per the Global Carbon Project (2021), and to a scalar that results in -4.2% vs. 2019 emissions for all other countries. Estimates can be found at the end of the tab ‘GHG’.

Figure 71: Summary of the CPAT v1.0 structure

Figure 3‑7: Summary of the CPAT v1.0 structure

3.3.4.5 Fuel transformation

In CPAT we transform balances into final energy consumption (buildings, industry, transport, other), power sector (part of energy transformation in balances) and fuel transformation. The fuel transformation sector (FTR) is determined as the difference between primary and final energy consumption, subtracting Fuel Transformation in the power sector. This residual is treated as an additional industrial sector called fuel transformation.

In addition, all oil products and natural gas are aggregated to avoid dealing with negative fuel consumption. The FTR, computed as a residual, is treated as an additional industrial sector called ‘transformation’. For the forecasted years, its consumption follows the main mitigation fuel equations.

3.3.4.6 Other energy use

The other energy use sector contains principally military fuel use. No carbon taxes are imposed in this sector.

3.3.5 Income and Price Elasticities of Demand

3.3.5.1 Overview

The current version of CPAT uses a derived set of elasticities based on Burke and Csereklyei (2016)¹⁵ using the relationship from Gertler and others (2016).¹⁶

3.3.5.2 Income elasticities

Income elasticities relate to general energy demand (electricity, transport, industry, services, residential and other).

Income elasticities of energy demand are selected based on a broad literature review, simplified, adjusted for development levels, and sense-checked to a large dataset of income elasticities and outputs of other models. There are 32 ‘base’ income elasticates in CPAT covering eight energy sources (coal; natural gas; gasoline; diesel; other oil products like LPG and kerosene; biomass; small-scale renewables like solar PV; and electricity) and four sectors (transport including road, rail, aviation and shipping; residential; heavy industries; and public and private services).

These are then sense-checked against a database of income elasticities collected by the authors, which covers over 250 studies 2,000 observations of income elasticities across countries. Next, these are each adjusted for income per capita of the country considered in each projection period (‘adjusted income elasticities’) to reflect the broad finding that income elasticities decline with development. Lastly, the elasticities are checked once more through model intercomparison: comparing the baseline projections from those of many other global, regional, and country-specific models. The process is described further below.

Figure 54: Income elasticities: Base income elasticities of energy demand in CPAT

Figure 3‑8: Income elasticities: Base income elasticities of energy demand in CPAT

Base income elasticities for sectors are selected based on Burke and Csereklyei (2016), which covers 132 countries from 1960-2010. Fuel-specific elasticities within sectors are then selected based on a literature review such that the weighted global average income elasticity across fuels is within one standard deviation of those found for sectors (left panel of Figure 3-55). Broadly, energy demand grows more quickly in services, industry, transport, and other sector than it does in the residential or agricultural sectors.

Figure 55: The relationship of fuel demand to GDP across countries – by sector (left panel, mean estimated elasticities 1960-2010) and by development levels (right panel, unadjusted and adjusted elasticities with respect to log GDP 1985-2010)

Figure 3‑9: The relationship of fuel demand to GDP across countries by sector (left panel, mean estimated elasticities 1960-2010) and by development levels (right panel, unadjusted and adjusted elasticities with respect to log GDP 1985-2010) – Source: left panel from Burke and Csereklyei (2016); right panel inferred from Gertler and others (2016), adjusted upwards to match the global average income elasticity for energy in left panel

It is then further assumed that income elasticities have a reverse-U shape with respect to income levels. This relationship has been found by numerous studies (Gertler et al. 2016; Zhu et al. 2018; Liddle and Huntington 2020; Caron and Fally 2022). This non-homothetic relationship between incomes and energy could be reflective of the rapid rise in ownership of key energy consuming assets like refrigerators, air conditioners, and vehicles whose ownership tends to binary in nature (e.g. households purchase one fridge but not additional fridges as they become wealthier; Gertler et al. 2016). It could also reflect the Environmental Kuznets effect (as incomes increase economies reduce their environmental destruction by, for example, consuming fewer fossil fuels) (Saqib and Benhmad 2021) or ‘dematerialization’ (richer countries tend to need fewer materials for marginal production and hence become more energy efficient).

The relationship between per capita incomes and energy demand is derived from Gertler and others (2016) based on data cross-country analysis 1985-2010. This is then adjusted upwards such that the inferred global average income elasticity from this shape equals that found by Burke and Csereklyei (0.74, 2016) over the same time period (1960-2010). This adjustment is then applied to each base income elasticity’s base for each country over the projection period (varying with each year). The impact for selected fuel-sector pairs is shown in left panel below for per capita GDP and in the right panel for log GDP. Income elasticities jump up as countries graduate from being lower-income to a peak around lower-middle income status (at around $3,000 per capita) and then asymptotically decline until reaching the developed country maximum (at around $22,000 per capita).

Figure 56: Per capita GDP adjusted income elasticities, selected fuels/sectors by GDP (left) and log GDP (right)

Figure 3‑10: Per capita GDP adjusted income elasticities, selected fuels/sectors by GDP (left) and log GDP (right) – Source: IMF staff using Burke and Csereklyei (2016), Gertler and others (2016), and various other sources.

Lastly, the results of these income elasticities on baseline energy consumption and emissions are then sense checked through a model inter-comparison. Overall, they allow for initially rapid accelerations in energy demand in developing countries (as households purchase energy-consuming goods like fridges, air conditioning units and cars) as well as broader structural change as countries increase the share of services in GDP and energy consumption.

3.3.5.3 Price elasticities

Own-price elasticities of energy demand are parametrized using a similar approach to income elasticities. A major meta-study to estimate elasticities for fuels, which are then simplified and calibrated to allow for sectoral coverage, sense- and then finally sense checked to a large in-house dataset through model-intercomparison. These steps are described in turn.

Price elasticities in CPAT separated into two broad margins (see below). CPAT contains two types of price elasticities to distinguish between behavioral responses: the direct reduction in demand from reduced intensity of use from existing capital-consuming goods like vehicles (‘intensive margin’) and changes in the composition and scale of those goods (‘efficiency and extensive margin’). The two effects combined less the rebound effect (described later) correspond to the total price elasticity of demand, which is parametrized to the empirical literature¹⁷.

Table 3‑1 Price elasticities of energy demand in CPAT – Source: IMF staff using various sources. Tables show price elasticities used for developed countries. For developing countries, extensive margin elasticities are uniformly increased (in absolute terms) by 0.1.

Figure 57: Price elasticities of energy demand in CPAT

The initial source for price elasticities is a meta-study by Labandeira and others (2017). This includes about 2,000 empirically estimated elasticities from 430 studies with broad global coverage of countries, seven fuels, and four sectors (refer to Table A for descriptive statistics). ‘Target’ estimates of elasticities for fuels and sectors are estimated, assuming that the base is the transport sector, plus deviations for the residential, industrial and services sectors (Table B)¹⁸. For any statistically insignificant values for fuels within sectoral regressions (natural gas in residential, for example), it is assumed that the difference between sectoral and base elasticities equal that sectors’ general elasticities multiplied by a scalar for all energy sources.

Additionally, there is evidence that price elasticities are slightly higher for developing countries (about 10%; Labandeira, Labeaga, and López-Otero 2017). Price elasticities are therefore adjusted slightly upwards for developing countries (on the extensive margin) such that they are a similar magnitude higher than for developed countries.

Simple price elasticities (rounded to 1 decimal point) on both the intensive and extensive margin are then calibrated to those targets. As shown in Table C, when weighting for developed and developing countries’ emissions, elasticities in CPAT are very similar (within 10%) to these target elasticities.

Table 3‑2: Comparison of price elasticities

Figure 58: Comparison of price elasticities

These, price elasticities are sense checked both against a large database of price elasticities (covering around 250 studies and 2,500 price elasticities), as well as through model intercomparison of CPAT results compared with those of other models. Both the baseline emissions projections and price responsiveness of emissions is broadly in line with that of other models, while median price elasticities are not significantly different for fuel-sector pairs collected across countries (though there is variation).

Lastly, all elasticities are long-term elasticities.

3.3.5.4 Rebound effect

When prices change, energy consumers also shift to more efficient energy-consuming goods. Marginal costs of fuel consumption are lower for more efficient goods (e.g. each km travelled is cheaper for a vehicle with higher fuel economy), hence there is a corresponding increase in demand for those same fuels (‘direct rebound effect’). As marginal costs of fuel consumption decline, consumers also increase the intensity of consumption of these capital goods (e.g. travel more miles in vehicles).

Table 3‑3: Implied direct rebound effects from prices (endogenous efficiency improvements increasing demand for energy)

The energy use equation outlined in Section 3.3 allows rebound effects, $\left( 1 + \epsilon_{U} \right),$ to be captured and compared to econometric estimates of rebound. Broadly, these align with the empirical literature. More specifically, the rebound effect is defined as the product of the energy efficiency elasticity and the usage elasticity, $\epsilon_{F}*\epsilon_{U}$, as follows in the term affecting prices change:

$\left( \frac{P_{t}}{P_{t - 1}} \right)^{\epsilon_{F} + \epsilon_{U} + \epsilon_{F}*\epsilon_{U}}$

With $\epsilon_{F} = \epsilon_{U} = - 0.3$, the rebound effect represents 15.5% (i.e. the rebound effect reduces the total price elasticity by 15.5%). This result is lower, but seems more reasonable, than the estimates in a meta-analysis of 74 studies in Dimitropoulos and others (26-29% rebound effect, 2018).

The estimated leakage effects in residential natural gas (31%) are similar to those found in studies (20% to 30%, Haas and Biermayr 2000).

3.3.5.5 Cross-price elasticities

CPAT contains three substitution or cross-price elasticities to account for the risk that households that face increases in costs for residential heating and cooking fuels shift to informal fuels like biomass. This ‘leakage’ effect can have a negative impact on household air pollution and hence welfare, which is calculated by CPAT’s air pollution module. These cross-price elasticities (biomass with respect to LPG and kerosene, as well gasoline with respect to diesel) are parameterized to the same broad literature review.

Table 3‑4: Cross-price elasticities of substitution in CPAT

Figure 60: Cross-price elasticities of substitution in CPAT

3.3.5.6 Rates of technological change and exogenous rebound effects

The annual rate of exogenous technological change (that is, not induced by policies under consideration in CPAT) are set at between 0.5 and 1 percent per year for each fuel-sector pair.

Table 3‑5: Exogenous efficiency improvements in energy-consuming capital goods (cars, buildings, factories)

Figure 61: Exogenous efficiency improvements in energy-consuming capital goods (cars, buildings, factories)

It should be noted that – as with efficiency induced endogenously by price changes – exogenous efficiency improvements reduce marginal costs of energy consumption, hence there is some rebound effect that partly offsets the reduction in demand from improved efficiency. A large literature exists that examines the rebound effect from efficiency improvements, with estimates varying significantly, from 0 to 300% (Saunders et al. 2021). In CPAT, this rebound from exogenous efficiency improvements depends on the fuel-sector pair and its corresponding intensive margin and efficiency, but broadly it is between 20% to 60% across fuels and sectors.

Table 3‑6: Rebound effect from exogenous efficiency improvements (% of emissions reduction reduced)

Figure 62: Rebound effect from exogenous efficiency improvements (% of emissions reduction reduced)

3.3.5.7 References

Belaïd, Fateh, Salomé Bakaloglou, and David Roubaud. 2018. “Direct Rebound Effect of Residential Gas Demand: Empirical Evidence from France.” Energy Policy 115: 23–31. https://doi.org/10.1016/j.enpol.2017.12.040.
Burke, Paul J., and Zsuzsanna Csereklyei. 2016. “Understanding the Energy-GDP Elasticity: A Sectoral Approach.” Energy Economics 58: 199–210. https://doi.org/10.1016/j.eneco.2016.07.004.
Caron, Justin, and Thibault Fally. 2022. “Per Capita Income, Consumption Patterns, and CO2 Emissions.” Journal of the Association of Environmental and Resource Economists 9 (2): 235–71. https://doi.org/10.1086/716727.
Dimitropoulos, Alexandros, Walid Oueslati, and Christina Sintek.
1. “The Rebound Effect in Road Transport: A Meta-Analysis of Empirical Studies.” Energy Economics 75: 163–79. https://doi.org/10.1016/j.eneco.2018.07.021.
Friedlingstein, Pierre, Matthew W. Jones, Michael O’Sullivan, Robbie M. Andrew, Dorothee C. E. Bakker, Judith Hauck, Corinne Le Quéré, et al. 2021. “Global Carbon Budget 2021.” Earth System Science Data Discussions, November, 1–191. https://doi.org/10.5194/essd-2021-386.
Gertler, Paul, Orie Shelef, Catherine Wolfram, and Alan Fuchs. 2016. “The Demand for Energy-Using Assets among the World’s Rising Middle Classes” 106 (6): 1366–1401.
Grassi, Giacomo, Jo House, Werner A. Kurz, Alessandro Cescatti, Richard A. Houghton, Glen P. Peters, Maria J. Sanz, et al. 2018. “Reconciling Global-Model Estimates and Country Reporting of Anthropogenic Forest CO2 Sinks.” Nature Climate Change 8 (10): 914–20. https://doi.org/10.1038/s41558-018-0283-x.
Haas, Reinhard, and Peter Biermayr. 2000. “The Rebound Effect for Space Heating Empirical Evidence from Austria.” Energy Policy 28 (6): 403–10. https://doi.org/10.1016/S0301-4215(00)00023-9.
Ian Parry, Simon Black, and Nate Vernon. 2021. “Still Not Getting Energy Prices Right: A Global and Country Update of Fossil Fuel Subsidies.” IMF Working Papers, Working Paper No. 2021/236, . https://www.imf.org/en/Publications/WP/Issues/2021/09/23/Still-Not-Getting-Energy-Prices-Right-A-Global-and-Country-Update-of-Fossil-Fuel-Subsidies-466004.
IEA. 2021. “World Energy Outlook 2021,” 386.
IMF. 2021. World Economic Outlook, October 2021. Washington DC. https://www.imf.org/en/Publications/WEO/Issues/2021/10/12/world-economic-outlook-october-2021.
IPCC. 2021. “Sixth Assessment Report (AR6) Contribution from Working Group I.” Climate Change 2021: The Physical Science Basis, August. https://www.ipcc.ch/report/ar6/wg1/.
IPCC, J. Penman, Michael Gytarsky, T. Hiraishi, W. Irving, and T. Krug. 2006. “2006 Guidelines for National Greenhouse Gas Inventories.” Directrices Para Los Inventarios Nacionales GEI, 12.
Labandeira, Xavier, José Labeaga, and Xiral López-Otero. 2017. “A Meta-Analysis on the Price Elasticity of Energy Demand.” Energy Policy 102: 549–68. https://doi.org/10.1016/j.enpol.2017.01.002.
Liddle, Brantley, and Hillard Huntington. 2020. “Revisiting the Income Elasticity of Energy Consumption: A Heterogeneous, Common Factor, Dynamic OECD & Non-OECD Country Panel Analysis.” The Energy Journal 41 (3). https://doi.org/10.5547/01956574.41.3.blid.
Luca, Oana, and Diego Mesa Puyo. 2016. “Fiscal Analysis of Resource Industries: (FARI Methodology).” Technical Notes and Manuals 2016 (01): 1. https://doi.org/10.5089/9781513575117.005.
Minx, J. C., T. Wiedmann, R. Wood, G. P. Peters, M. Lenzen, A. Owen, K. Scott, et al. 2009. Input-Output Analysis and Carbon Footprinting: An Overview of Applications. Economic Systems Research. Vol. 21. https://doi.org/10.1080/09535310903541298.
Saqib, Muhammad, and François Benhmad. 2021. “Updated Meta-Analysis of Environmental Kuznets Curve: Where Do We Stand?” Environmental Impact Assessment Review 86 (January): 106503. https://doi.org/10.1016/j.eiar.2020.106503.
Saunders, Harry D., Joyashree Roy, Inês M.L. Azevedo, Debalina Chakravarty, Shyamasree Dasgupta, Stephane de la Rue du Can, Angela Druckman, et al. 2021. “Energy Efficiency: What Has Research Delivered in the Last 40 Years?” Annual Review of Environment and Resources 46 (1): 135–65. https://doi.org/10.1146/annurev-environ-012320-084937.
World Bank. 2022. “Carbon Pricing Dashboard.” https://carbonpricingdashboard.worldbank.org/. Zhu, Xing, Lanlan Li, Kaile Zhou, Xiaoling Zhang, and Shanlin Yang. 2018. “A Meta-Analysis on the Price Elasticity and Income Elasticity of Residential Electricity Demand.” Journal of Cleaner Production 201 (November): 169–77. https://doi.org/10.1016/j.jclepro.2018.08.027.

3.4 Power sector models

The mitigation module has two models that can be used for the electricity sector: the elasticity-based model and the techno-economic (‘engineer’) model. The user can choose to use the elasticity, engineer model, or a simple average of the two models. We recommend the ‘average’ model for ‘off-the-shelf’ use of CPAT and the engineer model for more tailored usages and for non-marginal changes (like a high CO2 tax policy). Before presenting the two models, it is essential to note that by default, prices and generation costs are applied to both the techno-economic (‘engineer)’ and the elasticity-based power models. The main differences are as follows:

The ‘elasticity-based’ model uses marginal increases in fuel prices and price elasticities to determine the shares of each generation type. It is simple, transparently parameterized, easily explainable, and easily deployable in an Excel spreadsheet model used in previous versions of CPAT and IMF tools.
The ‘engineer model’ explicitly models the capacity of different generation types, with capacity¹⁹ expanding to meet desired power demand. Flexible capacity (gas and coal) is allocated according to marginal price, with a sigmoidal function of relative price. Investment is also a function of levelized cost, with a system penalty for the cost of integrating high levels of renewable penetration. Transmission losses are modeled as a fixed quantity of total generation. The model allows modeling decisions changing the stock of assets in the power sector (investment and retirement) and decisions changing the use of assets for power generation (dispatch). In addition, the model allows the user to define a constraint on Variable Renewable Energy (VRE) scale up rate. The rates reflect a ‘linear’ type constraint. It constrains generation in VRE additions to be a certain percentage of total generation (in gross additions, not net of retirements). The model is consistent with countries’ generation capacities and makes it possible to investigate the radically different power systems consistent with high carbon prices, while the empirical ‘elasticity-based’ model is valid only for more marginal changes.

In what follows, Section 3.4.1 defines power prices and generation costs, Section 3.4.2 describes the techno-economic model, and Section 3.4.3 the elasticity-based model. Finally, Section 3.4.4 presents the parameter choices of the power models.

3.4.1 Power prices and generation costs

This section describes the determination of generation costs and power prices in CPAT. These prices and generation costs are applied to the techno-economic (‘engineer)’ and the elasticity-based power models. However, in the latter case, the user has an alternative option to use a simpler set of prices based on the original IMF board paper, which are not covered here.

3.4.1.1 Overview

Power generation costs have the following components:

Variable (per kWh) operations and maintenance costs;
Fixed (per MW) operations and maintenance costs;
Decommissioning and waste disposal costs;
Fuel cost before the introduction of the carbon pricing policy;
Existing or new renewables subsidies;
Existing or new carbon price or other policy (feebate, excise duty on electricity); and
Systems cost of integration, modeled as short+long-term storage costs as a function of variable renewable energy (VRE; meaning wind+solar+other renewables, but not including hydro or biomass) share.

In addition, we impose an implicit price of coal relative to gas, reflecting unobserved environmental regulations on coal and the superior flexibility of gas. These aspects are not fully captured in a model as simple as this. We calibrate this price on observed coal shares and future (IEA) projections (see Section 3.4.2.4).

End-user (industrial and residential) power prices additionally have the following components:

Estimated transmission and distribution costs (different for industry and residential);
Net historical subsidy or tax (estimated either via a price gap or via independent data if provided by the user);
Any correction for under- or over-estimated transmission and distribution costs (exists only if we have concrete subsidy data);
New carbon tax as imposed on the generation types and passed on to the end user; and
Any electricity excise or rebate of the carbon price (Feebates/Output-based-rebating).

3.4.1.2 Notation

The tables below present the notations used in the section and the name of the variables to which they correspond. Note that the units are reported as they were input into CPAT, but further conversions are made to ensure that they match our calculations.

The first table gives overarching concepts relating to power generation.

Notation	Variable	Unit
$F$	Use of fuel	ktoe
$g$	Electricity generation	GWh
$\nu$	Thermal efficiency	%
$\text{cf}$	Capacity factor	%
$\text{cap}$	Capacity	MWy
$\text{PV}$	Present value of costs
$\text{tic}$	Levelized total investment costs	US$/kWh
$\text{wacc}$	Weighted Average Cost of Capital	%
$\text{lif}$	Lifetime	Years
$\text{dlf}$	Discounted lifetime	Years
$\Phi_{\text{inv}}$	New investment expressed as a proportion of total existing capacity less retirements	%
$\text{gns}$	Generation shares	%

This table denotes variables used to calculate the levelized cost of investment types (and also, indirectly the power price).

Notation	Variable	Unit
$\text{fc}$	Projected unit fuel costs	US$/kWh
$\text{opv}$	Variable costs for operating and maintenance (OpEx)	US$/kWh
$\text{vc}$	Current variable costs	US$/kWh
$\text{cax}$	Capital cost (CapEx)	US$/kW
$\text{opf}$	Fixed costs for operating and maintenance (OpEx)	US$/kW
$\text{tfc}$	Fixed OpEx	US$/kWy
$\text{sto}$	Storage cost	US$/kWh
$\text{dtc}$	Decommissioning costs	US$/kWh
$\text{ipc}$	Implicit price component for coal	US$/kWh
$\text{pusRen}$	Per-unit renewable subsidies	US$/kWh
$\text{LCOE}$	Levelized cost of electricity	US$/kWh

This table denotes variables used to calculate the price of electricity.

Notation	Variable	Unit
$\text{hrp}$	Historical retail prices in the electricity sector	US$/Gj
$\text{gnc}$	Current generation cost	US$/kWh
$\text{fix}$	Amortized fixed costs	US$/kWh
$\text{ca}x^{\text{av}}$	Weighted average CapEx	US$/kW
$\text{acc}$	Yearly amortization of capital costs	US$/kWh
$\text{int}$	Interest costs	US$/kWh
$\text{dec}$	Yearly amortization of decommissioning costs	US$/kWh
$sp_{T}$	Supply power price determined in the engineer model	US$/kWh
$\text{tmc}$	Transmission cost	US$/kWh
$mu^{T}$	Markup used in the calculation of supply power prices	US$/kWh
$\text{pex}$	Power excise	US$/kWh
$\text{reb}$	Rebate	US$/kWh
$p^{T}$	End-user power price (engineer model)	US$/kWh

3.4.1.3 Power generation cost and price concepts

We use four different power generation cost/price concepts in CPAT:

Current Variable Costs: For dispatch decisions the current variable costs are used (fuel and variable operations and maintenance).
Levelized Cost of Investment: For forward looking (investment) decisions, a levelized and forward-looking cost approach adding all cost components is used. For example, one part is forward-looking expectations of future fuel and carbon costs.
Cost-recovery generation cost: For estimating the total running cost of the power system, a cost-recovery generation cost is estimated. This includes current variable cost, running amortization of capital costs, plus average interest costs (and other components too). The cost-recovery generation cost by generation type is averaged and then transmission and distribution costs added to produce an overall estimate cost of generating and distributing electricity.
End user power prices (residential and industrial): these are based on observed prices with an adjustment for changes due to cost changes or carbon pricing. The user can decide what proportion of changes to overall generation cost are passed on. The user can also choose to phase out estimated electricity subsidy.

3.4.1.4 Concept 1: Current variable costs

Variable costs are used in the dispatch decision directly between gas and coal.²⁰

Current variable costs are defined as the sum of the following cost components:

$vc_{\text{ocft}} = \text{vo}p_{\text{ocft}} + fc_{\text{ocft}} + ip_{\text{cft}} = \text{vo}p_{\text{ocft}} + \frac{p_{\text{ocft}}}{\nu_{\text{cf}}} + ip_{\text{cft}}$

where:

$\text{vop}$ represents variable costs for operating and maintenance, that is variable OpEx in USD per kWh.
$\text{fc}$ denotes projected unit fuel costs before the introduction of the carbon pricing policy. These costs are calculated as the ratio of pre-tax prices (including producer-side subsidies) $\text{ps}$ and thermal efficiency $\nu$: $\frac{ps_{\text{cft}}}{\nu_{\text{cf}}}$. It is worth noting that no improvements in time is currently modeled. By default, fuel costs are considered as a moving average over a 5-year window. The option to use spot prices can be enabled in the dashboard:

Figure 3‑11: Dashboard: Use Spot Fuel Prices in Engineer Power Model

$\text{ip}c_{\text{cft}}$ denotes an implicit price component for coal. Note that this latter component could be turned off in the settings and not taken into account (for more information, see Section 3.4.2.4).

3.4.1.5 Concept 2: Levelized costs of generation (Forward-looking)

3.4.1.5.1 General approach

LCOEs by generation type are estimated as a forward-looking (discounted cashflow) approach.
Note these is different from the cost-recovery prices above as the cost-recovery approach uses an amortization of capital costs and running interest costs rather than discounting.
Fuel and carbon costs in these LCOEs are forward-looking, meaning they are the discounted value of future cashflows assuming full confidence in the proposed policy and full foresight.

Forward-looking generation costs are defined using a levelized cost of electricity (LCOE) methodology, which relies on discounting at the appropriate discount rate. Levelized cost enables the comparison of different energy technologies with different characteristics (operating lifetime, capacity factor, construction cost, and time) on an equivalent basis. To the levelized cost, we add system integration costs. The levelized cost can be defined, in general, as the discounted sum of costs divided by the discounted sum of electricity produced. Let’s assume that a generation technology produces power for $N$ years, and we start counting at year zero (so there are $N$ payments, with the first being $t_{0}$ and last being $t = N - 1$. We separate the components $q$ (capital cost) of the levelized costs, which can be treated equivalently. For each component $q$ of the levelized cost:

$\text{LCO}E_{q} = \frac{PV_{q}}{\text{dem}} = \frac{\sum_{t = 0}^{N - 1}C_{q,t}e^{- \text{rt}}}{\sum_{t = 0}^{N - 1}g_{t}e^{- \text{rt}}}$

where $PV_{q}$ is the present value of costs, $\text{dem}$ is the discounted power produced, $g_{t}$ is the power produced at time $t$ and $C_{q,t}$ is the $q$ component of costs at time $t$, breaking down into the following components:

The full investment cost contains the following components:

Capital expenditure
Decommissioning (all generation types) and waste disposal cost (nuclear only)
Variable OpEx
Fixed OpEx
Fuel Cost Before Carbon Price
Marginal system cost of storage (see next section)
Carbon Price
Implicit cost of coal

Each of these components is calculated using the levelized cost formula above. Almost all components are either fixed or increasing/decreasing at a fixed rate. In that case we can use a geometric series approximation. See the appendices for a derivation.

The weighted average cost of capital (WACC) is by default income-dependent:

Income Level	WACC Assumed
HIC	0.075
UMIC	0.100
LMIC	0.125
LIC	0.150

The WACC can also be technology-dependent, i.e. it can be specified for each technology. At the same time, the WACC can be specified for the baseline and the policy scenario. Finally, the WACC can be defined globally by the user.

The levelized total investment costs is defined as:

$\text{ti}c_{P,\text{cf}} = \frac{vc_{P,\text{cft}}*cf_{\text{cf}}*\text{df}c_{\text{cft}}}{cf_{\text{cf}}*\text{df}c_{\text{cft}}} + \text{fi}x_{\text{cft}}^{\text{fl}}$

where $\text{df}c_{\text{cft}}$ is the discount factor $1 + \text{wac}c_{\text{cft}}^{t - t_{0}}$ and $\text{fi}x^{\text{fl}}$ denotes the forward-looking levelized fixed costs, which is calculated as:

$\text{fi}x_{\text{cft}}^{\text{fl}} = \frac{\text{ca}x_{\text{cft}}}{cf_{\text{cf}}*365*24*\text{dl}f_{\text{cft}}} + \frac{\text{dt}c_{\text{cft}}}{cf_{\text{cf}}*365*24*\text{dl}f_{\text{cft}}} + \text{st}o_{\text{cft}} + \text{op}f_{\text{cft}} + \text{pusRe}n_{\text{cft}}$

where $\text{cax}$ is the capital cost, $\text{dtc}$ is th decommissioning total cost, $\text{sto}$ is the cost of storage, $\text{fro}$ correspond to fixed costs for operating and maintenance, $\text{dl}f_{\text{cft}}$ denoting the discounted lifetime of each generation type $f$ and $\text{re}s_{\text{cft}}$ reflects the per-unit renewable subsidies (if added).

In the dashboard, the following option allows the user to specify renewable subsidy under a baseline and policy scenarios:

Figure 3‑12: Dashboard: Renewable subsidy ($/kwh in nominal terms)

After the introduction of the carbon pricing policy, the current total cost is:

$\text{LCO}E_{P,\text{cft}} = vc_{P,\text{cft}} + \text{fi}x_{\text{cft}}^{\text{fl}}$

where $vc_{P,\text{cft}} = vc_{B,\text{cft}} + \text{nc}p_{\text{cft}}$.

3.4.1.5.2 LCOE methodology: Simplification

As mentioned in the main text:

$\text{LCO}E_{q} = \frac{PV_{q}}{g} = \frac{\sum_{t = 0}^{N - 1}C_{q,t}e^{- \text{rt}}}{\sum_{t = 0}^{N - 1}g_{t}e^{- \text{rt}}}$

where $PV_{q}$ is the present value of costs, $g$ is the discounted power produced, $g_{t}$ is the power produced at time $t$ and $C_{q,t}$ is the $q$ component of costs at time $t$, breaking down into various components described in the above section.

There is a simplification in the case of constant growth rates. If at and after time $n$ the residual components of the cashflow have consistent real (logarithmic) growth rate $\tau$, i.e., $C_{t} = C_{n}e^{g\left( t - n \right)}$, then they form a geometric series, which can be summed analytically:

$\begin{matrix} \text{PVofCosts} & = \sum_{t = 0}^{n - 1}C_{t}e^{- \text{rt}} + \sum_{t = n}^{N - 1}C_{n}e^{- \text{rn}}\left( e^{\tau - r} \right)^{t - n} & & & \\ \end{matrix}$

$= \sum_{t = 0}^{n - 1}C_{t}e^{- \text{rt}} + C_{n}e^{- \text{rn}}\sum_{t = n}^{N - 1}\left( e^{\tau - r} \right)^{t - n}$

$= \sum_{t = 0}^{n - 1}C_{t}e^{- \text{rt}} + C_{n}e^{- \text{rn}}\sum_{t = 0}^{N - n - 1}\left( e^{\tau - r} \right)^{t}$

$= \sum_{t = 0}^{n - 1}C_{t}e^{- \text{rt}} + C_{n}e^{- \text{rn}}\frac{1 - \left( e^{\tau - r} \right)^{N - n}}{1 - \left( e^{\tau - r} \right)}$

If a component is fixed in time, i.e. $\tau = 0$ and $n = 0$, there’s a further simplification:

$\text{PVofCosts} = C_{n}e^{- \text{rn}}\frac{1 - \left( e^{\tau - r} \right)^{N - n}}{1 - \left( e^{\tau - r} \right)} = C_{0}\frac{1 - e^{- \text{rN}}}{1 - e^{- r}}$

$\begin{matrix} \text{LCOE} & = \frac{\sum_{t = 0}^{N - 1}C_{t}e^{- \text{rt}}}{\sum_{t = 0}^{N - 1}g_{t}e^{- \text{rt}}} & = \frac{\sum_{t = 0}^{N - 1}C_{0}e^{\text{τt}}e^{- \text{rt}}}{\sum_{t = 0}^{N - 1}g_{t}e^{- \text{rt}}} & = \frac{\sum_{t = 0}^{N - 1}C_{0}\left( e^{\tau - r} \right)^{t}}{\sum_{t = 0}^{N - 1}g_{t}e^{- \text{rt}}} & = \frac{C_{0}\frac{1 - e^{- \text{rN}}}{1 - e^{- r}}}{g_{0}\frac{1 - e^{- \text{rN}}}{1 - e^{- r}}} & = \frac{C_{0}}{g_{0}} \\ \end{matrix}$

3.4.1.6 Concept 3: Cost-recovery estimated total cost of generation

Generation costs are modeled by component (CapEx, OpEx, Fuel costs etc). These are ‘cost recovery prices’ assuming amortization of CapEx, interest costs and so on.
Weighted average generation costs are then augmented by global assumptions on transmission costs, to give estimated cost recovery price.
Then the cost recovery price is compared to observed prices and the difference attributed to being a tax or subsidy (if no independent subsidy data is available) or an under/overestimated cost if independent (user entered) subsidy-data is available.
For cost recovery, a weighted average CapEx of the capital stock is needed. For most generation types, the CapEx per MW is constant, but for renewable energies it declines rapidly so the weighted average invested amount per MW is estimated by taking a weighted average of the current running total with the cost of new additions.

The current generation cost before tax, $\text{gn}c_{B,\text{cft}}$, is thus composed of both variable and fixed costs:

$\text{gn}c_{B,\text{cft}} = vc_{B,\text{cft}} + \text{fi}x_{\text{cft}}$

where $\text{vc}$ denotes current variable costs (defined in an earlier section) and $\text{fix}$ denotes amortized fixed costs.

Amortized fixed cost is the sum of the following elements:

$\text{fi}x_{B,\text{cft}} = \text{ac}c_{\text{cft}} + \text{in}t_{\text{cft}} + \text{de}c_{\text{cft}} + \text{st}o_{\text{cft}} + \text{op}f_{\text{cft}}$

Where:

$\text{acc}$ is the yearly amortization of capital costs per kWh produced: $\frac{\text{ca}x_{\text{cft}}^{\text{av}}}{\text{cf}*365*24*\text{li}f_{f}}$ with $\text{ca}x^{\text{av}}$ the weighted average CapEx, $\text{cf}$ the assumed capacity factor and $\text{lif}$ the lifetime for each fuel. The weighted average CapEx is defined as: $\text{ca}x_{\text{cf},t - 1}^{\text{av}}*\left( 1 - \Phi_{\text{inv}} \right) + \text{ca}x_{\text{cft}}*\Phi_{\text{inv}}$ with $\text{ca}x_{\text{cft}}$ the CapEx and $\Phi_{\text{inv}}$ the new investment expressed as a proportion of total existing capacity less retirements. It is worth noting that the base year, $t_{0}$, corresponds to $\text{ca}x_{\text{cft}}$. Over time, the CapEx is not varying, except for renewables (for more information see Section 3.4.4.4).
$\text{int}$ is the interest costs per kWh produced, assuming a straight-line amortization of CapEx: $0.5*\frac{\text{ca}x_{\text{cft}}^{\text{av}}*\text{wac}c_{\text{cf}}}{cf_{\text{cf}}*365*24}$ where $\text{wacc}$ is the WACC. The WACC can be adjusted according to different settings and both under a baseline and policy scenarios.

Figure 3‑13: Dashboard: WACC Settings

$\text{dec}$ denotes the yearly amortization of decommissioning costs²¹ per kWh produced: $\frac{\text{dt}c_{B,\text{cft}}}{cf_{B,\text{cf}}*365*24*\text{li}f_{f}}$ where $\text{dt}c_{\text{cft}}$ denotes the decommissioning and transmission costs in USD per kW (for more information see Section 3.4.4.4).
$\text{sto}$ defines the weighted average storage cost of vintages, which corresponds to the marginal storage costs for renewable energies.
Finally, $\text{opf}$ represents fixed costs for operating and maintenance, that is fixed OpEx expressed in USD per kWh according to the capacity factor of each fuel: $\frac{\text{tf}c_{\text{cft}}}{365*24*cf_{\text{cf}}}$ where $\text{tfc}$ is the fixed OpEx expressed in USD per kWy.

3.4.1.7 Concept 4: End-user prices

End-user prices are taken to be equal to current prices plus any change in underlying generation cost.
Observed power prices are used as the basis of the demand model.
Changes in generation costs (including those caused by carbon prices and any due to the phase-out of aforementioned subsidies) are assumed to be passed on to consumers (the proportion of pass-on defaults to 100% but can be altered.). If the parameter setting price controls is set to not one (could be 0, 0.25, 0.5, 0.75) then all price changes (from technology changes or carbon price) are diminished in the same proportion.

To estimate power prices (i.e. before the policy tax is introduced), the weighted current generation cost is calculated as follows:

$\text{gn}c_{B,\text{ct}}^{\text{av}} = \sum_{f}^{}gns_{B,\text{cft}}*\text{gn}c_{B,\text{cft}}$

For each country, the weighted average of generation cost $\text{gn}c_{B,c}^{\text{av}}$ is calculated according to generation shares $\text{gn}s_{B,\text{cft}}$ of each fuel $f$ and their respective current generation cost $\text{gn}c_{B,\text{cf}}$.

In the engineer model, power prices are processed specifically in the residential and non-residential sector (i.e. industrial sector). The supply price in the technoeconomic model $sp_{B,\text{cg}}^{T}$ (where the index $T$ holds for technoeconomic model) is determined in the residential and industrial sectors ($g = \text{Residential},\text{Industrial}$) via a fixed positive increment corresponding to transmission cost ($\text{tmc}$) to the weighted average generation cost such as:

$sp_{B,\text{cg}}^{T} = \text{gn}c_{B,\text{ct}}^{\text{av}} + \text{tmc}$

An allowance of $15/MWh and $40/MWh was added to account for transmission and distribution costs for industrial and residential uses, respectively²².

A markup $\text{mu}$ is then calculated specifically for residential and industrial electricity prices to equalize the starting year price (i.e. historical retail prices in the electricity sector, $\text{hr}p_{\text{cg}}$), as follows:

$mu_{B,\text{cgt}}^{T} = \text{gn}c_{B,\text{ct}}^{\text{av}} + \text{tmc} - \text{hr}p_{\text{cg}}.$

It is worth noting that when the markup is negative (i.e. retail prices are lower than modeled supply prices), the model captures a subsidy.

Carbon taxes are applied at the fuel-input stage to each generation. However, for the purposes of the overall generation cost, those costs are excluded as part of the generation cost average and averaged, and added on, separately. This is for the reason that doing this way allows us to calculate easily a needed rebate when rebating is employed.

The final residential and industrial end user power price in the technoeconomic power model, $p_{P,\text{cg}}^{T}$, is calculated as follows when a carbon price, $\text{nc}p_{\text{cg}}$, power excise, $\text{pe}x_{P,\text{cgt}}$, a rebate, $\text{re}b_{\text{cg}}$, are introduced:

$p_{P,\text{cgt}}^{T} = \text{gn}c_{B,\text{ct}}^{\text{av}} + \text{nc}p_{\text{cgt}} - \text{re}b_{P,\text{cgt}} + \text{pe}x_{P,\text{cgt}} + \text{tmc} + mu_{B,\text{cgt}}^{T}$

At this stage two end-user power price settings are included:

Output Based Rebating: the total carbon price is added to the generation types and then subtracted from overall power prices so that the overall policy is revenue-neutral.
Electricity Excise: a per-kwh tax is added at the end-user stage

3.4.2 Techno-economic (‘engineer’) power model

3.4.2.1 Overview

Electricity is widely acknowledged to be critical to ‘deep decarbonization’ scenarios, in the sense that alternatives such as renewables primarily generate electricity instead of solid, liquid, or gaseous energy vectors. Deep decarbonization involves decarbonizing the existing power sector and electrifying sectors that currently use fossil fuels directly. Electrification will also involve expanding the power sector to accommodate the increased power demand from this shift in energy vector. Such a structural model is important for the following reasons:

Marginal versus radical. Elasticity-based models are arguably best suited to price-based demand-side effects of marginal increases in fuel prices. They are less well suited to the non-marginal changes required for deep-decarbonization Paris-compliant scenarios.
Within bounds of equipment. Power systems involve two significant sets of decisions: decisions that change the stock of power generation assets (investment and retirement) and decisions that change the use of those assets for electricity generation (dispatch). Without determining the capital stock, it is unclear that a particular choice of generation is consistent with the actual generation capacities of a specific country. An elasticity-based approach can produce non-physically realistic results (i.e., power dispatched that requires implicit investment rates faster than what is realistic).
Responsiveness to absolute levels of renewable costs. Elasticity-based models can be unresponsive to actual levels of costs since it is based principally on the changes in cost.
Using accurate, referenced generation cost data. The elasticity-based model used data that was at times not clearly referenced and not recently updated. For example, the percentage of non-fuel costs in total coal generation costs seems inconsistent between the spreadsheet and the published IMF paper. Neither are directly referenced against currently published costs.
Renewables costs are rapidly changing, and it is helpful to model this explicitly.
The model should include, and the outcomes depend on, carbon price-dependent switching carbon prices for generation and investment. It’s helpful to know the ‘switching cost’ (for example, between coal and gas) in terms of the dispatch decision and the investment decision as a valuable marker of required carbon taxes to begin decarbonization.
Modeling the new reality. According to Bloomberg New Energy Finance data, newly built renewables have already achieved cost-parity with newly built fossil fuel plants in many parts of the world. Consequently, the near future is likely to look very different from the past, even without any policy-led acceleration of the deployment of renewables. Indeed, the recent deployment of renewables has tended to surprise on the upside (e.g., actual deployment has tended to outpace IEA projections). It’s unclear whether an elasticity-based model can fully capture these rapidly changing dynamics.

Summary of algorithm

As mentioned previously, the model has four types of prices:

Current Variable Costs: For dispatch decisions, the current variable costs are used (fuel and variable operations and maintenance).
Levelized Cost of Investment: For forward-looking (investment) decisions, a levelized and forward-looking cost approach adding all cost components is used. For example, one part is forward-looking expectations of future fuel and carbon costs.
Cost-recovery generation cost: For estimating the total running cost of the power system, a cost-recovery generation cost is calculated. This includes current variable cost, running amortization of capital costs, plus average interest costs (and other components too). The cost-recovery generation cost by generation type is averaged and then transmission and distribution costs are added to produce an overall estimated cost of generating and distributing electricity.
End user power prices (residential and industrial): these are based on observed prices with an adjustment for changes due to cost changes or carbon pricing. The user can decide what proportion of changes to overall generation cost are passed on. The user can also choose to phase out the estimated electricity subsidy.

The outlines of the algorithm are as follows:

End-user prices and GDP changes drive power demand by CPAT sector. (Some components of these prices are lagged one year to avoid circularity as Excel uses sequential rather than optimizing logic.)
According to historical energy balance data, transmission losses, own use, and net exports are added as fixed proportions of aggregated power demand.
Current inflexible capacity (renewable, nuclear) are assumed to dispatch at historical capacity factors, and the remainder is allocated to coal and gas according to available capacity using a logit formula based on variable cost.
Old capacity is retired according to either to defined data on retirement schedules (coal) or an exponential process (other generation types), with cost-based early retirement also included and an option to schedule retirement of coal.
Aggregate new generation capacity is added to meet expected demand assuming historical capacity factors.
Renewables are assumed to require both short- and long-duration storage, with assumed piecewise-quadratic total storage requirements, implying piecewise-linear marginal storage requirements. These storage requirements are approximately modelled based on global technical models. These storage costs are added to generation costs for Variable Renewable generation types.
Needed additions to aggregate ‘effective’ capacity (i.e. additions to expected generation) are then allocated according to another logit formalism based on total levelized costs by generation type, with the cheapest generation types taking the main share of the investment.
Renewables also have a maximum scale-up rate, set by default to 2 percentage points of total generation for wind and solar additional-generation. This setting can be changed by the user. Needed capacity beyond the limits are reallocated to other generation types according to the logit proportions. If there is still an unmet need for generation (for example in a high-hydro situation where new hydro investment is prohibited), the model will in extremis override VRE scaleup limits and the allowed investment types and invest in proportion to the current proportions of capacity in the system.
Capacities after retirement and new investment are passed forward as the starting point of the model for the next year.

3.4.2.2 Notation

Notation	Variable	Unit
$F$	Use of fuel	ktoe
$Y$	Total real GDP	US$
$p$	Retail price	US$/Gj
$\alpha$	Autonomous annual energy efficiency improvement	%
$\Psi$	Covid adjustment factor to energy demand	%
$\epsilon_{Y}$	Forward-looking real GDP-elasticity of fuel demand	%
$\epsilon_{U}$	Elasticity of usage of energy products and services	%
$\epsilon_{F}$	Efficiency price elasticity	%
$g$	Electricity generation	GWh
$E$	Total quantity of power demanded by sector	GWh
$\text{net}$	Net exports (imports)	ktoe
$\text{eiu}$	Energy industry’s own use	ktoe
$\Delta^{\text{dif}}$	Transmission and statistical differences	ktoe
$x$	The variable x is used in the logit formula to alternatively represent investment, $x = \text{inv}$, or generation $x = \text{gen}$	GWh
$K$	Parameter adjusting the shape of the sigmoidal function. It determines the speed of transitioning between generation types with a different cost.
$\text{reqge}n_{\text{COA} + \text{GAS}}$	Remaining generation allocated to coal and gas after nuclear, renewables, biomass and oil generation are subtracted	GWh
$\text{minge}n_{\text{COA},\text{GAS}}$	Minimum coal/gas needed assuming gas runs at maximum capacity	GWh
$\text{residualreqge}n_{COA/GAS}$	residual power generation from coal and gas	GWh
$\text{maxC}f_{\text{GAS},\text{COA}}$	Maximum capacity for coal/gas	GWh
$\lambda_{f}$	Proportion of the residual generation (after the ‘minimum coal’ and minimum gas’ allocation given limited capacity of the other) allocated to each of coal and gas	GWh
$\text{vc}$	Current variable costs	US$/kWh
$vc_{\text{lc}}$	Lowest current variable costs between coal and natural gas	US$/kWh
$\text{cf}$	Capacity factor	%
$\text{cap}$	Capacity	MWy
$\nu$	Thermal efficiency	%
$\widetilde{\gamma}$	Generation shares before PPAs	%
$\gamma$	Generation shares after PPAs	%
$\omega$	Percentage of PPAs	%
$\Omega$	Downscaling factor if needed generation is different from that which is determined by the raw capacity factors	%
$\text{inv}$	Generation investments	MWh
$\text{ret}$	Generation retirements	MWh
$\text{lif}$	Lifetime	Years
$\text{re}p_{\text{COA}}$	Proportion of coal replacement	%
$\zeta$	New investments permitted	MWh
$\text{ivp}$	Proportion of new investments	%
$\text{tic}$	Levelized total investment costs	US$/kWh
$\text{ti}c_{\text{lc}}$	Lowest levelized total investment costs between coal and natural gas	US$/kWh
$v$	Variable renewable energy (VRE)	%
$\text{sst}$	Short-term storage	Hours
$\text{slt}$	Long-term storage	MW/MW, i.e. dimensionless units (%)

3.4.2.3 Power demand

The power demand, $E_{\text{cgt}}$, determines the total quantity of power demanded by sector. At present, our power demand is determined the same way as the equations outlined in Section 3.3.3, with fuel type equal to power (electricity) ($f = P$):

$\frac{E_{\text{ocsf},t}}{E_{\text{ocsf},t - 1}} = \left( \frac{1}{1 + \alpha_{\text{sf}}} \right)^{1 + \epsilon_{U,\text{sf}}}\Psi_{\text{ct}}\left( \frac{Y_{c,t}}{Y_{c,t - 1}} \right)^{\epsilon_{G,\text{csf}}}\left( \frac{p_{\text{ocsf},t}}{p_{\text{ocsf},t - 1}} \right)^{\epsilon_{U,\text{csf}}}\left( \frac{p_{\text{ocsf},t}}{p_{\text{ocsf},t - 1}} \right)^{\epsilon_{F,\text{csf}}\left( 1 + \epsilon_{U,\text{csf}} \right)}$

where $E$ is expressed in ktoe, $Y$ is the total real GDP, $\alpha$, the autonomous annual energy efficiency improvement. The prices $p$ correspond to total (industrial and residential) power prices, as in Section 3.3.3). These prices respond to changes in weighted total generation cost, which is lagged by one year to avoid circularity issue.

A Covid adjustment factor to power demand $\Psi$ can be taken into account (see Section 3.3.4.4 - note this is specifically calibrated for the engineer model). Note that additional policies affecting the parameter $\alpha$ can be manually added.

That power demand from the elasticity model can also be used (it is very similar, just not disaggregated by sector):

Figure 41: Mitigation: Use Elasticity Model Power Demand In Engineer Model

Figure 3‑14: Mitigation: Use Elasticity Model Power Demand In Engineer Model

The total generation requirement (in ktoe), $g_{\text{oc},t}$, is therefore calculated as the sum of the total demand of all sectors augmented (subtracted) by the proportion – based on the base year – of net exports (imports), $\text{ne}t_{\text{oc},t_{0}}$, the energy industry’s own use, $\text{ei}u_{\text{oc},t_{0}}$, and transmission and statistical differences, $\Delta_{t_{0}}^{\text{dif}}$:

$g_{\text{oc},t} = \sum_{s}^{}E_{\text{ocs},t}*\left( 1 + \text{ne}t_{\text{oc},t_{0}} + \text{ei}u_{c,t_{0}} + \Delta_{c,t_{0}}^{\text{dif}} \right)$

3.4.2.4 Power supply

3.4.2.4.1 Logit function

Two different cost-based decisions are considered in the engineer model: the dispatch decision, determining how existing power plants are used, and new investment planning. In both of these decisions, the ‘multilogit’ function is used, with the probability of investment and dispatch of a technology increasing as a function of the price differential with alternatives. A parameter $K$ adjusts the shape of the sigmoidal function that can be refined upon review of leading power sector models employing a similar approach. They determine the speed of transitioning between generation types with a different cost. The $K$ parameters are set with defaults set subjectively at 2 for both dispatch and investment, which we believe produces realistic results. This parameter can be adjusted in the dashboard:

Figure 3‑15: Dashboard: K parameters

The formula of the multilogit is as follows:

$\frac{x_{\text{ocft}}}{\sum_{f}^{}x_{\text{ocft}}} = \frac{e^{- K.c}}{\sum_{i}^{}e^{- K.c}}$

where $\frac{x_{\text{ocft}}}{\sum_{f}^{}x_{\text{ocft}}}$ is the proportion (i.e. investment, $x = \text{inv}$, or generation $x = \text{gen}$) allocated to generation type $f$, and $c_{i}$ is the relative cost of generation type $f$ (i.e. the total levelized cost of electricity in the case of investment or variable costs $i$.

3.4.2.4.2 Dispatch decision

Dispatch decisions are based on a multi-step process.

The model first determines generation from nuclear, renewables, biomass and oil according to their capacity factor and the total supply required. In particular, renewables are assumed to produce power according to their installed capacity multiplied by historical capacity factors.

In the case of renewables, they are assumed to be non-dispatchable meaning their capacity factor is fixed. Nuclear, biomass, and oil generation are assumed to be semi-dispatchable meaning that if power demand falls relative to the base year, they too will reduce their capacity factor proportionally. But they will not increase their capacity factor. For nuclear, the low variable cost makes it economical always to run the plant when available. For biomass and oil, we simplify as we do not wish to model merit order decisions with many different fact (hourly peaking needs, environmental regulations etc).

Then, residual energy demand is determined by an explicit choice between coal and gas based on the variable cost of each (including the carbon tax). In other words, the remaining generation needed after nuclear, renewables, biomass and oil generation are subtracted, is allocated to coal and gas.

$\text{reqge}n_{\text{oc},\text{COA} + \text{GAS},t} = g_{\text{oc},t} - \sum_{\text{fϵ}\left( \text{RE},\text{NUC} \right)}^{}cap_{f}*cf_{f}$

First, we determine the minimum coal needed assuming gas runs at maximum capacity and vice versa for coal. The maximum capacity is by default set to 90%, but the user can adjust it in the dashboard:

Figure 44: Dashboard: Use energy balances or (CPAT) energy consumption data

Figure 3‑16: Energy balances and energy consumption

For example, for coal:

$\text{minge}n_{\text{oc},\text{COA},t} = \text{reqge}n_{\text{oc},\text{COAL} + \text{GAS},t} - \text{ca}p_{\text{GAS}}*\text{maxC}f_{\text{GAS}}$

Then, the remaining required generation after these minima are allocated to coal and natural gas, $g_{f}$, is determined based on their relative marginal costs, using the logit formulation:

$\lambda_{f} = \frac{e^{- K_{\text{dispatch}}.H_{f}}}{\sum_{f}^{}e^{- K_{\text{dispatch}}.H_{f}}}$

where $f$ is restricted to coal or natural gas and $\lambda_{f}$ is the proportion of the residual generation (after the ‘minimum coal’ and minimum gas’ allocation given limited capacity of the other) allocated to each of coal and gas. The term $H_{g}$ is the ratio $\frac{vc_{P,\text{cft}}}{vc_{P,\text{cft}}^{\text{lc}}}$, where the (marginal) variable cost is given by $vc_{P,\text{cft}}$ and $vc_{P,\text{cft}}^{\text{lc}}$ is the variable cost of the lowest cost option between coal and natural gas, i.e. $f \in \left\{ \text{coal},\text{naturalgas} \right\}$, and $K_{g}$ is the K parameter specific to generation.

Power generation for coal thus becomes:

$g_{\text{oc},\text{COA},t} = \text{minge}n_{\text{oc},\text{COA},t} + \lambda_{f}*\text{residualreqge}n_{\text{oc},\frac{\text{COA}}{\text{GAS}},t}$

where $\text{residualreqgen}$ denotes the residual power generation from coal and gas.

This procedure gives overall raw generation shares (assuming no PPAs), ${\widetilde{\gamma}}_{\text{ocf},t}$. It is worth noting that to the extent PPAs exist, a fixed capacity factor is used. Therefore, the latter is downscaled if the ‘needed’ coal and gas generation is less than what is implied by their default capacity factors. The total generation mix becomes:

$\gamma_{\text{ocf},t} = \left( 1 - \omega_{\text{oct}} \right)*{\widetilde{\gamma}}_{\text{ocf},t} + \omega_{\text{oct}}*\Omega*\left( \text{ca}p_{\text{ocft}}*CF_{\text{cft}} \right)$

where $\gamma_{\text{ocf},t}$ is the generation share after PPAs $\omega$ denotes the percentage PPAs and $\Omega$ a downscaling factor if needed generation is different from that which is determined by the raw capacity factors.

3.4.2.4.3 Retirement and capacity needed

At the start of the analysis, the capital stock is based on electricity generation capacity data by fuel type from Enerdata. Required effective capacity is equal to expected generation capacity and is defined as capacity multiplied by the expected capacity factor -– i.e., the investment is set such that the capacity is sufficient to cover expected peak demand, which is estimated using the power demand equation (see Section 3.4.2.2).

The economic system is expected to plan ahead a few years in advance so that investment takes place to meet the projected demand at the start of each year at the same time as retirement is modeled to happen. Capacity for the first year is thus determined based on IEA data.

For the following years, new capacity is thus equal to the old capacity, less retirements, and plus any new investments needed. The total required generation capacity is given by the expected power demand minus the generation capacity (last year’s capacity less retirements):

$g_{\text{ocft}} = g_{\text{ocf},t - 1} - \sum_{f}^{}ret_{ocf,t - 1} + inv_{ofc,t - 1}$

It is assumed that a generation dependent proportion, $\text{ret}$, of all generation assets retire each year, equal to the reciprocal of the average lifetime $\text{lif}$ of that generation type.

$\text{re}t_{\text{ocft}} = \frac{1}{\text{lif}}*\text{ca}p_{\text{ocft}}$

For coal, it is worth noting that planned retirement is adjusted based on the coal power plant tracker, which provides power plant data level for a number of countries. Therefore, based on these data, the retirement year of each power plant is determined and the capacity associated is determined from 2022 to 2050²³. When data do not exist, the above formula is used.

In addition to planned retirement, cost-based early retirement coal is also estimated as additional policies could accelerate retirement for coal power plants. In this respect, the model:

First finds the maximum of coal that could be replaced by wind and solar. The maximum coal retirement is estimated as a fixed proportion (default 80%) of coal total effective capacity.
Second, it compares the variable cost of coal with the total cost of wind and solar.
Third, it calculates through a logit formula a proportion of the maximum coal replacement (depending on relative costs):

$\text{re}p_{\text{oc},\text{coa},t} = 1 - \frac{e^{- K_{i}.H_{r,\text{COA}}}}{\sum_{f}^{}e^{- K_{i}.H_{r,f}}}$

where $H_{r,\text{coa}}$ is the ratio $\frac{vc_{\text{oc},\text{coa},t}}{vc_{\text{ocft}}^{\text{lc}}}$ and $H_{r,f}$ is the ratio $\frac{vc_{\text{ocft}}}{vc_{\text{ocft}}^{\text{lc}}}$ with $f \in \left\{ \text{coal},\text{solar},\text{wind} \right\}$. The term $\text{re}p_{\text{oc},\text{COA},t}$ denotes the proportion of coal replacement.

Finally, the estimated proportion $\text{re}p_{c,\text{coa},t}$ is multiplied by the maximum of coal retirement.

Therefore, the total retirement is equal to the sum of planned retirement and cost-based early retirement.

3.4.2.4.4 Investment decision and non-VRE and VRE scale up limitations

Investment decisions are constrained by non-VRE and VRE limits and are based on two rounds:

New investments permitted: A logit function capped by a VRE limit that spreads out investments across technologies based on the cheapest levelized costs.
Allocated remaining capacity needed: A least-cost merit order algorithm allocates remaining capacity needed according to generation costs across technologies.
- Logit function constrained by scale-up limits

Similarly as dispatch and retirement, new investment is spread out across the cheapest levelized possibilities, according to a multilogit formulation (with K parameter = 2):

$\frac{\text{iv}p_{\text{ocft}}}{\sum_{f}^{}{\text{iv}p_{\text{ocft}}}} = \zeta_{\text{cft}}*\frac{e^{- K_{i}.H_{i}}}{\sum_{i}^{}e^{- K_{i}.H_{i}}}$

Where: $\zeta_{\text{cft}}$ stands for new investments permitted in percentage. The user has the possibility to enable new investments (in MW). $\text{iv}p_{\text{cft}}$ denotes the proportion of new investments $K_{i}$ the K parameter specific to investment decisions. The term $H_{i}$ is the ratio $\frac{\text{ti}c_{P,\text{cft}}}{\text{ti}c_{P,\text{cft}}^{\text{lc}}}$, $\text{ti}c_{P,\text{cft}}$ and $\text{ti}c_{P,\text{cft}}^{\text{lc}}$ define, respectively, the levelized investment cost and the lowest levelized investment cost across fuel types. It is important to note that renewables face a penalty at high levels (i.e. above 75% penetration) as an additional ‘storage systems cost’ could increase costs (see Section 3.4.2.5 on Long-term storage).

Different options are possible for whether new investments are permitted ($iv^{\text{new}}$):

If present is the default option and allows new investments in the model if nameplate capacity > 0. Otherwise, no investment is accounted for.
Yes allows the user to introduced planned investments, that is specifying a start year.
No disables new investments.
Manual allows the user to enter data. These data will override the data determined by the model and new capacity will be accounted for as: New Nameplate Investments (MW) = Capacity data entered by the user + Planned Retirement.

Figure 3‑17: Dashboard: Plan or enable new investment

Maximum effective investments, $\text{iv}^{\max},$ are then capped by non-VRE and VRE limits ($\text{VRE}$):

${\text{iv}_{\text{ocft}}^{\max} = g}_{\text{oc},t}*\zeta_{\text{cft}}*VRE_{\text{cft}}$

Default non-VRE limits are set to 5% for coal and natural gas and 2% for hydro, oil, other renewables, nuclear and biomass. Default VRE limits are set to 2% (i.e. for wind and solar).

CPAT allows the user to define non-VRE and VRE scale up rates. The rates reflect a ‘linear’ type constraint. It constrains generation in VRE additions to be a certain percentage of total generation (in gross additions, not net of retirements). For VRE rates, the following rates can be selected: Low (1%), Medium (2%), High (3%), Very High (4%), UserDefined and CountrySpecific (currently set to 2% – except for China 2.5%). The default is country specific.

Figure 46: Dashboard: Scale up rate parameter

Figure 3‑18: Dashboard: Scale up rate parameters (right panel: non-VRE rate; left panel: VRE rates)

Figure 3‑19: Dashboard: Scale up rate specification for wind and solar

Least-cost merit order

The logit approach and the scale-up limitation determines ‘allocated’ investment. But there is still some needed investment that is not allocated. We use a least cost merit order approach to determine the currently ‘unallocated’ investment need.

The least cost algorithm ranks the generation types in terms of the cost and then use up all their available space (within the capacity limits) one by one, starting with the cheapest and so on.

First of all, the algorithm defines the remaining unallocated investment need. New effective investment before reallocation are defined as the minimum between maximum effective investments and new investments permitted in order to make sure investments cannot be superior to the maximum capacity. Therefore, this allows to determine the remaining investments needed, $iv^{\text{rem}}$:

${iv_{\text{ocft}}^{\text{rem}} = \ iv}_{\text{ocft}}^{\max} - \min{(\text{iv}_{\text{ocft}}^{\max},\text{iv}_{\text{ocft}}^{\text{new}})}$

Second, generation costs are ranked from the cheapest to the most onerous across technologies in order to allocate remaining capacity needed.

Third, remaining capacity are thus allocated in a second round of investment according to the cheapest technology in a cumulative way.

Finally, total new investments equals investments permitted over the two rounds of investments, that is before reallocation and after reallocation:

$iv^{\text{tot}} = \text{iv}_{\text{ocft}}^{\text{new}} + \ iv_{\text{ocft}}^{\text{rem}}$

3.4.2.4.5 Calibration and systems costs

Two calibrations are performed in the engineer power model, that is (1) a calibration on the total electricity generation and (2) an inferred value for systems cost, calibrated on the share of coal.

First, to ensure proper calibration of the engineer power model in 2020, a COVID adjustment factor can be used to calibrate total electricity generation. The latter, estimated by the model, is compared to observed data (IEA, 2020). The adjustment factor is calculated as the percentage difference between the estimated and observed data. Results per country can be found in the tab ‘CovidAdjust’. For countries not covered by the IEA database, the factor adjustment is similar to the Covid adjustment on energy consumption (see Section 3.3.4.4). Importantly, in 2021, a rebound effect is introduced.

By default, the adjustment factor is set to 0. However, the user can rely on the adjustment factor by modifying the setting to 1 (see below). It should be mentioned that the lower and upper limits are set at 25%, which means that the factor adjustment cannot be less (more) than -25% (25%).

Figure 3‑20: Dashboard: Covid Adjustment

Second, systems costs are currently inferred by using a calibration on the share of coal in the electricity generation. This exercise is carried out using observed data in 2019 based on observed data from the IEA and consists of matching observed data for the coal share in the electricity generation. Systerms costs are equivalent to an additional implicit price for coal, $\text{im}p_{c,\text{coa},t}$. Inferred value for system costs are thus used for the years after 2019, with the exception of the year 2020. The latter is considered as exceptional because of the Covid shock. Therefore, the exercise is repeated for this year, as systems costs could be higher. IEA’s forecasts on the share of coal in total electricity generation for the year 2030 are also reported for information only.

Figure 3‑21: Dashboard: Covid Adjustment

For the years 2019 and 2020, the following steps are taken:

The share of coal in total electricity generation is calculated for both the power model’s estimates and observed data from the IEA.
To account for the difference between these two values, the “goal seek difference” is expressed as the following distance between estimated and observed coal share: $\left( \text{co}a_{t}^{\text{est}} - \text{co}a_{t}^{\text{obs}} \right)^{2}$, where $\text{coa}l_{t}^{\text{est}}$ denotes the share of coal estimated by the power model and $\text{coa}l_{t}^{\text{obs}}$ represents the observed share of coal for $t \in \left\{ 2019,2020 \right\}$.
As estimated coal share is often over-estimated compared to observed data, the goal seek difference is thus addressed by increasing prices for coal (i.e. an implicit price component) in order to reduce the difference between estimated and observed coal share. Only positive implicit price components are considered.

Results of additional implicit prices are reported in the tab ‘GoalSeekCoal’ for both 2019 and 2020. By default, CPAT uses the additional implicit prices. However, an option in the dashboard allows the user to turn this assumption off or to manually add the implicit price component.

Figure 73: Dashboard: Coal share calibration

Figure 3‑22: Dashboard: Coal share calibration

If the “Manual” option is selected, the user overrides the implicit price component with their choice.

Figure 74: Dashboard: Coal share calibration (manual)

Figure 3‑23: Dashboard: Coal share calibration (manual)

3.4.2.5 Storage decision

CPAT has a simple model of electricity storage. The required storage consists of two elements, short and long-term. Both long and short-term storage is related to the proportion of renewable energy (VRE) generation as a percentage of total electricity generation. VRE includes wind and solar and other renewables but not hydro and biomass.

Because the model does not represent renewable energy generation profiles, relative quantification of balancing capabilities, or variability in demand, a “system integration cost” is imposed on higher shares of variable renewable energy (VRE). This cost is assumed to be an increasing function of VRE share. This additional cost forms part of the investment decision. The cost of integrating renewables is particularly significant at high levels (i.e. >50% by generation) of renewable penetration into an electricity mix. Against this background, two different types of storage are considered in the model:

Short-term storage, which are costly per kWh but cheap per kW (e.g. batteries measured in kWh).
Long-term storage, which are costly per kW but cheap per kWh (e.g. electrolysis and hydrogen tanks measured in kW).

For both types of storage there is an additional ‘hours’ ratio, measuring the ratio of battery capacity (kwh) to battery interface (kw), and electrolysers (kw) to hydrogen storage (kwh). Each storage aspect is two-dimensional, meaning that every storage technology is determined by an ‘interface’ (kW) and a ‘storage quantity’ (kWh). The model measures storage according to one ‘numeraire’ and one ratio. For short-term storage, we measure the kWh and assume a standard 4-hour ratio between the kWh and kW in determining the costs. We calculate the kW for long-term storage and assume 1000 hours of storage per kW.

3.4.2.5.1 Short-term storage

Short-term storage in CPAT is satisfied by the batteries. Total storage needs are calculated in hours, which means kWh of storage per kW of average generation (not peak capacity).

The model uses rounded versions of a parameterization derived from global data²⁴. The model assumes that the total number of storage for a 100% VRE system is 9 hours, with a quadratic form. We fit the short-term storage needed (in hours) as a (conservative) quadratic function of the VRE. We allocate some percentage of this (currently 100%) to the costs of the power system itself. VRE, $v$, includes solar and wind but not hydro (other renewables are neglected). Short-term storage $\text{sst}$ is measured in hours, i.e. kWh/(kWh/h). We also assume a ratio between the kWh of the storage and the kw interface. For conservatism (given our metric is in kWh), we use a low number (2 hours) for the ratio of kWh to kw:

$\text{sst} = 9v^{2}$

By way of example, for a 50% VRE system, the hours needed are $9*{0.5}^{2} = 2.25$ hours.

Therefore, the marginal storage needed is:

$\frac{\text{dsst}}{\text{dv}} = 18v^{2}$

The system has assumed to already have invested optimally in the existing storage at current VRE.

3.4.2.5.2 Long-term storage

CPAT also has a long-term storage model. Long-term storage is additional to short-term storage and is measured according to the cost of the interface (i.e., the electrolyzers rather than the cost of the storage tank). The interface is measured in units of KW. Therefore the proportion of long-term storage per kW of average generation is measured in dimensionless terms (kW per kW or %).

Long term storage $\text{slt}$ costs are treated as effectively punitively costly (in contrast to short term storage), reflecting current costs and technological uncertainties. The long-term storage model assumes zero need for long-term storage below a VRE penetration of 75 percent, raising to 100 percent at a VRE of 100 percent. To this end, long-term storage is viewed as additional to short-term storage, and is needed for VRE over 75%.

Since batteries and hydrogen have other uses, we also have a parameter that determines the proportion of the short-term and long-term storage allocated to the electricity system. This is set to 100% for short-term storage and 33% for long-term storage. This parameter can be modified in the dashboard:

Figure 3‑24: Dashboard: Percent allocation of LT storage costs to VRE

Given its interseasonal storage and geographic independence, we focus on the costs of electrolysers for storage. This storage cost is thus assumed as a long-term storage and is measured with the interface (i.e. electrolysers) as the numeraire. It is given by the following quadratic function:

$ = \left{

\[\begin{matrix} 0 & \text{for\ }v \leq 0.75 \\ \left( \frac{v - 0.75}{1 - 0.75} \right)^{2} & \text{for\ }v > 0.75 \\ \end{matrix}\]

Long term storage requirements are measured in MW/MW, i.e. dimensionless units (%). The marginal MW of electrolysers required once VRE penetration reaches 75% is thus varying according to the derivative $2*\frac{v - 0.75}{\left( 1 - 0.75 \right)^{2}}$. The table below shows the results for different levels of VRE.

VRE penetration	Marginal MW of electrolyzers required
85%	2.5
90%	5.0
95%	7.5
100%	10.0

3.4.2.5.3 Levelized cost of storage

The levelized cost of the marginal quantity of storage needed to maintain required quantities of total storage is added to the investment costs for VRE. This means that the storage-inclusive cost of renewables can rise in time as renewable penetrations increase, even if the cost of renewables without storage is falling.

3.4.3 Elasticity model

3.4.3.1 Overview

The elasticity-based model is derived from an IMF spreadsheet tool, with a methodology described in an IMF board paper²⁵. The CPAT mitigation module, and the IMF tool on which it is based, are primarily elasticity-based models, meaning that future fuel demand is dependent on projected total real GDP growth, and upon future energy prices, modified by mitigation policies such as carbon taxes. The power supply model is also based on elasticities, although it has a more complex structure than in other sectors. It separately models final power demand, and within that overall power demand the generation share of different generation types.

3.4.3.2 Notation

Notation	Variable	Unit
$E$	Total quantity of power demanded by sector	GWh
$Y$	Total real GDP	US$
$p$	Retail price	US$/Gj
$\alpha$	Autonomous annual energy efficiency improvement	%
$\Psi$	Covid adjustment factor to energy demand	%
$\epsilon_{Y}$	Forward-looking real GDP-elasticity of fuel demand	%
$\epsilon_{U}$	Elasticity of usage of energy products and services	%
$\epsilon_{F}$	Efficiency price elasticity	%
$g$	electricity generation	GWh
$\Phi$	Production share	%
$\text{gn}c^{*}$	Total unit cost adjusted of thermal efficiency	US$/kWh
$\epsilon_{\widetilde{E}}$	Conditional own-price elasticity of generation from fuel $f$ with respect to generation cost	%
$\delta^{\text{add}}$	Additional share of electricity generation attributed to non-nuclear and non-hydro energy	%
$\text{TotExcess}$	Total surplus of nuclear and hydro power generation to be redistributed	%
$F$	Use of fuel	ktoe

3.4.3.3 Generation costs

Importantly, by default, the power generation costs are taken from the engineer model (i.e. levelized fixed cost plus current variable costs, but excluding intangible coal cost). However, this assumption can be modified and the cost model from the IMF board paper can, if wished, be selected in the dashboard. The methodology for these ‘old’ costs is given the IMF paper mentioned above.

Figure 49: Dashboard: Use Spot Fuel Prices in Engineer Power Model

Figure 3‑25: Dashboard: Use old or new generation costs in elasticity model

Renewable producer subsidies under a baseline scenario, as well as under the policy scenario, can be specified in the dashboard:

Figure 3‑26: Dashboard: Renewable producer subsidies under a baseline scenario

3.4.3.4 Total power demand

As described above, power demand is determined by the energy use equation. As this is a total power demand, elasticities are averaged across all sectors. The autonomous efficiency improvements (or more especially, the annual generation productivity improvements) used across fuels are as follows:

Fuels	Change
Coal	0.5%
Natural gas	1.0%
Oil	0.5%
Nuclear	1.0%
Wind	5.0%
Solar	5.0%
Hydro	1.0%
Other renewables	5.0%
Biomass	1.0%

Productivity improvements at power plants reflect improvements in technical efficiency and gradual retirement of older, less efficient plants. Following the IMF Board Paper, for coal, annual average productivity growth is taken to be 0.5 percent based on IEA’s data. For natural gas, nuclear, and hydro, there is likely a bit more room for productivity improvements and baseline annual growth rate of 1 percent is assumed. For renewables, a productivity growth rate of 5 percent is used (i.e., costs halve every 15 years).

For the base year, energy consumption is extracted from energy balances, expressed as total energy consumption net of fuel transformation and transportation. The index $E$ denotes the sector Electricity.

For 2020, estimates are based on the previous year’s data adjusted for a one-time exogenous shock, i.e., Covid (see Section 3.3.4.4).

$\frac{E_{\text{oct}}}{E_{\text{oc},t - 1}} = \left( 1 + \alpha \right)^{- \left( 1 + \epsilon_{U} \right)}\left( 1 + 0.5*\Psi_{\text{ct}} \right)\left( \frac{p_{\text{cEt}}}{p_{\text{cE},t - 1}} \right)^{\epsilon_{U,\text{cE}}}\left( \frac{p_{\text{cEt}}}{p_{\text{cE},t - 1}} \right)^{\epsilon_{F,\text{cE}}}\left( \frac{Y_{\text{ct}}}{Y_{c,t - 1}} \right)^{\epsilon_{G,\text{cE}}}$

In the elasticity model, half the usual Covid adjustment is employed as power demand does not fall as far as other energy types.

3.4.3.5 Total power supply

Power generation fuels potentially include coal, natural gas, oil, nuclear, hydro, biomass wind, solar and other renewables.

Similar to the engineer model, total demand is scaled to generation (which includes additionally transmission losses, energy industry own use and transmission losses). The total production of electricity, $g_{\text{oct}}$, is driven by the total power demand multiplied by the ratio of generation to demand in the base year.

$g_{\text{oct}} = E_{\text{oct}}*\frac{g_{\text{oc},t_{0}}}{E_{\text{oc},t_{0}}}$

For the base year, total electricity generation is based on observed energy balance data, which is the sum of all electricity generation from each fuel $f$.

The elasticity model provides two types of information when it comes to forecast generation of each type of fuel: the electricity output and the primary energy used for electricity production for each technology.

The electricity output from technology $f$ is defined as the production share multiplied the total production. The production share, $\Phi_{\text{ocft}}$ is derived from observed data and is defined as the ratio between the observed electricity output from fuel $f$ and the total production, that is $\frac{g_{\text{ocft}}}{g_{\text{oct}}}$. The production share is assumed to be fixed until 2020. After this date, to accommodate flexible assumptions for the degree of substitution among fuels, the share of fuel $f$ in generation is defined as:

$\Phi_{\text{ocft}} = \Phi_{\text{ocf},t - 1}\left( \frac{\text{gn}c_{\text{ocft}}^{*}}{\text{gn}c_{\text{ocf},t - 1}^{*}} \right)^{\epsilon_{\widetilde{E}}} + \frac{\Phi_{\text{ocf},t - 1}\sum_{i \neq f}^{}\left\lbrack 1 - \frac{\text{gn}c_{\text{ocit}}^{*}}{\text{gn}c_{\text{oci},t - 1}^{*}} \right\rbrack^{\epsilon_{\widetilde{E}}}}{\sum_{j \neq f}^{}\Phi_{\text{ocj},t - 1}}$

where $i$ and $j$ are bound variables ranging over the same range as $f$ (i.e., OIL, NGA, COA, NUC, WND, SOL, BIO, REN, HYD). In addition, $\text{gn}c_{\text{ocft}}^{*}$ denotes the total unit cost adjusted of thermal efficiency and $\epsilon_{\widetilde{E}} < 0$ is the conditional own-price elasticity of generation from fuel $f$ with respect to generation cost. Conditional (indicated by $\\tilde$) here means the elasticity reflects the percent reduction in use of fuel $f$ due to switching from that fuel to other generation fuels, per one-percent increase in generation cost for fuel $f$, holding total electricity generation fixed. Generation cost elasticities are larger than corresponding fuel price elasticities as an incremental increase in fuel and non-fuel generation costs has a bigger impact than an incremental increase in fuel costs alone.

From the above equation, fuel $f$’s generation share decreases in own generation cost. It also increases in the generation cost of fuel $i \neq f$, where the increase in fuel $f$’s generation share is the reduced share fuel $i$ (i.e., $\Phi_{\text{ocft}}$ times the term in square brackets) multiplied by the (initial) share of fuel $f$ in generation from all fuel alternatives to $i$ (i.e., $\frac{\Phi_{\text{ocf},t - 1}}{\sum_{f \neq i}^{}\Phi_{\text{ocf},t - 1}}$:

NB: The actual equation in CPAT also reflects that nuclear and hydro should normally not grow beyond current levels. Therefore the model reallocates any excess growth for nuclear and hydro to other generation types. The equation above thus becomes:

$\Phi_{\text{ocft}} = \Phi_{\text{ocf},t - 1}\left( \frac{\text{gn}c_{\text{ocft}}^{*}}{\text{gn}c_{\text{ocf},t - 1}^{*}} \right)^{\epsilon_{\widetilde{E}}} + \frac{\Phi_{\text{ocf},t - 1}\sum_{f \neq i}^{}\left\lbrack 1 - \iota_{\text{cft}} \right\rbrack^{\epsilon_{\widetilde{E}}}}{\sum_{f \neq i}^{}\Phi_{\text{ocf},t - 1}}*\delta^{\text{add}}$

where $\iota_{\text{cft}} = \frac{\text{gn}c_{\text{ocft}}^{*}}{\text{gn}c_{\text{ocf},t - 1}^{*}}$ and $\delta_{\text{oct}}^{\text{add}} = \frac{\text{TotExces}s_{\text{oc},\text{NUC} + \text{HYD},t}}{\left( 1 - \Phi_{\text{oc},\text{HYD},t} - \Phi_{\text{oc},\text{NUC},t} \right)}$

The energy used of each technology $f$ in electricity production

Similarly, to electricity output, the base year corresponds to observed data, with the exception of wind, hydropower, solar and other renewables which are equal to electricity output. Therefore, for the following years, the energy used in electricity production is expressed as follows:

$F_{\text{ocft}} = E_{\text{ocft}}*\left( \frac{1}{1 + \alpha_{f}} \right)^{t}\frac{F_{\text{ocf},0}}{E_{\text{ocf},0}}$

The fuel use is equal to the electricity generated multiplied by an efficiency improvement over time $\alpha_{f}$ specific to the generation type $f$.

3.4.4 Power data sources and parameter choices

3.4.4.1 Introduction – Overview of Data Sources and Assumptions

The CPAT mitigation module offers two models that can be used for the power sector: the elasticity-based model and the techno-economic (‘engineer’) model. The former uses marginal fuel price increases and price elasticities to determine the shares of each type of generation, while the latter explicitly models the capacity of different types of generation, with capacity expansion to meet desired power demand. The user can choose to use elasticity, the engineer model, or a simple average of the two. Since the data documented in this section are fed into the engineer model, we will briefly review that model here.

The engineer model is based on four elements (see Figure 1):

The power demand model, which is based on income and price elasticity of electricity demand.
The retirement model, which includes cost-based ‘early retirement’ options for coal.
The investment model, which models the addition of new capacity.
The dispatch model, which models renewables and nuclear as operating continuously and accounts for the trade-off between coal and gas based on price.

For more information, please refer to Section 3.4. Power sector models in the online documentation.

3.4.4.1.1 Technology Definitions

Technologies are not always consistent across sources, and the CPAT model takes specific technologies into account. For transparency, Table 1 summarizes the mapping of technologies considered in the CPAT model. We select specific significant technologies to represent each CPAT technology. For instance, we use onshore wind to represent wind power in general (onshore and offshore), as it accounted for 92% of installed wind capacity in 2024, according to the IEA (2024). Other renewables constitute a separate category, as it includes all other renewable technologies. For more information, please refer to the Appendix A, Section A.1. Technology Mapping.

Table 1 - Technology Mapping
CPAT Technology	Technology
Coal (coa)	Coal, Subcritical
Natural gas (nga)	CCGT
Oil (oil)	Fuel Oil
Nuclear (nuc)	Nuclear (incl. ALWR, EPR, LWER, PHWR, PWR, SMR, VVER)
Hydro (hyd)	Hydro Large, Reservoir
Wind (wnd)	Wind onshore
Solar (sol)	PV fixed axis
Other renewables (ore)	Geothermal flash, waste, marine
Biomass (bio)	Biomass incineration, bioenergy
Battery (bat)	Utility-scale battery (4h), lithium-ion

3.4.4.1.2 Primary Data Sources

Power sector data components are organized into two primary methodological approaches:

Derived Data: Components directly extracted, or derived, from energy consumption capacity datasets. These provide empirical foundations based on operational data.
Study-Based Data: Components sourced from studies, research publications, and institutional assessments.

CPAT power models draw from the following key data sources (summarized in Table 2):

Main Technoeconomic Characteristics: Global data is derived from the CCDR EEX Methodology Note – Energy Transition Analysis FY24 (CCDR-EEX) , as well as Way et al., (2022) and the Global and National Energy Systems Techno-Economic (GNESTE) database . National data is derived from IRENASTAT (IRENA) , GNESTE and BloombergNEF (BNEF).
Time Evolution of CapEx: Data is derived from the CCDR-EEX (using IEA scenarios).
Decommissioning and Transmission Costs: Decommissioning data is derived from three studies: Raimi (2017) , the World Nuclear Association (2023) , and the Water Power & Dam (2009) . Transmission data us derived from Andrade and Baldick (2017) .
Storage: Data derived from Bogdanov et al. (2019) is used.
Installed Capacity: Current and forecast data are derived from IRENA .
Planned Retirement of Power Plants: Data from the Global Coal Plant Tracker is used.
Maximum RE Scale-Up Rate: Assumptions are used. We hope to revise these as part of the review of the investment equation.
WACC: A mixed approach is used, deriving data from Damodaran (2025) and Steffen (2020) .

Table 2 - Summary Table for Power Model Data
Data Section	Methodology	Unit	Data Level	Data Source
Main Technoeconomic Characteristics	The CCDR-EEX assumptions “National Policies in APS World” are used.	CapEx, variable and fixed OpEx in USD/kW; Capacity Factor, WACC and efficiency in %; Total lifetime in years	Global	CCDR-EEX (WBG), Way et al., 2022, GNESTE
	Simple averages of multiple sources are used; indexation to the CPAT year is performed when no more recent data is available. A script is available to update data at the country-level.	Country	IRENA (Red), GNESTE (Purple), BNEF (Green)
Time Evolution of CapEx	For solar and wind, the decline in CapEx over time is included. There are two scenarios: (1) Medium = uses CCDR-EEX Assumptions “National Policies in APS World”; (2) High = uses National PD2050 in NZE World scenario	Index (base year: 2021)	Global	CCDR-EEX (WBG)
Decommissioning & Transmission costs	Decommissioning and transmission costs are based on estimates provided by several data sources. The average is computed and then transformed to be expressed as percentage of CapEx. NB: Transmission costs are not currently used in CPAT.	Percentage of CapEx	Global	Decommissioning costs (Raimi, 2017; WNA, 2023; Water Power & Dam, 2009) & Transmission costs (Andrade & Baldick, 2017)
Storage	Data are directly retrieved from the LUT model and interpolated when missing.	CapEx, fixed and variable OpEx in USD/kWh, lifetime in years	Global	LUT model (Bogdanov et al., 2019)
Installed capacity	Data prior to 2019 is from the EIA, data after 2019 is from IRENA. A script is available to update data at the national level.	Installed capacity in MW	Country	EIA, IRENA
Planned retirement	Based on power plant data, the retirement year of each power plant is determined and the capacity associated is determined from 2000 to 2050.	MW per year	Country	Coal Power Plant tracker
Maximum Scale Up Rate	Constraint on renewable scale up rate. Based on assumptions.	%	Country	Assumption
WACC	Using a combination of LIBOR, a country factor (risk premium) taken from the literature, a policy factor (accounting for PPAs) and a technology factor, a WACC is estimated	%	Country	Damodaran, 2023; Steffen, 2020

3.4.4.2 Data Harmonization Process

Integration process: Where multiple sources provide data for the same parameter, we employ a simple average methodology after applying necessary adjustments for consistency. This approach balances the strengths of different sources while mitigating individual source limitations. Table 17 in Appendix A, Section A.2. Assumptions outlines the different assumptions underlying the construction of variables in the power sector according to various data sources and correction in CPAT.

Standardization Requirements: Due to different underlying assumptions across data sources, several standardization adjustments are implemented:

Costs in time: The latest version of CPAT is based on 2021 data, including costs expressed in USD and in real terms (net of inflation). As costs may vary in time depending on the status of the power plant, the approach aims to establish a time series based on available data points across different sources. The IRENA, GNESTE and BNEF databases display nominal data and are adjusted to the model year. Other monetary data are adjusted according to the US GDP deflator indicator (including historical CPAT data that could not be updated).
Efficiency Standardization in Net Caloric Value (NCV): Differences between net and gross calorific values (GCV) are typically about 5% to 6% of the gross value for solid and liquid fuels, and around 10% for natural gas. Based on the original BNEF GCV data, we estimate the NCV by applying a 10% increase for natural gas and 5.5% for other technologies. For more information, please refer to Appendix A, Section A.2. Definitions.
Overnight Costs: Capital costs in principle exclude interest payments during the construction phrase. For more information, please refer to Appendix A, Section A.2. Definitions.
Capacity factor: This factor measures how often a power plant operates during a given period. It is expressed as a percentage and calculated by dividing the actual power output of the unit by the maximum possible output. This ratio indicates the share of a unit’s capacity that is used.
Lifetime Assumptions: Lifetime information is provided for all types of technologies in CPAT except for biomass. A lifetime of 35 years for power plants specialized in biomass is assumed.

3.4.4.3 Data Update Schedule, Implementation, and Responsibilities

Overview: This section outlines the recommended update frequency for different data categories in the power models, along with the implementation process and the responsibilities of CPAT users for maintaining data accuracy and relevance. Since different processes are used for different data sets used in the power sector, a practical guide is provided to assist the user.

Table 3 - Update Schedule by Data Category
Data Section	Update Frequency	Responsibility	Rationale
Main Technoeconomic Characteristics	Every 2 years (Next Update: FY27)	Main CPAT Team	Technoeconomic parameters, especially for RE, evolve rapidly. Regular updates ensure CPAT reflects current costs, efficiencies, and operational parameters at the global and national levels.
Time Evolution of CapEx	Every 2 years (Next Update: FY27)	Main CPAT Team	CapEx, especially for clean technologies, can decline sharply within a few years. Regular updates are needed to capture cost learning trends and investment dynamics.
Decommissioning & Transmission costs	Every 2 years (Next Update: FY27)	Main CPAT Team	Decommissioning and transmission costs depend on regulation, plant age, and technology. These factors shift over time, requiring periodic updates to maintain accuracy in cost estimates.
Storage	Every 2 years (Next Update: FY27)	Main CPAT Team	Battery prices are highly dynamic, with frequent cost reductions driven by innovation and scale. Frequent updates are therefore essential to model storage competitiveness in the power sector.
Installed capacity	Every 2 years (Next Update: FY27)	Main CPAT Team	Capacity changes continually due to new projects and retirements. It forms the foundation of the power model and needs to be as accurate as possible.
Planned retirement	Every 2 years (Next Update: FY27)	Main CPAT Team	Coal retirement schedules reflect national policies or economics. These plans must be regularly updated to track the changes.
Maximum Scale Up Rate	Every 2 years (Next Update: FY27)	Main CPAT Team
WACC	Every 2 years (Next Update: FY27)	Main CPAT Team	Regular updates are needed to reflect significant changes in market conditions.

Responsibilities of Primary Model Users: - Monitor data relevance and accuracy - Ensure updates align with WBG standards - Document all data modifications and sources

3.4.4.3.1 Update Workflow

Assessment phase: Assess current data against update criteria.
Planning phase: Coordinate with relevant teams and identify data sources.
Implementation phase: Execute updates following technical procedures (detailed below).
Validation phase: Verify data integrity, take the pen and implement in the main CPAT model.
Documentation phase: Record changes and communicate updates to other CPAT users.

3.4.4.3.1.1 Implementation Procedures

Folder Structure and Organization: All elements required for updating power sector data are centrally located in the CPAT folder (currently in <CPAT\Mitigation module\Power Model Data Update>). Users should ensure they have access permissions and are working with the most current version of the folder structure.

Note: The current implementation procedure uses different processes for various data categories. While these procedures are scheduled for simplification in the future, the following methods are currently in use.

Data Update Methods: The implementation process is divided into Excel-based and Python-based workflows depending on the data type (see Table 4 below).

Table 4 - Data Update Methods Summary
Table	Update Process
Main Technoeconomic Characteristics (Global)	Excel-based
Time evolution of CapEx	Excel-based
Main Technoeconomic Characteristics (National)	Python scripts
Decommissioning and Transmission Costs	Excel-based
Storage	Excel-based
Installed capacity	Python scripts
Planned Retirement of Coal Power Plant	Excel-based
Maximum Scale-Up Rate	Excel-based
WACC	Excel-based

Excel-Based Process: To update Excel-Based data categories, follow these steps: - Locate the relevant sub-folders (see Figure 2). - Extract the required data manually from the relevant source(s). - Process the data if needed in the relevant Excel file. - Update the corresponding sections in the CPAT power data tab.

Figure 2 - Excel-Based Process Folder Structure

Python-Based Process: To update Python-Based data categories, follow these steps: - Download input files - Obtain necessary input files from designated sources. - Store files in directory: \Power Model Data\Python_Based_Process\3. Input Data (see Figure 3). - Rename files according to the specified naming structure to ensure script compatibility: - \BNEF_LCOE_data_viewer_2023.xlsb - \GNESTE_{technology}_Power.csv - \IRENA_{technology}_Power.csv - \IRENA_Capacity.csv - Execute Data Processing Scripts - Run the main processing script: \Power Model Data\Python_Based_Process\1. Scripts\run_all.py. - Monitor script execution for any error messages or warnings. - Verify that all input files are processed successfully. - Add into CPAT - Copy the updated data tab from the script output. - Perform verification checks to ensure data accuracy and formatting. - Cross-reference with source data to confirm successful processing. - Integrate into the main CPAT file.

Figure 3 - Python-Based Process Folder Structure

Integration into Main CPAT File: Both processes require manual implementation into the main CPAT file. Since the model is an Excel file shared with multiple users, this step allows the modeler to check all the updated data when implementing it. The data is compiled in a Power tab (see Figure 4).

Figure 4 - Power data tab in main CPAT file

3.4.4.4 Main Technoeconomic Characteristics

3.4.4.4.1 Global Technoeconomic Characteristics

To estimate power sector characteristics at the global level in 2024, the recommended cost characteristics data from various sources. The units are updated when needed and mapped to CPAT fuel.

Data Sources: - CCDR Energy Transition Analysis FY24 Methodology Note (or CCDR-EEX) – in green in Table 5 - Way et al., (2022) – in purple - GNESTE – in red - Modeler assumptions (for average time for construction)

Methodology: CapEx, OpEx (both fixed and variable), and lifetime data are taken from the CCDR-EEX methodology (see Table 21 in Appendix B, Section B.1. Global). Capacity Factor is updated from Way et al., 2022, and efficiency and construction time from GNESTE, when available.

Table 5 - CPAT Global Technoeconomic Characteristics
CPAT Technology	Capacity Factor	CapEx (USD/kW)	Efficiency (NCV)	Fixed OpEx (USD/kW/year)	Variable OpEx (USD/kWh)	Lifetime (year)	Construction (year)
Coa	0.54	2000	34%	60	0.003	30	5.25
Nga	0.57	900	52%	30	0.002	30
Oil	0.13	1345	38%	23.5	0.005	35
Nuc	0.93	4000	38%	150	0.004	50	7.4
Hyd	0.43	3300		50	0.001	50	4
Wnd	0.3	1300		40	0	30	2
Sol	0.18	800		15	0	25	1.5
Ore	0.75	3500	38%	100	0	30	4.5
Bio	0.69	2000	25%	100	0.003	30	4
Eys		794		31.4	0.001	30
Bat		300	85%	40	0	20	1
Bat-int		166		0	0	20

3.4.4.4.2 Time Evolution of CapEx

The engineer power model is based on CapEx forecasts, subject to a learning rate methodology for renewable energies. This methodology is essential for projecting future costs and planning investments in these technologies. The data source and methodology differ for historical and forecast data. The methodology used for historical data (2014 to 2023) is included in Appendix B, Section B.2. Time Evolution of Capex, as it is not updated here.

Data Source: - CCDR-EEX

Methodology: For wind and solar, we use the learning curve method to forecast global investment expenditure from 2023 to 2050. Other technologies, namely coal, oil, natural gas, and nuclear, are not subject to a learning rate or different scenarios and are assumed to be constant over time. We use capacity projection from the IEA National Policies in APS World (APS) and the IEA National Power Decarbonization 2050 in NZE World (NZE), used in the Country Climate and Development Reports Energy Transition Analysis (CCDR EEX) methodology. The APS scenario is used as the medium scenario and the NZE scenario is used as the high scenario, in line with the recommendation in the CCDR EEX Approach Note.

Table 6 - CapEx Trajectories
CPAT Technology	Solar	Wind
Scenario	Medium	High
2023	1.000	1.000
2025	0.909	0.894
2030	0.682	0.628
2035	0.628	0.580
2040	0.575	0.532
2045	0.522	0.484
2050	0.469	0.436

Table 7 - Yearly Change in Wind and Solar CapEx
CPAT Technology	Solar	Wind
Scenario	Medium	High
2025	-0.048	-0.056
2030	-0.062	-0.078
2035	-0.017	-0.015
2040	-0.019	-0.017
2045	-0.021	-0.020
2050	-0.021	-0.022

3.4.4.4.3 National Technoeconomic Characteristics

To estimate power sector technoeconomic characteristics, simple averages of the available data points are computed. The process includes averaging the values by data source. This step is important because data sources may provide different data at a given time for the same technology. Different data sources are used and prioritized depending on their availability.

Data Sources: - IRENA - GNESTE - BNEF

Methodology:To construct a dataset with 2021 as the CPAT as-of-date year, we accept data between 2021 and 2023, taking the latest available year. We convert the data where necessary to include in the final dataset (see Table 8):

Capital expenditure (CapEx) in USD/kW
Fixed operational expenditure (OpEx) in USD/kW/year
Variable OpEx in USD/kWh
Capacity, weighted average cost of capital (WACC), and efficiency in percentage
Lifetime in years

To maintain consistency with the rest of the model, the data is indexed to the currency of the base year (see Appendix A, Section A.3. Adjusting for inflation). This process is also used to fill in data gaps (see Table 9). The methodology then differs slightly for each dataset but ensures that the data is accurately processed and standardized for subsequent use (see the Section Update Workflow for a technical guide through the update process).

For clarity and easier reviewing of the data, we also express the processed data as a percentage of global values for CapEx and OpEx variables (see Table 10). To do so, we apply the following formula:
% of global = (value / (global value)) * 100

Table 8 – Main Technoeconomic Characteristics for Selected Countries
Country	Technology	Capacity Factor	CapEx (USD/kW)	Efficiency (NCV)	Fixed OpEx (USD/kW/year)	Variable OpEx (USD/kWh)	Lifetime (year)
USA	bat	0	1637	0.884	46	0.026	19
	bio	0.625	4605	0.401	34	0.002
	coa	0.45	2098		45	0.005	30
	hyd	0.65	6888	0.594	110	0.001	50
	nga	0.7	1064	0.348	13	0.002	20
	nuc	0.95	8397		129	0.003	40
	oil	0.134	729		56	0.012
	ore	0.9	7060		18	0
	sol	0.193	1000		13	0	30
	wnd	0.42	1353		29	0	21
China	bio	0.571	1126		36	0.004	20
	coa	0.6	596	0.38	15	0.003	25
	hyd	0.525	2130		20	0
	nga	0.35	573		16	0.003	25
	nuc	0.85	4615	0.348	85	0.006	50
	oil		1104	0.443	24	0.008
	sol	0.16	605		5	0	28
	wnd	0.28	889		19	0.002	25
India	coa	0.65	805	0.4431	13	0.002	30
	hyd	0.441	1687		20	0
	nga	0.4	676		28	0.001	25
	oil		885	0.422	28	0.009
	sol	0.19	641		5	0	30
	wnd	0.335	1089		10	0	25

Table 9 - Impact of Inflation Adjustment
Country	Technology	Parameter	Value before	Value after
China	Oil	CapEx	104	124
		OpEx Fixed	23	27
		OpEx Variable	0.007	0.009
France	Biomass	CapEx	1643	1931
		OpEx Fixed	224	263
		OpEx Variable	0.003	0.004
Brazil	Coal	CapEx	1483	1744
		OpEx Fixed	17	20
		OpEx Variable	0.003	0.004

Table 10 – Main Technoeconomic Characteristics for Selected Countries, Expressed as Percentage of Global Values for CapEx and OpEx
Country	Technology	CapEx (USD/kW)	Fixed OpEx (USD/kW/year)	Variable OpEx (USD/kWh)
USA	bat	546%	116%	0.026%
	bio	230%	34%	80%
	coa	105%	75%	167%
	hyd	209%	220%	200%
	nga	118%	42%	100%
	nuc	210%	86%	86%
	oil	54%	239%	232%
	ore	202%	18%	0%
	sol	125%	88%	0%
	wnd	104%	74%	0%
China	bio	56%	36%	160%
	coa	30%	25%	100%
	hyd	65%	39%	0%
	nga	64%	54%	150%
	nuc	115%	56%	171%
	oil	82%	103%	155%
	sol	76%	35%	0%
	wnd	68%	47%	0.002%
India	coa	40%	22%	67%
	hyd	51%	39%	0%
	nga	75%	92%	50%
	oil	66%	121%	174%
	sol	80%	32%	0%
	wnd	84%	25%	0%

3.4.4.5 Decommissioning, Transmission, and Storage

3.4.4.5.1 Decommissioning and Transmission

Decommissioning costs are one of the components of power generation costs. It takes place after a power plant has been taken out of service. It should be noted that retirement and decommissioning are two different things. Decommissioning indicates that the power plant is no longer producing electricity, but that assets such as buildings, turbines, boilers, or other equipment are left in place. The decommissioning process refers to the dismantling, environmental remediation, and restoration of the site. While much of the literature focuses on the cost of decommissioning for nuclear power plants, data on decommissioning costs for other types of technology is scarce. Thus, data from older sources sometimes remain the most reliable. Prices are therefore indexed to inflation (reference year: 2021), but more recent sources need to be found. For more information, please refer to Section 3.4.1. Power prices and generation costs in the online documentation.

NB: Transmission costs as a percentage of capital expenditure are not currently used in CPAT.

Data Sources: - Raimi (2017) provides estimates of decommissioning costs by technology type (offshore and onshore wind, coal, concentrated solar, solar photovoltaic, oil, and gas) based on a literature review. The data are expressed in 2016 US dollars and adjusted to inflation using a normalization factor for 2023. - The Nuclear Energy Agency (NEA) states that “the lack of cost data from actual decommissioning projects is a major hindrance to the benchmarking and validating of decommissioning cost estimates.” For the time being, the World Nuclear Association (WNA) estimates decommissioning costs at around 9 to 15% of initial CapEx. An approximation is used to take into account an average of 13% of CapEx. - Hydro Power & Dam construction estimates, based on information on dam destruction in the United States, that decommissioning costs can be 20-40% of new construction costs.

Methodology: In CPAT, decommissioning costs are expressed as a percentage of overall upfront costs. Decommissioning and transmission costs are based on estimates provided by several data sources. The average is calculated and then transformed to be expressed as a percentage of capital expenditure (see Table 11). For nuclear, estimates from two studies are averaged. The ratio of available data for decommissioning costs to overall CapEx (USD/MW) data by technology type is then used to express decommissioning costs as a percentage of CapEx. For hydroelectricity, based on the study mentioned below, decommissioning costs are assumed to be 20% of capital expenditure. For other renewables and bioenergy, the average decommissioning costs estimated for the other technologies are used as decommissioning costs for now.

Table 11 - Decommissioning Costs
CPAT Technology	Decommissioning Costs
Coal	5%
Natural gas	1%
Oil	2%
Nuclear	13%
Wind	3%
Solar	6%
Hydro	20%
Other RE	7%
Biomass	7%

3.4.4.5.2 Storage

Utility-scale battery storage systems differ slightly from other technologies as they store electricity produced by generators or pulled from the electric grid. These systems then redistribute the power based on the demands. It is worth noting that battery storage costs are commonly expressed in kWh, although one fraction of these costs – the power cost – is measured in kW. Several types of batteries exist, typically varying from 1h to 4h storage batteries. In CPAT, costs for battery correspond to 2h storage battery. For more information, please refer to Section 3.4.2.5. Storage decision in the online documentation.

Data Sources:

Bogdanov et al., 2019 (LUT model)

Methodology: For storage data, data directly extracted from the LUT model is used (see Table 12). Since the study provides data every five years (i.e., starting from 2015), estimates for the year 2021 are approximated using the following weighting approach: \[ \text{CAPEX}_{2021} = 0.8 \times \text{CAPEX}_{2020} + 0.2 \times \text{CAPEX}_{2025} \] - Battery: CapEx, variable, and fixed OpEx are in USD/kWh - Battery interface: CapEx and fixed OpEx are in USD/kW and variable OpEx in USD/kWh - Water Electrolysis: CapEx and fixed OpEx are in USD/kW and variable OpEx in USD/kWh - Lifetime in years

Table 12 - Battery Storage Costs
Technology	Variable	Unit	2020	2021	2025	2030
Battery	CapEx	USD/kWh,el	346	323	233	172
	OpExFix	USD/kWh,el	12	6	5	4
	OpExVar	USD/kWh,el	0	0	0	0
	Lifetime	Years	20	20	20	20
Battery Interface	CapEx	USD/kWh,el	173	162	117	86
	OpExFix	USD/kWh,el	0	0	0	0
	OpExVar	USD/kWh,el	0	0	0	0
	Lifetime	Years	20	20	20	20
Water Electrolysis	CapEx	USD/kWh,el	877	705	544	395
	OpExFix	USD/kWh,el	35	28	22	14
	OpExVar	USD/kWh,el	0	0	0	0
	Lifetime	Years	30	30	30	30

3.4.4.6 Capacity and Retirement

3.4.4.6.1 Installed Capacity

Capacity is used directly in the model. It is also used to derive the capacity factor and efficiency.

Data Sources: Installed capacity data comes from two sources: - The Environmental Investigation Agency (EIA): Used for data prior to 2019. The data must be supplemented by the breakdown of fossil fuels, as these are aggregated. The methodology is not covered here since it is not used anymore. - IRENA: Used for data after 2019.

Methodology: IRENA data on renewable energy capacity represents the maximum net capacity of power plants and systems using renewable energy sources. Data is collected from a variety of sources, including national statistics, industry reports, and questionnaires. The IRENA data processing script is designed to process and transform IRENA data on electricity installed capacity for integration into the CPAT model. The script classifies technologies and maps countries and regions from the database to the CPAT model. It extracts data from 2020 to 2023, already expressed in MW. This methodology ensures accurate regional mapping and categorization of power capacities.

Table 13 – Example of Installed Capacity Data (MW)
Country	Fuel Type	2019	2020	2021	2022	2023
CHN	coa	1,129,352	1,127,833	1,171,068	1,205,451	1,252,999
SCHN	nga	46,633	94,029	97,408	100,186	104,097

3.4.4.6.2 Planned Retirement of Coal Power Plant

Planned coal retirement plays a role in investment decisions within the model. For each future year, the model adjusts the available coal-fired generation capacity by subtracting the planned retirements derived from detailed coal plant monitoring data. This closure schedule is incorporated into the model to ensure that capacity shortfalls created by these closures are identified and can be filled by new investments in a timely manner. In the absence of plant-level closure data, a standard depreciation rule is applied. For more information, see Section 3.4.2.4.3 Retirement and capacity needed in online documentation.

Data Source: - Coal Power Plant tracker

Methodology: Based on the power plant data level, the retirement year of each power plant is determined from 2024 to 2050. Data is downloaded from the Coal Power Plant tracker, mapped to CPAT country/region, and implemented in the tab. See Table 14 for an example of coal retirement data.

NB: Power plants are removed if status = cancelled, shelved, mothballed.

Table 14 - Example of Coal Retirement Data (MW per year)
Year	Australia	China
2019	0	7872
2020	0	12318
2021	0	1663
2022	700	2938
2023	1534	4011
2024	0	1085
2025	200	2660
2026	0	0
2027	350	0
2028	2180	0
2029	3334	0
2030	0	600

3.4.4.6.3 Maximum Scale Up Rate

Maximum scale up rate is used to include a constraint on renewable energy scale up. It consists of simple assumptions (2% for all countries, except China and India set at 3%, as illustrated in Table 15). They can be defined in the dashboard and are included in CPAT defaults. For more information, please refer to renewable scale up rate in Section 3.4.2.4 ‘Power supply’ in online documentation.

Table 15 - Maximum Scale Up Rate Assumptions
Country	Max scale up rate assumptions
China	3%
India	3%
All other countries	2%

3.4.4.7 Finance

3.4.4.7.1 WACC Calculation

In CPAT, there are four ways to consider the weighted average cost of capital (WACC). It is by default income-dependent (see Table 11) but can also be technology-dependent (i.e., it can be specified for each technology). It can be specified for the baseline and policy scenario, and finally defined globally by the user, as shown in Figure 1. For more information, please refer to section 3.4.1.6. Concept 3: Cost-recovery estimated total cost of generation in online documentation.

Data Sources: - Damodaran (2025) - Steffen (2020)

Methodology: The cost of capital is a “forward-looking measure comprising the time value of money and a premium for risk (as well as potentially further factors, such as taxes and transaction costs). The cost of capital is equal to the discount rate as used in investment appraisals, such as net present value calculations.”

According to Steffen (2020), four dimensions are key in defining WACC: - LIBOR: Used to compare the cost of capital over time. - Country Factor: Affects the overall investment risk of a project. - Technology Factor: Investment risk differs between different technologies. - Time or Policy Factor: Investment risks can vary over time, and regulatory frameworks can affect investment risks.

LIBOR: Steffen (2020) uses the 12-month London Interbank Offered Rate (LIBOR) as a common benchmark interest rate, in different currencies, to compare the cost of capital over time.

Figure 5 - General Interest Rate Level Over Time,(Steffen, 2020, p.5)

Country Factor: Country risk premium determined by Damodaran (2023) is used. The author considers the degree of indebtedness, pension/social service commitments, revenues/inflows to government, the stability of revenues, political risk, and the implicit backing from other entities to compute a country risk premium dataset. He estimates an adjusted country risk premium by multiplying the default spread by the relative equity market volatility for that market (Std dev in country equity market/Std dev in country bond).

Technology Factor: Different technologies do not have the same risk, depending on their maturity, even among renewable technologies. For instance, solar PV has been deployed significantly since 2015, leading to a lower operational risk than wind, and therefore to a comparably lower WACC.

Policy Factor: The methodology includes an adjustment in the case of new power purchase agreements (PPAs), which leads to a reduction in the WACC of 4% (based on IEA 2021 methodology).

3.4.4.8 References

Andrade, J., & Baldick, R. (2017). The Full Cost of Electricity (FCe-). http://energy.utexas. Augustine, C., & Blair, N. (2021). Storage Futures Study: Storage Technology Modeling Input Data Report. https://www.nrel.gov/docs/fy21osti/78694.pdf
Bogdanov, D., Farfan, J., Sadovskaia, K., Aghahosseini, A., Child, M., Gulagi, A., Oyewo, A. S., de Souza Noel Simas Barbosa, L., & Breyer, C. (2019). Radical transformation pathway towards sustainable electricity via evolutionary steps. Nature Communications, 10(1), 1–16. https://doi.org/10.1038/s41467-019-08855-1
Cole, W., Frazier, A. W., & Augustine, C. (2021). Cost Projections for Utility-Scale Battery Storage: 2021 Update. <www.nrel.gov/publications>
EIA. 2021. “FORM EIA-860 INSTRUCTIONS ANNUAL ELECTRIC GENERATOR REPORT.” <www.eia.gov/cneaf/electricity/page/forms.html>
Eurostat, IEA, and OECD. 2004. “Energy Statistics Manual.” Energy Statistics Manual, 1–196. https://doi.org/10.2307/2987710
Feldman, D., Ramasamy, V., Fu, R., Ramdas, A., Desai, J., & Margolis, R. (2020). U.S. Solar Photovoltaic System and Energy Storage Cost Benchmark: Q1 2020. <www.nrel.gov/publications>
IEA&NEA. (2020). Projected Costs of Generating Electricity.
Ioannis Tsiropoulos, Dalius Tarvydas, & Andreas Zucker. (2018). Cost development of low carbon energy technologies - Scenario-based cost trajectories to 2050, 2017 edition. In JRC Science and Policy Reports. https://doi.org/10.2760/23266
IRENA. (2020). Renewable Power Generation Costs in 2020. In International Renewable Energy Agency. https://www.irena.org/-/media/Files/IRENA/Agency/Publication/2018/Jan/IRENA_2017_Power_Costs_2018.pdf
OECD&NEA. (2016). Costs of Decommissioning Nuclear Power Plants.
Raimi, D. (2017). Decommissioning US Power Plants Decisions, Costs, and Key Issues Decommissioning US Power Plants: Decisions, Costs, and Key Issues.
Rubin, E. S., Azevedo, I. M. L., Jaramillo, P., & Yeh, S. (2015). A review of learning rates for electricity supply technologies. In Energy Policy (Vol. 86, pp. 198–218). Elsevier Ltd. https://doi.org/10.1016/j.enpol.2015.06.011
Steffen, B. (2020). Estimating the cost of capital for renewable energy projects. Energy Economics, 88. https://doi.org/10.1016/j.eneco.2020.104783
Way, R., Ives, M., Mealy, P., & Farmer, J. D. (2021). Empirically grounded technology forecasts and the energy transition.

3.5 Emissions

This section describes how GHG emissions estimation and emissions are accounted for in CPAT and how they are projected in each sector.

3.5.1 Overview

In CPAT, emissions are projected in two ways: i) energy-related emissions are based on a model, that is estimations of energy consumption (see Section 3.3) in the different sectors are converted into GHG emissions by the means of an emission factor; and ii) non-energy related emissions are forecasted based on particular assumptions. The table below summarizes the approach taken to forecast emissions forward.

Emission type	Assumptions to forecast emissions
Energy-related sectors
and	Corresponding emissions are calculated by multiplying energy consumption by emissions factors. Total energy-related emissions are augmented by energy distribution losses and methane energy-related emissions. Emissions are scaled to UNFCCC inventory emissions, meaning they are multiplied by a factor such that base-year emissions are equal in the model and the inventory. This allows the model to start from observed value for emissions.
	emissions are scaled to emissions
F-gases	These emissions are historically equal to zero and are thus assumed to be equal to zero.
Non-energy related sectors
Industrial emissions		The growth rate is based on changes in energy-related industrial emissions.
Agricultural emissions	Non-energy agriculture emissions are forecasted based on the GDP and population growths (and a proxy for additional mitigation efforts – if selected by the user).
LULUCF	, , and F-gases	Forecasted non-energy emissions for LULUCF are driven by a sink activity growth and the ratio of the growth in emissions for the carbon tax scenario to the increase in emissions for the baseline scenario. Net sources and net sinks are treated differently (see below)
Waste and other	For waste and other emissions, forecasted estimates are determined by population growth.

Emissions have two dimensions:

Pollutants: Carbon dioxide ($CO_{2}$), Methane ($CH_{4}$), Nitrous oxide ($N_{2}O$) and Fluorinated gases (F-gases). GHG emissions include those in the UNFCCC inventories ($CO_{2}$, $CH_{4}$, $N_{2}O$ and Fluorinated Gases (or F-gases), including PFCs, HFCs SF_6, and NF₃). Note that the mitigation also presents short-lived air pollutants (PM_2.5, NOx, SO₂, CO₂, NMVOC, BC, OC, CH₄ and CO); the methodology for these is covered in the air pollution module documentation.
Sectors: Energy-related sectors (i.e., Transport, Power, Industry, Building, and Other energy use), as well as non-energy-related sectors (i.e., Agriculture, Industrial Process, LULUCF, Waste and Other). It is important to note that some parts of the sectors accounted for in the non-energy sectors are also reflected in energy-related sectors. For instance, Agriculture also appears under the ‘Building’ sector, under ‘Food and Forestry’ sub-sector (for more information, see Appendix B).

CPAT considers territorial rather than consumption-based emissions. This means that, for example, if some natural gas is imported but subject to leaks upstream in extraction before it arrives at the country concerned, these methane emissions are not counted in the emissions of a natural gas power station. However, an extracting country will include those leaks. Similarly, the emissions from imported goods are not included, whereas those associated with exported goods are included.

In what follows, we first define the role of emission factors and their sources. Second, we present the approach adopted for energy-related $_{}$ and non- $_{}$ by fuel and sector. Third, we describe the estimation of emissions in non-energy sectors. We use the index $p$ to refer to the type of GHG ($CO_{2}$, $CH_{4}$, $N_{2}O$ and F-gases). The variable $em_{\text{ocupt}}$ denotes the estimation of emissions under scenario $o$, country $c$, UNFCC sector $u$ , and for pollutant $p$ and at year $t$. Total GHG emissions are the sum of both energy and non-energy related emissions: $em_{\text{oc},\text{GHG},t} = em_{\text{ocER},\text{GHG},t} + em_{\text{ocNER},\text{GHG},t}$. Finally, the section explains how NDCs are accounted for in CPAT.

3.5.2 Notation

Notation	Variable	Unit
$\text{em}$	Emissions	$\text{tC}O_{2}$/GJ
$\text{Δe}m_{\text{LUCF},t}$	LULUCF emissions decline	% per annual in absolute value of start year
$\text{ef}$	Emission factors	$\text{tC}O_{2}$/ktoe
$F$	Use of fuel	ktoe
$\text{fug}$	Methane fugitive and venting emissions	$\text{tC}O_{2}$/ktoe
$\text{gwp}$	Global warming potential from methane emissions	$\text{tC}O_{2}$/ktoe
$Y_{\text{grow}}$	GDP growth	%
$lp_{\text{grow}}$	Population growth	%
$\text{ame}$	Additional (e.g. non-pricing) mitigation effort	%
$\epsilon_{Y}$	Forward-looking real GDP-elasticity of fuel demand	%
$\epsilon_{\text{lp}}$	Population elasticity	%

3.5.3 Emission factors

An emission factor is a coefficient that converts activity data into GHG emissions. It represents the average emission rate for a given fuel relative to consumption units. For instance, in the power sector, coal emits 3.931 ton of $_{}$ per ktoe.

The emission factors used are (as a default) fuel-, country- and sector-specific emissions from IIASA’s GAINS model²⁶. The user also has the option to use global emissions factors from the IEA.²⁷ The emission factors given by the IEA are scaled at a worldwide level, while those from IIASA are country specific. Also, IIASA emission factors include process and fugitive emissions in the distribution network from natural gas (which is why it is necessary to rescale them through the overall calibration to 2019 emissions). All emission factors are sector and fuel specific.

The user has the possibility in the dashboard to select the source of emission factors to be used. Global IEA emissions factors are also an option.

Figure 63: Selection of the source of emission factors

Figure 3‑28: Selection of the source of emission factors

The emissions are given originally in $\frac{\text{tC}O_{2}}{\text{GJ}}$, then converted in $\frac{\text{tC}O_{2}}{\text{ktoe}}$ via a $\text{ktoe}$ to $\text{GJ}$ conversion factor of $41,868$.

$ef_{\text{cgf},\frac{\text{tC}O_{2}}{\text{ktoe}}} = ef_{\text{cgf},\frac{\text{tC}O_{2}}{\text{GJ}}}*41,868$

Furthermore, it is worth noting that we do not have data for emission factors for sector-fuel types when the energy consumption is close to zero. Therefore, the following rules are applied to define emission factors when missing:

Sector-Fuel types	Assumptions
Power sector-LPG	Equal to emission factors in the industrial sector
Road-LPG	Equal to emission factors in the building sector
Power sector-Kerosene and Road-Kerosene	Equal to emission factors in the building sector
Road-Coal	Equal to emission factors in the power sector
Road-Other oil products	Equal to emission factors for diesel
All sectors-Biomass	Emission factors are equal to zero

3.5.4 Energy-related emissions

Energy-related emissions are estimated across sectors and by aggregating sectors (i.e., Transport, Power, Industry, Building, and Other energy uses) for the four GHGs (i.e. $\text{CO}_{2}$, $CH_{4}$, $N_{2}O$ and F-gases). In this section, the index $u = E$, denotes the energy-related sectors.

3.5.4.1 Carbon dioxide ($CO_{2}$) and methane ($CH_{4}$)

Energy-related $CO_{2}$ and $CH_{4}$ emissions are calculated by multiplying energy consumption by emissions factors. Emissions are multiplied by $10^{- 6}$ as the emission factor $\text{ef}$ is given in tCO2e/ktoe and the fossil fuel consumption $F$ is given in ktoe, to obtain emissions in mtCO2e. We neglect this unit transformation in the description below.

In 2019, these emissions (both $CO_{2}$ and $CH_{4}$ energy-related emissions) are scaled to UNFCCC inventory emissions, meaning they are multiplied by a factor such that base-year emissions are equal in the model and the inventory. In other words, the model is adjusting $_{}$ and $_{}$ emissions to match the model and inventory. This scaling factor is close to 1 for $CO_{2}$, but are typically greater than one for $CH_{4}$. This scaling applies only to the aggregate emissions and not to the price effect. It only applies to the core modelled emissions of energy related $CO_{2}$, and $CH_{4}$ and not to any other gas or any other UNFCCC sector.

After 2019, these emissions are thus calculated, for each fuel $f$ and for a year $t$, as the multiplication of the fossil fuel’s consumption for year $t$ by the sector’s associated to emission factor:

$em_{\text{ocEsfpt}} = F_{\text{ocEsft}}*ef_{\text{cEsfp}}$

where $o$ represents scenario, $s$, sector, $f$, fuel type, $p$, GHG (e.g., $CO_{2}$) and $t$ the year.

$CO_{2}$ and $CH_{4}$ emissions are determined across all fuels and across all sectors (and grouping sectors). Total energy emissions are determined as the sum across sectors and fuels (for energy related emissions u=E)

$em_{\text{ocpt}} = \sum_{s}^{}{\sum_{f}^{}e}m_{\text{ocsfpt}}$

Furthermore, total energy-related $_{}$ and $_{}$ emissions are augmented by energy distribution losses and methane energy-related emissions are subject to a calibration. In particular:

Total energy-related $\mathbf{C}\mathbf{O}_{\mathbf{2}}$ emissions include energy distribution losses, that is the sum of combustion emissions and the fugitive and venting $CO_{2}$ emissions. The latter are mostly from natural gas pipes plus coal mines. These are a part of energy-related $CO_{2}$ emissions but they are not combustion.

Total energy-related $\mathbf{C}\mathbf{H}_{\mathbf{4}}$ emissions are calibrated to 2019 shares. The factor is the 2019 ratio of methane emissions to the sum of the total global warming potential²⁸ from methane emissions $\text{gwp}$ and the methane fugitive and venting emissions $\text{fug}$. Then, projections are made by multiplying this factor with the sum of the $\text{gwp}$ and the $\text{fug}$ for the current year $t$. For $t \geq 2019$:

$em_{ocE,CH_{4},t} = \frac{em_{ocE,CH_{4},2019}}{\text{gw}p_{ocE,CH_{4},2019} + \text{fu}g_{ocE,CH_{4},2019}}*\left( \text{gw}p_{ocE,CH_{4},t} + \text{fu}g_{ocE,CH_{4},t} \right)$

CPAT also covers the other parts of the UNFCCC inventories (i.e. GHGs other than $CO_{2}$ and methane, and other categories than energy-related GHGs). For these emissions, the UNFCCC inventories are scaled by various growth rates, detailed in the next section.

3.5.4.2 Nitrous oxide ($N_{2}O$) and Flourinated gases (F-gases)

$N_{2}O$ and F-gases energy-related emissions estimates follow the below rules:

Total energy-related $\mathbf{N}_{\mathbf{2}}\mathbf{O}$ emissions are scaled to $CO_{2}$ emissions. For $t > 2019$:

$em_{oc,N_{2}O,t} = em_{oc,N_{2}O,\left( t - 1 \right)}*\frac{em_{\text{oc},CO_{2},t}}{em_{\text{oc},CO_{2},\left( t - 1 \right)}}$

Total energy-related F-gases emissions ($p = \text{PF}C_{s}$, $\text{HF}C_{s}$, $SF6$, $NF3$) are historically zero for the energy category. For $t > 2018$: $em_{\text{ocpt}} = 0$.

3.5.5 Non-energy related emissions

Non-energy-related emissions are estimated across non-energy-related sectors (i.e. Agriculture, Industrial Process, LULUCF, Waste, and Other) for the four GHGs (i.e. $\text{CO}_{2}$, $CH_{4}$, $N_{2}O$ and F-gases). Non-energy-related emissions in the different sectors considered above are determined based on various sector-specific assumptions. In particular:

In the industrial processes and product use sector, the growth rate is based on changes in energy-related industrial $CO_{2}$ emissions.
Non-energy agriculture emissions are forecasted based on the GDP and population growths.
Forecasted non-energy emissions for LULUCF are driven by a sink activity growth and the ratio of the growth in emissions for the carbon tax scenario to the increase in emissions for the baseline scenario. Net sources and net sinks are treated differently (see below)
For waste and other emissions, forecasted estimates are determined by population growth.

3.5.5.1 Industrial processes and product use

In the industrial processes and product use sector, the growth rate is based on changes in energy-related industrial $CO_{2}$ emissions.

In what follows, the index $u = I$, standing for Industrial Processes and Product Use.

Non-energy-related industrial $CO_{2}$ emissions are forecasted based on an industrial $CO_{2}$ emissions rate ($\text{Δe}m_{ocP,CO_{2},t + 1}$). Therefore:

$m_{ocI,CO_{2},t + 1} = \left{

\[\begin{matrix} \max\left( 0;\frac{em_{\text{ocEind},CO_{2},t + 1}}{em_{\text{ocEind},CO_{2},t}} - 1 \right) & \text{for\ }t = 2019 \\ \frac{em_{\text{ocEind},CO_{2},t + 1}}{em_{\text{ocEind},CO_{2},t}} - 1 & \text{for\ }t > 2019 \\ \end{matrix}\]

The index $\text{Eind}$ stands for the energy-related emissions in the industrial sector.

Importantly, it is assumed that other pollutants $p$ are scaled on the same industrial $CO_{2}$ emissions rate. In other words, emissions of each pollutant for a year $t$ is the sum of emissions from the previous year $t - 1$ adjusted by the change in industrial $CO_{2}$ emissions $\text{Δem}$.

For $t > 2019$: $em_{\text{ocIpt}} = em_{\text{ocIp}\left( t - 1 \right)}*\left( 1 + \text{Δe}m_{\text{ocI},CO_{2},t} \right)$

3.5.5.2 Agriculture

Non-energy agriculture emissions are forecasted based on the GDP and population growths (and a proxy for additional mitigation efforts – if selected by the user).

For this section, $u = A$.

Agricultural emissions are projected using a similar approach to the rest of CPAT: a reduced-form approach with elasticities, notably per capita income $\epsilon_{Y}$ (GDP growth: $Y_{\text{grow}}$) and population $\epsilon_{\text{lp}}$ specific to each UNFCCC emissions sector (population growth: $lp_{\text{grow}}$).

In addition, the user has the option to assume that non-$CO_{2}$ GHGs scale with fossil $CO_{2}$, which is a proxy for additional (e.g., non-pricing) mitigation effort $(ame$) in the UNFCCC categories. This option, in effect, turns a carbon price into an all-sector (incl non-energy sectors) GHG tax (incl. methane, N20 etc).

For each pollutant and for $t > 2019$:

$em_{\text{ocApt}} = \frac{em_{\text{ocAp},t - 1}}{\text{am}e_{A,t - 1}}(1 + Y_{\text{growth}})^{\epsilon_{Y}}*\left( 1 + lp_{\text{grow}} \right)^{\epsilon_{\text{lp}}}*\text{am}e_{\text{At}}$

3.5.5.3 Land use, land-use change and forestry

LULUCF GHG are assumed to be flat in the baseline and policy scenario for net sink countries (where sinks of GHGs exceed sources). For countries where LULUCF is a source, we assume an exogenous decline of 2.5% per annum in both the baseline and policy scenario. The user should note that this rate can be adjusted in the dashboard.

Figure 3‑29: LULUCF emissions decline rate

At the global level, this aligns with approximately the midpoint of IAMs’ projection for LULUCF. Where the country assumes ‘additional mitigation effort in non-energy sectors’ LULUCF GHGs decline at the rate of energy $_{}$.

For this section, $u = L$.

It is considered that a defined amount of emissions can be subtracted yearly, based on the 2019 level. Therefore, we introduce the LULUCF emissions decline $\text{Δe}m_{L,t}$ (in annual %, in absolute value of the start year).

For $p = CO_{2}$:

In the case of $CO_{2}$, we create a condition to model the sink activity of LULUCF ($em_{\text{ocLpt}} < 0$ or $> 0$). In both cases, we subtract an annual capture of $CO_{2}$ based on the LULUCF emissions decline $\text{Δe}m_{\text{Lt}}$. If the emissions of the previous year $t - 1$ are positive, we scale the emissions with the ratio $\frac{a\text{me}_{cLp,t}}{\text{ame}_{\text{cLp},t - 1}}$ with $a\text{me}_{cLp,t} = \ \frac{em_{P,cLt}}{em_{B,cLt}}$, which represents the ratio between energy-related emissions under a policy and baseline scenario.

For $t > 2019$:

$em_{} = \left{

\[\begin{matrix} em_{ocLp,t - 1} - \left| em_{\text{ocLp},2019}*\text{Δe}m_{L,t} \right| & \text{if\ }em_{ocLp,t - 1} < 0 \\ \frac{em_{ocLp,t - 1}}{a\text{me}_{\text{cLp},t - 1}}*\text{am}e_{\text{cLpt}} - \left| em_{\text{ocL},2019}*\text{Δe}m_{L,t} \right| & \text{if\ }em_{ocLp,t - 1} \geq 0 \\ \end{matrix}\]

For $p = CH_{4}$:

The same logic as for $CO_{2}$ is used, without considering the condition for sinks.

For $t > 2019$:

$em_{\text{ocLpt}} = \frac{em_{\text{ocLp}\left( t - 1 \right)}}{\text{am}e_{B,L,t - 1}}*\text{am}e_{P,Lt} - \left| em_{\text{ocLp},2019}*\text{Δe}m_{L,t} \right|$

For $p = N_{2}O$:

In the case of $N_{2}O$, we assume the level of emissions to grow accordingly to the population growth $lp_{\text{grow}}$.

For $t > 2019$:

$em_{\text{ocLpt}} = \frac{em_{ocLp,t - 1}}{\text{am}e_{B,L,t - 1}}*\text{am}e_{P,Lt}*\left( 1 + lp_{\text{grow}} \right) - \left| em_{\text{ocLp},2019}*\text{Δe}m_{L,t} \right|$

For F-gases ($p = \text{PF}C_{s}$, $\text{HF}C_{s}$, $SF6$, $NF3$):

In the case of F-gases, we assume the level of emissions to grow accordingly to the population growth $lp_{\text{grow}}$. However, it is the only case where we do not consider the LULUCF emissions decline.

For $t > 2019$:

$em_{\text{ocLpt}} = \frac{em_{\text{ocLp},t - 1}}{\text{am}e_{B,Lp,t - 1}}*\text{am}e_{P,Lt}*\left( 1 + lp_{\text{grow}} \right)$

3.5.5.3.1 Waste and Others

For waste and other emissions, forecasted estimates are determined by population growth.

For this section, we consider that $u = W$ and $O$, denoting respectively Waste and Others type of emissions.

Waste emissions are projected using a similar approach to Agricultural emissions: a reduced-form approach with population growth elasticity $\epsilon_{\text{lp}}$ (population growth: $lp_{\text{grow}}$). We include again the additional (e.g. non-pricing) mitigation effort $\text{ame}$.

For each pollutant and for $t > 2019$:

$em_{\text{ocupt}} = \frac{em_{\text{ocup},t - 1}}{\text{am}e_{B,u,t - 1}}*\text{am}e_{P,ut}*\left( 1 + lp_{\text{grow},t} \right)^{\epsilon_{\text{lp}}}$

3.5.6 National Determined Contributions

CPAT harmonizes National Determined Contributions (NDCs) for 192 countries to show target GHG emissions levels (excluding LULUCF) in 2030, based on several major NDC characteristics, that is conditionality and sectoral coverage. This section presents the different types of NDCs. Country cases illustrating how NDCs are calculated in CPAT are presented in Appendix D - Examples of NDCs calculations.

3.5.6.1 Types of NDCs

There are different types of NDCs:

Business as usual (BAU) targets: NDC target is a percent reduction from the country’s BAU scenario. For example, Albania’s NDC is 11.5% reduction in CO2 emissions compared to the baseline scenario in 2030.
Fixed targets: NDC target is a fixed level of GHG/CO2 emissions in target (future) year. For example, Argentina’s NDC is a cap of 359 MtCO2e net emissions in 2030.
Historical targets: NDC target is a percent or fixed reduction from the level of emissions in past years. For example, Australia’s NDC is 26 to 28% reduction below 2005 levels by 2030.
Intensity targets: NDC target is a reduction in emissions intensity. For example, Uruguay’s NDC is emissions intensity reduction (GHG/GDP) of 24% in CO2 from 1990 levels.
Unquantifiable targets: NDCs with no specific emissions reduction commitments. For example, Saudi Arabia’s NDC: “The Kingdom will engage in actions and plans in pursuit of economic diversification that have co-benefits in the form of greenhouse gas (GHG) emission avoidances and adaptation to the impacts of climate change, as well as reducing the impacts of response measures.”

NDCs could also present conditional and unconditional targets:

Unconditional targets: Countries would use their own resources and technologies to achieve unconditional goals.
Conditional targets: Countries would need international support to achieve these (more ambitious) goals.

3.5.6.2 Harmonization of NDCs: Country cases

CPAT excludes LULUCF emissions from NDC calculations, so in case LULUCF emissions were included in initial document, the goals are recalculated with LULUCF, using the latest available data for LULUCF GHG emissions and user-identified growth parameters for these emissions. If not stated, we assume that the NDC target includes LULUCF.

By default, CPAT models the impact of carbon pricing on energy-related emissions. Hence, for countries with high levels of emissions from non-energy related sources (agriculture, waste, LULUCF), the calculations would imply a high burden on energy sector to achieve NDC goals. For more information, see Appendix D - Examples of NDCs calculations, which presents examples of NDCs calculations.

3.6 Fiscal revenues

The fiscal revenues section in the mitigation tab of CPAT is organized as follows:

Additional information, including total fuel expenditure broken down per fuel and sector grouping and revenues/losses from price controls broken down per fuel. These data are not used in the calculation of fiscal revenues.
Policy coverage showing the percentage coverage of CO2 emissions under the policy selected and for each sector group and fuel.
The different components of the fiscal revenues detailed in the subsequent section.

3.6.1 Overview

Revenues from mitigation policies are estimated by comparing any revenues from the policy and fuel taxes, net of any outlays from fuel subsidies, in the baseline scenario with those in the policy scenario. Fiscal revenues in CPAT are calculated for several types of taxes, by fuel and sector. Revenue-raising policies include carbon taxes, ETSs with auctioned allowances, increases in fuel/electricity excises, and reductions in fossil fuel subsidies. Revenue-reducing policies include expenditures (e.g., on renewable subsidies) and regulations (which reduce the base of pre-existing fuel taxes).

CPAT differentiates two types of revenues:

Carbon tax revenues, which are the result of the carbon tax multiplied by emissions factor and energy use.
Full revenues, which include other taxes, VAT changes, excise duties, existing ETS schemes, etc. The changing revenues according to a carbon tax are not just simple revenues but also any changes associated with full revenues. For instance, there could be changes in subsidies due to changes in energy consumed.

A general formula for fiscal revenues calculations is:

$\text{re}v_{\text{ocfgt}} = F_{\text{ocfgt}}*\varphi_{\text{cgft}}*\text{nc}p_{\text{ocfgt}}$

where $\text{re}v_{\text{cfgt}}$ is the fiscal revenues from fuel $f$ in sector $g$, $F_{\text{cfgt}}$ is the energy consumption, $\varphi_{\text{cgft}}$ is the sector-fuel coverage and $\text{nc}p_{\text{cfgt}}$ denotes the tax (policy) rate per unit of energy consumption.

In the dashboard, the graph below shows total additional (vs. baseline) fiscal revenues from the policy net of renewable energy subsidies. Note that this includes base effects on existing taxes and subsidies, so even a revenue-neutral policy that nevertheless changes the base of existing taxes will have some effects on these, net, revenues.

Figure 64: Dashboard: Fiscal revenues raised by fuel and total as % of GDP

Figure 3‑30: Dashboard: Fiscal revenues raised by fuel and total as % of GDP

The user can also see total revenues (i.e. not against the baseline scenario) according to the different fuels net of subsidies.

Figure 65: Dashboard: Total revenues by fuel source net of subsidies

Figure 3‑31: Dashboard: Total revenues by fuel source net of subsidies

The remaining of the section presents the calculations of revenues and its breakdown in more details.

3.6.2 Notation

Notation	Variable	Unit
$\text{rev}$	Fiscal revenues	Real 2021 US$bn
$F $	Energy consumption	ktoe
$\varphi$	Sector-fuel coverage	%
$\text{ncp}$	New Carbon Price	US$/ton of CO2
$\text{revExi}$	Revenues from existing excises and other taxes	Real 2021 US$bn
$\text{cs}$	Consumer-side subsidy	US$/Gj
$\text{fao}$	Fixed/ad val part/other	US$/Gj
$\text{xct}$	Current carbon tax	US$/Gj
$\text{xetsp}$	Current ETS permit price	US$/Gj
$\text{revVAT}$	Revenues from VAT	Real 2021 US$bn
$\text{vat}$	Value added tax	US$/Gj
$\text{cstPs}$	Losses from producer-side subsidies	Real 2021 US$bn
$\text{subDem}$	Subsidized demand	Billion liters for oil, GJ for coal and natural gas and GWh for electricity
$\text{pusF}$	Per-unit fossil fuels subsidies	US$/liters for oil, US$/GJ for coal and natural gas and US$/GWh for electricity
$\text{cstRen}$	Cost of renewable subsidies	Real 2021 US$bn
$\text{pusRen}$	Per-unit renewable subsidies	US$/kwh

3.6.3 Total revenues raised by policy

Fiscal revenues are calculated according to the selected power model (Elasticity, Engineer or Average) and are expressed in billions of dollars (in real terms based on the year 2021) and % of GDP. Please note that revenues can be broken down per fuel. Total revenues are composed of:

Revenues from the baseline scenario raised for each fuel and sector coverage. The estimation of these revenues follows the general formula for fiscal revenues presented above (i.e. the carbon tax multiplied by emissions factor and energy use).
Revenues from existing excises and other taxes, including consumer-side subsidies. This describes all existing taxes and consumer side subsidies. Excise and other taxes are composed of:
- Consumer-side subsidy: $cs_{\text{ft}}$;
- Fixed/ad val part/other: $\text{fa}o_{\text{ft}}$;
- Current carbon tax: $\text{xc}t_{\text{ft}}$; and
- Current ETS permit price: $\text{xets}p_{\text{ft}}$.

For each fuel, we multiply the fuel consumption (minus the other energy use part, which is assumed not to be covered by excises) by the sum of all the current excises. If the existing ETS is EU ETS, then the excise and other taxes from current ETS permit price are not taken into account. It is worths noting that for coal and natural gas, the formula below is used across sectors as these fuels are broken down per data on excise taxes in the sector groupings (i.e. industry, buildings and power sectors).

Revenues from existing excises and other taxes, $\text{revEx}i_{\text{ft}}$, are thus estimated as follows:

$i_{} = \left{

\[\begin{matrix} \left( F_{\text{ocft}} - F_{\text{oc},\text{oen},\text{ft}} \right)*\left( cs_{\text{cft}} + \text{fa}o_{\text{cft}} + \text{xc}t_{\text{cft}} \right) & \text{if\ }\text{ExistingETS} = \text{EUETS} \\ \left( F_{\text{ocft}} - F_{\text{oc},\text{oen},\text{ft}} \right)*\left( cs_{\text{cft}} + \text{fa}o_{\text{cft}} + \text{xc}t_{\text{cft}} + \text{xets}p_{\text{cft}} \right) & \text{if\ }\text{ExistingETS} \neq \text{EUETS} \\ \end{matrix}\]

where $F_{\text{ft}}$ denotes energy consumption and $F_{\text{oen},\text{ft}}$ energy consumption in the Other Energy Use sector grouping.

For electricity, revenues from additional excise tax are also estimated based on the power prices determined in the engineer power model. The additional excise tax is multiplied by the energy use and the consumer-side tax/subsidy in the residential sector and the tax/subsidy on industrial users in the non-residential sector.

Revenues from additional excise tax (if it exists – additional excise tax can be inputted in the Manual Inputs tab.) raised for each fuel and sector, calculating as the additional excise tax multiplied by the energy use. For electricity, however, it is worth noting that revenues from additional excise tax relies on the engineer power model estimations.
Revenues from VAT. Following the same logic as for existing excises and other taxes and additional excise taxes, revenues from VAT are calculated across sector grouping as the multiplication of the fuel consumption (minus the other energy use part $F_{\text{oen},f,t}$, which is assumed not to be covered by the VAT) by the associated VAT payment rate $\text{va}t_{\text{cft}}$:

$\text{revVA}T_{\text{ft}} = \left( F_{\text{ocft}} - F_{\text{oc},\text{oen},\text{ft}} \right)*\text{va}t_{\text{cft}}$

For electricity, revenues from VAT are obtained by multiplying the energy use by the VAT payment in the residential non-residential sectors.

Losses from producer-side subsidies. Producer-side subsidies represent a loss and are thus subtracted from total fiscal revenues. They do not affect the calculation of prices in CPAT and thus revenues unless they are phased out, if they exist. Note that implicitly the underlined that we are using has already been adjusted for producer-side subsidies, in particular in the case of coal. Producer-side subsidies, $\text{cstP}s_{\text{ocft}}$, are defined as the product between the per-unit subsidies²⁹, $\text{pus}F_{\text{ocft}}$, and the subsidized demand, $\text{subDe}m_{\text{ocft}}$:

$\text{cstP}s_{\text{ocft}} = \text{subDe}m_{\text{ocft}}*\text{pus}F_{\text{ocft}}$

where:

Subsidized demand is determined based on both global demand data from the IEA and domestic demand data directly estimated in CPAT. The estimation of subsidized demand differs depending on the fuel considered. For oil, subsidized demand is equal to global demand as it is a global traded product. Subsidized demand for coal and natural gas represent 50% of global demand and 50% of domestic demand. Finally for electricity, only domestic demand is used and depends on the power model selected. Subsidized demand can also vary according to the global energy demand scenario selected in the dashboard.

Figure 66: Dashboard: Global energy demand scenario

Figure 3‑32: Dashboard: Global energy demand scenario

Per unit subsidies are taken from the Prices section of CPAT. For coal, gasoline and natural gas, per unit subsidies correspond to the average across all sectors. Importantly, per unit subsidies are equal across sector grouping. For electricity, producer-side subsidies are retrieved from the non-residential sector (i.e. denoted as industrial sector) of the Power Prices section of CPAT, determined in the engineer power model.

Cost of renewable subsidies (if applicable – renewable subsidies are defined by the user in the dashboard). If specified by the user, $\text{cstRe}n_{\text{ocft}}$ represents the cost of implementing renewable electricity subsidy (or tax). In addition, the user can also add renewable subsidies under the baseline scenario. This cost is thus equal to the product between $\text{pusRe}n_{\text{ocft}}$, the cost of renewable subsidies in $/kWh (in real terms) and, $g_{\text{ocft}}$, the electricity supplied in the power sector according to the power model chosen.

$\text{cstRe}n_{\text{ocft}} = \text{pusRe}n_{\text{ocft}}*g_{\text{ocft}}$

These costs are estimated for each renewable energy, that is wind, solar, hydropower and other renewables.

3.6.4 Additional information

Revenue or losses from price controls and total fuel expenditures can also be found in the Fiscal Revenues section of CPAT. These estimations are not used in the calculation of the total fiscal revenues.

3.6.4.1 Revenues/losses from price controls

Revenues/losses from price controls, $\text{ct}r_{\text{ocft}}$, are calculated by multiplying fuel consumption across sectors (minus the other energy use part, on which price control does not apply) by the difference in fuel’s international prices from the current year to the previous one, $\text{pIn}t_{\text{ocft}} - \text{pIn}t_{\text{ocf},t - 1}$, and by the portion of global energy price changes not passed-through into domestic prices, $\text{pt}h_{\text{ocft}} - 1$.

$\text{ct}r_{\text{ocft}} = \left( F_{\text{ocft}} - F_{\text{oc},\text{oen},\text{ft}} \right)*\left( \text{pt}h_{\text{ocft}} - 1 \right)*\left( \text{pIn}t_{\text{ocft}} - \text{pIn}t_{\text{ocf},t - 1} \right)$

3.6.4.2 Total fuel expenditures

Total fuel expenditures are not part of the fiscal revenues, but show the expenditures on fuel from a whole country perspective, as this is often relevant in developing countries wishing to minimize their import bill. Fuel expenditures are estimated for each fuel considered in CPAT and are expressed as the product between prices and energy consumption across all sectors.

3.7 Monetized social costs and benefits

In this section, the theoretical framework is first presented in order to explain the approach used to assess efficiency costs and domestic environmental co-benefits. Then, this section describes how energy externalities costs are estimated. Finally, these costs are used to calculate monetized welfare benefits.

3.7.1 Overview

Figure 3‑33 provides a representation of the fossil fuel market, where supply and demand interact. Importantly, it is assumed that the energy demand responds to prices in the private sector, although the institutional setup could, in some markets, play a role in preventing prices from determining supply and demand.

Figure 67: Efficiency costs and co-benefits in the presence of prior-tax and carbon charge

Figure 3‑33: Efficiency costs and co-benefits in the presence of prior-tax and carbon charge

At any point, the height of the demand curve reflects the benefit to consumers from an extra unit of consumption, while the height of the supply curve (drawn as flat here because constant returns to scale is assumed) reflects the cost to firms of producing an extra unit. If there is no pre-existing tax or subsidy in the market, the consumer and producer price are equal, and the market equilibrium is efficient (leaving aside environmental impacts) because the benefit to consumers from the last unit consumed equals the cost to firms of supplying that unit.

3.7.1.1 Efficiency costs without a prior tax

Introducing a carbon tax in a country is distortionary by nature from a local perspective (since it does not correct for a local externality per se), but with the aim of contributing to a global reduction in emissions (i.e., it contributes to reducing global externalities). Suppose a carbon charge, equal to a carbon tax times the fuel’s CO2 emissions factor, is now applied to the fuel. The charge drives a wedge between the price paid by fuel users and the price received by fuel producers and reduces fuel use, resulting in an economic efficiency cost indicated by the shaded triangle abg. This efficiency cost is equal to the loss of benefits to consumers from the fuel reduction, the integral under the demand curve or trapezoid adeg, less savings in production costs to firms, rectangle bdeg.

Alternatively, the efficiency cost can be interpreted as the loss in consumer and producer surplus (jkga) less revenue gains to the government where the latter is rectangle jkba. Consumer surplus reflects the benefits of fuel use to consumers less the amount they pay for the product (jkga) and is reduced from triangle hkg to triangle hja by the carbon charge. Producer surplus reflects revenue gains to firms less production costs consumption but is zero with and without the carbon charge as constant returns are assumed.

3.7.1.2 Efficiency cost in the presence of a prior tax

It is now supposed that a prior tax on fuel use is applied. This prior tax drives a wedge between the consumer and producer price in the initial equilibrium as indicated in Figure 3‑33. The efficiency cost of the carbon charge is now given by trapezoid acfg. Again, this reflects losses in benefits to consumers from the fuel reduction, trapezoid adeg, less savings in production costs, rectangle cdef. Alternatively, it is the loss in consumer surplus, trapezoid jlma, less revenue gains to the government, rectangle jlca.

In this case the efficiency cost has two components: (i) one-half times the carbon charge (per ton of CO2) times the overall CO2 reduction; and (ii) the pre-existing tax per unit of fuel use, times the fuel reduction, and aggregated across fuel markets.

3.7.1.3 Efficiency costs in CPAT

The efficiency cost can be (approximately) computed by the ‘Harberger triangle’, that is, one-half times the carbon charge expressed per unit of fuel use times the fuel reduction. If the carbon charge is applied to multiple fuel products, the efficiency cost is the sum of Harberger triangles across the fuel markets. Equivalently, the efficiency cost is simply one-half times the carbon charge (per ton of CO2) times the overall CO2 reduction, which corresponds to the integral under the marginal abatement cost (MAC) schedule where the latter is the horizontal summation of individual MAC curves for all the behavioral responses promoted by the carbon charge.

In CPAT, the efficiency costs follow the Harberger methodology, i.e., efficiency costs are treated as deadweight costs, $\text{ddw}$. These costs correspond to the area of the trapezoid described above, which is expressed as follows:

$\text{dd}w_{\text{ft}} = \frac{\left( \text{nc}p_{\text{ft}} - xcp_{\text{ft}} \right)}{2}*(F_{P,ft} - F_{B,ft})$

Where the first term $\frac{\left( \text{nc}p_{\text{ft}} - xcp_{\text{ft}} \right)}{2}$ represents the average of new and pre-existing tax, respectively denoted $\text{nc}p_{\text{ft}}$ and $\text{xc}p_{\text{ft}}$, and $F_{P,ft} - F_{B,ft}$ corresponds to the change in fuel consumption from the baseline to the policy scenario.

3.7.1.4 Co-benefits

If it is now supposed that there are also local air pollution or other domestic environmental costs associated with use of the fuel product as indicated in Figure 3‑33. The reduction in fuel use from the carbon charge reduces these costs by rectangle ncfo, which corresponds to the domestic environmental co-benefits. In short, the area acfg is presumably due to the externality created from fossil fuel use in the first place – and hence that is why the entire ncfo area could be a benefit. The net economic benefit is defined as the domestic environmental co-benefits—excluding global climate benefits—less efficiency costs. This is shown by trapezoid noga, as the co-benefits exceed the efficiency cost. More generally co-benefits might offset a portion of (rather than more than offsetting) efficiency costs in which case net economic benefits are negative.

3.7.2 Energy externalities costs

Externalities are deadweight losses from the tax before revenue recycling and do not include revenue recycling and tax interaction effects. In the dashboard of CPAT, energy externality costs are calculated under the baseline scenario and include costs above the marginal cost, that is costs related to air pollution, congestion, road damage and accidents and global warming. The sum of these externalities, including the supply costs and the potential VAT, actually defines what is called the ‘efficient price’.

Figure 3‑34: Dashboard: Global energy demand scenario

These costs are displayed by fuel (i.e. coal, natural gas, electricity and liquid fuel, gasoline, diesel, LPG and kerosene) and sectors grouping (except for liquid fuels) and broken down by various components:

Supply costs as defined in the Prices section of CPAT.
Air pollution costs. These costs are associated mortality and morbidity attributed to air pollution. Averted mortality is valued using a Value of the Statistical Life (with the method selected by the user) and morbidity, measured as years lived with disabilities, is valued using a fraction of wages. See Section 6.7 of the Air Pollution module for methodological details.
Road accident costs and Congestion costs³⁰. The main road transport co-benefits of a carbon tax are a reduction in road accidents (from a reduction in driving, changes in the vehicle fleet, less aggressive driving, etc.) and a reduction in congestion (from a reduction in driving, an increase in car sharing, changes in the vehicle fleet, changes in transport timing decisions, etc.). Externality costs are estimated based on the baseline and policy forecast (i.e. adjusted for the fuel price change using a country-specific elasticity) accidents/congestion. The monetary value of accidents (multiplying fatalities by value of statistical life) and congestion (multiplying time lost in traffic times value of travel time) is then computed. Finally, the change in value of accident/congestion is divided by the change in motor fuel consumption.
Global warming costs are by default defined at the global level. These costs are estimated based on the damage per ton CO2 (in real USD$ 2021) and the level of CO2 emissions under both scenarios. Note that several social cost of carbon can be selected:
- The damage per ton of CO2 is by default set to a social cost of carbon, fixed to 75USD$ in 2030, implying an annual rise in real terms from 2018 of the social cost of carbon of 4%.
- Estimated social costs by Ricke et al. (2018) for which the national social cost of carbon discount rate and elasticity of marginal utility can be modified. Note that Ricke et al. (2018) estimates are country specific. More information can be found in the tab “SCC” of CPAT.
- The social cost of carbon can also rely on the Global US EPA estimates with a 2.5% discount rate.
- Finally, the user can manually enter a social cost of carbon (in US$2021 per ton of CO2), assuming that the latter starts in year

These options can be modified in the dashboard:

Figure 69: Dashboard: Social cost of carbon (SCC) assumptions

Figure 3‑35: Dashboard: Social cost of carbon (SCC) assumptions

Potential VAT can be calculated on the supply cost only or on the supply cost augmented by all externalities (the default).

3.7.3 Monetized welfare benefits

CPAT provides an assessment of climate co-benefits associated with carbon pricing and fossil fuel price reform. Welfare benefits induced after the introduction of the carbon tax include the monetized following items (in real USD$ 2021), which are estimated based on the description of the costs described in the above section:

Averted climate damages (national) is defined as the difference between the total national global warming costs in the baseline and the policy scenario.
Averted air pollution mortality/morbidity is taken from the Air Pollution module. The air pollution welfare gains are calculated from reduced mortality and morbidity attributed to improvements in air pollution. Averted mortality is valued using a Value of the Statistical Life (with the method selected by the user) and morbidity is valued as a fraction of wages. See Section 6.7 of the Air Pollution module for methodological details.
Averted road accidents are taken from the transport module and represent the change in the number of road accidents induced by the implementation of the policy selected by the user, which thus corresponds to externality benefits.
Reduced congestion is taken from the transport module. In the same vein, external benefits from reduced congestion results from the change in traffic induced by the implementation of the policy selected by the user.
Efficiency costs are defined as the deadweight costs resulting from the carbon tax (i.e. the average of existing and new carbon tax introduced) and the change in fuel consumption for each fuel considered, including electricity.

CPAT dashboard shows monetized net welfare benefits as percentage of GDP.

Figure 70: Dashboard: Total monetized welfare

Figure 3‑36: Dashboard: Total monetized welfare

3.8 Validation

3.8.1 Overview

It is important to note that the validation exercise differs from the calibration. While the calibration performed for some variables throughout the mitigation module prevents the model from deviating from observed data (i.e. for 2019 to 2021), particularly in the context of Covid, the validation analysis covers a broader time horizon and aims to explore how the mitigation module performs against other models or to compare it against the literature. The analysis also includes sense-checking and parameter sensitivity analysis of the parameters defined in the mitigation module. The validation is organized as follows:

Elasticities estimations. As CPAT is mainly driven by elasticities with respect to prices and economic activity, an econometric analysis is carried out to compare the elasticities used in CPAT and those obtained from an empirical analysis.
Comparison of CPAT against other models.
Ex-post studies. This section presents the literature’s estimates of the effectiveness of carbon pricing with respect to emissions and compares them to the CPAT results.
Hindcasting. The hindcasting exercise aims at testing CPAT’s forecasts against observed data. It searches to evaluate the performance of the used assumptions when trying to reproduce historical information.
Parameter Sensitivity Analysis. The analysis explores the sensitivity of a set of selected parameters.

Before deep diving into the validation analysis, a first step in the validation process is performed to ensure that CPAT produces reliable data, especially for the data fed into the rest of the validation analysis. To further validate CPAT and check its functionality for all countries the T and Tt scenarios have been created in the Multiscenario Tool to test 826 parameters used in CPAT. The T-scenarios use average power models and show how CPAT behaves under different carbon taxation and how these parameters change. There are six testing scenarios:

T0-T6, when T0 has no carbon tax;
T1 (small carbon tax scenario) introduces 12$ carbon tax with 20$ target carbon tax;
T3 (medium carbon tax scenario) introduces 36$ carbon tax with 60$ target carbon tax;
T6 (high carbon tax) introduces 120$ carbon tax with 200$ target carbon tax; and
The T2, T4 and T5 introduce intermediate rates for comparison.

In addition to these scenarios, the scenarios denoted Tt (i.e. T0t-T6t) use engineer model instead of Average power models and hold the same assumptions and carbon tax rates as the T scenarios described above (i.e. T0-T6). In order to test CPAT, the following steps were performed:

Settings. The T0-T6 use average model, while T0t – T6t scenarios use engineer model.
Model runs. The MT is run using the same defaults.
Data. The database is then compiled, retaining CPAT’s output on 826 parameters for 218 countries.

The scenarios aim to provide data for further Parameter Sensitivity, hindcasting and comparison analysis, as well as signal any problems with country specific results, i.e. due to the poor data quality. Based on the outcomes, we classify countries into working and ones which produce spurious results. The Table on Countries coverage presented in the User Guide results from this testing.

3.8.2 Panel estimation of energy demand

3.8.2.1 Introduction

This section describes the results from the estimation of some of the fuel demand equations incorporated in CPAT. The aim is to

Deliver an empirical view of the elasticities with respect to price and economic activity;
Establish the size and direction of any linear trend in fuel consumption; and
Reflect on the difference between the value of the elasticities and trends estimated in this study and those currently used in CPAT.

Elasticities describe the percentage change in a dependent variable in response to a percentage change in an independent (driving) variable. As an example, a price elasticity equal to -0.3 implies that a 100% increase in the price delivers a 30% reduction in fuel consumption. In the case of models using data undergoing a logarithm transformation, the elasticity with respect to a given variable is simply the estimated coefficient on that variable.

3.8.2.2 Methodology

The approach used here reflects underlying CPAT model and database structure in relation to:

Frequency of data and timespan. In the estimation we used annual data ranging between 2000 and 2018, i.e. the dataset currently incorporated in CPAT. This is a panel dataset in which information for a set of fuels consumed in a set of sectors (and their driving variables) is observed across time and countries (here taken as the unit dimension of the panel).
Driving factors. Consumption of a fuel in a specific sector is assumed to be a function of fuel price (in that sector) and of the overall level of economic activity (as measured by the GDP), with both variables expressed in real terms.
Static functional form. The whole impact of a change in a driving variable, say, price, unfolds within the year covered by that observation. This means that last year’s prices have no impact on this year’s and future consumption.
Sectorial disaggregation. Results are reported based on the disaggregation underlying the current set of elasticities in CPAT (industrial, service, residential and transport) but data are available for a number of industrial subsectors and transport modes (as shown in Appendix B - Energy balances, Figure 3‑47) which are used in the estimation. This implies that we are able to produce estimates for the elasticities of a fuel consumed in any industrial subsector, so that the range of these estimates for the industrial sector as a whole is indicated as with a boxplot in Figure 3‑37 and Figure 3‑38.
Fuel disaggregation. Results are reported based on the fuels underlying the current set of elasticities in CPAT (coal, electricity, natural gas, other oil products, biomass, diesel and gasoline). In the case of other oil products, we are able to rely on two fuels in the estimation: kerosene and lpg.

We estimated the fuel demand below for each combination of sector and fuel for which estimation was deemed relevant and feasible:

$\begin{matrix} \text{ln\:f}c_{\text{it}} = \alpha_{i} + \beta_{1}\text{\:ln\:}y_{\text{it}} + \beta_{2}\text{\:ln\:}p_{\text{it}} + \beta_{3}\text{\:t} + \epsilon_{\text{it}} \\ \end{matrix},$

where $fc_{\text{it}}$ indicates the consumption of a specific fuel at time t in country i in a specific sector, $p_{\text{it}}$ indicates the price for that fuel and $y_{\text{it}}$ the overall level of GDP in the country. There are no indices in relation to the sector and the fuel in the equation as estimation is conducted for each combination of fuels and sectors. The individual effects $\alpha_{i}$ reflect constant (across time) factors which affect fuel consumption in a specific sector in a specific country given the value of the independent variables in the model. An example for these factors could be energy efficiency policies affecting fuel consumption regardless of the level of economic activity and price. Finally, $t$ is a linear time trend. We also introduced a time effect $\lambda_{t}$ but it was never found to be statistically significant when a linear trend was also included.

In terms of relevance, we excluded sectors for which the CPAT dataset contained data covering less than 0.5 GTOE while in terms of feasibility we required a minimum of about 300 observations for a sector-fuel combination to be included in the analysis. As a consequence, the number of units (countyries) used in the analysis varied from more than 150 in the case of gasoline used for road transport to 13 in the case of coal used for non-energy use or otherwise not included in other industrial subsectors.

3.8.2.2.1 Adopted estimators

The following estimators were implemented: 1) the between estimator (BE); 2) the pooled OLS estimator (POLS) and; 3) the Common Correlated Effects Mean Group (CMG) estimator of Pesaran (2006). The results from the Between and Pooled OLS estimator are reported only for those cases when they produce consistent estimates, ie. when regressors are not correlated with individual effects as assessed by the Hausman test. The choice of these estimators was motivated by the aim of assessing the long-term impact of driving factors on fuel consumption - despite the use of a static functional form in CPAT - and evidence of Cross-Sectional Dependence (i.e. correlation across the units in a panel dataset).

More precisely, the choice of adopting these estimators is motivated by the following considerations:

The BE produces consistent estimates of long-run coefficients for a panel with adequate number of observations across time and units (in our case countries) as formally discussed in Pesaran and Smith (1995). It also produced the best estimate of long-run price coefficient for gasoline in the Monte Carlo simulation discussed in Baltagi and Griffin (1984), although estimates from POLS were not markedly different.
The POLS produced the most robust forecasts (assessed based on the RMSE) in the Monte Carlo study in Baltagi and Griffin (1984). In the same study, the BE produced very similar results, although with (slightly) higher errors.
The CMG estimator produces unbiased estimates when cross-sectional dependence (CSD), which was assessed based on the test in Pesaran (2015), is correlated to included regressors in the model. We used robust standard errors (Beck and Katz 1995; Driscoll and Kraay 1998) to take into account cross-sectional dependence but this is a valid approach only if the unobserved factors responsible for correlation across units are not correlated to variables in the model, in our case fuel price and GDP. Although the CMG estimator is robust to any form of Cross-Sectional Dependence, the extent to which it captures long-term impact of driving variables in a static model is not clear.

Two versions of the equation above are implemented in the case of the POLS and CMG estimators: one with a global linear trend, one with a trend allowed to vary across countries. Considering the number of estimates we obtain we report only those which were statistically significant at the 10% level and conform to economic theory, e.g. positive elasticity on economic activity and negative on the fuel price.

3.8.2.2.2 Data

Data used in this study reflects the dataset underlying CPAT. This means using:

fuel consumption data from IEA energy balances;
nominal GDP data from the IMF World Economic Outlook (WEO) database converted into real terms by using the Consumer Price Index (CPI) also from IMF’s WEO;
nominal fuel prices data from IMF’s database, also converted into real terms by using the CPI index.

All the variables were converted into logarithms before the estimation.

3.8.2.3 Results

3.8.2.3.1 Price elasticities

Figure 3‑37 compares the estimates of price elasticities obtained here with those used in CPAT for the transport (quadrant A), residential (quadrant B), industrial (C) and service sector (D). Estimated elasticities are similar to those used in CPAT in the case of the:

residential sector, with the exception of electricity for which we estimated -0.1 - considerably lower than the -0.4 value used in CPAT;
industrial sector, with the of exception of diesel for which CPAT uses the high value of -1.1.

Difference between the elasticity in CPAT (-0.61) and the value estimated here (-0.19) for gasoline in the transport sector might be related to the fact that only the estimate from the CMG estimator can be used in the comparison with CPAT. Low estimates for price elasticities of gasoline in road transport are however very established in the literature. A recent survey, Galindo et al (2015), indicated -0.10 and -0.30 for short- and long-term elasticities, respectively, with our estimate (-0.19) falling right in the middle of this range.

The difference between elasticities estimated here and those used in CPAT is noticeable in the case of the Service sector. CPAT postulates fuel consumption being more price responsive than demand in industrial sector while our estimates point at elasticities being similar to those estimated in the residential sector. Assuming that there is considerable overlap between fuel uses in the service sector and in households (space heating, air conditioning and everyday electrical appliances), our findings of similar elasticities in the service and the residential sector seem plausible. Considering the difference between our estimates and CPAT and the growing importance of the service sector globally, this is a topic which should be explored further in the next iteration of CPAT.

Figure 3‑37 Comparison between price elasticities used in CPAT and those estimated in this study for transport ( A), residential (B), industrial (C) and service (D) sectors. The red triangles indicate an estimate obtained from one of the adopted estimators, while the blue triangles indicate the value of the elasticity used in CPAT. The boxplot in subplot C indicates the range of the estimates obtained for the industrial subsectors included in the study.

3.8.2.3.2 Elasticities with respect to economic activity

Figure 3‑38 compares the estimates of the elasticities with respect to economic activity with the values used in CPAT for the transport (quadrant A), residential (quadrant B), industrial (C) and the service sector (D). Estimated elasticities are similar to those in CPAT in the case of the:

residential sector, with the exception of electricity for which we estimated a relatively low (0.16) value compared to the value (0.65) used in CPAT;
industrial sector, with the of exception of natural gas for which CPAT uses a value of 0.81 while estimates here range between 0.33 and 0.56.

Differences still emerge in the transport (quadrant A) and in the service sector (quadrant D). With regard to the former, our estimates (ranging between 0.31 and 0.53 across fuels) are close to the results from the meta-analysis in Galindo et al (2015) indicating short- and long-run income elasticities equal to 0.26 and 0.46, respectively. CPAT is currently using the higher value of 0.57 for gasoline and 0.65 for other oil products. With regard to the service sector, CPAT incorporates a stark difference between elasticities for biomass and diesel (with values up to 0.41) and those for electricity and natural gas (with elasticity as high as 0.9). In contrast, our estimates are more homogeneous across fuels with values at most as high as 0.7.

Figure 3‑38: Comparison between income elasticities used in CPAT and those estimated in this study for Transport (A), Residential (B), Industrial (C) and Service (D) sectors. The red triangles indicate an estimate obtained from one of the adopted estimators, while the blue triangles indicate the value of the elasticity used in CPAT. The boxplot in subplot C indicates the range of the estimates obtained for the industrial subsectors included in the study.

3.8.2.3.3 Linear trend

CPAT includes a term called “annual autonomous improvement in efficiency” which conveys the annual percentage reductions in fuel consumption due to increasing energy efficiency. The intensity of this factor is stronger in the case of transport (average of about -0.5% across fuels) compared to the other sectors for which average for each fuel varies between -0.27 and -0.06%

Our estimate of a global linear trend for the sector-fuel combinations included in this study presents quite a different picture, as a negative trend in consumption could be estimated only for coal and other oil products. In the case of biomass, electricity and natural gas the trend is positive. In the case of diesel and gasoline consumption in the transport sector, not reported in Figure 3‑39, the estimated models pointed out at non-statistically significant linear trend.

Figure 3‑39: Comparison between the assumed annual autonomous improvement in efficiency in CPAT and the global linear trend estimated in this study. The red triangles indicate the average of the estimates from the models allowing for a global linear trend.

3.8.2.4 Conclusions and areas for improvement

The empirical validation pointed out that the elasticities with respect to price and economic activity in CPAT tend to be on the same ballpark as those estimated here, with some exceptions mainly related to road transport and the service sector.

This exercise pointed out that estimated global linear trends are considerably different from the assumed impact of energy efficiency used in CPAT. With hindsight, this is not surprising, as estimated global linear trends include the impact of energy efficiency but also changing preferences for a specific fuel or the impact of changing sector decomposition. As an example, one would expect a positive linear trend in the case of biofuels in the transport sector due to the impact of policies facilitating substitution away from fossil fuels to renewable sources. CPAT might benefit from continuing to disentangle the perceived impact of energy efficiency (as currently done) especially if that coefficient could be linked to explicit policymaking.

This empirical validation has provided an opportunity for a thorough assessment of CPAT and how econometric analysis may inform values used in the model. This resulted in a number of considerations that will be explored in the next iteration of model development. In particular, CPAT is likely to benefit from including:

Elasticities estimated on an extensive dataset spanning about 4 decades which has been recently put together. Although this is a key development allowing the implementing of more sophisticated approaches and functional forms described below, as a first step, it seems helpful to focus on the estimators considered in this note.
A more focused measure of economic activity. The use of GDP to measures economic activity for each sector included in CPAT is not supported by best practice in the energy literature and involves the risk of producing unstable estimates, and therefore forecasts. As an example, if the share of a sector’s economic activity in the whole economy changes in a specific direction, CPAT would under- or over-forecast fuel consumption in that sector. As historical data for more focused economic activity indicators are available for all sectors in CPAT, one would need to assess whether one could obtain forecast time series which are needed by the model to make this approach feasible.
A more explicit treatment of long-run estimates. CPAT can incorporate the long-run / short-run distinction explicitly through an Error Correction Model (ECM) specification which is included in the macro-economic model of the World Bank or - perhaps more simply
- maintain its current specification but include two sets of elasticities, one for long-run and the other for short-run forecasts, with the timing of the switch between the two informed by empirical evidence.
A more explicit analysis of the impact of cross-price elasticities. This is a very important factor for a model assessing consumption for each fuel like CPAT. Systematic approaches to fuel substitution bring their own set of challenges (Agnolucci and De Lipsis 2020), to the extent that a simpler ad-hoc method may be preferable at least as a starting point, perhaps focused only on the substitution of specific fuels in specific sectors.
Exploring feedback mechanisms between the variables incorporated in the model and their possible endogeneity. This does not seem a considerable concern considering the variables currently used in CPAT but may deserve its own empirical exploration if more focused indicators of economic activity (as consequence of point 2 and more likely to be endogenous) are used in the model.
Assessing the extent to which elasticities vary across sectors and countries. The current version of CPAT includes the possibility of differentiating elasticities with respect to price and economic activity based on whether a sector is in a country belonging to the Lower Income, Lower Middle Income and Upper Middle-Income group on one side, and High-Income Country. The next phase of model development should thoroughly explore this possible source of heterogeneity alongside other sources, e.g. the possibility of allowing heterogeneous responses across industrial subsectors.
Trying to disentangle the impact of energy efficiency from changing preferences for a specific fuel, either through variables related to explicit policymaking or incorporating evidence from specific policy events

3.8.2.5 References

Agnolcucci, P. & de Lipsis, V. (2020). Fuel Demand across UK Industrial Subsectors. The Energy Journal, 41, pp.65-86
Baltagi, B. & Griffin, J. M. (1984). Short and Long Run Effects in Pooled Models, International Economic Review, 25, pp.631-45
Beck. N & Katz, J. N. (1995) What to do (and not to do) with Time-Series Cross-Section Data. The American Political Science Review, 89, pp. 634-647
Driscoll, J. & Kraay, A. (1998). Consistent Covariance Matrix Estimation With Spatially Dependent Panel Data, The Review of Economics and Statistics, 80, pp. 549-560
Galindo, L. M., Samaniego, J., Alatorre, J. E., Carbonell, J. F. and Reyes, O. (2015). Meta-analysis of the income and price elasticities of gasoline demand, CEPAL review, 117, pp.7-24
Pesaran, M. H., (2006) Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure, Econometrica, 74,pp. 967-1012
Pesaran, M. H. (2015). Testing Weak Cross-Sectional Dependence in Large Panels, Econometric Reviews, 34, 1089-1117
Pesaran, M. H., and Smith R. (1995). Estimating long-run relationships from dynamic heterogeneous panels, Journal of Econometrics, 68, pp. 79-113

3.8.3 Model comparisons

Over the current section, we will compare CPAT results and projections with other models over a selection of indicators. We will therefore:

Compare CPAT’s baseline results against Enerdata and the IEA;³¹
Assess the sensitivity to carbon price against the Enerdata POLES model;
Put the two together: compare CPAT time trend for different carbon prices vs alternative models.
Explore the power sector results compated against selected results from EPM

3.8.3.1 Baseline validation

This section is dedicated to the assessment of the CPAT baseline results. The latter is observed and compared with other models/sources through time series. We use two sources for comparison. The first and main source used is the Stated Policies (STEPS) scenario of the IEA World Energy Outlook 2021, extracted from RFF’s Global Energy Outlook 2022 database. The second source used for comparison is Enerdata’s long-term Marginal Abatement Cost Curves (MACC).

In both cases, the comparison is established based on specific indicators available in the different datasets (from Enerdata and from the IEA). We will therefore challenge both Average and Engineer models of CPAT.

3.8.3.1.1 Comparison with the STEPS scenario of the IEA

The IEA’s STEPS scenario reflects current policy settings based on a sector-by-sector assessment of the specific policies that are in place, as well as those that have been announced by governments around the world.

Data for solar has been added manually from the IEA WEO 2021 as it was not included originally in the RFF dataset.

We only have 3 points of data from the IEA: 2019, 2020, and 2030. The indicators selected are: Total CO2 emissions, Primary energy consumption by fuel, and Electricity generation by fuel.

Overall, the comparison shows comparable results between CPAT and the IEA STEPS scenario. Indeed the figures below suggest outcomes of same order of magnitude for the observed year (i.e. 2019, 2020 and 2021) and long-term projections are similar.

Note that it is not possible to observe the inflection point in 2022 in the IEA projection, as data point for the year 2022 is not available. As defined by RFF, Primary energy consumption displays the estimated energy content of fuels consumed prior to any conversion process.

Oil in CPAT is the aggregation of Diesel, Gasoline, LPG, Kerosene, and Other Oil Products. A different aggregation could explain the difference observed in order of magnitude for Oil.

In Europe and Eurasia, discrepancies are mainly driven by the results of Russia. It is important to note that there is no data for Solar Electricity Generation per country in the RFF-GEO dataset for the IEA STEPS scenario. Strong divergence should be noted between the two models on the nuclear generation.

3.8.3.2 Carbon Price Sensitivity

The sensitivity analysis is the observation of the evolution of the emissions depending on the carbon tax level. We will use the data from Enerdata in order to establish the analysis. We are taking into account both Average and Engineer models of CPAT. The graphs are indexed on the baseline scenario, as a 100% of emissions.

We will only consider 3 indicators: Total CO2 emissions, Energy related CO2 emissions - Power sector, and GHG emissions, exc. LULUCF. The focus is at the world level, for the year 2030. We see good alignment between the two models for all three indicators and both CPAT power model choices (average or engineer).

Note here we abstract for any differences in baseline. See the previous and next sections for that topic.

Total CO2 emissions

Energy related CO2 emissions - Power sector

**
**

Total GHG emissions, exc. LULUCF

3.8.3.3 Comparison with Enerdata’s long-term Enerbase scenario

It should be noted that Enerdata’s scenarios were formed before the Covid crisis.

This comparison is based on different carbon tax scenarios (including the baseline scenario), target for 2030: 0 USD/tCO2, 20 USD/tCO2, 40 USD/tCO2, 60 USD/tCO2, 80 USD/tCO2, 100 USD/tCO2, and 120 USD/tCO2. These scenarios are computed using the average and the engineer models of CPAT in order to add another layer of comparison. Enerdata presents CO2 MACC, which is going to be used as an equivalent to the target carbon tax. There are 3 points of data: 2025, 2030 and 2035.

We consider 5 indicators: Total CO2 emissions, Energy related CO2 emissions - Power sector - Industry - Buildings - Transportation, and GHG emissions, exc. LULUCF.

Results show comparable results, with both models having similar slops. Enerdata’s outcomes are, however, higher and aligned with pre-covid results of CPAT, suggesting that the Covid adjustment implemented in CPAT may explain the difference. In addition, it is worth mentioning that CPAT is calibrated on IEA’s data in the year 2019 to 2021, and IEA’s assumptions are less conservative than Enerdata when it comes to the share of coal power plant in the future.

Overall, CPAT’s results are similar to Enerdata’s results. With a few exceptions, the figures below report a similar order of magnitude and comparable directions. In this comparison, the average power model of CPAT provides closer estimates to Enerdata’s scenarios.

The figures below compare CPAT’s GHG emissions (exc. LULUCF) against Enerdata’s results. Similarly, outcomes are very close worldwide, although some discrepancies are observed in some regions.

3.8.3.4 Power sector comparison vs. EPM

The power sector validation is made using the World Bank’s EPM model. The World Bank’s Electricity Planning Model (EPM) is a long-term, multi-year, multi-zone capacity expansion and dispatch model. The objective of the model is to minimize the sum of fixed (including annualized capital costs) and variable generation costs (discounted for time) for all zones and all years considered, subject to:

Demand equals the sum of generation and non-served energy
Available capacity is existing capacity plus new capacity minus retired capacity
Generation does not exceed the max and min output limits of the units
Generation is constrained by ramping limits
Spinning reserves are committed every hour to compensate forecasting errors
renewable generation constrained by wind and solar hourly availability
Excess energy can be stored in storage units to be released later or traded between the other zones
Transmission network topology and transmission line thermal limits

The model is an abstract representation of the real power systems with certain limitations. EPM is used mostly to perform least cost expansion plans as well as dispatch analyses.

3.8.3.4.1 Objectives

The main objective of this analysis is to validate the accuracy of the CPAT results by comparing them with selected results from the EPM model, for different countries. The following outputs are compared:

Electricity Demand
Electricity Generation
New Investments

3.8.3.4.2 Methodology

The EPM model presents several different scenarios per country. Each scenario is defined by a 2030 carbon budget, most of the time defined as a 40% emission reduction relative to the BAU scenario. However, while the carbon budget is an input for the EPM model, it is an output for CPAT. Therefore, we used a goal seek in order to define a 2030 target carbon price in CPAT, which brought us to $40 t/CO2. This is an only approximately equivalent comparison: exact matching was difficult.

We use the Engineer model of CPAT for the entire comparison.

3.8.3.4.3 Caveats

Please note the following caveats on the approach followed:

EPM has a constraint in emissions and look to 2040 (80% emission reduction relative to BAU on average), but we work with 2030. In other words, we use a proportional ratio to set the target goal seek.

The fuel classification in CPAT does not exactly match the EPM ones. Therefore EPM “Fuel oil” will be considered as CPAT “Other oil products” (“Oil” in the legend), EPM “Onshore wind” and “Offshore wind” will be considered as CPAT “Wind”, and EPM “Geothermal” as CPAT “Other RE”. Storage is invested in CPAT but not reported so we do not compare it here.
CPAT’s New Investments (MW) are considered spreaded in time, which explains their continuous aspect.

3.8.3.4.4 Comparison

The comparison in terms on types of fuels in the energy mix and the order of magnitude of the shares reflect similar results. It is worth noting that the EPM model shows a higher share of wind in the electricity generation for some countries (e.g. Vietnam).

It is however more complicated to establish parallels in the case of developing countries, as EPM can suggest discontinuous generation/investments.

3.8.3.4.5 Graphs

The following pages show, for a number of mostly African countries available in the EPM dataset, comparisons for the larger countries between CPAT and EPM of:

Overall electricity demand.
Electricity generation by generation type.
New investment by fuel type.

Comparison for a bigger set of countries, including smaller countries than previously, are available in the Appendix H.

3.8.3.4.6 Electricity Demand Comparison

3.8.3.4.7 Electricity Generation By Fuel Type

3.8.3.4.8 New Investments By Fuel Type

3.8.4 Ex-post studies

3.8.4.1 How effective is the carbon pricing, really? A literature review

Despite voluminous literature on the carbon tax, few empirical works have investigated the effectiveness of a carbon tax and ETS in reducing emissions. Figure 3‑40 provides a first attempt to compare the estimates according to three different methods employed in the literature, that is counterfactual scenario and the estimation of semi-elasticity. It is worth noting that this comparison might be imperfect as under a counterfactual scenario some estimates have been annualized based on the policy implementation window, similarly to Green (2021). Moreover, Figure 3‑40 reports both short- and long-term estimates.

Two main key findings stand out from ex-post quantitative assessments of carbon pricing policies since 1990.

First, experience with carbon pricing and hence the empirical evidence is primarily from developed and emerging economies. In particular, studies assessing the effectiveness of a carbon tax focus on OECD countries or Northern European countries, which implemented a carbon tax earlier and for which time series data are available. Only few recent studies evaluate ex-post estimates of the effects of carbon tax on CO2 emissions across the world. At the national level, particular emphasis is placed on British Columbia, Sweden and the United-Kingdom. With respect to the assessment of the ETS, the focus is, not surprisingly, on the EU, China, Germany and the United States.

Second, the estimates for overall emission reductions from carbon pricing are minimal to modest, falling in the range of 0 – 2 percent per annum, with significant variations across sectors, but also across countries (Green, 2021).

Nonetheless, several caveats have to be factored in before drawing conclusion:

Carbon prices so far have had low coverage, low prices, or both. The sample size as well as the time horizon might still be too restricted to accurately examine the effect of a carbon pricing instrument. In this respect, empirical results acknowledge that the effects of taxes on emission reductions largely depend on the comprehensiveness of the instrument design and the level of the carbon tax (Metcalf, 2021).
The carbon price appears to have a non-linear effect, indicating that its effect becomes stronger above a certain threshold (Aydin & Esen, 2018). For instance, emissions reductions attributable to the EU ETS during the second phase (2008-2012) are greater than during the first stage (2005-2007). In the first phase, allowances were freely allocated. In the second phase, the cap was tightened and prices higher.
Control variables introduced in empirical studies may poorly capture the effect of the instrument alone. At the same time, isolating the effect of the carbon pricing instrument from other policies - which are not always considered as environmental policy measures - may lead to insignificant results. However, evaluating a carbon pricing instrument in conjunction with other instruments can lead to effectiveness (see, for example, Shmelev & Speck, 2018, who find that a carbon tax is effective when evaluated with a set of policies).
The effects of rational ignorance may kick in and eliminate any impact. Given the transaction costs of investing in low-carbon technologies, agents may not be responsive to a price signal set below a certain threshold.
When it comes to the ETS, generalized free allocation can mitigate incentives (e.g., through the creation of resource rents and barriers to entry). In addition, as more and more emissions are covered by ETSs (such as in China or in the EU) uncertainty on future prices may blunt the responsiveness of agents.

Figure 3‑40: Effects of carbon pricing instruments on average annual emission reductions: A literature review.

Notes: The numbers correspond to studies listed in the reference section (Section 3.8.4.3). Study estimates are adjusted to derive annual emission reduction effects of the carbon tax and the ETS to make estimates comparable. ST = Short-Term semi-elasticity; LT = Long-term semi-elasticity; CA-BC = British Columbia (Canada)

3.8.4.2 How does CPAT compare to the literature?

In order to compare CPAT’s semi-elasticity of CO2 emissions against the literature, the following settings are used:

Due to low carbon prices, we employ a low step function, that is $10 per ton of CO2. Such a step function is comparable to studies estimating semi-elasticities.
The model is run for all countries for which data are available and factors in the total CO2 emissions of 171 countries.
As CPAT is forward-looking, it covers the period 2019-2035.
As most of studies analyzed their results against a counterfactual scenario, CO2 emission changes in CPAT are compared to the baseline scenario. The estimation of the short- and long- term semi-elasticities is calculated as follows:

The total CO2 emissions in ton/CO2 are retrieved from CPAT under the baseline and policy scenarios over the period 2019-2035.
Annual changes are thus computed between the baseline and the policy scenarios.
Short-term semi-elasticities are arbitrarily calculated as an average of the annual changes over the period 2019-2023.
Long-term semi-elasticities are estimated as an average of the annual changes over the entire period (i.e. from 2019 to 2035).

Finally, CPAT holds the advantage to compare C02 emission changes across sectors (i.e. industry, power, residential and transport).

The table below presents the results. Long-term semi-elasticities are greater than short-term ones, indicating that changes that are not possible in a short period of time are more realistic over a longer time period. When looking into the range of CPAT’s estimates across all sectors, results are comparable with those of the literature (see Figure 3‑40 above). At the sector level, the power sector records the highest decrease on the long run, which is consistent with Rafaty et al. (2020)³².

Table 3‑9: Short- and long-term semi-elasticities of CO2 emission in CPAT

Sector	Short-term semi-elasticities	Long-term semi-elasticities
All sectors	-2.4%	-6.2%
Industry	-2.7%	-6.2%
Power sector	-2.3%	-8.4%
Residential	-2.2%	-4.9%
Transport	-0.9%	-2.0%

3.8.4.3 References

1. Rivers, N., & Schaufele, B. (2015). Salience of carbon taxes in the gasoline market. Journal of Environmental Economics and Management, 74, 23–36. https://doi.org/10.1016/j.jeem.2015.07.002

2. Metcalf, G. E. (2019). On the Economics of a Carbon Tax for the United States.

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3.8.5 Hindcasting

3.8.5.1 Objectives

The hindcasting exercise aims at testing CPAT’s forecasts against observed data. It searches to evaluate the performance of the used assumptions when trying to reproduce historical information. In short, the process assumes an historical point in time as its base year, and projects all relevant variables. Key indicators are selected and their projections are compared to real/observed data.

3.8.5.2 Methodology

The current results were obtained using a hindcastable version of CPAT (CPAT 1.0pre_043) with the help of the Multiscenario tool (MT v219). This is an out-of-sample forecasting exercise that simulates data from the year 2000 onward. The analysis uses CPAT methods to forecasts domestic prices, energy consumption and resulting emissions. Observed international prices for the forecasted period were fed as inputs to the simulation.

At the first stage, the focus is set on the forecasts of emissions; in particular, on GHG emissions (excl. LULUCF) and on energy-related CO2 emissions. The scenarios are run using six countries as test samples:

Australia (AUS)
Brazil (BRA)
China (CHN)
South Africa (ZAF)
United Kingdom (GBR)
United States (USA)

No Policy interventions were modeled, so the results correspond to the ‘Baseline’ output of the model.

The hindcasting exercise relies on an adapted version of CPAT and the MT files, where the first year of calculations is set to an historical point in time. All relevant data tables (e.g. energy consumption and domestic energy prices) are provided for that same base year. The exercise focuses on testing emissions projections, and hence not all features of CPAT are used.

The analysis covers annual data from 2000 to 2017, and assumes that consumption of a fuel in a given sector is a function of sector-specific fuel prices and overall level of economic activity, as measure by the GDP. Default settings and no-policy interventions are used for simulations.

The exercise consists of projecting key modeled variables and comparing those simulations with observed information. The checks are done on a country level basis, with a subset of those being presented here as a sample of results. Results are presented by means of figures, and tables of key statistics, namely the Root Mean Square error (RMSE) and its normalized version.³³

3.8.5.3 Comparing projected emissions across selected countries

For the selection of countries, CPAT has been able to capture the global trend in emissions. However, there are periods where the volatility of projections is larger than that of observed data, and where local trends, and in particular levels, are not properly captured. For a fixed set of elasticities, this gaps with respect to observed historical information can result from projected prices showing higher volatility than observed ones. This is explored in a subsequent stage.

3.8.5.3.1 GHG (excl. LULUCF)

CPAT shows a good performance on projecting the trend of emissions in most tested countries. A deeper look at the vertical axis’ scale of each plot will show periods of increasing gaps between projected and observed emissions. For a given set of price elasticities of demand, this could be explained by an inverse gap in projected versus observed domestic prices.

Figure 3‑41: Total GHG (mt.CO2e) excluding LULUCF

Table 3‑10 RMSE and Normalized RMSE . Total GHG Excluding LULUCF. Selected Countries

Country	RMSE	Normalized RMSE
Australia	25.9641	0.0505
Brazil	278.5110	0.2551
China	9021.2421	0.9151
United Kingdom	207.1026	0.3285
United States of America	672.3218	0.0966
South Africa	73.7134	0.1383

3.8.5.3.2 CO2 (energy-related)

The previous conclusions extends to the CO2 energy-related emissions. This data, however, should be considered with care as the observed emissions series exclude some years and a linear trend has been assumed to interpolate data for these periods (see for instance, 2007-2014).

Figure 3‑42: Total energy-related CO2 emissions (mt.CO2e)

Table 3‑11 RMSE and Normalized RMSE. Total energy-related CO2 emissions. Selected Countries

Country	RMSE	Normalized RMSE
Australia	35.8338	0.1011
Brazil	127.3467	0.3635
China	8687.0478	1.3373
United Kingdom	155.2571	0.3231
United States of America	637.0707	0.1179
South Africa	85.9752	0.2142

3.8.5.4 A potential source of discrepancies: In-model price forecasts

CPAT is an elasticity-based model where Emissions depend on fossil fuel consumptions, which in turn depend on fuel prices. It follows that, given the negative price elasticity of demand, an over-estimation (under-estimation) of prices with respect to the ones observed in reality, may lead to an under-estimation (over-estimation) of energy consumption, and hence emissions. The case of China, is a clear example of this. Projected prices are below observed historical ones. Since elasticities were computed based on historical prices, this results in higher hindcasted emissions than observed.

It should be noted, however, that the case of the UK escapes this explanation. The hindcasting tool projects lower emissions despite the lower modeled domestic prices. This gap in projected emissions would be amplified if considering in the model the policies that the UK implemented in the mid 2010s. These discrepancies remain for further analysis.

The tracking of historical information by the simulations may also be improved when setting short and long-term elasticities to model the energy consumption behavior. The current exercise only considers the former, and leaves the latter for further research.

As an additional remark, by construction, CPAT domestic prices for fossil fuels track international market prices for these fuels, and are adjusted with the help of an historical factor. The factor helps tame the volatility. However, for some countries, domestic observed prices remain smoother than projected ones. This may follow as well from policies like existing price regulations, not modeled in the current runs, and also left for further research.

3.8.5.4.1 Coal prices (historical vs CPAT)

Figure 3‑43: Domestic retail prices of coal used in the power sector

Table 3‑12 RMSE and Normalized RMSE. Domestic retail prices of coal used in power. Selected Countries.

Country	RMSE	Normalized RMSE
Australia	35.8338	0.1011
Brazil	127.3467	0.3635
China	8687.0478	1.3373
United Kingdom	155.2571	0.3231
United States of America	637.0707	0.1179
South Africa	85.9752	0.2142

3.8.5.4.2 Coal prices (projected, historical domestic and international)

Figure 3‑44: Historical retail prices of coal (domestic and international)

3.8.5.4.3 All countries

When considering the coal prices used for the power sector in all countries, it can be seen that CPAT forecasts are, on average, above observed prices. The set of figures below, shows this through the distribution of the relative difference (Projections/Observed), and its concentration under the value of “1”.

A subset of years is taken as a reference, but the behavior is consistent for all years. This reinforces the idea that a second set of price elasticities of demand based on price projections may be needed.

Figure 3‑45: Coal prices, relative differences: $CPAT projection$ / $Observed domestic prices$

3.8.5.5 Conclusions and additional analysis needed

The hindcasting exercise was focused on projecting emissions (GHG and energy-related CO2). It consists of a partial hindcasting, as the international prices used as inputs correspond to the outturn of prices (observed), instead of projections of prices dating from before the base year selected. It can, hence, serve to better study how the forecasting of domestic prices takes place once the true values of some inputs are known.

For the countries analyzed, CPAT generally shows a good performance capturing the historical trends of the respective variables. In most cases, however, the volatility of observed data is not replicated with CPAT projections. Moreover, depending on the country, CPAT’s projections appear to be persistently under (over) estimating values with respect to historical ones. While this may result from the implementation of policies that were not modeled in the exercise, it can also result from discrepancies in price forecasting, and may be subject to additional country-specific adjustments.

3.8.6 Parameter Sensitivity Analysis

3.8.6.1 Objectives

The parameter sensitivity analysis explores the sensitivity of a set of selected parameters with regard to:

The power sector assumptions;
Macroeconomic adjustments;
Elasticity adjustments; and
Price source adjustments.

The analysis aims to propose a classification of the sensitivity of the parameters, i.e. how CPAT behaves when changing the default parameters, and more especially how the change in parameters affects the emissions’ reductions.

3.8.6.2 Methodology

In order to test the sensitivity of the parameters, the following steps were performed:

Settings. Default parameters are used for G20 countries and for a carbon tax increasing from 10$ to 75$.
Model run. The MT is run using the same defaults but changing one parameter only.
Data. The database is then compiled, retaining CPAT’s output on emissions for G20 countries.
Computation.
1. Change in Emissions: Carbon Tax $75 in 2030 vs Baseline
2. Relative change (i.e. to the default parameter) in percentage points (pp). The difference between the change of CO2 emissions recorded under the default setting and the change in CO2 emissions under the other options is computed in order to analyse how each option is sensitive to the baseline parameter.
Output. Create a sensitivity classification of parameters affecting CPAT’s behavior (no sensitivity/negligible/sensitivity/high sensitivity).

3.8.6.3 Results

Based on the methodology described above, the sensitivity of the parameters to CPAT to CO2 emissions varies from no effect to very sensitive when focusing on the relative changes (i.e. CO2 emissions reduction relative to the default parameter). The following rule-of-thumb is used to classify the sensitivity of the parameters:

No effect: no variation
Negligible: less than 2 percentage points
Sensitivity: between 2 and 5 percentage points
High sensitivity: more than 5 percentage points

The table below summarizes the results of the sensitivity analysis.

Table 3‑: CPAT’s parameters sensitivity results

Parameters	Assumptions	Description	Change in Emissions: Carbon Tax $75 in 2030 vs Baseline	Relative change (i.e. to the default parameter) in percentage points (pp)	Sensitivity
Power model	Average*	Average between the elasticity and engineer models. The two models differ in their assumptions on generation cost so that even though they share a power demand framework, they can differ in modeled power demand despite the equations being the same.	-29%	-	-
	Elasticity	The ‘elasticity’ model is the original IMF power sector model explained in IMF board paper (2019)	-34%	5% more sensitive	High
	Engineer	The power demand model in the engineering model is based on specific sectors, and the elasticity model is more aggregated.	-22%	7% less sensitive	High
K parameter	k = 2*	The k parameter determines the speed of transitioning between generation types with a different cost. K is a measure of local cost variability and other reasons (such as load matching) for higher cost choices still being included in the generation mix.	-29%	-	Negligible
	k = 6		-29%	0	Negligible
	k = 10		-29%	0	Negligible
Renewables’ growth rate	Very high	2*Maximum historical rate or 4% of capacity, whichever is higher	-32%	3% more sensitive	Medium
	High	Maximum historical rate	-30%	1% more sensitive	Negligible
	Medium*	Halfway between maximum and average historical rate.	-29%	-	-
	Low	Average historical rate	-29%	0	Negligible
Fiscal multipliers adjustment	High	Increase all fiscal multipliers by 1 standard deviation	-29%	0	No effect
	Medium*	No adjustment	-29%	-	-
	Low	Decrease all fiscal multipliers by 1 standard deviation	-29%	0	No effect
GDP growth adjustment	High	Increase forecast GDP growth by 50%	-30%	1% more sensitive	Negligible
	Medium*	No adjustment	-29%	-	-
	Low	Reduce forecast GDP growth by 50%	-29%	0	Negligible
International energy prices forecast	Average*	Average of above four sources	-29%	-	-
	IMF-IEA	Average of IEA and IMF	-28%	1% less sensitive	Negligible
	EIA	Institutions’ forecasts for international prices for oil, gas, and coal	-32%	3% more sensitive	Medium
	IEA		-28%	1% less sensitive	Negligible
	IMF		-28%	1% less sensitive	Negligible
	WB		-30%	1% more sensitive	Negligible
International energy prices adjustment	High	Increase forecast prices by 50%	-20%	9% more sensitive	High
	Medium*	No adjustment	-29%	-	-
	Low	Reduce forecast prices by 50%	-31%	2% less sensitive	Medium
Adjust income elasticities for GDP level	Yes*	Adjusts income elasticities for electricity, gasoline and diesel with GDP levels (elasticities decrease as countries increase their per capita GDP). The intuition is that, for example, in middle-income countries households purchase fridges, but do not purchase additional fridges as their income increase further.	-29%	-	-
	No		-30%	1% more sensitive	Negligible
Income elasticities adjustment	Very high	Increase by 2 standard deviations	-29%	0	Negligible
	High	Increase by 1 standard deviation	-29%	0	Negligible
	Medium*	No adjustment	-29%	0	Negligible
	Low	Reduce by 1 standard deviations	-29%	0	Negligible
	Very low	Reduce by 2 standard deviations	-29%	0	Negligible
Prices elasticities adjustment	Very high	Increase by 2 standard deviations	-39%	10% more sensitive	High
	High	Increase by 1 standard deviation	-35%	6% more sensitive	High
	Medium*	No adjustment	-29%	-	-
	Low	Reduce by 1 standard deviations	-20%	9% less sensitive	High
	Very low	Reduce by 2 standard deviations	-7%	22% less sensitive	High
* Denotes the default parameter

3.9 Appendices

3.9.1 Appendix A - Macro data of CPAT: Sources and codes

This table shows the sources for all macro data in CPAT.

Indicator	Variable	Unit	Source
NGDP_D	GDP Deflator	Index	WEO
	Discount index - 2021	Index	WEO
	GDP growth - nominal (current prices, LCU)	% change	WEO
NGDP_RPCH	GDP growth - real (constant prices)	% change	WEO
NGDP_R	GDP - real (constant prices)	LCU bn	WEO
	GDP - real (current prices)	USD bn	WEO
	GDP - real (constant prices) - 2021 USD	USD bn	WEO
NGDP	GDP - nominal (current prices)	LCU bn	WEO
NGDPRPC	GDP per capita - real (constant prices)	LCU	WEO
NGDP_R_PPP_PC	GDP per capita - real (constant prices)	PPP; 2011 international dollar	WEO
LP	Population	mm	GBD, WEO, WDI
	Population	% change	GBD, WEO, WDI
LE	Employment	mm	WEO
ENDA	Exchange rate	LCU/USD	WEO
ENDA	Euro exchange rate	EUR per US$	WEO
	GDP growth - real (constant prices)	% change	WEO
SP.URB.GROW	Urban population growth - latest available	% change	WDI
SP.URB.GROW	Urban population growth (annual %)	% change	WDI
NGDP_D	GDP Deflator (2012=100)	index	WEO
PCPI_PCH	CPI Change	%	WEO
pcpi	Inflation index	%	WEO
gdgg.base.pct	GDP growth - real (constant prices)	% change	IMF WEO
gdpl.base.lcu	Baseline GDP - real (constant prices) - LCU	LCU bn	IMF WEO
gdpl.base.usd	Baseline GDP - real (constant prices) - USD bn	USD bn	IMF WEO
	Baseline ln(GDP per capita)		IMF WEO
	Deflator- 2021 - used hereafter - World		IMF WEO

3.9.2 Appendix B - Energy balances

Energy balances are a key source of information for CPAT. While the model uses energy consumption as a main input for the mitigation module, energy consumption is itself built based on the structure and information provided in the energy balances framework. This document presents the main principles used to transform the energy balances information into a structure consistent with CPAT’s fuels and sectors, as well as the steps taken to build energy consumption tables based on the CPAT energy balances.

Figure 3‑46: Mitigation module overview

We use the IEA Extended World Energy Balances, and Enerdata Energy Balances as the main sources to build the energy consumption tables used in CPAT.

3.9.2.1 CPAT fuels

The main energy products in CPAT are presented in the table below.

CPAT energy products	Corresponding IEA energy products codes	Corresponding IEA energy products
Coal	HARDCOAL	Hard coal
	BROWN, BKB	Brown coal, Brown coal briquettes
	ANTCOAL	Anthracite
	COKCOAL, OVENCOKE, GASCOKE, COKEOVGS	Coking coal, Coke oven coke, Gas coke, Coke oven gas
	BITCOAL, SUBCOAL	Other bituminous coal, Sub-bituminous coal
	LIGNITE	Lignite
	PEAT, PEATPROD	Peat, Peat products
	BLFURGS, GASWKSGS, OGASES	Blast furnace gas, Gas works gas, Other recovered gases
	COALTAR, PATFUEL	Coal tar, Patent fuel
Natural gas	NATGAS	Natural gas
	NGL	Natural gas liquids
Gasoline	NONBIOGASO	Motor gasoline excl. biofuels
Diesel	NONBIODIES	Gas/diesel oil excl. biofuels
LPG	LPG	Liquefied petroleum gases
Kerosene	OTHKERO	Other kerosene (other than kerosene used for aircraft transport)
Jet fuel	NONBIOJETK	Kerosene type jet fuel excl. biofuels
	AVGAS	Aviation gasoline
	JETGAS	Gasoline type jet fuel
Other oil products	CRUDEOIL; CRNGFEED	Crude oil; Crude/NGL/feedstocks (if not details)
	RESFUEL	Fuel oil
	OILSHALE, BITUMEN, PETCOKE	Oil shale and oil sands, Bitumen, Petroleum coke
	ETHANE	Ethane
	LUBRIC, NAPHTHA, PARWAX, WHITESP, ADDITIVE	Lubricants, Naphtha, Paraffin waxes, White spirit & industrial spirit (SBP), Additives/blending components
	REFFEEDS, REFINGAS	Refinery feedstocks, Refinery gas
	NONCRUDE, ONONSPEC	Other hydrocarbons, Other oil products
Biomass	PRIMSBIO	Primary solid biofuels
	CHARCOAL	Charcoal
	BIOGASOL	Biogasoline
	BIODIESEL	Biodiesels
	OBIOLIQ	Other liquid biofuels
Wind	WIND	Wind energy
Solar	SOLARPV	Solar photovoltaics
	SOLARTH	Solar thermal
Hydro	HYDRO	Hydro energy
Other renewables	BIOJETKERO; BIOGASES	Bio jet kerosene; Biogases
	GEOTHERM	Geothermal
	INDWASTE; MUNWASTEN; MUNWASTER	Industrial waste; Municipal waste (non-renewable); Municipal waste (renewable)
	TIDE	Tide, wave and ocean
	RENEWNS	Non-specified primary biofuels and waste
Nuclear	NUCLEAR	Nuclear energy
Electricity	ELECTR	Electricity

The table below provides indications on the code names used in CPAT.

Fuel code	Energy use by fuel and sector
bio	Biomass
bgs	- in which: biodiesel
bdi	- in which: biogasoline
obf	- in which: other liquid biofuels
coa	Coal
die	Diesel
ecy	Electricity
gso	Gasoline
hyd	Hydro
jfu	Jet fuel
ker	Kerosene
lpg	LPG
nga	Natural gas
nuc	Nuclear
oop	Other oil products
ore	Other renewables / Total self-generated renewables
ren	Renewables
sol	Solar
wnd	Wind

Starting from CPAT Prototype version 1.478, we separate biomass to biogasoline, biodiesel and other biofuels.

3.9.2.2 CPAT energy sectors

The energy sectors in CPAT are based on the IEA Extended Energy Balances dataset. We divide all energy flows into three main categories:

Raw energy supply,
Energy transformation, and
Final energy consumption.

For each country $j$, the balancing flow in raw energy supply category is Total Primary Energy Supply (TPES), which should be equal to the sum of Imports, Production, Exports (negative), Stock changes, International marine bunkers (only on the world level) and International aviation bunkers (only on the world level). Stock changes and bunkers were combined in “Stock and bunker changes (STOCKCHA)” flow.

$\text{TPE}S_{j} = \text{Productio}n_{j} + \text{Import}s_{j} - \text{Export}s_{j} + \text{STOCKCH}A_{j}$

Energy transformation category includes the following IEA flows: transformation processes (TOTTRANF, includes electricity generation), transfers (TRANSFER), energy industry own use (OWNUSE), distributional losses (DISTLOSS), and statistical differences (STATDIFF). The balancing equation for total final consumption (TFC) is:

$\text{TF}C_{j} = \text{TPE}S_{j} + \text{TOTTRAN}F_{j} + \text{TRANSFE}R_{j} + \text{OWNUS}E_{j} + \text{DISTLOS}S_{j} + \text{STATDIF}F_{j}$

In transformation processes, we separate the power sector - transformation of fuels into electricity. We include main activity producer electricity plants, autoproducer electricity plants, main activity producer CHP plants, and autoproducer CHP plants. The main sector groups in final energy consumption are:

Industry
Transport
Building
Power sector

We disaggregate transport and industry further to sectors.

Figure 77: Sectors disaggregation in CPAT

Figure 3‑47: Sectors disaggregation in CPAT

3.9.2.3 CPAT fuels and sectors overlap

The fuels and sectors specified above form an energy balances table in the mitigation module, which shows the amount of fuels consumed by each subsector in industry, transport, residential or other sector for energy purposes, and the amount of fuels consumed in the power sector to generate electricity (see the screenshot).

Figure 3‑48: Energy Balances

As the energy balances and prices are the main inputs for the Mitigation module, it is also essential to understand the overlap between energy prices and energy consumption by sector and fuels. The table below depicts the energy consumption table obtained in CPAT following transformations from international sources and CPAT’s own projections. For fossil fuels and electricity we have sector-specific or general energy prices and taxes per energy unit (please see a separate documentation on CPAT Prices and Taxes), for renewables we use price indices instead.

Figure 3‑49 explains the overlap of CPAT energy prices and sectors.

Figure 79: CPAT energy prices and sectors overlap

Figure 3‑49: CPAT energy prices and sectors overlap

3.9.2.4 Energy Consumption (EC) construction for CPAT

The purpose of this section is to present the sequence of processes applied to build and project Energy Consumption data in CPAT format, that is also sufficiently derived from original international sources. This process is applied as well to build a set of time series of Energy Consumption used for regression analysis and hindcasting.

Raw Inputs:

Energy Balances (EB) from IEA (yearly information. 2018 and 2019)
Energy Balances (EB) from Enerdata (yearly information. Last update:

Intermediate inputs:

CPAT projected Energy Consumption (EC) (2019)
User defined parameters for projections and for EC adjustment

Outcome:

Energy Consumption tables created using CPAT own structure, assumptions and projections based on raw data published by international databases. The table below depicts an example structure of such table:

Figure 3‑50: Energy Consumption

The CPAT energy consumption projections for the base year include a sub-process under which the fuel transformation sector is created. In CPAT we transform balances into final energy consumption (buildings, industry, transport, other), power sector (part of energy transformation in balances) and fuel transformation. Fuel Transformation sector is determined by the difference between primary and final energy consumption, subtracting Fuel Transformation in the power sector. Additionally, all oil products plus natural gas are aggregated to avoid dealing with negative fuel consumption.

Summary: The following diagram summarizes the process.

Figure 3‑51: Energy Balances process

3.9.3 Appendix C - Prices And Taxes Methodology

Energy prices and taxes are among the main inputs of the Mitigation module. They include information on (1) domestic energy prices by fuel and sector, (2) governmental price controls, (3) international energy prices and forecasts, and (4) existing carbon pricing mechanisms (carbon taxes and ETS). This document reflects the main principles and data sources used to build the CPAT Prices and Taxes part of the Mitigation module and information on assumptions used in calculations and the main outputs of the Mitigation module that directly depend on the prices and taxes data.

Figure 82: Mitigation module scheme: prices and taxes

Figure 3‑52: Mitigation module scheme: prices and taxes

The main data sources for prices and taxes inputs include:

For international energy price forecasts: energy price scenarios from the World Bank (Commodity Markets Outlook, “Pink Sheet” data), IMF (World Economy Outlook), IEA (World Energy Outlook), and EIA (International Energy Outlook);
For domestic energy prices and forecasts: historical fuel- and sector-specific prices from Enerdata, IEA, IMF FAD, and other sources;
For current carbon pricing mechanisms: historical and planned carbon taxation or ETS information, mainly based on the Carbon Pricing Dashboard;
For subsidies: IMF Energy Subsidies Template, ODI, other data sources

Based on the historical data and policy specifications, including sub-sectoral exemptions, the Mitigation module calculates the changes in energy prices and their impact on energy consumption (please see the Mitigation module’s documentation for more details). These energy prices also act as an input for other modules, including the distributional module and the Transport module.

As one of the outputs, the Mitigation module calculates fiscal revenues based on taxation, price controls, and energy consumption data.

3.9.3.1 User options affecting prices in CPAT

This section lists the user’s choices and briefly explains how these choices will affect further calculations. For more details, please refer to specific parts of this document.

Figure 3‑53: Dashboard

3.9.3.1.1 Policy coverage and exemptions

The user can choose what sector and fuel to tax on the Dashboard:

Figure 3‑54: Dashboard: Policy coverage

Additionally, the user decides whether to phase out exemptions or not and the period to phase out exemptions.

Figure 3‑55: Dashboard: Exemptions

Note: if the fuel is exempt and the phase-out is active, the carbon pricing policy (new carbon tax or ETS) will increase by 1/n every year starting from the chosen year, where n is the number of years to phase out exemptions. The user can trace exemptions in the “New policy coverage: CO2 emissions covered” graph on the Dashboard.

3.9.3.1.2 Choices of the sources for key inputs

The user can choose the source for international and domestic energy prices:

Figure 86: Dashboard: Sources for key inputs

Figure 3‑56: Dashboard: Sources for key inputs

The options for key inputs include “manual,” which the user can fill in a separate “Manual inputs” tab:

Figure 3‑57: Manual inputs

3.9.3.1.3 Policy options: Existing carbon pricing policies

The user can choose to apply existing carbon tax or ETS (if they exist) on the Dashboard:

Figure 3‑58: Dashboard: Policy Options

The user also has an option to specify carbon tax or ETS permit price growth for future years in the “Advanced options” of the Dashboard:

Figure 89: Dashboard: Advanced Policy Options

Figure 3‑59: Dashboard: Advanced Policy Options

Note 1: even if the user decides not to apply existing carbon pricing mechanisms, it will not affect historical prices, only forecasted.

Note 2: existing policy coverage for carbon tax and ETS permit prices are fractional. When considering sector and fuel coverage, for existing policies, CPAT accounts for the fraction of the consumption that is affected by the policy. This differs from the treatment of coverage under the new, user-defined, policies. There, the option to include or not a sector or fuel is binary. For new policies, a fractional coverage only occurs when the user selects to exempt a sector or fuel, and to phase out that exemption in time.

3.9.3.1.4 Policy options: New excise / existing excise exemptions

The user can add a manual per-unit of energy excise by choosing the “Add additional excise” option on the Dashboard and filling a relevant part of the “Manual inputs” tab.

Figure 90: Manual inputs: Manual Policy Options

Figure 3‑60: Manual inputs: Manual Policy Options

The user also has an option not to apply existing excise taxes starting from the policy year (existing excises used by default):

Figure 91: Dashboard: Existing tax removal

Figure 3‑61: Dashboard: Existing tax removal

Note 1: if the user decides not to apply existing non-carbon taxes, this decision will affect only policy forecast, not baseline and historical data. Moreover, it the user decides to keep existing policies in place, by default those will be projected with the existing sector and fuel coverage and not with the one the user may use for newly-introduced policies.

Note 2: As discussed before, existing policy coverage for carbon tax and ETS permit prices are fractional, while the coverage for new policies is binary. Indeed, when considering sector and fuel coverage, for existing policies, CPAT accounts for the fraction of the consumption that is affected by the policy. This differs from the treatment of coverage under the new, user-defined, policies. There, the option to include or not a sector or fuel is binary. For new policies, a fractional coverage only occurs when the user selects to exempt a sector or fuel, and to phase out that exemption in time.

3.9.3.1.5 Policy options: VAT reforms

The user can include externalities to be part of the VAT base for optimal taxation (included by default):

Figure 3‑62: Dashboard: VAT Reform

Also, the user can choose to apply the same VAT tax rate in the residential and transport sectors if it is different from the general VAT in the economy (“advanced options” in the Dashboard):

Figure 93: Dashboard: Adjusting VAT per sector

Figure 3‑63: Dashboard: Adjusting VAT per sector

3.9.3.1.6 Fossil fuel subsidies reform

The user can choose to phase out fossil fuel subsidies (producer- and/or consumer-side) over a specified period (n years). The fossil fuel subsidy will decrease linearly by 1/n every year starting from the year the user chose to start the phase-out until they reach zero or a specified limit.

Figure 94: Dashboard: Fossil Fuel Subsidies Reform

Figure 3‑64: Dashboard: Fossil Fuel Subsidies Reform

Additionally, the user can choose to phase out only a part of the fossil fuel subsidies in the “advanced options” of the Mitigation module.

Figure 95: Dashboard: Fossil Fuel Subsidies Reform (Advanced Options)

Figure 3‑65: Dashboard: Fossil Fuel Subsidies Reform (Advanced Options)

3.9.3.1.7 Price liberalization

The user can choose to calculate the impact of the government energy price control in the “advanced options” of the Dashboard and the source for price control coefficients (manual or regional). The choice will not affect historical price components but will affect calculations of fiscal revenues or losses.

Figure 96: Dashboard: Price liberalization (Advanced Options)

Figure 3‑66: Dashboard: Price liberalization (Advanced Options)

Note. Do not use price liberalization and fossil fuels subsidies phase out simultaneously to avoid double-counting.

3.9.3.2 Price components

3.9.3.2.1 Assumed pricing mechanism

Figure 3‑67 below presents the main components of prices in the baseline.

Figure 97: Main components of baseline prices

Figure 3‑67: Main components of baseline prices

Supply cost is an average price that includes all price components like production and transformation costs, transportation and distribution costs, profits, and others, except taxes.

Retail price is an average end-user price paid by the final user in the corresponding sector (power generation, industry, transport, residential) per unit of energy, including all applicable taxes and subsidies. According to IEA, the historical retail prices are calculated as a ratio of total sales of energy to the sold volume. The retail price should equal the supply cost plus all relevant taxes:

$p_{\text{cgf},t} = sp_{\text{cgf},t} + \text{tt}x_{\text{cgf},t}$

where $p$ is the average retail price, $\text{sp}$ is the price before taxes and $\text{ttx}$ is the total taxes for country $j$, fuel $f$ in sector $s$ and year $t$. This holds for both the baseline and the policy scenarios.

Note: In general, carbon pricing policies and the phasing out of consumer-side subsidies will affect the $\text{ttx}$ component, while the phasing out of existing producer-side subsidies will instead affect the supply cost $\text{sp}$.

Price gap/total taxes/subsidy: the gap between the supply cost and retail price. This is a function of any type of taxation and/or subsidization that causes the supply cost to deviate from the import/export parity price plus mark-ups and the any taxes applied to the price before tax, such as VAT, excise taxes, and other taxes (environmental, renewable support taxes, energy security taxes, social taxes, and others). The historical values of $\text{ttx}$ are calculated in the dataset as a difference between average retail price and price before taxes and, thus, are negative in the case of a net subsidy. For forecasted years, the value of $\text{ttx}$ will instead be computed as the sum of the forecasted subcomponents (different types of taxes and consumer-side subsidies).

$\text{tt}x_{\text{cgf},t} = p_{\text{cgf},t} - sp_{\text{cgf},t}$

where $\text{ttx}$ stands for the total net taxes (or net subsidy if negative), $p$ is the average retail price and $\text{sp}$ is the supply cost (i.e. the price before tax). By construction, this relationship holds for all scenarios.

VAT payment: historical values are calculated in the dataset as VAT base (price before tax plus all other taxes except VAT) multiplied by the VAT rate. The VAT rate is assumed to be 0 for industrial and power generation users since these users receive a credit on their input VAT.

$\text{va}t_{c,f,g,t} = \left( sp_{c,f,g,t} + \text{tx}o_{c,f,g,t} \right)*\text{vatrat}e_{c,f,g,t}$

where $\text{VAT}$ is the VAT payment per energy unit, $\text{txo}$ represents the excise and other taxes/subsidies and $\text{VATrate}$ is the VAT rate.

Excise and other taxes: calculated in the historical dataset as a difference between retail price, supply cost, and VAT payment.

$\text{tx}o_{\text{cgf},t} = p_{\text{cgf},t} - sp_{\text{cgf},t} - \text{va}t_{\text{cgf},t}$

For the forecasted years, instead, it is computed as the sum of its projected components. This, as in the scenarios we decompose the Excise and other taxes category to several additional price components, such as current carbon tax, current ETS permit price, new policy, new excise tax (if applicable), and fixed/ad-valorem part / other, which includes price controls (if applicable).

These categories (except new policy and new excise tax), being the Excise and other taxes category components, do not affect the retail price.

Carbon tax/ETS permit price: ‘effective’ carbon tax/ETS permit price as a component of total taxes is calculated separately in CPAT based on existing carbon pricing mechanisms and emission factors. Details are provided below.
New policy/new excise tax: the main driver of the change in retail prices. They are calculated as components of the excise and other categories, depending on the chosen policy (new carbon tax, ETS, road fuel tax, others) and emission factors. By default, in the baseline scenario, new policy/new excise taxes are equal to zero.
Subsidies: per unit of energy subsidy is calculated as a sum of all subsidies over the total final consumption by sectors (power, industry, residential, transport). The details are provided below.

3.9.3.2.2 Assumptions used for price reconstruction and projections

Retail prices:

Takes user-provided data if there is any in the ‘manual inputs’ tab
Uses CPAT generated prices if the data exist
Otherwise, calculated as a sum of the supply cost, VAT and other (excise + environmental) taxes

Supply costs:

Takes user-provided data if there is any in the ‘manual inputs’ tab
Uses CPAT generated prices if the data exist
Otherwise:
- For the first year: if no data whatsoever, uses the global (regional if possible) price
- For the second year and after, calculated as the previous year’s supply cost multiplied by the global (regional) prices’ growth rate

VAT payments:

Takes user-provided data if there is any in the ‘manual inputs’ tab
Uses CPAT generated prices if the data exist
Otherwise:
- For the first year:
  - For the power and industry sectors, assumes 0
  - for the residential and “all” sector, calculated as the sum of the supply cost and excise and other taxes multiplied by the general VAT rate in the country
- For the second year and after, if no data, uses a proportion to the supply cost with other taxes from the previous year

Excise and other taxes:

Takes user-provided data if there is any in the ‘manual inputs’ tab
Uses CPAT generated prices if the data exist
Otherwise, if no data whatsoever: Assumes 0 for the first year, and uses a proportion to the supply cost from the previous year for the second year and after (would be changed later when we’ll have working carbon pricing mechanisms tab)

Current carbon tax and ETS permit price: Uses CPAT generated prices if the data exist (would be changed later when we’ll have working carbon pricing mechanisms tab)

3.9.3.3 Forecasted prices (after 2021)

3.9.3.3.1 Assumptions for forecasted prices

Retail prices: Sum of the supply cost and all applicable taxes: excise and other + existing ETS/carbon tax + new ETS/carbon tax

Supply costs: Previous year’s supply cost multiplied by the growth rate of the respective global fuel prices

VAT payments: Ratio of the previous year’s VAT payment to the supply cost with excise and other taxes multiplied by the current year’s sum of the supply cost and excise and other taxes (plan: should give the user an option to apply VAT before or after taxes)

Excise and other taxes:

If “fixed” – equals to the previous year’s absolute value of the price gap that is not covered by the current ETS/carbon tax, plus applicable carbon pricing mechanisms (current/new ETS/carbon tax)
If “ad-valorem” – equals to the ratio of the previous year’s part of the price gap that is not covered by the current ETS/carbon tax to the supply cost, multiplied by the current year’s supply cost, plus applicable carbon pricing mechanisms (current/new ETS/carbon tax)
Plan: additionally, should be corrected to the price control (as a part of the retail price that the government would change in order to keep the retail price controlled)

Current carbon tax and ETS permit price:

Values from the “Existing carbon pricing mechanisms (ETSs and carbon taxes) and price controls” New carbon tax and ETS permit price:
Values from the respective scenarios (zeroes for the baseline scenario)

3.9.3.3.2 Calculations: Modeling assumptions

For years starting from 2021, the price components are modeled by following rules.

Retail price for fuel f in sector s in year t is a sum of the supply cost and all applicable taxes (VAT payment, excise and other taxes):

$p_{\text{cgf},t} = sp_{\text{cgf},t} + \text{tx}o_{\text{cgf},t} + \text{va}t_{\text{cgf},t}$

Supply cost for fuel $f$ in sector $s$ in year $t$ is calculated using a coefficient of supply costs to base years (2017-2019) to the global prices in the same period, multiplied by the respective international fuel price in year $t$:

$sp_{\text{cgf},t} = \frac{sp_{\text{cgf},t_{0}}}{gp_{f,t_{0}}}*gp_{\text{cf},t}$

where $sp_{\text{cgf},t}$ denotes the average supply costs for country $j$, fuel $f$ in sector $s$ in base years $b$, $gp_{\text{cgf},t_{0}}$ is the average global fuel price in base years, $gp_{\text{cf},t}$ – global fuel price based on the chosen international energy price forecast in year $t$. Notice that the global price for certain fuels change from country to country, as the reference market differs.

Producer-side fossil fuel subsidy is equal to the previous year’s per unit of energy producer-side fossil fuel subsidy unless the user decides to phase out fossil fuels.

VAT payment equals the previous year’s VAT payment ratio to the supply cost multiplied by the current year’s supply cost:

$\text{va}t_{\text{cgf},t} = \frac{\text{va}t_{\text{cgf},t - 1}}{sp_{\text{cgf},t - 1}}*sp_{\text{cgf},t}$

Excise and other taxes components are decomposed into five categories: current carbon tax, current ETS permit price, new policy component, new excise tax, and fixed/ad-valorem part/other taxes.

Current carbon tax and ETS permit price: if the user decides to apply existing carbon pricing mechanisms, the values will be calculated based on historical values and planned policies. If a country’s carbon pricing policy is not specified for years after 2020, the current carbon tax / ETS permit price per energy unit, $\text{xcp}$, is calculated as:

$\text{xc}p_{\text{cgf},t} = \text{xc}t_{\text{cgf},t} + \text{xets}p_{\text{cgf},t}$

$= \text{xc}t_{\text{cgf},t_{0}}*\left( 1 + \delta_{\text{CT}} \right)^{t - t0} + \text{xets}p_{\text{cgf},t_{0}}*\left( 1 + \delta_{\text{ETS}} \right)^{t - t_{0}}$

$= \text{XC}T_{c,t_{0}}*ef_{\text{cgf}}*\varphi_{\text{XCT},\text{cgf},t_{0}}*\left( 1 + \delta_{\text{CT}} \right)^{t - t_{0}} + \text{XETS}P_{c,t_{0}}*ef_{\text{cgf}}*\varphi_{\text{XETS},\text{cgf},t_{0}}*\left( 1 + \delta_{\text{ETS}} \right)^{t - t_{0}}$

As show above, the existing carbon price per energy unit results from scaling the existing carbon taxes and ETS permit prices from the base year, $\text{XCT}$ and $\text{XETSP}$ respectively, by their specific coverage $\varphi$, the fuel-sector-specific emissions factor $\text{ef}$, and the user-defined growth rate of the nation-wide price for the forecasted years $\delta$.

New policy component:

$\text{nc}p_{\text{cgf},t} = \text{nc}t_{\text{cgf},t} + \text{nets}p_{\text{cgf},t} = \text{NC}T_{c,t}*ef_{\text{cgf}}*\varphi_{\text{NCT},\text{cgf},t} + \text{NETS}P_{c,t}*ef_{\text{cgf}}*\varphi_{\text{NETS},\text{cgf},t}$

where $\text{nc}t_{\text{cgf},t}$ and $\text{nets}p_{\text{cgf},t}$ stand for the new carbon tax per energy unit and the new ETS price per energy unit, respectively. In both cases, the value per energy unit is obtained based on the national price per ton of $CO2$ ($\text{NC}T_{c,t}$ or $\text{NETS}P_{c,t}$), and scaling it by the country-sector-fuel specific emission factors, $ef_{\text{cgf},t}$, and the sector-fuel coverage for the new policies within the country in question ($\varphi_{\text{NCT},\text{cgf},t}$ and $\varphi_{\text{NETS},\text{cgf},t}$).

Among the options available, the user can select the sectors or fuel that will be exempt of the policy implemented, as well as the linear phase out of those exemptions, if selected by the user. This is already considered in the sector-fuel coverage $\varphi$.

New excise tax: the user can specify additional per energy unit excise tax in the “Manual inputs” tab.
Fixed/ad-valorem part/other:
- If the country’s taxation regime is “fixed,” this category equals the previous year’s absolute value of the price gap not covered by the current ETS/carbon tax and VAT payment, corrected to price controls.
- If the taxation regime in the country is “ad-valorem,” this category is equal to the ratio of the previous year’s part of the price gap not covered by the current ETS/carbon tax and VAT payment to the supply cost, multiplied by the current year’s supply cost, corrected to price controls.

$o_{,t} = \left{

where $\frac{\text{Σfa}o_{\text{cgf},t_{0}}}{n_{t_{0}}}$ represents the average value of $\text{fao}$ during the base years.

3.9.3.4 Power generation costs: ‘Old’ cost model from IMF paper used only in elasticity based power model and only if ‘Old’ costs are selected.

Elasticity-based generation costs are defined as follows. The total unit costs of generation (i.e. for each fuel type considered), $\text{gn}c_{\text{ocft}}$, is estimated as:

$\text{gn}c_{\text{ocft}} = \text{ef}c_{\text{ocft}} + \text{nf}c_{\text{ocft}} + \text{rp}s_{o,\text{cgft}} + \text{nc}t_{P,\text{cgft}}*\left( 1 - \text{te}x_{P,\text{cft}} \right)$

where:

$\text{ef}c_{\text{ocft}}$ denotes the effective fuel unit costs (i.e. after autonomous efficiency gains), which is defined as the retail price before any new policies adjusted from the autonomous efficiency improvement in generation.
$\text{nf}c_{\text{ocft}}$ is the effective non-fuel unit costs (i.e. after autonomous efficiency gains). For the base year, non-fuel unit cost is assumed as a fixed proportion through the period of costs that are non-fuel, $\gamma$:

$\text{nf}c_{\text{ocf},t_{0}} = \frac{\text{ef}c_{\text{ocf},t_{0}}}{\left( 1 - \gamma \right)}*\gamma$

For the following years, effective non-fuel unit costs are equal to effective non-fuel costs from the previous year, adjusted from the autonomous efficiency improvement. – $\text{rp}s_{o,\text{cgft}}$ denotes the renewable producer subsidies, which only apply to wind, solar, hydro and other renewables.

3.9.3.5 New price target: Goal seek

When simulating the introduction of a new ETS permit, CPAT allows the user to define, among others, the year of implementation, the initial price/tax to be considered, and the level at which it should reach in a ‘target’ year. While still on a development phase, CPAT incorporates a ‘goal seek’ feature to help the user determine the new policy’s target price based on an goal on the emissions level.

Figure 3‑68: ETS target price - Goal Seek

Located to the right of the Advanced Options in the dashboard, the goal seek allows the user to input:

The sectoral inclusion
The proportion of the industrial sector to be covered (if Industry is included)
The emissions target (in absolute terms, or the reduction percentage)

The lower part of the goal seek shows the emissions, by sector, for the baseline and the policy. The ‘Total’ row shows, first, the aggregated emissions (considering only the sectors included by the user), second, the emissions goal, and third, the squared difference of emissions between the baseline and the policy scenario.

While the user can apply the goal seek functionality in Excel, the algortihm is not particularly useful in this case, and it is more convenient to test the different target prices manually, step-by-step.

In brief, once the inputs of the Goal Seek feature are provided, the user should check different alternatives of a target price and evaluate how emissions perform under each one. This simplified tool aims at giving a broad approximation of the price level required to achieve the emissions goal for the target year.

3.9.4 Appendix D - Examples of NDCs calculations

3.9.4.1 Example 1: Paraguay (BaU NDC)

NDC overview:

Unconditional target: 10% reduction relative to baseline emissions by 2030
Conditional target: 20% reduction relative to baseline emissions by 2030
GHG covered: CO2, CH4, N2O
LULUCF emissions: included

Calculations in CPAT:

Baseline GHGs, excl. LULUCF in 2030: 48.8 MtCO2e
Baseline GHGs, incl. LULUCF in 2030: 94.9 MtCO2e

Based on NDC targets:

Unconditional NDC target: 10% reduction relative to baseline emissions by 2030 * GHG excluding LULUCF: $48.8*\left( 1 - 10\% \right) = 43.9$ MtCO2e
- GHG including LULUCF: $94.9*\left( 1 - 10\% \right) = 85.4$ MtCO2e
Conditional NDC target: 20% reduction relative to baseline emissions by 2030
- GHG excluding LULUCF: $48.8*\left( 1 - 20\% \right) = 39.0$ MtCO2e
- GHG including LULUCF: $94.9*\left( 1 - 20\% \right) = 75.9$ MtCO2e

Figure 99: Rebound effect from exogenous efficiency improvements (% of emissions reduction reduced)

Figure 3‑69: Rebound effect from exogenous efficiency improvements (% of emissions reduction reduced)

3.9.4.2 Example 2: Colombia (fixed NDC)

NDC overview:

Unconditional target: 169.44 MtCO2e in 2030
Conditional target: N/A
GHG covered: CO2, CH4, N2O, HFCs, PFCs, SF6 and black carbon
LULUCF emissions: included

Calculations in CPAT:

Baseline GHGs, excl. LULUCF in 2030: 218.8 MtCO2e
Baseline GHGs, incl. LULUCF in 2030: 302.6 MtCO2e

Based on NDC targets:

Unconditional NDC target: 169.44 MtCO2e (including LULUCF) in 2030
- GHG excluding LULUCF: $169.4 - \left( 302.6 - 218.8 \right) = 85.6$ MtCO2e
- GHG including LULUCF: $169.4$ MtCO2e
Reformatting to baseline reductions in 2030:
- GHG excluding LULUCF reduction: $1 - \frac{\left( 85.6 \right)}{218.8} = 60.9$
- GHG including LULUCF reduction: $1 - \frac{\left( 169.4 \right)}{302.6} = 44.0$
Since NDC included LULUCF, we use 44% reduction as a target:
- GHG excluding LULUCF target level: $218.8*\left( 1 - 44\% \right) = 122.5$ MtCO2e

Figure 100: Rebound effect from exogenous efficiency improvements (% of emissions reduction reduced)

Figure 3‑70: Rebound effect from exogenous efficiency improvements (% of emissions reduction reduced)

NB: CPAT models the impact of carbon pricing on energy-related emissions. Colombia’s LULUCF emissions are 83.8 MtCO2e, about a half of GHG emissions target in 2030. The harmonized calculations would imply a high burden on energy sector to achieve NDC goals. However, the user should also consider measures that the country would take in other sectors (agriculture, forestry, land use, sectoral policies) to achieve NDC goals.

3.9.4.3 Example 3: Australia (historical NDC)

NDC overview:

Unconditional target: 26-28% reduction relative to 2005 emissions levels
Conditional target: N/A
GHG covered: CO2, CH4, N2O, HFCs, PFCs, SF6 and NF3
LULUCF emissions: included

Calculations in CPAT: * 2005 GHGs, excl. LULUCF: 526.2 MtCO2e * 2005 GHGs, incl. LULUCF: 617.2 MtCO2e * Baseline GHGs, excl. LULUCF: 568.5 MtCO2e * Baseline GHGs, incl. LULUCF: 546.0 MtCO2e

Based on NDC targets:

Unconditional NDC target: 28% reduction relative to 2005 levels:
GHG excluding LULUCF: $526.2*\left( 1 - 28\% \right) = 378.8$ MtCO2e
GHG including LULUCF: $617.2*\left( 1 - 28\% \right) = 444.4$ MtCO2e
Reformatting to baseline reductions in 2030: * GHG excluding LULUCF reduction: $1 - \frac{378.8}{568.5} = 33.4\%$ * GHG including LULUCF reduction: $1 - \frac{\left( 444.4 \right)}{546.0} = 18.6\%$
Since NDC included LULUCF, we use 18.6% reduction as a target:
- GHG excluding LULUCF target level: $568.5*\left( 1 - 18.6\% \right) = 462.7$ MtCO2e

Figure 101: Rebound effect from exogenous efficiency improvements (% of emissions reduction reduced)

Figure 3‑71: Rebound effect from exogenous efficiency improvements (% of emissions reduction reduced)

3.9.4.4 Example 4: Uruguay (intensity NDC)

NDC overview:

Unconditional target: 24% reduction in emissions intensity relative to 1990
Conditional target: 29% reduction in emissions intensity relative to 1990
GHG covered: CO2
LULUCF emissions: excluded

Calculations in CPAT: * 1990 CO2 emissions intensity: 4.62 (tCO2e/LCU) * 2030 baseline CO2 emissions intensity: 3.593 (tCO2e/LCU) * 2030 baseline GHG emissions, excl. LULUCF: 37.4 MtCO2e

Based on NDC targets: * Unconditional NDC target: 24% reduction in emissions intensity relative to 1990 levels: * CO2 intensity: $4.62*\left( 1 - 24\% \right) = 3.51$ MtCO2e * Conditional NDC target: 29% reduction in emissions intensity relative to 1990 levels: * CO2 intensity: $4.62*\left( 1 - 29\% \right) = 3.28$ MtCO2e * Reformatting to baseline reductions in 2030: * Unconditional CO2 intensity reduction: $1 - \frac{3.509}{3.593} = 2.4\%$ * Conditional CO2 intensity reduction: $1 - \frac{3.28}{3.593} = 8.8\%$ * Converting to GHG emissions reduction goal: * Unconditional GHG excluding LULUCF target level: $37.4*\left( 1 - 2.4\% \right) = 36.5$ MtCO2e * Conditional GHG excluding LULUCF target level: $37.4*\left( 1 - 8.8\% \right) = 34.1$ MtCO2e

Figure 102: Rebound effect from exogenous efficiency improvements (% of emissions reduction reduced)

Figure 3‑72: Rebound effect from exogenous efficiency improvements (% of emissions reduction reduced)

3.9.5 Appendix E – Defaults and parameter options in the mitigation module

These tables show the different parameter options related to the mitigation module in the dashboard of CPAT.

This tables presents the general settings.

Figure 3‑73: Dashboard: General settings

Settings	*Defaults () and additional options**	Description
Key policy option
Additional mitigation effort in non-energy sectors?	Yes*/No/Manual	Whether complementary policies are implemented alongside the main policy to target GHGs in non-energy sectors (industrial processes, agriculture, LULUCF, waste, and fugitive emissions). No macro/welfare effects are estimated.
Price pathway continues to rise after target year?	Linear*/No/Percentage	No = policy remains flat after target year Linear = price continues to rise in a linear manner after target year Percentage = price continues to rise at the same % growth rate in the target year of the linear pathway
Policy pathway is in nominal or real terms?	Real*/Nominal	If nominal, tax rate reduces with inflation.
Power price: portion of cost change passed-on:	1*/0.75/0.5/0.25/0	The portion of the increase in generation costs from the policy that are passed on in consumer prices. <1.0 for e.g. countries with state-owned utilities where the utility is not allowed to pass-on input cost increases to retail electricity prices.
Power feebate: power revenues rebated per kwh	No*/Yes	If selected, this means revenues raised from additional taxes/ETSs in power sector are kept within the sector through an output-based rebate to generators.
Phase out existing electricity taxes/subsidies?	No*/Yes	If there are existing electricity taxes or subsidies, phases them out over the same time period as fossil fuel subsidies (defined above). For mitigation purposes it is preferable to tax the fuels going into electricity generation rather than the electricity itself, which could be sourced from renewables as well as fossil fuels.
Harmonize VAT rates in residential and transport?	No*/Yes	Applies general economy’s VAT rate on residential and transport prices
Sources for key inputs
International energy price forecasts	AVG*/WB/IMF/EIA/IEA/IMF-IEA	WB/IMF/EIA/IEA = use institutions’ forecasts for international prices for oil, gas, and coal AVG = average of above four sources IMF-IEA = average of IEA and IMF Manual = defined in ‘Manual inputs’ tab
GDP growth forecasts	WEO*/Manual	WEO = growth forecasts from IMF’s World Economic Outlook Manual = see ‘Manual Inputs’ tab
Price elasticities of demand source	Simple*/Manual	Simple = elasticities drawn from literature review Manual = defined in ‘Manual inputs’ tab
Income elasticities of demand source	Simple*/Manual	Simple = elasticities drawn from literature review Manual = defined in ‘Manual inputs’ tab
CO2 emissions factors	IIASA*/IEA	Use CO2 emissions factors (CO2e per ton of pollutant) from IIASA or IEA.
Fiscal multipliers	Income-grp*/Estimated/Manual	Income-grp/global = multipliers extracted from macrostructural model and averaged for countries in same income group/global Estimated = fiscal multipliers estimated econometrically and averaged for regions Manual = user-defined (in ‘Manual inputs’ tab)
Power sector model (elasticity or engineer)?	Average*/Elasticity/Engineering	Engineering = use engineering-type power sector supply model Elasticity = use elasticity-based power sector supply model
Uncertainty adjustments
International energy prices adjustment	Base*/High/Low	Base = no adjustment High = increase forecast prices by 50% Low = reduce forecast prices by 50%
GDP growth adjustment	Base*/High/Low	Base = no adjustment High = increase forecast GDP growth by 50% Low = reduce forecast GDP growth by 50%
Price elasticities adjustment	Base*/Vhigh/High/Low/Vlow	VLow = reduce by 2 standard deviations Low = reduce by 1 standard deviations Base = no adjustment High = increase by 1 standard deviation VHigh = increase by 2 standard deviations
Income elasticities adjustment	Base*/Vhigh/High/Low/Vlow	VLow = reduce by 2 standard deviations Low = reduce by 1 standard deviations Base = no adjustment High = increase by 1 standard deviation VHigh = increase by 2 standard deviations
Adjust income elasticities for GDP levels?	Yes*/No	Adjusts income elasticities for electricity, gasoline and diesel with GDP levels (elasticities decrease as countries increase their per capita GDP). The intuition is that, for example, in middle-income countries households purchase fridges, but do not purchase additionals fridges as their income increaes further.
Fiscal multipliers adjustment	Base*/High/Low	Base = no adjustment High = increase all fiscal multipliers by 1 standard deviation Low = decrease all fiscal multipliers by 1 standard deviation
Max power sector renewable scaleup rate	Medium*/Vhigh/High/Low	Maximum investment rate for solar and wind per year. Please see the power sector section for the meaning of the options.
Renewable cost decline rate	CtryDefault*/Medium/Vhigh/High/Low	A learning rate methodology is applied, indicating the price reduction of the considered technology arising from every doubling of cumulative installed capacity (experience rate). CtryDefault = 2% increase of the installed capacity and 2.5% for China Low = 1% increase of the installed capacity Medium = 2% increase of the installed capacity High = 3% increase of the installed capacity Vhigh = 4% increase of the installed capacity
Miscellaneous
Include endogenous GDP effects?	Yes*/No	Use fiscal multipliers to model effects on GDP, which increases projected energy demand (‘rebound effect’)
Residential LPG/kerosene always exempted	No*/Yes	Exempts LPG/kerosene used in residential sector in all scenarios
National social cost of carbon (SCC) source	Target*/Ricke2018/GlobalUS-EPA	Shows national social cost of carbon source, which are the estimated cost of climate damages for the country, excluding costs to other countries (real US$2018 per ton of CO2) Target = global average Paris-consistent carbon price (set to $75 by 2030) Ricke2018 = uses Ricke et al. 2018 global estimates (further parametrization in ‘Advanced options’ in mitigation module) Global - US EPA - use global SCC estimate from the US EPA ($62 in 2018) Manual = see ‘Manual inputs’ tab
Congestion & road damage attributable to fuels	0.01	The portion of baseline congestion and road damage externalities attributable to motor fuels
Add non-climate Pigouvian tax on top?	No*/Yes/FFS	Adds additional Pigouvian tax for non-climate externalities (based on costs in baseline years)
Years to phase-in non-climate Pigouvian tax?	5	Number of years to gradually add non-climate Pigouvian tax on top of main policy
Add additional excise tax (see ‘Manual inputs’ tab)?	No*/Yes	Adds manual excise tax, as specified in ‘Manual inputs’ tab

This table presents the advanced mitigation options.

Figure 3‑74: Dashboard: Advanced mitigation options

Settings	*Defaults () and additional options**
General assumptions
First year of model calculations?	2019
Nominal results in real terms of which year?	2021
Use energy balances or (CPAT) energy consumption data	Consumption*
Generate Matrix of Energy Consumption Projections for Year	2019
NDC submission	Latest*/First round
Use ‘world’ (USA) or country-specific discount factors?	World*/Country
Sum all oil products in industrial transformation sector	Converted*/Raw
Adjust Annex I country energy-related CO2 EFs to match UNFCCC GHG inventories?	Yes*/No
Adjust non-Annex I country energy-related CO2 EFs to match CAIT GHG inventories?	Yes*/No
Industrial process emissions scale with industrial CO2 energy emissions?	Yes*/No
LULUCF emissions decline at % pa (in absolute value of start year)?	2.5%
Global energy demand scenario	Stated Policies*/Announced Pledges/Sustainable Development/Net Zero
Social cost of carbon (SCC) assumptions
Target-consistent carbon price by 2030 (for ‘Target’ option)	$75
NSCC discount rate (ρ)	2%*/1%
NSCC elasticity of marginal utility (μ)	1.5%*/0.7%
Global social cost of carbon (GSCC) source	Target*
SCC (both NSCC and GSCC) - annual rise in real terms from 2018	0.04
Apply existing non-carbon taxes?	Yes*/No - This setting can be broken down per fuel
Existing carbon tax
Apply existing carbon tax (if exists)?	Yes*/No
Assumed existing carbon tax growth per annum (real terms)	0
Existing ETS
Apply existing ETS (if exists)?	Yes*/No
Existing ETS permit price growth per annum (real terms)	0
New carbon tax complementary to existing ETS coverage	No*/Yes
Energy pricing assumptions
Use manual domestic energy prices?	No*/Yes
Use uniform global assumption for fuel prices (normally ‘No’)	No*/Yes
Externalities are part of VAT base for optimal taxes?	Yes*/No
Phase out Subsidies
Producer-side subsidy
Share of subsidies to phase-out in the policy scenario	100%
Apply phaseout in the baseline scenario?	No*/Yes
Period to reach full phaseout (baseline scenario)	5 years
Share of subsidies to phase-out in the baseline scenario	50%
Consumer-side subsidy
Share of subsidies to phase-out in the policy scenario	100%
Apply phaseout in the baseline scenario?	No*/Yes
Period to reach full phaseout (baseline scenario)	5 years
Share of subsidies to phase-out in baseline	50%
Price liberalization
Government energy price controls	None/Bucketed*/Manual
Phase-out price controls in the baseline?	No*/Yes

This table presents the advanced power sector options.

Figure 3‑75: Dashboard: Advanced power sector options

Settings	*Defaults () and additional options**	Description
Elasticity Model Parameters
Elasticity model uses economy-wide or sectoral power demand?	Economy-wide*/Sectoral
Use old or new generation costs in elasticity model?	New*/Old	Old: use Elasticity model original prices. New: use Engineer Model (without coal adjusment)
Engineer Model Parameters
k Parameter dispatch	2	Speed of transitioning between generation types with a different cost
k Parameter investment	2	Speed of transitioning between generation types with a different cost
Hydro retirement rate set to zero	Yes*/No
Baseline renewable energy subsidy, $/kwh nom	$0
Apply additional RE subsidy to hydroelectric power?	No*/Yes
Minimum (post subsidy) generation cost $/kwh real	$0.01
Maximum Coal Capacity Factor	90%
Maximum Gas Capacity Factor	90%
Use additional coal intangible cost	Yes*/No/Manual	Default Yes*: Account for intangible cost of coal. No: Do not account for implicit prices of coal. Manual: User can manually add data.
Manual Value for coal intangible cost (base year)	0
Manual Value for coal intangible cost (2030)	0
Maximum cost based early coal retirement proportion	80%
More Engineer Model Parameters
WACC: User-, Income- or Tech-dependent?	Income*/Tech/Use
If User-selected global WACC, what value?	7.5%	The WACC can also be technology-dependent, i.e. it can be specified for each technology. The WACC can be defined globally by the user.
Minimum WACC	1%
Percent allocation of ST storage costs to VRE	100%
Total hours short term strorage for 100% VRE	9 hours
kwh storage to kw interface ratio (hours)	2 hours
Percent allocation of LT storage costs to VRE	33%
Starting point of long term storage requirement (%VRE)	75%
GW electrolyzer per Gwy/y for 100% VRE (%)	1
kWh of LT storage per kW electrolysis	1000kWh
Use Spot Fuel Prices in Engineer Power Model	No*/Yes	It uses 5 year centred moving average, where we have data (3y for first year, 4y for second)
Use Engineer Covid Adjustment (1=Yes 0=No)	0
Max coal/gas invsmnt as a percentage of total gen	5%
Max hyd/ore/nuc/bio invsmnt as a percentage of total gen	2%
Max fossil/nuclear growth rate	2%
Engineer: Investment, Overrides and Financing
Plan or enable new investment	If present*/Yes/No/Manual	If present* = If Nameplate Capacity > 0, then an investment is accounted for in the model, otherwise no. Yes = Planned investments are enabled. No = Disable new investments. Manual = Allows the user to enter data. These data will overwrite the data determined by the model and new capacity will be accounted for as: New Nameplate Investments (MW) = Capacity data entered by the user + planned retirement.
Override Capacity Factor		The minimum of capacity factor for solar and wind, as well as for other technologies, and the maximum capacity factor can be modified.
WACC override (baseline and policy scenario)		The WACC can be specified for the baseline and the policy scenario.
Solar/Wind Max Investment	Medium*/Low/High/Vhigh	Percentage of total generation and of existing capacity of generation type

3.9.6 Appendix F - Notation in CPAT

This table presents CPAT four key components (‘Modules’) and their corresponding codes.

• Mitigation module – a reduced form energy model for projecting emissions and estimating impacts of pricing and other mitigation instruments on energy consumption, prices, GHG and local air pollutant emissions, revenues, GDP, and abatement

• Air pollution module – a reduced form air pollution and health model for estimating impacts on premature deaths and disease for local air pollutants like PM2.5 and ozone;

• Distributional module – a cost-push model for estimating impacts of changes in energy prices on industries and households (by income decile and region), including recycling of revenues from mitigation policy.

• Transportation module – a reduced form model for estimating the impacts of motor fuel price changes on congestion and road fatalities.

TabCode	CPAT Module
mit	Mitigation
ap	Air Pollution
dist	Distribution
tra	Transport

3.9.6.1 Sectors

This table displays the sector grouping used in CPAT. It shows the main sectors (industry, power, buildings, transport, other) and the corresponding codes. Each sector breaks into SubSectors, which have their corresponding codes.

SectorGroup	SectorGroupCode	SubSector	SubSectorCode
industry	ind	cement	cem
industry	ind	construc	cst
industry	ind	food_forest	foo
industry	ind	nonpowertrans	ftr
industry	ind	ironstl	irn
industry	ind	machinery	mac
industry	ind	mining_chemicals	mch
industry	ind	nonenuse	neu
industry	ind	nonferrmet	nfm
industry	ind	other	oen
industry	ind	other_manufact	omn
industry	ind	services	srv
industry	ind	worldav	wav
power	pow	power	pow
buildings	bld	residential	res
buildings	bld	food_forest	foo
buildings	bld	services	srv
transport	tra	domesair	avi
transport	tra	domesnav	nav
transport	tra	road	rod
other	oth	other	oth
all	all
eloutput	ele

3.9.6.2 Fuel types

This table presents the types of fuels used in CPAT and corresponding fuel codes used within CPAT. Additionally, there are three extra expanded fuel codes assigned to the biomass.

Fuel types	FuelCode	Expanded Fuel Code
Biomass	bio
in which: biodiesel		bgs
in which: biogasoline		bdi
in which: other liquid biofuels		obf
Coal	coa
Diesel	die
Electricity	ecy
Gasoline	gso
Hydro	hyd
Jet fuel	jfu
Kerosene	ker
LPG	lpg
Natural gas	nga
Nuclear	nuc
Other oil products	oop
Other renewables / Total self generated renewables	ore
Renewables	ren
Solar	sol
Wind	wnd

3.9.6.3 Scenarios

This table shows CPAT Scenarios and their corresponding numbers. Baseline, Carbon Tax, and ETS belong to General policies. The remaining scenarios are under Fuel or sector-specific policies.

Policy coverage	Scenario	Number
	Baseline	1
General policies
	Carbon tax	2
	ETS	3
Fuel or sector-specific policies
	Feebates	4
	Energy efficiency regulations	5
	Coal excise	6
	Road fuel tax	7
	Electricity emissions tax	8
	Power feebate	9
	Electricity excise	10
	Vehicle fuel economy	11
	Residential efficiency regulations	12
	Industrial efficiency regulations	13

3.9.6.4 Sub-models

This table displays sub-models that could be selected for analysis in CPAT.

ModelCode	Model
t	Techoeconomic Model
e	Elasticity Model
b	Both models
a	All

3.9.6.5 Pollutants

This table shows pollutants used in CPAT, their corresponding codes, and additional notes.

Pollutant	Code	Note
Black carbon	bc
Organic carbon	oc
Total carbon	tc	bc+oc
Nitrous oxides	nox
Sulphur dioxide	so2
Volatile organic compounds (VOC)	voc
Carbon monoxide	co
Methane	ch4
Ammonia	nh3

3.9.6.6 Unit codes

This table shows the energy units description used across CPAT and their corresponding codes.

UnitCode	Unit Name
twh	Terawatthour
gwh	GigawattHour
ktoe	Thousand (kilo) Tons of Oil Equivalent

3.9.7 Appendix G - Data sources

This table shows the data sources used in CPAT mitigation module.

Particular data set	CPAT data tabs	Openness category	Data source:	Link to data or Terms and Conditions (as applicable)
Greenhouse Gas Emissions	GHGs	Open	UNFCCC & WRI CAIT	WRI CAIT: https://www.wri.org/our-work/project/cait-climate-data-explorer UNFCC: https://unfccc.int/process-and-meetings/transparency-and-reporting/greenhouse-gas-data/ghg-data-unfccc/ghg-data-from-unfccc
Nationally Determined Commitments	NDCs	Open	Climate Watch	https://www.climatewatchdata.org/ndcs-explore
Domestic Fuel Prices	dom_prices	Open. CPAT (IMF side) derivatives from proprietary data	Various: IEA, Enerdata country offices, OECD. Openly available BNEF climatescope data. Refined.	IEA: https://iea.blob.core.windows.net/assets/3bf6ce57-3df6-4639-bf60-d73ee8f017c0/IEA-Terms-April-2020.pdf Enerdata: https://www.enerdata.net/terms-conditions.html OECD: https://www.oecd.org/termsandconditions/?_ga=2.92732957.129827420.1622686486-574055691.1595441182
Elasticities & Annual Efficiency Improvements	Elasticities	Open	Various (literature review)	N/A
Existing Carbon Prices	ECPPC	Open	WB Carbon Pricing Dashboard	https://carbonpricingdashboard.worldbank.org/
Power Sector Data	Power	Derivatives from open data	CPAT calculations from EIA data (Electrical Capacity); Energy GP calculation from IRENA (VRE scale-up); General Power Data is an average of openly available sources including: IEA, EIA, IRENA, Bogdanov et al and JRC (EU)	N/A
Social Cost of Carbon	SCC	Open	Ricke, K., L. Drouet, K. Caldeira and M. Tavoni. “Country-level social cost of carbon” (2018)	https://www.nature.com/articles/s41558-018-0282-y
Energy Consumption	Energy Consumption		CPAT calculations and projections from multiple data sources
World Development Indicators	WDI	Open	World Development Indicators	https://databank.worldbank.org/source/world-development-indicators
Macro data and projections from World Economic Outlook	WEO2020	Open	IMF WEO	https://www.imf.org/en/Publications/SPROLLs/world-economic-outlook-databases#sort=%40imfdate%20descending
Macro Balance of Payments from World Economic Outlook	WEOBOP	Open	IMF WEO	https://www.imf.org/en/Publications/SPROLLs/world-economic-outlook-databases#sort=%40imfdate%20descending
Emissions Factors	EF_GHG	Used with Permission	IIASA’s GAINS model	https://iiasa.ac.at/web/home/research/researchPrograms/air/GAINS.html
	CalVal	Used with Permission	IIASA’s GAINS model	https://iiasa.ac.at/web/home/research/researchPrograms/air/GAINS.html
International Energy Price Forecasts	int_prices	Open	World Bank Commodity Price Forecasts, IMF World Economic Outlook, IEA World Energy Outlook	WB: https://www.worldbank.org/en/research/commodity-markets; IMF: https://www.imf.org/en/Publications/WEO IEA: https://www.iea.org/topics/world-energy-outlook EIA: https://www.eia.gov/outlooks/aeo/tables_ref.php
Population	Popn	Open	Global Burden of Disease (2020); Vollset et al (2020)	https://www.thelancet.com/article/S0140-6736(20)30677-2/fulltext
Multipliers	Multipliers	Open	CPAT team	N/A

3.9.8 Appendix H – Validation with the EPM model

The following shows more comparisons with the EPM model, using a larger set of countries.

3.9.8.1 Electricity Demand Comparison

3.9.8.2 Electricity Generation By Fuel Type

3.9.8.3 New Investments By Fuel Type

The mitigation chapter of the CPAT documentation was prepared by Alexandra Campmas, Daniel Bastidas, Olivier Lelouch, Faustyna Gawryluk, Paolo Agnolucci, and Stephen Stretton. Some sections are based on earlier papers by Ian Parry, Simon Black, Karlygash Zhunussova, Nate Vernon, Alexandra Campmas, and Stephen Stretton. Thanks to the whole CPAT team – and, in particular, to Simon Black, Karlygash Zhunussova, Paulina Schulz Antipa, and Samuel Okullo for useful comments, clarifications, and assistance in preparing this paper. CPAT has benefited from the extremely helpful comments of our initial reviewers in early 2021 including, among others, Charl Jooste and Claire Nicolas; thanks also to Claire and Adam Suski for providing EPM comparison data. CPAT relies on the assistance of many parties for data and support, including other WB Global Practices (including Phillip Hannam from Energy GP, who helped develop the techno-economic power model) and other academic groups, including IIASA (who provided emissions factors). Thanks to Dirk Heine, Stephane Hallegatte, Simon Black, and Ian Parry for leadership and direction, and for originating what became CPAT. Thanks also to Somik Lall for leadership and guidance.↩︎
Income and price elasticities are based on a literature review. Income elasticities might depend (implicitly) on the level of GDP per capita (user option).↩︎
IMF (2019), Fiscal Policies for Paris Climate Strategies, From Principle to Practice $<https://www.imf.org/en/Publications/Policy-Papers/Issues/2019/05/01/Fiscal-Policies-for-Paris-Climate-Strategies-from-Principle-to-Practice-46826>$↩︎
Burke, Paul J., and Zsuzsanna Csereklyei. 2016. “Understanding the Energy-GDP Elasticity: A Sectoral Approach.” Energy Economics 58: 199–210. https://doi.org/10.1016/j.eneco.2016.07.004.↩︎
Gertler, Paul J., Orie Shelef, Catherine D. Wolfram, and Alan Fuchs. 2016. “The Demand for Energy-Using Assets among the World’s Rising Middle Classes.” American Economic Review 106 (6): 1366–1401. https://doi.org/10.1257/aer.20131455↩︎
Please note that more comparisons are available upon request.↩︎
With $o$=(B) for baseline; $o$=(P) for policy e.g., carbon tax.↩︎
Used in the emissions accounting section. This category distinguishes between energy-related (E), (which includes power, transport, buildings, industry and other energy use), Industrial Processes and Product Use (I), Agriculture (A), Land Use, Land-Use Change and Forestry (L), Waste (W), and Other (O) emissions.↩︎
For the aggregation of energy and emissions, sector groupings refer to buildings (i.e., residential, services, and food & forestry) industry, transport, and power. Some other calculations have different aggregations. For prices, sector groupings refer to residential, industry including services, transport, and power; for elasticities, sector groupings refer to residential, industrial, services (including food & forestry), transport, and power.↩︎
The following abbreviations for fuels considered are used in the documentation: Coal (COA), Natural gas (NGA) Oil (OIL), Nuclear (NUC), Wind (WND), Solar (SOL), Hydro (HYD), Other renewables (REN) and Biomass (BIO).↩︎
$t_{0}$ represents the first year of model calculations, also known as the base year (as of the time of writing, 2019).↩︎
IMF (2019): $<https://www.imf.org/en/Publications/Policy-Papers/Issues/2019/05/01/Fiscal-Policies-for-Paris-Climate-Strategies-from-Principle-to-Practice-46826>$ (Fiscal Policies for Paris Climate Strategies, From Principle to Practice.)↩︎
A shadow price translates a non-pricing policy type into an explicit carbon price.↩︎
Efficiency in the residential sector is retrieved from Malla & Timilsina (2014), Household Cooking Fuel Choice and Adoption of Improved Cookstoves in Developing Countries, The World Bank Development Research Group Environment and Energy Team, Policy Research Working Paper 6903. https://documents1.worldbank.org/curated/en/542071468331032496/pdf/WPS6903.pdf ↩︎
Burke, Paul J., and Zsuzsanna Csereklyei. 2016. “Understanding the Energy-GDP Elasticity: A Sectoral Approach.” Energy Economics 58: 199–210. https://doi.org/10.1016/j.eneco.2016.07.004.↩︎
Gertler, Paul J., Orie Shelef, Catherine D. Wolfram, and Alan Fuchs. 2016. “The Demand for Energy-Using Assets among the World’s Rising Middle Classes.” American Economic Review 106 (6): 1366–1401. https://doi.org/10.1257/aer.20131455↩︎
Empirical studies generally include rebound effects when estimating the total price elasticity of demand.↩︎
Transport sector studies accord to the highest share of elasticity studies, mostly gasoline and diesel. For estimates see Tables A1-A4 in Labandeira and others (2017).↩︎
Capacity factors are assumed to be as in the base year (unless those capacity factors are outside of normal ranges, when default values are used)

↩︎
They are also components of the forward-looking levelized cost (see investment costs/LCOEs, later)↩︎
Decommissioning costs are not discounted.↩︎
See https://www.iea.org/topics/energy-subsidies#methodology-and-assumptions ↩︎
Power plants are removed if status is cancelled, shelved, mothballed.↩︎
Bogdanov, D., Farfan, J., Sadovskaia, K., Aghahosseini, A., Child, M., Gulagi, A., Oyewo, A. S., de Souza Noel Simas Barbosa, L., & Breyer, C. (2019). Radical transformation pathway towards sustainable electricity via evolutionary steps. Nature Communications, 10(1), 1–16. https://doi.org/10.1038/s41467-019-08855-1 ↩︎
IMF (2019): $<https://www.imf.org/en/Publications/Policy-Papers/Issues/2019/05/01/Fiscal-Policies-for-Paris-Climate-Strategies-from-Principle-to-Practice-46826>$ (Fiscal Policies for Paris Climate Strategies, From Principle to Practice.)↩︎
Note that IIASA Emission Factors include process emissions, but we scale them to UNFCCC inventory emissions to only cover energy-related emissions↩︎
See https://pure.iiasa.ac.at/id/eprint/17552/↩︎
We calculate the Global Warming Potential (GWP) of GHG according to international norms (using GWP100, over 100 years timescale). This allows us to calculate a total Carbon Dioxide Equivalent (CO₂^e) value. GWP is also calculated for short-term pollutants which have a cooling effect.↩︎
For oil, it is worth noting that the component ‘other oil products’ is removed from the calculation as these types of fuels (e.g. light fuel oil) are not subsidized.↩︎
Note that road damage costs are also calculated in the Transport module. Resulting reduced road damage are currently not accounted for in welfare benefits, although they are also estimated in the Transport module (see Chapter Transport Module, Section Road damage).↩︎
Note that additional comparisons are available on demand. Notably, additional comparisons were done disaggregating the results per country, per sector and per fuel when available.↩︎
Rafaty et al. (2020) is comparable to CPAT in the sense that semi-elasticities are assessed globally and across different sectors.↩︎
The RMSE and its normalized version measure how far the projections are from observed historical data. The RMSE is scale-dependant, while the normalized RMSE is not, allowing for comparison across series or countries. Here, the normalization was done using the averages of the observed series as reference.↩︎