metadata: authors: 0: author: Fischer,Carolyn
1: author: Qu,Chenfei
2: author: Goulder,Lawrence H.
count: China
docna: 0: docna: Rate-Based Emissions Trading with
            Overlapping Policies : Insights from Theory and an
            Application to China
docty: Policy Research Working Paper
abstracts: cdata!: Jurisdictions that rely on emissions
            trading to control emissions often utilize other
            environmental or energy policies as well, including policies
            to support renewable energy and reduce energy consumption.
            Overlapping policies produce economic interactions that can
            lead to quite different outcomes from what might be
            predicted after examining individual policies separately.
            Prior literature on policy interactions has primarily
            focused on cap-and-trade systems, where aggregate emissions
            are fixed by regulation but emissions prices respond.
            However, jurisdictions are increasingly turning to
            alternative forms of emissions markets, including a range of
            rate-based emissions trading systems, in which both
            emissions quantities and prices are flexible and the
            significance of policy interactions is less understood. This
            paper extends the literature by considering the outcomes
            under a range of emissions trading systems&#x2014;not
            only cap-and-trade, but also several forms of tradable
            performance standards&#x2014;and under a variety of
            overlapping policies, including subsidies to renewables and
            taxes on electricity. An analytical model stylized on the
            electricity sector demonstrates that an overlapping subsidy
            to renewable energy drives down emission prices and expands
            output under all types of emissions trading systems, but
            emissions quantities differ with tradable performance
            standards&#x2014;emissions increase with renewable
            subsidies under a uniform, sectorwide tradable performance
            standard but decrease when the performance standard only
            covers emitters, excluding clean sources from receiving
            tradable credits. Taxing electricity consumption reduces
            emission prices and total output under all types of
            emissions trading systems and reduces emissions under all
            tradable performance standards. With cap-and-trade, the
            presence of an overlapping renewables subsidy or electricity
            consumption tax implies higher efficiency costs. Under
            certain tradable performance standards, however, these
            measures can reduce distortions and enhance
            cost-effectiveness. A numerical general equilibrium model
            offers quantitative assessments of the impacts of overlaps
            on emissions, production, prices, and costs, under
            China&#x2019;s planned emissions trading system and
            alternative designs. The overlaps in China&#x2019;s
            current stated policy for 2020 to 2035 reduce the cost per
            ton of abatement of its system of differentiated emitter
            performance standards by 20&#x2013;30 percent;
            optimizing renewable portfolio standards could further
            reduce costs by 10 percent, and transitioning to uniform
            benchmarks for emitting power generators could save another
            10&#x2013;15 percent. Still, cap-and-trade without
            overlapping policies would be most cost-effective. The
            findings highlight the need to consider the choice of
            emissions trading systems and overlapping policies together
            when undertaking reforms.
display_title: Rate-Based Emissions Trading with
            Overlapping Policies : Insights from Theory and an
            Application to China
listing_relative_url: /research/2024/08/34380085/rate-based-emissions-trading-overlapping-policies-insights-theory-application-china
topicv3: Climate Change Mitigation m1327079 579,Energy and Climate Change m1327080 1756,Environmental Management m1327125 598
publishtoextweb_dt: 2024-08-21T00:00:00Z
dois: 10.1596/1813-9450-10872
origu: Off of Sr VP Dev Econ/Chief Econ (DECVP)
no_of_pages: 69
author_keys: 0: author_key: 812983
1: author_key: 2238375
2: author_key: NA
model_extractions: Policy Research Working Paper 10872 Rate-Based Emissions Trading with Overlapping Policies Insights from Theory and an Application to China _Carolyn Fischer Chenfei Qu Lawrence H. Goulder_ Development Economics Development Research Group August 2024
Policy Research Working Paper 10872

# **Abstract**

Jurisdictions that rely on emissions trading to control emissions often utilize other environmental or energy policies as well, including policies to support renewable energy and reduce energy consumption. Overlapping policies produce economic interactions that can lead to quite different outcomes from what might be predicted after examining individual policies separately. Prior literature on policy interactions has primarily focused on cap-and-trade systems, where aggregate emissions are fixed by regulation but emissions prices respond. However, jurisdictions are increasingly turning to alternative forms of emissions markets, including a range of rate-based emissions trading systems, in which both emissions quantities and prices are flexible and the significance of policy interactions is less understood. This paper extends the literature by considering the outcomes under a range of emissions trading systems—not only cap-and-trade, but also several forms of tradable performance standards—and under a variety of overlapping policies, including subsidies to renewables and taxes on electricity. An analytical model stylized on the electricity sector demonstrates that an overlapping subsidy to renewable energy drives down emission prices and expands output under all types of emissions trading systems, but emissions quantities differ with tradable performance standards—emissions increase with renewable subsidies under a uniform, sectorwide tradable performance standard but decrease when the performance standard only covers emitters, excluding clean sources from receiving tradable credits. Taxing electricity consumption reduces emission prices and total output under all types of emissions trading systems and reduces emissions under all tradable performance standards. With cap-and-trade, the presence of an overlapping renewables subsidy or electricity consumption tax implies higher efficiency costs. Under certain tradable performance standards, however, these measures can reduce distortions and enhance cost-effectiveness. A numerical general equilibrium model offers quantitative assessments of the impacts of overlaps on emissions, production, prices, and costs, under China’s planned emissions trading system and alternative designs. The overlaps in China’s current stated policy for 2020 to 2035 reduce the cost per ton of abatement of its system of differentiated emitter performance standards by 20–30 percent; optimizing renewable portfolio standards could further reduce costs by 10 percent, and transitioning to uniform benchmarks for emitting power generators could save another 10–15 percent. Still, cap-and-trade without overlapping policies would be most cost-effective. The findings highlight the need to consider the choice of emissions trading systems and overlapping policies together when undertaking reforms.

This paper is a product of the Development Research Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at cfischer2@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **: Rate-Based Emissions Trading with Overlapping Policies Insights from Theory and an Application to China**<sup>*****</sup>

Carolyn Fischer,<sup>†</sup> Chenfei Qu,<sup>‡</sup> and Lawrence H. Goulder<sup>§</sup>

**Keywords** : emissions trading; market-based regulations; subsidies; renewable energy **JEL codes** : Q21, Q28, Q48, O38

* The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.

- World Bank Group, CESifo, and Resources for the Future (cfischer2@worldbank.org)

- Institute of Energy, Environment and Economy, Tsinghua University

- § Stanford University, NBER, and Resources for the Future
# **I. Introduction**

Economists for years have urged policy makers to adopt market-based mechanisms for controlling emissions of pollutants like greenhouse gases (GHGs). More and more jurisdictions have been introducing carbon pricing, either through carbon taxes or via tradable allowance systems (World Bank, 2022). Importantly, these jurisdictions typically have other energy or environmental policies in place, including support for renewable energy to promote the transition to a low-carbon economy. This overlap of policies leads to economic interactions that give rise to outcomes quite different from what one might predict after examining the individual policies separately. The overlaps affect outcomes for emissions, the prices of emission allowances, and levels of production.

A substantial literature has evolved to look at interactions between overlapping marketbased policies. Most have focused on the response of emissions tax and cap-and-trade (CAT) systems to additional interventions such as various supports for renewable energy (Sijm, 2005; De Jonghe _et al._ , 2009; Böhringer and Rosendahl, 2010; Fischer and Preonas, 2010; Fankhauser _et al._ , 2010; and Flues, Löschel _et al._ , 2014; Böhringer and Behrens, 2015).

The prior literature has often contrasted the case where a new policy intervention overlaps with an emissions tax (e.g., a carbon tax) and the case where it overlaps with an emissions trading system. In the former case, the emissions prices are fixed by statute; in the latter, these prices are determined by supply and demand in the market for allowances. The new intervention affects the shadow cost of meeting the regulatory obligations, thereby affecting emissions prices under CAT, a phenomenon that has come to be known as the “waterbed effect.” An example of this effect: when a binding renewable energy target is introduced in the presence of a CAT system, the requirement for more renewables than the market would otherwise provide lessens the need for other abatement measures to meet a binding emissions cap. This fall in demand for allowances causes emission prices to decline. Meanwhile, total emissions remain unchanged, as this total is determined by the emissions cap.

This paper extends the literature by considering the implications of overlaps for a wider range of emissions trading systems (ETSs), including not only cap and trade (CAT) but also several forms of tradable performance standards (TPSs). We also consider a range of policies with which the ETS overlaps, including subsidies to renewables and taxes on electricity. We 2
present analytical results that contrast the impacts of the different types of overlaps. We then describe and apply a numerical general equilibrium model that indicates quantitative impacts in the context of China’s economy.

CAT is a mass-based ETS: the total quantity (mass) of allowable emissions for each compliance period is pre-determined.<sup>1</sup> However, rate-based approaches are becoming more prevalent for emissions control. These approaches allocate allowances in proportion to output (or, occasionally, to input use), allowing total emissions to vary with the level of economic activity. Examples include China’s nationwide ETS for CO2 (Goulder _et al._ , 2022, 2023) and Canada’s federal and provincial output-based pricing systems for power and industrial sectors, which use intensity standards and credit trading. Rate-based ETSs may also be called tradable performance standards (TPSs), since the emissions allocation to regulated producers is determined by an emissions intensity benchmark.

Both the type of ETS and the type of overlap matter. ETSs vary in important ways. CAT is a mass-based ETS: the total quantity (mass) of allowable emissions for each compliance period is pre-determined. In contrast, TPSs are rate-based approaches that allocate allowances based on an assigned benchmark and the firm’s level of output; consequently, aggregate emissions are market-determined, depending on the level and, in some cases, the composition of production within a sector.

Within the general TPS category, there are also significant differences. Some TPSs set a uniform sector-wide performance standard for fossil- and non-fossil-based producers alike, such as a maximum emission intensity per kWh of generation from all sources. Other TPSs employ benchmarks that differ depending on (status quo) emissions intensities. Under the Chinese and Canadian TPSs, sources with higher emissions intensities face higher (less stringent) benchmarks, and non-emitting sources are unregulated and receive no benchmarks. We will use the label “SPS” for a rate-based ETS in which the performance standard is applied sector-wide, covering both fossil- and non-fossil-based producers. In contrast, we will apply the label “EPS” (for “emitter performance standard”) to refer to rate-based ETSs that cover only relatively highemitting sources such as fossil-based power generators, while relatively clean or non-emitting

> 1 In practice, some “flexibilty mechanisms” within a CAT system can allow the number of allowances to vary.

3
sources are excluded from benchmark allocations. The US EPA’s Affordable Clean Energy Rule (ACE) of 2019 is an example of an EPS: it establishes performance standards for existing coalfired generators only, based on modest goals for heat rate (efficiency) improvements.<sup>2</sup> Under all of these forms of rate-based ETSs, a covered firm’s allocation of emissions allowances is proportional to its production; it is the product of the assigned benchmark and the level of output. Such systems implicitly subsidize output, since additional production generates additional emission credits (Fischer, 2001). The subsidy discourages the use of output reductions or conservation as mechanisms for reducing emissions. In addition, differentiated forms of TPSs tend to discourage source-switching away from firms that enjoy relatively lax (i.e., high) benchmarks, while relatively clean sources receive less output support.

The TPSs we consider will differ in terms of both coverage (sectoral or emitter) and in terms of whether the benchmarks are uniform or differentiated. We will focus primarily on the following four types of ETS: (1) cap-and-trade (CAT); (2) a uniform sector-wide performance standard (USPS); (3) a uniform emitter performance standard (UEPS), which imposes uniform standards on covered sectors but includes no benchmarks for clean sources; and (4) a differentiated emitter performance standard (DEPS), in which higher emitting categories among the fossil energy sources are afforded higher benchmarks. Table 1 displays the main features of the different ETSs.

The nature of the interactions between such rate-based trading systems and overlapping energy or environmental policies differs from the interactions of CAT with such policies, as this paper will reveal. Under a (well-enforced) CAT system, total emissions are determined by the cap, apart from potential leakage outside the relevant domain of the system. In contrast, under a USPS, the presence of an overlapping subsidy to renewable energy lowers generation costs and electricity prices, and the expansion of electricity consumption and output gives rise to larger allowance allocations and emissions. Under an EPS, an overlapping subsidy yields outcomes that differ from both the CAT case and the USPS case; in this case, an overlapping subsidy to low- or zero-carbon energy crowds out production from higher-intensity sources and thereby lowers overall emissions. Under all forms of TPS considered, an accompanying increase in taxes on

> 2 However, since the ACE excludes trading, it is not an EPS as defined in this paper.

4
electricity reduces electricity production from all sources and thereby contributes to reduced emissions.

**Table 1. Features of Emissions Trading Systems Considered**

|**Compliance**<br>**Basis:**|**Mass-Based**|**(Tradable**|**Rate-Based**<br>**Performance Stand**|**ards, TPS)**|
|---|---|---|---|---|
|**Coverage:**|**Designated**<br>**Sectors or**<br>**Emitters**|**Designated**<br>**Sectors**|**Emitting Se**|**ctors Only**|
|**Benchmark**<br>**Specification:**|||Uniform|Differentiated|
|**ETS**<br>**Description**<br>**and Label:**|Cap and Trade<br>(CAT)|Uniform Sectoral<br>Performance<br>Standard (USPS)|Uniform Emitter<br>Performance<br>Standard (UEPS)|Differentiated<br>Emitter<br>Performance<br>Standard(DEPS)|

We derive these and other results analytically using an energy demand and supply model that considers a range of opportunities for fuel-switching and demand-reduction, as well as different types of emissions-control policies. The theoretical model reveals the effects of a range of potential policy overlaps, bringing out how the economic consequences differ depending on the combination of policies involved.

We complement this analysis with quantitative results using a numerical general equilibrium model that considers the different types of ETSs and overlaps. Its general equilibrium structure captures interactions across sectors and changes over time. The model is designed and calibrated to simulate the context of China’s recent introduction of a nationwide TPS (specifically, a DEPS) to reduce CO2 emissions. The issue of overlapping policies with ratebased trading is highly relevant to this new initiative, as the nation has also introduced overlapping subsidies to promote renewables-based electricity. Policy discussions suggest a significant possibility that China’s ETS will be revised to address the current incomplete passthrough of electricity prices. We apply the numerical model to assess the impact of a range of current and potential overlaps under alternative ETS designs.

5
The numerical model yields unique and policy-relevant findings regarding the implications of policy overlaps. First, overlapping policies improve the cost-effectiveness of China’s TPS (a DEPS), while reducing the cost-effectiveness of the CAT alternative. The overlaps in China’s stated policy<sup>3</sup> —a renewable portfolio standard, which implicitly taxes electricity consumption to subsidize renewable energy, and an additional requirement that TPScovered industrial sectors pay for their indirect emissions—reduce the cost disparity between China’s DEPS and an equivalent CAT by two-thirds.<sup>4</sup> Second, combining the stated policy overlaps with China’s DEPS is estimated to reduce the costs of meeting the given emissions reduction target by approximately 30%. Third, aligning renewable share targets more closely with China’s emissions targets could further enhance the existing system’s cost-effectiveness by approximately 10%. Fourth, reforming the ETS by phasing out differentiated benchmarks in the electricity sector could lower costs by 10%-15%, although the additional benefits from moving to a uniform, sector-wide performance standard are small in the presence of the given overlaps. These results highlight the need to consider the choice of ETS and overlapping policies together when undertaking reforms.

The rest of the paper is organized as follows. Section II offers the structure of the analytical model and derives and interprets results from that model under various types of overlaps. Section III offers results from numerical simulations of potential outcomes in China. Section IV presents the sensitivity analysis. Section V concludes.

# **II. Insights from theory**

The theoretical model of energy and environmental markets builds on those of Fischer and Preonas (2010, henceforth FP) and Fischer (2009), which use linearized supply and demand functions to analyze incremental policy changes from an equilibrium point. The framework is simple yet general enough to incorporate multiple ETSs and overlaps. The theoretical model focuses on incentives to reduce overall emissions by switching from higher-emitting to loweremitting sources or by reducing the supply of intended output (e.g., electricity). These incentives

> 3 This study employs the term “stated policy” to refer to the climate policies currently in place as well as those under development. Section IIIA provides a detailed discussion of these policies.

> 4 China is contemplating transitioning from its DEPS to a CAT system. These findings suggest smaller benefits from such a transiton than what otherwise might be expected, absent reforms to the overlapping policies.

6
align with the crucial differences among the policies, which include the differences in implicit output subsidies created by different allowance allocation systems. The model abstracts from some activities that can make individual sources less emissions-intensive, such as the adoption of efficiency improvements or new abatement technologies. This simplification helps sharpen the focus of our analytical model. Key outputs from this model are the impacts of overlapping subsidies or taxes on emissions, allowance prices and output under various ETSs. These results provide a foundation for the quantitative results from our numerical simulations.

# **A. Model framework**

The theoretical model considers the example of electricity generation, the industry most frequently regulated with emissions trading, but the results generalize to other industries as well. Four main types of generation are represented: higher-emitting fossil fuels _f_ , such as coal; loweremitting fossil fuels _g_ , such as natural gas; non-emitting renewable energy _r_ ; and baseload technologies _x_ , such as nuclear energy and large-scale hydropower, which are also non-emitting. Baseload generation is characterized as fixed and fully utilized generation capacity. Renewable energy sources include wind, solar, biomass, geothermal, and so on, and the structure also pertains to new, small-scale hydropower. Natural gas-fired generation has an emissions rate of _mg_ , while that from other fossil fuels has a higher emissions rate of _m f_ > _mg_ .

The model comprises a collection of upward-sloping, source-specific inverse supply curves and a single downward-sloping inverse demand curve,<sup>5</sup> thus offering the standard relationships between price (on the y-axis) and quantities (on the x-axis). Whereas the baseload supply curves are fixed and perfectly inelastic (i.e., _dx =_ 0), the non-baseload types of generation are assumed to have inverse supply curves _Sg_ ( _g_ ) ,<sup>_S_</sup> _f_ ( _f_ ) , and<sup>_S_</sup> _r_ (<sup>_r_</sup> )<sup>that are weakly upward-</sup> sloping (<sup>_S_</sup> _i_<sup>′ ≥</sup> 0 for all _i_ ); that is, the prices demanded by suppliers are either flat or increasing

> 5 Thus, the outputs of the industry are regarded as perfect substitutes.

7
with generation load.<sup>6</sup> The inverse consumer demand function is _D_ ( _f+g+r+x_ ), where _D_ ′ < 0 .<sup>7</sup> Let total output _Y_ = _g_ + _f_ + _r_ + _x_ .

If markets are competitive, the supply curves can be interpreted as marginal cost curves. When these technologies receive competitively determined (i.e., exogenous) prices, their marginal costs are equal to the price received. More generally, the supply curves represent whatever price is demanded by producers for an additional unit of generation at the amount supplied. This characterization can then more generally encapsulate producer responses, such as in imperfectly competitive or regulated electricity markets; the key feature is that supply curves are upward-sloping. For our narrative, we will assume competitive markets.

Let _P_ be the market price of electricity received by producers (the “wholesale price”). Policies to reduce emissions and promote renewables cause the after-tax prices received by suppliers to diverge according to the energy source and may also create a wedge between consumer (“retail”) prices and producer prices.

All of the major market-based policies for renewable energy and climate mitigation can be expressed as a combination of taxes and subsidies (see also Fischer and Newell 2008). We consider three: a price on emissions _t_ , a tax on electricity consumption _b_ , and a production subsidy for renewables _s_ . To this, we add a key feature of many tradable performance standards: namely, source-specific benchmarks or emissions rates that determine allowance allocations. The benchmarks are _ai_ , for _i=_ { _f_ , _g,r_ }. We will refer to “ _mi_ − _ai_ ” as the net emissions rate for electricity from generator type _i_ . The implicit subsidy to a source is the product of the benchmark and the emissions price. Since baseload generation sources are assumed to have fixed output, we ignore output-based allocations for these sources, which could equivalently be subsumed into a total lump-sum allocation, _A_ . In practice, large existing nuclear and hydropower sources are frequently exempt from performance standards, both by virtue of being clean and the fact that their capacity is not possible to adjust.

> 6 The symbols _f, g, r,_ and _x_ are used both to index the applicable industry and to indicate output levels. Steepness or flatness of the supply curves may depend on the timeframe being considered (short run or long run), and interactions with fossil fuel or land markets. We essentially assume that there are no increasing returns to scale for any overall supply curve.

> 7 FP used direct demand, so our equations will have the inverse of those slopes.

8
The market-clearing conditions are simply that the inverse supplies and demand equal the relevant prevailing market prices, inclusive of applicable policy interventions: To evaluate the effects of changes in different policy combinations on consumer prices, we first totally differentiate the market-clearing equations. From this, we derive a system of equations governing the responses to the different policies: Substituting (2)–(4) into (1) and solving for _dP_ , we can derive the electricity price impacts as a function of the various policy changes. Let χ = − _D_ ′ / ( _S_ ′ _f Sg_ ′ _Sr_ ′ − _D_ ′ ( _Sg_ ′ _Sr_ ′ + _S_ ′ _f Sr_ ′ + _S_ ′ _f Sg_ ′ ) ) > 0. Then we can define weights for source-specific policy changes as a function of the supply curve slopes of competing sources and χ , which ′ ′ ′ ′ ′ ′ determine the incidence of those changes: ω _r_ = χ _S f Sg_ , ω _f_ = χ _Sg Sr_ , ω _g_ = χ _S f Sr_ , and ω _D_ = 1 − ω _f_ − ω _g_ − ω _r_ . Note that 0 < ω _i_ < 1, for all _i_ .

The resulting price change can be expressed as a weighted average of the net tax and subsidy changes for fossil and renewable energy sources: where ~~μ~~ ≡ (ω _f_ ( _m f_ − _a f_ ) + ω _g_ ( _mg_ − _ag_ ) + ω _r_ ( _mr_ − _ar_ ) ) is a weighted average of the embodied emissions liability for generation, in which the slopes of the supply curves weight the individual 9
per-unit compliance obligations.<sup>8</sup> For sensible price responses to allowance cost changes, we make the following assumption restricting the policy design:

**Assumption 1** . Allowance allocations for each policy _j_ are such that ~~μ~~ _j_ > 0 (the weighted net emissions rate is positive) and _dP_ / _dt_ > 0 is assured.

From (5), we see that the wholesale price of electricity is increasing in the emissions tax _t_ , assuming that the weighted average benchmarks are lower than the average emission rates. It is decreasing in the electricity consumption tax _b_ , as well as in the renewable energy subsidy, _s_ . The net effect of changes in multiple policy variables on the price of electricity depends on the relative weights, which in turn are functions of the slopes of all the supply curves, as well as electricity demand.

Emissions trading systems that embrace fossil fuels but do not cover renewables have stronger price effects, the steeper the renewable energy supply and the flatter the fossil energy supply; these cases imply less flexibility to switch toward renewables. The opposite is true for policies targeting the renewables sector: price impacts are stronger when the renewable energy supply curve is flatter or the fossil energy supply curves are steeper (see also Fischer 2010).

Substituting (5) back into (2)–(4), we solve for the impacts on electricity supplies: From equation (8), we see that renewables generation is increasing with higher subsidies to renewables and higher emissions prices (as long as ~~μ~~ > −<sup>_a_</sup> _r_ ). From equations (6) and (7), we see that fossil energy sources are decreasing with increased support for renewables, which tend to displace fossil sources. Higher emissions prices also reduce production from the fossil source _i_ if _mi_ − _ai_ > ~~μ~~ ; that is, if its net emissions liability is higher than the average among fossil

> 8 This follows the presentation in FP, now including the benchmarks.

10
sources. From all three equations, we see that all energy sources are decreasing with higher taxes on electricity consumption in inverse proportion to the slope of their supply curve.

Since our model focuses on the fuel-switching options for reducing emissions, for emissions pricing to have sensible results, we assume that the higher-intensity fossil source (coal) is always relatively under-allocated: that is, it has a higher-than-average net emissions rate ( _m f_ − _a f_ > ~~μ~~ ) , leaving it with a net emissions liability. On the other hand, the less intensive fossil source (natural gas, which emits CO2 at about half the intensity of coal) may be relatively overallocated on net (i.e., _mg_ − _ag_ < ~~μ~~ ), depending on the stringency of the emissions regulation and the treatment of renewable generation for compliance.

The above equations reveal the basic responses to the policy price levers (renewables subsidies or electricity consumption taxes). In reality (and as discussed below), one or more of these levers may be endogenous.

Notably, we have the additional policy constraint that total emissions ( _E_ = _m f f_ + _mg g_ ) cannot exceed the total allowance allocation: We will restrict ourselves to binding regulations, implying that in equilibrium this constraint will hold with equality. Totally differentiating this market-clearing requirement yields the requirement that the total change in emissions must equal the total change in allowance allocation: With this additional equation, we can solve the system with the endogenous change in the emissions price, _dt_ , needed to bring the total change in emissions into balance with the total allowance allocation. This response depends on the particular combination of ETS and overlapping policy. We consider several combinations below.

# **B. Overlaps between ETSs and a subsidy or tax**

We focus on how outcomes differ depending on the magnitudes of the subsidy to renewable energy or the tax on electricity consumption that overlaps with the ETS. Specifically, 11
we explore the implications of changes to a subsidy to renewable energy ( _ds_ ) or to a tax on electricity consumption ( _db_ ) in the presence of various ETSs.<sup>9</sup> We begin with exogenous changes in the tax or subsidy. In Section II.C, we then consider combination cases in which the tax and subsidy may be linked by a policy requirement. Examples of linkage arise when subsidies to renewables are funded by taxes on electricity consumption, either explicitly (as in with many feed-in tariff programs) or implicitly (as with renewable portfolio standards, which require energy suppliers to purchase renewable energy credits in proportion to their energy sales (Fischer, 2010). Electricity consumption taxes may also be applied to fund transmission infrastructure or energy efficiency programs. We are particularly interested in the case where they are levied as an indirect tax on the embodied emissions associated with generation. The results that follow in this section provide the building blocks for analyzing the effects of those combinations.

# **1. Cap and trade**

We start with the case in which the ETS takes the form of cap and trade. Under a fixed CAT cap, _ar_ = _ag_ = _a f_ = _dA_ = 0. As a result, emissions are fixed ( _dE_ = 0) .<sup>10</sup> What does respond is the emissions price. Solving the system, we get The effect on overall output is

> 9 The change could be relative to an initial value of zero (which indicates the impact of the introduction of the subsidy or tax) or from an initially positive value. Although the focus is on marginal changes, the impact of a “large” change to the subsidy or tax can be viewed as the integral of successive marginal changes.

> 10 In this paper, we make the assumption that the subsidy does not apply to sectors that are not included in the emissions cap. Furthermore, although the emissions level determined by the emissions cap remains unaffected, there may still be an impact on overall emissions due to emissions leakage into sectors that are not covered. To evaluate this effect, a general equilibrium model like the one in secton III is necessary.

12
Ceteris paribus, _dY CAT_ / _ds_ > 0 and _dY CAT_ / _db_ < 0 . Overall output rises with a higher renewables subsidy, which directly lowers renewable energy costs and indirectly lowers the compliance cost burden on fossil sources, as allowance prices decline. However, the shift towards meeting the cap with more renewables and less conservation entails a loss in efficiency (in the absence of other market failures).

Furthermore, we see the result of Böhringer and Rosendahl (2010) that the subsidyinduced fall in the allowance price will allow the relatively emissions-intensive source to increase its output, at the expense of the less emissions-intensive fossil source. Since emissions only come from the two fossil sources, and total emissions are given by the cap, if generation from one falls, generation by the other must rise ( _m f df_ + _mgdg_ = 0) . The emissions-intensive source thus has a negative relationship with the carbon price, while the less intensive source has a positive relationship: Since both policy changes lower the equilibrium carbon price, both cause the more carbonintensive source to expand, while the less carbon-intensive source contracts.

Renewables, of course, are helped to a greater extent by the subsidy than they are harmed by the fall in electricity and emissions prices: The sign of the change is clearly positive, since supply curves are upward sloping and demand is downward sloping, and the squared terms and denominator are positive. Indeed, if renewables did not expand, there would be no crowding out to cause the price changes.

On the other hand, a tax on electricity tends to crowd out renewables as well as fossil sources on average: We summarize these results in the following proposition: 13
**Proposition 1:** _In the presence of a CAT system, a higher renewable energy subsidy implies a lower emissions price and greater output of both renewables and the higher-emitting source, as well as higher overall output. A higher electricity consumption tax implies a lower emissions price and less total output._

# **2. Uniform sector-wide performance standards**

With uniform sector-wide performance standards (USPS), the goal set by the regulation is to meet an average emissions intensity for all generators. Uniformity of the benchmark means that _a f_ = _ag_ = _ar_ = _a_ . The policy essentially combines a price on emissions ( _t_ ) with an implicit subsidy to output ( _ta_ ), which incentivizes production equally for all non-baseload sources (Fischer and Newell 2008).

**Proposition 2:** _Ceteris paribus, increasing a renewable energy subsidy in the presence of a USPS will lower the emissions price and increase both output and emissions._

**Proof.** Solving our set of equations using this form of allowance allocation, and setting _db_ = 0, we find that

where Ψ USPS = _Sr_ ′ _S_ ′ _f_ ( _a_ − _mg_ )2 + _Sr_ ′ _Sg_ ′ ( _a_ − _m f_ )2 + _S_ ′ _f Sg_ ′ _a_ 2 − _D_ ′( _Sg_ ′ _m f_ 2 + _Sr_ ′ ( _m f_ − _mg_ )2 + _S_ ′ _f mg_ 2 ) > 0 and Μ = ( _Sg_ ′ _m f_ ( _m f_ − _a f_ ) + _S_ ′ _f mg_ ( _mg_ − _ag_ ) ) . The proof for the numerator being positive follows from ~~μ~~ USPS = χ( _Sg_ ′ _Sr_ ′ ( _m f_ − _a_ ) + _S_ ′ _f Sr_ ′ ( _mg_ − _a_ ) + _Sg_ ′ _S_ ′ _f_ ( _mr_ − _a_ ) ) > 0 , which implies _Sg_ ′ ( _m f_ − _a_ ) + _S_ ′ _rf_ ( _mg_ − _a_ ) > _aSg_ ′ _S_ ′ _f_ / _Sr_ ′ . Thus Μ USPS = ( _Sg_ ′ _m f_ ( _m f_ − _a_ ) + _S_ ′ _f mg_ ( _mg_ − _a_ ) ) > _mg_ ( _Sg_ ′ ( _m f_ − _a_ ) + _S_ ′ _f_ ( _mg_ − _a_ ) ) > _mgaSg_ ′ _S_ ′ _f_ / _Sr_ ′ > 0. Emissions increase in proportion to output and the benchmark: _dE_ USPS / _ds_ = _a_ ⋅ _dY_ USPS / _ds_ > 0. □ 14
Under the USPS, total emissions are (by definition) proportional to output. In the presence of the USPS, adding a subsidy to renewables generation has three effects: i) it lowers costs for renewable supply directly; ii) by expanding production of a source with emissions below the benchmark, it depresses the emissions price, lowering costs for fossil energy sources; and iii) it depresses the value of the implicit output subsidy, which is tied to the emissions price. The first two factors would tend to expand overall production, but the third factor puts a drag on production.

With a USPS, the more emissions-intensive (under-allocated) fossil source gains unequivocally from an increase in renewables support, while the less-intensive source necessarily loses market if _a_ > _mg_ : For coal-fired generation, the fall in the carbon price lowers its net costs more than the fall in the price it receives for electricity. Natural gas-fired generation loses not only from lower prices but, to the extent it is overallocated, from lower values for its net allowance sales as well. As a result, the additional emissions from more coal-fired generation can outweigh the additional emissions savings from less gas-fired generation. If natural gas sources are also under-allocated, then the carbon price fall can help them expand as well, leading naturally to higher total emissions.

In contrast with a renewables subsidy, a tax on electricity consumption directly affects both renewable and fossil energy sources. From Equation (5), we know that consumption taxes reduce demand and depress the electricity price for all sources, causing each to decrease their supply in inverse proportion to the slope of their supply curve (by _db_ ( ω _D_ / _Si_ ′ ) ). As a result, demand for emission allowances also falls, and we can demonstrate the following:

**Proposition 3:** _Ceteris paribus, under a USPS, increasing an electricity consumption tax will cause overall output, emissions, and the emissions price to fall._

**Proof.** Solving the system of equations, we get

15
Since emissions are simply proportional to demand, any reduction in demand will lower emissions. □ Although an electricity consumption tax does not directly distinguish among sources, the indirect effects on the emissions price do discriminate. We find that an increase in the tax necessarily decreases total output, as well as production by the _less_ intensive emitting source. If that source is under-allocated ( _mg_ > _a_ ), renewable energy generation also falls, but the dirtiest generation may not (whereas the opposite is true if the less intensive source is over-allocated): In other words, two of the three types of sources reduce generation in response to the tax, while the third expands some of its share of the shrinking market; the dirtier source benefits if the emissions market is tight and both emitting sources are net buyers of allowances, whereas renewables benefit if the emissions market is looser and both it and the less intensive emitting source are net sellers of allowances.

# **3. Emitter performance standards**

Under emitter performance standards, the benchmark standards and compliance requirements are applied only to emitting sources. Since clean sources are thus excluded from the regulation, they receive no benchmark allocation value and thus no corresponding output subsidy.

We can distinguish two categories of EPSs. A uniform EPS (UEPS) applies the same benchmark to all emitting sources (and only to emitting sources). A differentiated EPS (DEPS) 16
applies different benchmarks to the emitting sources, distinguishing, for example, coal-fired from gas-fired generation, or blast furnaces from electric arc furnaces in steelmaking. Canada and China have implemented DEPSs. In those countries, more generous benchmarks are given to higher emitting sources: i.e., _a f_ > _ag_ > _ar_ = 0. In Canada, after a transition period, the intent is for this additional differentiation across electricity generators to be phased out, shifting from a DEPS to a UEPS.

As previously mentioned, the present analysis focuses on the incentives for fuel switching and conservation, rather than fuel efficiency or direct abatement options. Consequently, for an EPS policy to have a meaningful effect on reducing emissions, the policy must be designed such that the relatively emissions-intensive source is under-allocated, while the less intensive source is overallocated ( _m f_ > _a f_ ≥ _ag_ > _mg_ ) . The following results apply to any EPS, recognizing that the main distinction between a UEPS and DEPS is that the high-intensity fossil sources receive a more generous allocation under a DEPS than under a UEPS, which limits the reductions that can be achieved relative to the case under the UEPS.

**Proposition 4:** _In the presence of an EPS that excludes clean sources, increasing a subsidy to renewable energy will lower both the emissions price and emissions while raising output._

**Proof.** Let ∆ _f_ = _m f_ − _a f_ > 0 and ∆= _g ag_ − _mg_ > 0 . Assuming that<sup>_a_</sup> _r_<sup>=</sup> 0 and defining

> where ( _Sg_ ′ ∆− _f S_ ′ _f_ ∆ _g_ )χ _Sr_ ′ = ~~μ~~ EPS ≡ (ω _f_ ( _m f_ − _a f_ ) + ω _g_ ( _mg_ − _ag_ ) ) > 0 by Assumption 1 for sensible energy price responses to emissions price changes. □

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As indicated by equation (19) above, supplementing an EPS with a higher subsidy for renewables lowers emissions. In a sense, the subsidy to renewables corrects the distortion of that source’s under-allocation relative to fossil sources. Expanding renewables helps displace fossil energy sources, which reduces the number of allowances allocated and thus emissions. In fact, both types of emitting sources are crowded out, which could not happen under a CAT and was not certain under a USPS: Since total output rises, the increase in renewables is obviously greater than the decrease in emitting sources.

The overall effects of an electricity consumption tax increase are similar under a differentiated and uniform TPS, but now it is clear that the emissions price adjustment does not prevent all sources from contracting.

**Proposition 5:** _Ceteris paribus, under an EPS, increasing an electricity consumption tax will cause a decline in output from all sources, along with a decline in emissions and the emissions price._

**Proof.** Under an EPS,

Since all sources contract to some extent, emitting sources overall receive a lower allocation. □ 18
Note that an important distinction between a UEPS and a DEPS is the size of ∆ _f_ and ∆ _g_ . With a DEPS, both are smaller, since benchmarks are more closely aligned with emission intensities, which also means that Ψ EPS is smaller. With smaller numerators and denominators, it is not clear from the theory whether that differentiation amplifies emissions and price effects.

# **4. Summary of insights from theory**

Table 2a summarizes the effects of the various policy overlaps on the three variables of interest: the emissions price, sector emissions, and sector output.

**Table 2a. Summary from Theory: Effects of Overlapping Exogenous Subsidies and Taxes**

|**Overlapping Policy**|**Existing ETS**|**Allowance Price**<br>**Change**|**Emissions**<br>**Change**|**Output**<br>**Change**|
|---|---|---|---|---|
||CAT|–|0|+|
|Renewables Subsidy|USPS|–|+|+|
||EPS|–|–|+|
||CAT|–|0|–|
|Electricity<br>Consumption Tax|USPS|–|–|–|
||EPS|–|–|–|

Note: CAT – cap and trade; USPS – uniform sector-wide tradable performance standard, EPS – emitter performance standard. In the cases shown here, the changes in the subsidy and tax rates are regarded as exogenous rather than linked to each other.

The theory reaffirms results from prior studies that consider overlaps with cap and trade, while also offering new results for overlaps with other ETSs. Specifically, policies that drive additional renewable energy or conservation cause allowance prices to fall, not only when the ETS is CAT but also when it is a TPS. Under all of the forms of ETS considered, total sector output increases with overlapping policies like renewable subsidies that reduce supply costs but falls with policies like consumption taxes that increase product costs.

However, the effect of overlapping policies on emissions—the main target of ETS regulations—depends critically on the type of ETS. Under CAT, aggregate emissions are determined by a fixed cap; overlapping policies do not change total emissions. But when emissions are regulated by a TPS – a rate-based ETS -- the results depend on both the particular 19
type of TPS (USPS or ETS) and the type of overlap (renewables subsidy or tax on electricity consumption).

When a TPS overlaps with an exogenous subsidy to renewables, the overlapping subsidy leads to higher emissions when the TPS is a USPS: both the subsidy and the ensuing lower emissions prices lower production costs, allowing an expansion of generation and thereby higher emissions. In contrast, when the TPS is an EPS (under which renewables are not allocated allowances), an overlapping subsidy only changes the overall allocation of emission allowances to the extent it changes the output of covered sources; by crowding out production by emitting sources, the allocations and emissions of these sources fall. When a TPS overlaps with an exogenous tax on electricity consumption, there is less demand for output from all sources, reducing allowance allocations and thus emissions. The direct effect of the tax increase dominates any indirect cost savings from lower allowance prices, whether the TPS takes the form of a USPS or EPS. This stands in contrast to the CAT, where the allowance price change must fully absorb the change in demand for allowances.

# **C. Overlaps with linked electricity consumption taxes**

Up to now, we have examined the interaction of an ETS with exogenously implemented overlapping subsidies or taxes. Now we extend the analysis to consider situations in which the electricity consumption tax is endogenously determined. This additional focus is policy-relevant: as part of climate policy, taxes on electricity are often linked to the emissions or to renewables policies rather than introduced as independent rates. We concentrate on two main examples. First, we consider a case where the ETS policy includes a tax on electricity based on the emissions embodied in electricity consumption. Second, we consider a case where the emissions policy includes an electricity tax surcharge designed to finance the renewables support mechanism _._ The first case—involving a tax related to the value of emissions embodied in electricity consumption —is commonly proposed to address issues of incomplete price pass-through. The linkage arises when that value is determined by the prevailing ETS price. Incomplete price passthrough may occur, for example, due to rigidities in electricity markets with rate regulation, or due to the output subsidies implicit in benchmark allocations, which often aim to address 20
competition with unregulated goods (Neuhoff et al. 2016). California prices embodied emissions in imported electricity. The Republic of Korea's ETS and China’s regional ETS pilots both cover the indirect emissions from electricity consumption (IEA, 2020; ICAP, 2023).<sup>11</sup> A planned feature of the Chinese ETS is an implicit tax on the emissions embodied in electricity through a requirement that covered industrial emitters surrender emission allowances not only for their direct emissions but also for the indirect (embodied) from power generation.

A second case of linkage can arise from a requirement of revenue-neutrality.<sup>12</sup> As previously mentioned, many countries—including China—have committed goals for the expansion of renewable energy, and subsidies to renewables are frequently funded by earmarked taxes on electricity consumption, either explicitly through ratepayer-financed feed-in tariffs or implicitly through renewable portfolio standards. In such cases, revenue-neutrality requires the electricity consumption tax rate to equal the renewables subsidy multiplied by the renewable market share.<sup>13</sup>

# **1. Electricity tax linked to emissions embodied in electricity consumed**

When linked with an ETS, a tax on the emissions embodied in the consumption of the regulated good (in this case, electricity) is the product of two endogenous variables: 1) the emissions price from the ETS, and 2) the emissions intensity of electricity production, as influenced by the regulation. In our terminology, _db_ is the (now endogenous) tax on electricity consumption, equal to the per-unit embodied emissions cost. We will use the suffix “-2” to identify the cases involving embodied emissions taxes. Indirect emissions from electricity are commonly referred to as Scope 2 emissions, in contrast to Scope 1 direct emissions and Scope 3 other indirect emissions.

> 11 Korea’s ETS is a mass-based system with indirect emissions from electricity consumption covered. Similarly, China’s ETS pilot in Chongqing follows a mass-based approach that also accounts for indirect emissions from electricity consumption. Consequently, we have examined a CAT system linked with an embodied emissions tax in both theoretical and numerical applications, as this reflects certain policy practices in reality.

> 12 Many emissions-reduction policies are effectively a combination of policy instruments (Fischer and Newell 2008).

> 13 A renewable portfolio standard is functionally equivalent to the combination of a subsidy to renewables (the value of a renewable energy credit) and a tax on consumption (the credit value multiplied by the standard). See, for example, Goulder, Hafstead, and Williams (2016).

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> Suppose electricity consumers face an emissions price _b_ = _t_ _~~a~~_ , where _~~a~~_ = _E_ / _Y_ = ( _a f f_ + _ag g_ + _arr_ + _A_ ) / _Y_ is the average emissions per unit of electricity, equal to the average per unit allocation. Then _db_ = ( _dt_ ) _~~a~~_ + ( _d_ _~~a~~_ ) _t_ . The change in embodied emissions intensity with respect to changes in the source variables is

The equilibrium change in embodied emissions depends on the type of ETS. Under CAT, average intensity falls with output: _d_ _~~a~~_ CAT = − _~~ad~~ Y_ / _Y_ . With a USPS, average intensity is USPS fixed by design: _d_ _~~a~~_ = 0.With an EPS, the change in the average emissions rate depends on the change in the composition of output: _d_ _~~a~~_ EPS = ( ( _ag_ − _~~a~~_ ) _dg_ + ( _a f_ − _~~a~~_ ) _df_ − _~~ad~~ r_ ) / _Y_ .

The following propositions explain the intuition of the effects of changes in an overlapping subsidy to renewables in a context with an embodied emissions tax linked to the ETS price. For clear and coherent results, we restrict the range of the embodied emissions tax such that _t_ _~~a~~_ < − _D Y_ ′ . This restriction is akin to assuming that, with linear demand, a price equal to the embodied emissions charge would lie in the elastic portion of the demand curve.<sup>14</sup>

**Proposition 6:** _In a CAT system with a linked embodied emissions tax, increasing a subsidy to renewable energy raises output and lowers emissions prices._

**Proof.** From Proposition 1, a renewable subsidy increases output, which lowers the average emissions intensity, given that total emissions are fixed under a CAT. It also lowers the emissions price. These effects in turn lower the embodied emissions tax ( _db_ / _ds_ = ( _A_ / _Y_ ) _dt_ / _ds_ − _t_ ( _A_ / _Y_ )( _dY_ / _ds_ ) / _Y_ ) < 0) , and a lower electricity consumption tax amplifies the output increase, while only partially attenuating the emissions price change. (Mathematical proof in Appendix A).□

> 14 This restriction is akin to avoiding a Laffer-Curve-type of response.

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**Proposition 7:** _In a USPS system with a linked embodied emissions tax, increasing a subsidy to renewable energy lowers emissions prices and raises both output and emissions._

**Proof.** With a USPS, the embodied emissions tax change depends only on the emissions price effect of the additional intervention ( _db_ = _a_ ⋅ _dt_ ) . From Proposition 2, a higher renewable subsidy increases total output and lowers the emissions price, which implies a decrease in the linked consumption tax. From Proposition 3, a lower consumption tax amplifies the output increase. Since emissions are proportional to output, emissions rise. (Mathematical proof provided in Appendix A.)□

In other words, while adding indirect emissions pricing to a USPS can reduce emissions, it makes the system more sensitive to other overlapping policies. For example, renewable subsidies become more environmentally counterproductive: with linked embodied emissions pricing, increasing a subsidy to renewables drives larger increases to output and emissions under USPS than without indirect emissions pricing.

**Proposition 8:** _In an EPS system with a linked embodied emissions tax, increasing a subsidy to renewable energy will lower the embodied emissions tax, lower total emissions, and allowance prices, and raise total output._

**Proof.** With an EPS, the change in the electricity consumption tax has three drivers: the change in the emissions price, the change in emissions, and the change in output ( _db_ = _~~ad~~ t_ + _t_ ( _dE_ − _~~ad~~ Y_ ) / _Y_ ). From Proposition 4, an increase in the renewable subsidy puts downward pressure on both emissions and emissions prices and upward pressure on output. All of these drive down the embodied emissions tax. From Proposition 5, a reduction in the consumption tax puts upward pressure on output, as well as on emissions and emissions prices. Thus, the direct and indirect effects of an increase in the renewable subsidy align to expand output, but they push emissions and the emission price in opposite directions. The mathematical proof in Appendix A demonstrates that the first effects from the renewable subsidy dominate the indirect effects of the embodied emissions tax changes, at least when _t_ _~~a~~_ < − _D Y_ ′ .

# **2. Electricity-tax – funded renewables subsidy**

Here we briefly consider the effect of changes in the renewable energy subsidy when the subsidy and tax are linked through the requirement that the subsidy be financed through a tax on 23
electricity consumption. Many countries, including China, have committed to such financing of renewables subsidies.

With such linkage, we have _b_ = _s_ ⋅ _r_ , so _db_ = _ds_ ⋅+ _r s_ ⋅ _dr_ . In this case, higher renewable subsidies raise revenue requirements and the needed electricity consumption tax rate. Using the results in Section II.B (Table 2a), we can infer the effects of _ds_ and _db_ on prices, output, and emissions. The results are in Table 2b below.

Both of these actions depress allowance prices across all policies. Therefore, an increase in an electricity-tax-funded renewable subsidy unambiguously lowers emissions prices, regardless of the ETS in play. This price decrease should be larger than if the electricity consumption tax were exogenously determined.

Regarding total output, ceteris paribus, a higher renewable subsidy raised output under all ETSs, while a higher consumption tax reduced it. These actions work in opposite directions, so the output impacts are ambiguous and depend on the size of the subsidy and the share of renewables in output. The question is whether the supply cost reduction from the renewable subsidy is more than offset by the consumer cost increase from the tax. Fischer (2010) demonstrated that renewable portfolio standards could increase or decrease retail electricity prices for consumers, depending on the relative slopes of the supply curves and the stringency of the policy. Therefore, it is possible that such a linked renewable energy policy could increase or decrease total output under any ETS scenario.<sup>15</sup> Regarding emissions, the directions of the effects depend on the ETS type. As was the case with exogenous taxes and subsidies, emissions do not change when the ETS is in the form of CAT. With a USPS, emissions rise or fall in proportion to total output, so the impact of the linked subsidy is ambiguous in this case. However, both actions cause emissions to fall under an EPS; therefore, increasing an electricity consumption tax-funded renewable subsidy will drive down emissions when overlapping with an EPS.

> 15 For this reason, a mathematical treatment is not offered, as it does not yield unambigous results.

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**3. Summary of overlapping linked subsidies and taxes**

**Table 2b. Summary from Theory: Effects of An Increase in An Overlapping Policy**

|**Overlapping**<br>**Policy**|**Existing ETS**|**Allowance Price**<br>**Change **|**Emissions**<br>**Change **|**Output**<br>**Change **|
|---|---|---|---|---|
|Renewable Subsidy|CAT-2|–|0|+|
|with Embodied|USPS-2|–|+|+|
|Emissions Taxes|EPS-2|–|–|+|
|Renewable Subsidy|CAT-T|–|0|+?–|
|Financed by|USPS-T|–|+?–|+?–|
|Consumption Tax|EPS-T|–|–|+?–|

Note: CAT - cap and trade; USPS - uniform sector-wide tradable performance standard, EPS - emitter performance standard.

Under each type of ETS, a sector consumption tax linked to embodied emissions costs affects the magnitude but not the direction of impacts from a change in an overlapping renewable subsidy. The renewable subsidy tends to expand output and drive down the emissions price, which serves to lessen the embodied emissions costs, further allowing output to expand. The consumption tax response has an attenuating impact on the emissions price but does not undo the direct effects.

By contrast, when the electricity consumption tax is used to fund renewable subsidy costs, an increase in the subsidy rate requires a higher tax. Both of these actions drive down the emissions price necessary to meet any of the ETS requirements. But they push output in different directions. In the case of the USPS, this means the effect on emissions is uncertain. By contrast, with an EPS, both actions drive down emissions.

# **D. Efficiency considerations**

Our results have important implications for understanding the consequences of overlapping policies on the overall efficiency or cost-effectiveness of emissions trading.<sup>16</sup> When

> 16 Here we are measuring efficiency in terms of the costs of achieving given targets for emissions reductions. Thus it is synonymous with cost-effectiveness. A broader notion of efficiency would consider the environment-related benefits (avoided damages) as well as the costs from the reducitons. Such benefits are beyond the scope of this study. We simply note here that two policies that produce the same aggregate emissions reductions can yield different net benefits insofar as the environmental consequences from the reductions differ.

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the only market failure is from the emissions-related externality, CAT is the most cost-effective, and adding renewable subsidies or electricity consumption taxes increases costs per ton of abatement. TPSs alone are less cost-effective, but overlapping policies have the potential to increase (or decrease) cost-effectiveness,<sup>17</sup> and in some cases, a TPS can emerge as more efficient than a CAT system with the same overlaps.

For example, with a uniform sector-wide TPS (the USPS) achieving the same emissions outcomes as CAT, in the absence of overlaps, the emissions price will be too high and the electricity price too low in terms of efficiency. An overlapping electricity tax (a tax on output) can help undo the distortion from the implicit subsidy stemming from the policy’s output-based allocation. In contrast, an overlapping renewables subsidy expands the USPS’s efficiency handicap by further depressing output prices and putting upward pressure on emissions and requiring more stringent intensity standards to compensate.

An EPS, by virtue of applying the performance standard only to emitting sources, introduces inefficiencies by subsidizing the output of emitting sources to the exclusion of clean sources. Relative to a uniform EPS (UEPS), a differentiated EPS (DEPS) adds to inefficiency by offering different benchmarks (and associated subsidies) to emitting sources that depend on their emissions intensities. For a given emissions target, the allowance price will have to be even higher to achieve comparable overall incentives to reduce emissions. Linking the electricity tax to the embodied emissions in electricity consumption can offset some of the output subsidies _on average_ , thereby helping to improve efficiency. However, it does not undo the inefficiency from the benchmark differentiation. A renewables subsidy can make up for the lack of comparable benchmark allocation to renewables under a DEPS, promoting efficiency by in effect making the standard more uniform.

These efficiency considerations provide a springboard for the more detailed treatment and quantitative results from the numerical model. The numerical model has an explicit treatment of production costs, which yields quantitative results in terms of cost-effectiveness. It also considers an additional emission-reduction channel beyond the fuel-switching and demandreduction channels captured by the theoretical model: this is the potential of covered firms to reduce emissions intensities through changes in production methods. It also addresses general

> 17 See Braathen (2007) and Fischer, Huebler and Schenker (2019).

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equilibrium interactions across sectors. These additional channels can be expected to influence the quantitative outcomes but do not yield outcomes that differ qualitatively from the main findings obtained in this section. As part of a sensitivity analysis (detailed in Appendix D), we identify the relative significance of the various channels mentioned here.

# **III. Results from numerical simulations**

To understand the quantitative importance of ETS design and the role of overlapping policies, we conduct numerical simulations using a general equilibrium model applied to China. The evolving Chinese national ETS is a DEPS with several proposed overlaps, including a price on indirect CO2 emissions arising from electricity consumption for certain industrial sectors and mandates for renewable energy shares. The numerical model allows us to explore how policy outcomes depend on the specific design of China’s ETS and the overlapping policies.

# **A. The context: China’s ETS and other policies**

China’s announced climate goals are to have CO2 emissions peak before 2030 and achieve carbon neutrality before 2060. The national ETS, introduced in 2021, is expected to contribute importantly to meeting those goals.

In its current phase, the system covers the electricity sector, which is responsible for over 40 percent of China’s CO2 emissions. Coverage is scheduled to expand to other sectors in several phases and eventually include most of the significant energy-intensive industries. The second phase is likely to begin sometime in 2024, when the system’s coverage will expand to include the cement and aluminum sectors, and possibly the iron and steel sector as well. These three sectors currently account for about two-thirds of China’s CO2 emissions. One or more further phases are expected, during which the system will expand to cover other emission-intensive sectors, including pulp and paper, other non-metal products, other non-ferrous metals, chemicals, and refined petroleum. At that point, the system would likely account for at least 65 percent of China’s CO2 emissions.

China’s emissions trading system employs different benchmarks for different kinds of covered entities, both across and within sectors. Within the electricity sector, there are three benchmarks for different categories of coal-fired power plants and one for gas-fired power 27
plants. These plants receive free allowances equal to the product of their electricity generation and the corresponding benchmarks. Renewable electricity is not covered: it receives no free allowances. Thus, the Chinese ETS is a DEPS under our terminology.

In phases 2 and 3, when the system expands to industrial sectors, the non-electricity sectors likely to be covered will be required to surrender allowances not only for their own direct emissions but also for the indirect emissions associated with the electricity used by these sectors, following the precedence set by China’s pilot ETSs (Zhang _et al._ , 2021). If this requirement applies, the free allowance allocation given to these industrial sectors via their own benchmarks will also be adjusted to reflect these indirect emissions requirements. As mentioned, this pricing of indirect emissions functions as a tax on electricity consumption for which the value is tied to the prevailing emissions price and the average emissions intensity of electricity. This additional compliance liability has the effect of partially offsetting the implicit output subsidy inherent in China’s tradable performance standards for the electricity sector. The industrial consumers facing the charge on indirect emissions in electricity could be expected to consume roughly 10 percent and 25 percent of total electricity in Phase 2 and Phase 3, respectively.

China has to date been relying on subsidies to encourage the development of renewable energy. Before 2017, China deployed feed-in tariffs (FIT) to promote the development of wind and solar electricity. The FIT scheme offered a 20-year contract to eligible projects, featuring fixed FIT rates determined by the specific renewable technology, resource availability at the project site, and the year of plant construction. In keeping with the trend of cost decrease of renewable electricity generation, China has continuously lowered its FIT rates since 2014 and phased out FIT subsidies from the central government for new wind and solar projects by the end of 2020 (China, NDRC, 2021b). The National Development and Reform Commission (NDRC) has announced that the central government will discontinue direct production subsidies for new solar and wind power plants that are approved after 2021.

In 2019, China removed the FIT scheme. In its place, it introduced an RPS to promote sustainable development and better integration of renewables (NDRC and NEA, 2019). The RPS can be viewed as the major instrument to support the continued development of renewables in China, and thus it represents the most important policy with which China’s ETS overlaps. The plan includes a provision for green electricity trading, Provincial governments are required to 28
purchase enough renewable electricity to meet minimum targets for the share of renewable electricity in total electricity consumption for individual provinces (NDRC, 2023). Obligated parties can fulfill the targets by generating their own renewable electricity, by a bilateral agreement with those exceeding their RPS quota, or by buying green power through Green Power Trading or Green Certificates Trading. As discussed in the theory section above, this RPS is equivalent to an electricity-consumption-tax-funded subsidy, in which the subsidy rates are endogenously determined by the renewable share targets under TPS.

# **B. Numerical model**

To evaluate China’s nationwide ETS, we employ a multi-sector, multi-period general equilibrium model. The model is adapted from the version documented in Goulder _et al._ (2023). Thirty-one production sectors in China’s economy are distinguished. In each sector (or subsector, as applicable), a representative firm employs inputs of primary factors (capital, labor, and natural resources) along with intermediate inputs (energy and material goods) to produce goods for the domestic market and export. A representative household earns income from returns to the factors of production and devotes that income to consumption, savings and transfers to the government. The government uses the transfers for government consumption and public savings. Private and public savings finance investment. The final demand for goods and services consists of household consumption demand, public and private investment demand, and the government’s demand for goods and services. The model incorporates emissions allowance trading. For each year in the interval 2020 through 2035, it solves for the equilibrium factor prices and allowance prices as well as the prices of all produced goods. Details on the model’s structure and parameters are provided in Appendix B.

The model has several features that make it especially suitable for this study. It has considerable flexibility to examine CAT and various types of TPSs and the interactions between these systems and various overlapping policies. Its treatment of heterogeneous fuels and technologies enables it to capture the fuel-switching options under CAT and TPS systems. The electricity sector in the model distinguishes nine coal-fired generation technologies, two gasfired generation technologies, two renewable generation technologies, and two baseload technologies (hydropower and nuclear power).

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Additional features of the model enable it to address dimensions not captured by the theoretical model. In particular, its multi-period structure allows it to examine how impacts evolve with changes in coverage and policy stringency. Its general equilibrium framework enables it to consider the impacts of CAT and various types of tradable performance standards not only in the covered industries but in other industries as well. The incorporation of trade responses also allows it to consider changes in imports and exports and the corresponding emission leakage associated with these changes.<sup>18</sup>

# **C. Cases**

Our numerical simulations consider a range of ETSs and overlapping policy scenarios. Building on the preceding insights, we define the following scenarios that differ according to the type of ETS in place—CAT, USPS, UEPS, and DEPS—and the policy or policies with which the ETS overlaps. We consider scenarios where these overlapping policies are implemented individually or in combination. These overlapping policy settings are summarized in Table 3. The labels R and S refer to overlapping RPSs and subsidies. The labels “2” and “N” respectively refer to scenarios with or without Scope 2 emissions pricing of electricity. NO indicates no overlaps.

The DEPS-R2 policy most closely approximates China’s actual policy environment, resulting in economy-wide emissions reductions of 7 percent, 8 percent, and 20 percent in the first, second, and third phases, respectively. For comparability, in the USPS and UEPS cases, relative benchmarks for fossil electricity versus non-fossil electricity are determined by the weighted average benchmarks under the DEPS, but the absolute benchmarks in each period across scenarios are scaled so that the resulting emissions in each year equals that of DEPS-R2.

> 18 Relative to the model in Goulder et al. (2023), this paper’s model incorporates some simplifications to permit a closer match with the theoretical model. It ignores pre-existing taxes on labor and capital and thus it disregards some second-best issues. Pre-existing distortions offer some justification for output-based rebating (Fischer and Fox 2011; Fischer and Springborn 2011); we reserve these aspects for future research. It also disregards some pre-existing regulations and associated distortions in the electricity sector. Historically, China’s electricity prices and supplies have faced significant government regulation. However, the system has been going through rapid reform in recent decades. Currently, about half of the electricity generated in China faces market prices. The nation aims to go further and achieve a fully liberalized electricity market system before 2025 (NDRC and NEA, 2021). Correspondingly, the numerical model treats electricity prices as market-determined. Also, the model includes a relatively simple treatment of capital dynamics, representing the real investment as fixed shares of gross domestic product.

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China’s stated policy overlaps (“R2”) include the RPS as the renewable promoting policy and the scope-2 indirect emission pricing (IEP) for the ETS-covered sectors. In the model, the RPS policy is an endogenous electricity-consumption-tax-funded renewable subsidy, where the rates fulfill the projected RPS targets each year. The RPS target shares for non-hydro renewable electricity at the national level in 2025 and 2030 are drawn from NEA’s consultation draft (NEA, 2021). The 2035 target is projected assuming consistent annual growth rates between 2030 and 2035 using linear trends.

**Table 3. Overlapping Policies Considered**

|**Overlapping Policy**<br>**Cases**|**Renewable Support**|**Electricity Taxes**|
|---|---|---|
|**NO**|None|None|
|**R2**|RPS|RPS+ IEP|
|**RN**|RPS|RPS|
|**S2**|IRS|IEP|
|**SN**|IRS|None|
|**N2**|None|IEP|

Notes: i) Each overlapping policy case can pair with each of the four ETS types, indicated by a hyphen between the ETS type and the overlapping policy case.

ii) NO: No overlaps. R: overlapping RPS set according to projected national targets each year. S: Independent renewable subsidy (IRS) set to meet projected RPS targets each year. 2: indirect emissions pricing (IEP) applied to the electricity consumption of ETS-covered industrial sectors.

Alternative overlapping cases reveal how different elements in the stated policy overlap R2 affect the abatement costs. The RN scenario simply removes the IEP from R2. The S scenarios remove the implicit electricity taxes on all electricity consumers by replacing the RPS scheme with an independent renewable subsidy (IRS), funded by general revenues, that achieves the national renewable share target. S2 would retain the IEP obligation, while SN eliminates it. N2 has no renewable support but retains the IEP.<sup>19</sup> All policies are compared to a reference case with no ETS, renewables subsidies, or electricity taxes. Throughout, the cost per ton of abatement is measured as the present value of the equivalent variation of household consumption in each phase, divided by the cumulative

> 19 Some scenarios defined here for completeness are reported only in extended simulations in the Appendix.

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The detailed simulation results reported in Table 4 reveal three ways that the stated overlapping policies in R2 improve the DEPS’s cost-effectiveness. First, the renewable subsidy helps correct the inefficiency from the DEPS’s under-allocation of allowances to renewables. The resulting renewables shares—in the “Share of Wind and Solar Electricity Output” panel in Table 4—align better with their levels in the CAT-NO case, which would yield optimal shares in the absence of other market distortions.

Second, the implicit electricity taxes, introduced by the RPS across all consumption and by the IEP for covered industrial sectors, help address the incomplete pass-through of embodied emissions costs under DEPS. As discussed in the theoretical section, both of these policies help to exploit the abatement potential of reduced electricity consumption under a TPS. Results in the “Change in Total Electricity Output” panel of Table 4 show that, during Phases 2 and 3 with the IEP in effect, the decrease in total electricity output under DEPS-R2 surpasses that of DEPS-NO, moving towards the more efficient levels of conservation in CAT-NO. Even so, results in the “Change in (Wholesale) Electricity Prices” panel reveal that electricity prices rise 2.3% under DEPS-R2, less than a quarter of those under CAT-NO. This suggests that consumers are better insulated from cost increases under DEPS-R2.

**Table 4. Results without and with Stated Overlaps**

|**ETS policy:**<br>**CA**|**T**|**DE**|**PS**|
|---|---|---|---|
|**Overlap Scenario:**<br>**-NO**|**-R2**|**-NO**|**-R2**|
|**Cost Per Ton of Abatement (yuan/t)**||||
|_Phase 1_<br>5.4|12.1|19.6|15.3|
|_Phase 2_<br>8.8|14.2|21.0|17.3|
|_Phase 3_<br>14.1|15.1|32.0|22.5|
|_All_<br>13.1|14.8|30.2|21.5|
|**Allowance Price (yuan/t)**||||
|_Phase 1_<br>27.2|14.5|151.7|64.9|
|_Phase 2_<br>44.2|27.2|143.6|70.9|
|_Phase 3_<br>88.9|79.8|313.3|206.7|
|_All_<br>73.3|62.2|262.3|164.4|
|**Change in (Wholesale) Electricity Price (%)**||||
|_Phase 1_<br>4.1|2.3|0.9|0.4|
|_Phase 2_<br>6.5|4.2|1.5|0.8|
|_Phase 3_<br>12.7|11.2|4.1|3.1|
|_All_<br>10.1|8.4|3.1|2.3|

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|**Implied Rate of Renewable Subsid**<br>|**y under the RPS (**|**%)**<br>|||
|---|---|---|---|---|
|_Phase 1_||9.6||11.2|
|_Phase 2_<br>||12.5||16.3|
|_Phase 3_||2.9||10.3|
|_All_||5.7||11.5|
|**Change in Total Electricity Output**|**(%)**||||
|_Phase 1_|-2.4|-1.3|-1.2|-0.5|
|_Phase 2_|-3.8|-3.2|-1.3|-1.4|
|_Phase 3_|-7.3|-7.9|-2.8|-4.5|
|_All_|-5.9|-6.0|-2.3|-3.3|
|**Share of Wind and Solar Electricit**<br>|**y Output (%)**<br>||||
|_Phase 1_<br>|9.5|11.3|9.0|11.3|
|_Phase 2_|14.3|16.8|13.3|16.8|
|_Phase 3_|27.8|28.3|25.3|28.3|
|_All_|22.3|23.4|20.5|23.4|
|**Leakage Rates (%)**|||||
|_Phase 1_|0.9|0.6|0.2|0.3|
|_Phase 2_|1.1|0.9|0.2|0.3|
|_Phase 3_|1.2|1.3|0.4|0.3|
|_All_|1.2|1.2|0.4|0.3|

Note: All the changes refer to percentage changes as compared with the reference scenarios, where there is no ETS or overlapping policy. Leakage rates are emissions leakage to foreign countries as a percentage of domestic emissions reduction.

Third, both the RPS and the IEP lower the carbon price of the DEPS, as the theory section suggested. Since both policies also enhance emissions reductions, the benchmarks are relaxed to meet the same emissions target as without overlaps, amplifying this price reduction. Table 4’s “Allowance price” panel shows that the average carbon price of DEPS-R2 in all phases is around 40 percent lower than in DEPS-NO. The value of associated implicit output subsidies under DEPS equals the product of benchmark and carbon prices. The fall in carbon prices exceeds the increase in benchmarks, meaning the distortions from the implicit output subsidy and the benchmark differentiation are also lowered.

It is worth noting that the carbon price that results in these cases does not represent the marginal cost of abatement, but rather the marginal cost of residual abatement. As such, it is not a good indicator of the impact of overlapping policies on marginal abatement costs. In the case of DEPS-R2, both the allowance price and average abatement cost fall relative to DEPS-NO, indicating that overlap improves cost-effectiveness. In contrast, for CAT, any overlapping policy 34
undermines the cost-effectiveness of emissions reduction. In Phases 1 and 2, the cost per ton of abatement of CAT-R2 is 120 percent and 60 percent higher than that of CAT-NO, although allowance prices are lower. The presence of the RPS targets results in an inefficiently high renewable share, particularly in Phases 1 and 2.

Finally, we report “Leakage Rates” at the bottom of Table 4. The potential relocation of production and emissions to foreign countries that are not bound or less bound by emissions regulations is an important policy concern for countries implementing carbon pricing in traded sectors. The leakage rate is defined as the rise in emissions abroad relative to the domestic reductions achieved by the climate policy. Its magnitude is assessed using China’s import and export data and the average emissions intensity of imported and exported goods. We find that emissions leakage, across all cases, is generally small when compared to China’s emissions reduction.<sup>21</sup> Prior literature has demonstrated that TPS can mitigate emissions leakage due to their implicit output subsidies (Fischer & Fox, 2007; Holland, 2012). Our results confirm this: leakage rates under DEPS are approximately a quarter of those observed under the CAT system.

# **2. Relative contributions of overlapping policies**

While Table 4 focused on the stated overlaps, Figure 2 explores the contributions of different policy components to cost reductions under the DEPS, by comparing the impacts of the scenarios S2 and RN, as well as R2. In all three cases, the benchmarks are set to meet the same renewable energy and national emission targets.<sup>22</sup> Here, we focus on Phase 3, when IEP applies to a significant portion (25%) of electricity consumption.

Individually, both IEP and the implicit electricity tax under the RPS improve the costeffectiveness of the DEPS, with the most benefits coming from the RPS-introduced endogenous electricity taxes. The difference in cost per ton of abatement between the R2 and RN cases under the DEPS highlights the impacts of IEP, which helps reduce the cost by 8%. The difference between the RN and SN cases highlights the impact of RPS-introduced endogenous electricity taxes, which reduce the cost by 17%. The difference between the SN and NO cases reveals the

> 21 We also compared scenarios holding global emissions constant. Since the leakage rates are relatively small, controlling for emissions leakage has little influence on the results and does not affect policy rankings. For this reason, we focus on the cost per ton of domestic emissions reduction in discussions in the following sections.

> 22 Table C1 in the Appendix presents the full results in all periods.

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Figure 3 reveals that the stated-policy RPS share and associated renewable subsidy (the red dot on the blue line) is higher than what would best complement the DEPS (the blue triangle on the blue line) in the first two phases, but a bit lower than optimal in the third phase. It shows that cost-effectiveness under CAT is maximized with a non-binding RPS and no overlapping subsidy.

It is interesting to note from the right-hand panels that the lines for CAT and DEPS cross, revealing that, beyond a sufficiently high renewable (and tax-funded) subsidy, the costeffectiveness advantage of CAT relative to the DEPS disappears. Under such circumstances, CAT exacerbates the over-supply of renewables, while the benchmark differentiation of the DEPS that excludes renewables helps counteract it.

By contrast, the lines do not cross for any given RPS target within the range of the lefthand panels. This reveals a benefit of having a renewables support instrument with its own tradable credit mechanism, which allows the subsidies to adjust to the choice of ETS. Since CAT provides more incentives for renewables through its carbon price pass-through, a smaller, lessdistorting renewables subsidy is needed; with the DEPS, a higher subsidy is needed to offset the lack of benchmark allocation to renewables and the less efficient incentives. The fact that suboptimal overlapping policies can change the rankings of ETS policies underscores the importance of evaluating them together. Overall, we find that optimizing the RPS that accompanies China’s DEPS can lower costs per ton by about 10% compared to the actual RPS.<sup>24</sup>

# **4. Optimized overlapping policies under different ETSs**

The above sections focus on cases where policies overlap with China’s DEPS. Here we discuss cases involving overlaps with different forms of the ETS. Such cases are policy-relevant, since China continues to consider alternative ETS designs.

> 24 Theoretically, one could further enhance the cost-effectiveness of TPSs through an exogenously optimized electricity tax rate. However, our findings indicate that when a significant portion of electricity consumers are covered by the IEP in Phase 3, the system can already capture most of the cost-saving opportunities from policy overlap. In Appendix C, we explore the cost-saving potential of an optimized electricity tax. Such a tax can further reduce costs by roughly another 10% compared to optimized RPS with DEPS. Both of these improvements, while not negligible, are relatively modest compared to the nearly 40% cost savings of optimized RPS with DEPS over DEPS-NO.

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Table 5 shows the optimized renewable subsidy rates in the different cases. As mentioned, under CAT no subsidy is warranted, whether or not embodied emissions are priced and whether the subsidy is independent or electricity tax-funded. Nor can an independent renewable subsidy lower costs under a USPS. However, a USPS can benefit from a modest RPS, due to the implicit electricity tax component introduced by the RPS. Both the UEPS and DEPS benefit directly from the independent renewable subsidies, as proper levels of renewable subsidy can address the output subsidy disparities and level the playing field between renewable and fossil-based plants in both systems; implementation with RPS can confer additional benefits.

Optimized subsidy rates vary based on the type of TPS and other overlapping policies. With IEP in place, the allowance price decreases, reducing implicit output subsidies for fossilbased plants and necessitating smaller renewable subsidies to compensate for the distortions. When the renewable support policy is an RPS rather than an independent subsidy, the optimized subsidy level is significantly higher, as higher renewable subsidies under RPS not only provide support for renewables but also raise the implicit electricity tax, enhancing cost-effectiveness. The IEP then allows an even greater reduction in the renewable subsidy, since the improved carbon cost pass-through to consumers means less implicit tax is needed from the RPS.

**Table 5. Optimized Renewable Subsidy Rates under Different ETSs (%)**

|||**Type **<br>|**of ETS**<br>||
|---|---|---|---|---|
|**Overlapping Policies**|**CAT**|**USPS**|**UEPS**|**DEPS**|
|RPS+IEP (R*2)|0.0|2.0|12.0|14.0|
|RPS (R*N)|0.0|2.5|13.5|16.0|
|IRS+IEP (S*2)|0.0|0.0|7.5|9.0|
|IRS (S*N)|0.0|0.0|8.0|10.0|

Note: See Table 3 for the definitions of the overlapping policies. The asterisk (*) represents the cases with optimal renewable subsidy rates. Optimal renewable subsidy rates shown here refer to the renewable subsidy level that leads to the lowest cost per ton over the entire simulation period.

Figure 4 compares the outcomes of cost-minimizing overlapping policies across ETS types and phases.<sup>25</sup> The least-cost policy enabling China to achieve its emission targets is CAT with no overlapping policies.<sup>26</sup> Evidently, if the ETS is a CAT, additional policies are not needed

> 25 A full set of results of all policy cases are provided in Table C2 in Appendix C.

> 26 Although the numerical model includes several features (more sectors, international trade, and general equilibrium effects) not incorporated in the theroretial model, these numerical findings reinforce the theoretical model’s predictions.

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easier to reduce energy intensity through factor-energy input substitution, the cost-effectiveness gap between the DEPS-NO and CAT-NO cases narrows, and the necessity for overlapping policies such as RPS and IEP diminishes. This follows from the fact that when it is easier to reduce the emission intensity within a given subsector, the need for fuel switching and energy efficiency improvements also decreases, lowering the need for overlapping policies to compensate for DEPS’s inefficient use of these channels.

We also find that lowering capital transformation elasticities between subsectors of a given sector and raising the electricity demand elasticity both produce ambiguous impacts on the cost-effectiveness gap between DEPS-NO and CAT-NO, as it may increase or decrease the distortions brought by the implicit output subsidies under the DEPS. Regarding the effectiveness of overlapping policies, we find that altering capital transformation elasticity has a minimal impact, while a higher electricity demand elasticity enhances the benefits of implementing an electricity consumption tax, either through RPS or IEP.

Although quantitative outcomes depend on the parameters employed, our sensitivity analysis indicates that our main qualitative findings are robust over a wide range of parameter choices. Overlapping policies have quantitatively important implications for the cost of meeting emissions targets, as well as for other variables of concern, including prices and output levels. Furthermore, the choice of ETS matters a great deal for the consequences of overlapping policies and the resulting cost-effectiveness of the policy portfolio.

# **V. Conclusion**

As part of meeting their nationally determined commitments under the Paris Agreement, nearly all countries have clean energy plans and CO2 emission reduction goals. In most cases, countries aiming to achieve given clean energy and emissions targets will employ multiple policies to achieve the goals. Interactions across the policies significantly affect the outcomes.

Policy mixes often include both an emissions trading system and other policy instruments, such as subsidies to low-emitting fuels or taxes on electricity use. In the past, the ETSs have tended to take the form of cap and trade, but an increasing number of newer entrants to emissions trading employ rate-based approaches, where total emissions become a function of total output and the performance benchmarks set by the regulation.

41
Given the prevalence of overlapping policies, it is important to understand the nature of their interactions and the associated economic consequences. Such considerations should inform the choices both of emissions trading systems and of subsidies and other policies to promote transitions to low-carbon energy supplies.

Our analytical model reveals how outcomes differ depending on the nature of the ETS and the types of policies with which it overlaps. It highlights when overlapping policies may have counterproductive impacts with rate-based ETSs, and when they can enhance effectiveness in ways that differ from the effects with mass-based trading systems. The insights are complemented by results from a numerical general equilibrium model representing important characteristics of the recently implemented Chinese nationwide ETS context.

Several features of rate-based systems compromise efficiency, but the judicious use of overlapping policies can offset a substantial share of the potential efficiency losses. One source of inefficiency stems from the implicit subsidies to output inherent in rate-based allowance allocation. We show that this output-related distortion can be offset by combining a renewables subsidy with an electricity consumption tax (as in the case of renewable portfolio standards or feed-in tariffs with surcharge), or by putting a price on the embodied emissions in all or part of the electricity consumption. A second source of inefficiency relates to the relative support for different sources of energy. The cost-effectiveness of emitter performance standards is handicapped as a result of its exclusion of clean sources from the carbon market. Support for renewable production can offset this limitation and thus boost cost-effectiveness.

In our simulations for China’s context, pricing embodied emissions of industrial consumers—even if they only represent 25% of electricity consumption in the third phase—can lower the cost per ton by up to 8%. An optimized independent renewable subsidy can reduce the overall average cost per ton by 9%-15%, depending on the phase. By addressing both sources of inefficiency, using an RPS to meet China’s existing renewable energy target can reduce the cost per ton of abatement by 24% over all three phases of the given ETS. If those renewable share targets were better aligned with China’s TPS, the existing system’s cost-effectiveness could be further enhanced by approximately 10% in all three phases.

Overlapping policies also influence the cost-effectiveness of cap and trade. Without overlapping policies (and absent other market failures), CAT is the most cost-effective ETS 42
option, since it avoids introducing output subsidies that distort incentives to switch between energy sources as a means to reduce emissions. CAT also encourages efficient pass-through of emissions costs, meaning additional taxation of electricity is not needed. Thus, overlapping the stated RPS and embodied emissions pricing increases by about 10% the costs of a CAT system that would achieve the same emissions reductions as China’s actual TPS. Together, China’s stated policy overlaps reduce the cost differential between China’s TPS and an equivalently stringent CAT system by about two thirds.

These insights are relevant not only to China, but also to other countries considering or implementing a rate-based ETS, such as Indonesia, Kazakhstan, and India, as well as Canada.

In future work, we plan to consider how other pre-existing distortions or market failures might influence the outcomes from overlaps and suggest useful policy responses. For example, output-based allocations can have some benefits in the presence of distortionary taxes on labor, capital, or other factors of production, or investment dynamics under macroeconomic volatility. Clean energy policies are often needed to address technology market failures. Another area for extension is attention to the effects of a range of flexibility mechanisms often incorporated into ETSs to address uncertainty, including banking and borrowing, price corridors, or quantity adjustment mechanisms that make mass-based emissions targets more malleable. Incorporating more real-world policy settings and constraints would provide needed nuance to the recommendations for optimal ETS design and supplemental policy recommendations.

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**Rate-Based Emissions Trading with Overlapping Policies: Insights from Theory and an Application to China**

# **APPENDIX**

46
# **A. Additional Mathematical Proofs**

**Mathematical Proof of Proposition 6.** With CAT, the introduction of the renewables subsidy does not affect total emissions, which are determined by the cap. The average emissions intensity of production can change, however. The numerator in _~~a~~_ is fixed by the emissions CAT − 2 target, so average embodied emissions change only with total output: _d_ _~~a~~_ = _~~a~~_ ( _dY_ / _Y_ ) . Solving our system of equations with the new definition of _db_ :

**Mathematical Proof of Proposition 7.** With USPS, since average emissions always _UTPS_ − 2 equal the standard, _d_ _~~a~~_ = 0 . Solving our system of equations, we find that:

In the presence of linked embodied emissions pricing, an overlapping renewable subsidy has the same effect on the numerator of the emissions price response (which is negative) as in the case without such taxes, but the denominator is altered. The effect on emissions and output still takes the opposite sign of the emissions price effect.

**Mathematical Proof of Proposition 8.** With an EPS, substituting the equilibrium change in emissions, we see the change in average embodied emissions

47
_d_ _~~a~~_ EPS − 2 = (( _~~a~~_ − _a f_ ) _df_ + ( _~~a~~_ − _ag_ ) _dg_ + ( _~~a~~_ − _ar_ ) _dr_ ) / _Y_ . Assuming<sup>_a_</sup> _r_<sup>=</sup> 0 as in the EPS and solving for the change in emissions and their price from a change in the renewable subsidy, we get is positive with a (possibly unnecessary) restriction on the size of _t_ , which ensures that the direction of change in the embodied emissions tax follows the first-order effects of the renewable subsidy ( _db_ / _ds_ < 0). The range restriction of _t_ _~~a~~_ < − _D Y_ ′ is sufficient. Recall that ~~μ~~ EPS > 0 ′ ′ implies ∆ _f S g_ −∆ _g S_ > 0 .

This fact also allows us to demonstrate that the numerator of _dY_ EPS-2 / _ds_ is also positive: _dYds_ EPS-2 = _t_ ( ∆+ ∆ _f g_ ) <u>(∆</u> _gm f_ + ∆ _f mg_ <u>)</u> + Ζ _Y_ EPS <u>(</u> ( _S_ − 2 ′ _f_ ∆ _g_ ( ∆+ _g_ _~~a~~_ ) + _Sg_ ′ ∆ _f_ ( ∆− _f_ _~~a~~_ ) <u>)</u> > 0 ′ ′ ′ ′ ′ ′ 2 since ( _S f_ ∆ _g_ ( ∆+ _g_ _~~a~~_ ) + _Sg_ ∆ _f_ ( ∆− _f_ _~~a~~_ ) > ( _Sg_ ∆ _f_ ( ∆+ _g_ _~~a~~_ ) + _Sg_ ∆ _f_ ( ∆− _f_ _~~a~~_ ) = _Sg_ ∆∆+ _f g Sg_ ∆ _f_ > 0 .□ 48
<!-- Start of picture text --> Factor Capital<br>inputs ' Income<br>H H |<br>ie Factor: i<br>| Factor Natural Resources market | Transfers! |<br>Payments Toe<br>|J<br>|<br>Productiroduction Publiublic || ; PrivateF<br>Firms Saving’<br>i Input 1<br>|; Payments |ocr t rss Sacer seen nese cee eee a es| Final. demand | Investment f+<br>Material inputs: Produced Imports<br>' Inputs<br>Energy inputs :<br>Product market ‘ Rest of the World<br>_<br>Emissions pacetennerecon reer eee n een e enee neen eensene Exports<br>allowances<br><!-- End of picture text -->
below, some sectors subdivide into subsectors. The representative firm of each of the sectors (and subsectors) employs inputs of primary factors along with intermediate inputs (energy and material goods) to produce goods for the domestic market and export.

In the electricity sector, the model differentiates between renewable sources of electricity (such as solar, wind, and hydro) as well as nuclear power, and the conventional fossil-based sources of electricity. To capture the diversity among fossil-based electricity generators, the model takes into account eleven distinct subsectors, listed in the Figure B2. The cement, aluminum, and iron & steel sectors also distinguish subsectors with production technologies differing in their emissions intensities and production technologies. The model treats the outputs from subsectors of a given sector as homogeneous; thus they have the same market price.

Production is represented by nested constant elasticity of substitution (CES) functions. A general equation for this functional form is shown as Equation B1.

> _n_ 1

> where ∑α _i_ = 1. The parameter ρ is equal to 1 − , where σ is the elasticity of substitution _i_ = 1 σ among<sup>_v_</sup> _i_<sup>in producing</sup><sup>_V_. Equation (B1) indicates the relationship between a given composite</sup> and its underlying elements at any given point of the nest.

In each sector, including the subsectors within the electricity, cement, aluminum, and iron & steel sectors, producers employ material inputs ( **_x_** ), energy inputs ( **_e_** ), and factors ( **_mw_** ) to produce output. Figure B3 illustrates how the material inputs _x_ 1, _x_ 2, ..., _x_ 24 combine to produce the composite material input **_x_** . Each of the material inputs _x_ i is a composite of a domestically produced material input _dx,_ i and, if applicable, a foreign-produced material input _nx,i_ . The energy composite ( **_e_** ) is a composite of electricity ( _s_ ), heat ( _h_ ) and fossil fuels ( _f_ ), and the fossil fuel is a composite of five fuel inputs _f_ 1, _f_ 2, ..., _f_ 5 (coal, crude oil, natural gas, gas manufacture & distribution and petroleum products). Producers also employ factors of production labor ( _m_ ), capital ( _w_ ) and, if applicable, land ( _lnd_ ). Equation B1 applies in each level of the structure in Figure B3.

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Output _Y_ is allocated toward the domestic market, which is represented by _Ydm_ , and to export, which is represented by _Yex_ .

**Table B1. Sectors**

|**Name**|**Description**|
|---|---|
|Cement<sup>1</sup>|Cement|
|Iron & steel<sup>2</sup><br>|Iron and steel|
|Aluminum<sup>3</sup>|Aluminum products|
|Pulp & paper|Pulp and paper|
|Other non-metal products|Non-metal processing other than cement|
|Other non-ferrous metals|Non-ferrous metals other than aluminum|
|Raw chemicals|Raw chemical materials, chemical products|
|Agriculture|Crop cultivation, forestry, livestock and livestock products, and fishery|
|Mining|Metal minerals mining and non-metal minerals, and other mining|
|Food|Food and tobacco|
|Textile|Textile|
|Clothing|Clothing|
|Log & furniture|Log and furniture|
|Printing & stationery|Printing and stationery|
|Daily chemical products|Chemical fibers, medicines, rubber & plastics products|
|Metal products|Metal products|
|General equipment|General equipment manufacturing|
|Transport equipment|Transport equipment manufacturing|
|Electronic equipment|Electronic equipment manufacturing|
|Other manufacturing|Other manufacturing|
|Water|Water|
|Construction|Construction|
|Transport|Transport and post|
|Services|Services|
|Electricity|Electricity generation|
|Petroleum refining|Petroleum refining|
|Heat|Heat distribution|
|Coal|Coal mining and processing|
|Crude oil|Extraction of crude oil|
|Natural gas|Primary production of natural gas|
|Gas manufacture & distribution|Manufacture, processing,and distribution of natural or syntheticgas|

1 The cement is divided into 3 subsectors: high, medium, and low-efficiency cement production.

2 The iron & steel sector is divided into 6 subsectors: high, medium, and low-efficiency basic oxygen steel production, and high, medium, and low-efficiency electric-arc furnace steel making.

3 The aluminum sector is divided into 3 subsectors, including high, medium, and low-efficiency aluminum production.

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<!-- Start of picture text --> Ultra-super critical units with capacity > 1000MW<br>Ultra-super critical units with capacity > 600 MW and < 1000MW<br>Supercritical units with capacity > 600 MW<br>Supercritical units with capacity > 300 MW and <= 600 MW<br>ower Pan Subcritical units with capacity > 300 MW<br>Subcritical units with capacity < 300 MW<br>Circulating Fluidized Beds Units with capacity > 300 MW<br>e<br>= Circulating Fluidized Beds Units with capacity < 300 MW<br>v<br>vu<br>:<br>S<br>2<br>Gas-fired eh-p<br>Power Plants ;<br>Wind- and Wind electricity<br>Solar-<br>Electricity Solar electricity<br>Hydropower<br>Baseload<br><!-- End of picture text -->
**Figure B3. Nested CES Production Structure for Each Sector**

53
# **2. Household Behavior**

A representative household earns income from returns to the factors of production and devotes that income to consumption, savings, and transfers to the government.

Real private investment is set as a fixed share of real gross domestic production (GDP) and remains unaffected by the real return on investment. The value of savings is used to finance the real private investment.

Lumpsum transfers are endogenously determined to finance government expenditure, which is described in the following subsection.

Consumption choices reflect its utility maximization subject to a budget constraint. A nested CES utility function governs the allocation of consumption expenditure across specific consumer goods and energy.

# **3. Government Behavior**

We did not include pre-existing taxes and subsidies in the version of the model, so the tax revenue that finances the government’s activity in the input-output table is modeled as lump sum transfers from the households to the government. The government receives transfers from households that are devoted to government consumption and public savings.

Public consumption is set as a fixed share of GDP and is characterized by a CES preference function defined over the material-energy composite. Government saving finance public investment, which is also set as a fixed share of GDP.

In each period, an endogenously determined lumpsum transfer from the households finances these government expenditures.

# **4. Foreign Trade**

The model regards China as a price-taker on the world market: the foreign-currency prices of imports are exogenous, as are the foreign-currency prices at which exports can be sold. Domestically produced and imported goods in a given sector category are regarded as imperfect substitutes; hence their market prices can differ. Import and export quantities are functions of the relative prices of domestic and foreign goods.

The emissions leakage rate to foreign countries is calculated by multiplying the change in net exports in sector _j_ between China and country _c_ by the emissions intensity of _j_ in _c_ , and 54
dividing the sum across sectors and countries by the change in domestic emissions, using the following equation: _IC_ denotes import-origin countries, and _EC_ denotes export-destination countries. ∆ _EmissionD_ is the domestic emissions abatement. This formula assumes that any decrease in China’s bilateral exports will be perfectly offset by an equivalent increase in foreign production by the trade partner. This assumption tends to over estimates the leakage rate: In a more complicated model with trade response, the leakage rate would be even smaller. The data on emission intensities of each sector by country is from the Global Trade Analysis Project database (version 10) (2019).

# **5. Equilibrium**

The general equilibrium requires supply-demand balance in each period for each factor and produced goods. Under policies with emissions allowance trading, the allowance supply and demand must match as well. In each period, these requirements determine (a) the prices for the 31 sectors’ produced goods; (b) the wage rate; (c) the rental prices of capital, which differ across sectors (as well as subsectors in the electricity, cement, aluminum, and iron &steel sectors); (d) the four different rental prices of the natural resources, for these resources employed in the solar, wind, hydro, and nuclear electricity production subsectors, respectively; and (e) the CO2 allowance price.

# **6. Dynamics**

The model is solved as a mixed complementarity problem (MCP) with a Newton-based solver, and solves at one-year intervals from 2020 through 2035. Changes in equilibria from one period to the next depend on the increments to the stocks of labor and capital. There is one aggregate capital stock. As discussed earlier, domestic real investment in each period is set as a fixed share of GDP. The stock in the next period is aggregate real domestic investment in the current period net of depreciation over that period. The stocks of land and the four kinds of natural resources (wind, solar, hydro, and nuclear) are treated as fixed at the base year level.

55
The model incorporates technological progress as exogenous improvements in energy factor productivity, as well as the cost reduction trend in renewable electricity generation.

# **7. Parameters and Calibration Methods**

In this section, we provide a brief overview of the calibration process for our model. For a more comprehensive understanding of the data sources, data processing methods, and calibration techniques, we recommend referring to Goulder _et al_ . (2023).

For any CES function of the form in Equation (A1), the Lagrangian equation for obtaining the composite _V_ at minimum cost is given by: where _pi_ is the price of input<sup>_v_</sup> _i_<sup>. From this minimization problem, the optimal demand of input</sup><sup>_v_</sup> _i_<sup>per unit of the composite</sup><sup>_V_is derived as:</sup> Therefore, the share parameters of CES functions that have the functional form of Equation (A1), α _i_ can be calibrated by inverting the optimal input intensity function:

> where α _i_ is the share parameter of the CES production function, _V_ the output quantity,<sup>_v_</sup> _i_<sup>the</sup> quantity of input _i_ ,<sup>_p_</sup> _i_<sup>the benchmark price of input</sup><sup>_i_and</sup><sup>_p_the benchmark price of output.</sup>

Data for calibration includes the 2017 China’s input-output table and a firm-level dataset<sup>_v_</sup> _<u>i</u>_ from the Ministry of Ecology and Environment of 2017, which can be used to derive the “ _V_<sup>”</sup> component in Equation (A4). The elasticities of substitution ( σ ) at different levels of the nested CES structure are obtained from calibrations and various sources. Table B2 provides the 56
summary of the value and sources of these elasticities of substitution used in the version of the model in this study.

# **Table B2. Elasticities**

|**Parameter**|**Source**<br>**Values**|
|---|---|
||**Production elasticities**|
||Solar: 0.27|
|σrr<br>|Calibrated<br>Wind: 0.28|
||Hydro, Nuclear: 0|
|σxrx|GTAP, EPPA, RTI-ADAGE, DIEM<br>0|
||Electricity:<br>LUSC: 0.229<br>SUSC: 0.219<br>LSC: 0.259<br>SSC: 0.253|
||LSUB: 0.299|
|σrx|Calibrated<br>SSUB: 0.295|
||LCFB: 0.373|
||SCFB: 0.340|
||OTHC: 0.361|
||<br>HPG: 0.041<br>LPG: 0.161|
||Other sectors: 0.4|
|σr<br><br>|Calibrated<br>Other sectors: 0.50; Electricity: 0.01|
|σh<br>|Hu_et al._(2019)<br>0.30|
|σf|Cossa (2004), RTI-ADAGE<br>Other sectors: 1.00; Electricity: 0.10|
||Agriculture: 0.24|
||<br>Coal, Crude oil, Natural gas, Mining: 0.20|
|σx|Jomini_et al._(1991)<br>Food: 1.12<br>Services: 1.36|
||Transportation: 1.48|
||<br>Other sectors: 1.26|
|σx<br><br>|GTAP, EPPA, DIEM<br>0|
|σn<br>|Set to zero to suppress international leakage 0|
|σdr<br>|GTAP<br>0|
||**Consumption elasticities**|
|σxr<br><br>|GTAP<br>0|
|σr<br><br>|Calibrated<br>0.55|
|σf<br>|DIEM<br>0.50|
||<br>Household consumption: 1.00|
|σx<br>|GTAP<br> <br>Government consumption investment: 0|
||,<br>**Transformation elasticities**<sup>1</sup>|
|σw<br><br>|GTAP<br>1.50 for capital, +∞ for labor<br>|
|σxk<br>|GTAP<br>3.00 for capital, +∞ for labor<br>|
|Note: σwreprese<br>elasticities betwe|nts the factor transformation elasticities between sectors;σwkrepresents the factor transformation<br>en subsectors within a sector.|

57
Other parameters are closely related to intertemporal choices and economic growth. Capital growth from period _t_ to _t_ +1 is calculated as the investment of period _t_ net of depreciation during period _t_ . We apply an annual depreciation rate of 5 percent according to Herd (2020). The initial capital stock for the base year (2020) is derived from Holz & Sun (2018).

Technological progress takes two forms: autonomous energy efficiency improvement (AEEI) and Hicks-neutral technological change. Regarding AEEI: for sectors excluding the fossil-based electricity sector, we follow Chen _et al._ (2017), applying a 1 percent annual AEEI rate. For the fossil-based electricity subsectors, we again follow Chen _et al._ (2017), applying an annual AEEI rate of 0.4 percent.

Hicks-neutral technological change applies to all sectors but at different rates across sectors. The rates of Hicks-neutral technological change are set in a way that aligns the model’s reference path with the projections provided by the State Information Center (2020) and the International Renewable Energy Agency (IRENA) (2019a, 2019b). Specifically, the projections indicate that the contributions of agriculture, industry, and service sectors to GDP are expected to change from 7%, 37%, and 56% to 6%, 30%, and 64%, respectively, over the period of 20202035.

The growth rate of effective labor is calibrated so that the resulting GDP is consistent with the government projection, averaging 5.5% during 2020-2025, 4.5% during 2026-2030, and 3.5% during 2031-2035.

# **C. Additional Numerical Results**

## **1. Results of DEPS in Scenarios of Various Overlaps**

In Figure 2 in the main text, we compared the cost per ton of abatement associated with DEPS with various overlapping policy cases. Table C1 includes more details of the results, from which we can further understand why the stated policy overlaps – R2 – could help improve the cost-effectiveness of emissions reductions under a DEPS.

58
**Table C1. Results of Policy Overlaps under DEPS in Scenarios of Various Overlaps**

||**Electricity**<br>**Price**<br>**(yuan/kWh)**|**Marginal**<br>**Revenue of**<br>**Renewables**<br>**(yuan/kWh)**|**Marginal**<br>**Revenue of**<br>**Fossil-**<br>**based**<br>**Electricity**<br>**(yuan/kWh)**|**Unit Cost of**<br>**Electricity**<br>**Used by**<br>**Covered**<br>**Sectors**<br>**(yuan/kWh)**|**Allowance**<br>**Price**<br>**(yuan/t)**|**Cost Per**<br>**Ton of**<br>**Abatement**<br>**(yuan/t)**|
|---|---|---|---|---|---|---|
|**Phase 1**|||||||
|**R2**|0.692|0.769|0.746|0.711|65|15.3|
|**RN**|0.692|0.769|0.746|0.701|65|15.3|
|**SN**|0.690|0.767|0.747|0.690|68|19.4|
|**NO**|0.695|0.695|0.695|0.695|152|19.6|
|**Phase 2**|||||||
|**R2**|0.686|0.798|0.743|0.747|71|17.3|
|**RN**|0.687|0.799|0.744|0.706|72|17.5|
|**SN**|0.685|0.798|0.685|0.685|101|22.9|
|**NO**|0.695|0.695|0.695|0.695|152|19.6|
|**Phase 3**|||||||
|**R2**|0.675|0.745|0.821|0.790|207|22.5|
|**RN**|0.673|0.754|0.838|0.694|227|24.2|
|**SN**|0.673|0.760|0.673|0.673|263|29.0|
|**NO**|0.681|0.681|0.681|0.681|313|32.0|

# **2. DEPS with Optimized Renewable Subsidy and Electricity Taxes**

Additional cost savings are possible with exogenous renewable subsidies and electricity taxes by optimizing tax and subsidy rates together. Figure C1 presents the relationship between cost per ton, a broad-based electricity consumption tax rate, and renewable subsidy rates with DEPS. As the existence of an optimal level of renewable subsidy, there also exists an optimal level of electricity tax that corrects the incomplete cost passthrough just correctly. The optimal rate of the tax also depends on the rate of overlapping renewable subsidies. The higher the renewable subsidy rates, the lower the electricity price, the higher the needed overlapping electricity tax. Therefore, the two overlapping policies (electricity tax and renewable subsidies) are interdependent.

59
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# **3. Cost Per Ton Abatement of All Cases**

Table C2 includes the cost per ton abatement under all scenarios listed in section III C.

# **Table C2. Cost Per Ton Abatement of Different ETS in Different Scenarios**

|||**CAT**|**USPS**|**UEPS**|**DEPS**|
|---|---|---|---|---|---|
|**NO**||||||
||Phase1|5.4|9.5|12.7|19.7|
||Phase2<br>|8.8<br>|12.7<br>|16.3<br>|21.0<br>|
||Phase3|14.1|18.2|25.5|32.1|
|**R2**||||||
||Phase1|12.1|13.5|13.7|15.3|
||Phase2|14.2|15.8|15.9|17.3|
||Phase3|15.1|17.8|18.5|22.5|
|**R*2**||||||
||Phase1|5.4|9.4|10.0|13.7|
||Phase2|8.9|12.4|12.9|15.6|
||Phase3|14.4|17.3|17.8|20.4|
|**RN**||||||
||Phase1|12.1|13.5|13.7|15.3|
||Phase2|14.1|15.9|16.0|17.5|
||Phase3|14.8|18.4|19.1|24.2|
|**R*N**||||||
||Phase1|5.4|9.4|10.0|13.7|
||Phase2|8.8|12.7|13.1|16.0|
||Phase3|14.1|17.9|18.5|21.7|
|**S2**||||||
||Phase1|12.3|15.1|17.2|20.0|
||Phase2|14.3|17.9|20.3|22.4|
||Phase3|15.1|18.2|22.0|25.5|
|**SN**||||||
||Phase1|12.3|15.1|17.2|20.0|
||Phase2|14.4|18.1|20.7|22.9|
||Phase3|14.9|19.0|23.9|29.0|
|**S*2**||||||
||Phase1|5.4|9.4|11.4|16.7|
||Phase2|8.9|12.4|14.5|18.2|
||Phase3|14.4|17.4|21.2|24.8|
|**S*N**||||||
||Phase1|5.4|9.4|11.4|16.7|
||Phase2|8.8|12.7|14.9|18.9|
||Phase3|14.1|18.1|23.1|25.0|
|**N2**||||||
||Phase1|5.4|9.4|12.6|19.6|
||Phase2|8.9|12.4|15.8|20.1|
||Phase3|14.4|17.4|23.2|27.5|

61
# **D. Sensitivity Analysis**

We conducted a sensitivity analysis around the key parameters of the numerical model. Results are summarized in Tables D1 – D3. We focus on three parameters: the substitution elasticity between energy and factor inputs; the capital transformation elasticity within a sector; and the substitution between electricity and non-electricity inputs.

The substitution elasticity between energy and factor inputs determines how easily energy intensity can be reduced within a given subsector or sector. Higher elasticity indicates that production facilities can more easily substitute factor inputs for energy inputs. In the central case of our numerical model, the elasticity values for different electricity generation technologies are calibrated based on data on the cost of reducing the heat rate in the electricity sector, ranging from 0.16 to 0.37, depending on the specific technology. For industrial sectors, the elasticity value is sourced from the literature and is set at 0.4.<sup>27</sup> To account for uncertainties associated with these parameter choices, we considered two alternative settings: doubling and halving the elasticity. The results are summarized in Table D1. Higher energy-factor input substitution elasticity facilitates the use of factor inputs to replace energy inputs, thereby reducing abatement costs and achieving greater emissions reductions, as shown in Table D1. Additionally, increased elasticity correlates with a lower relative cost of DEPS-NO compared to CAT-NO. Greater elasticity signifies less difficulty in reducing emissions from fossil-based power plants, enabling more substantial emissions reductions by these plants. As a result, the need for augmenting renewable energy sources and reducing electricity demand diminishes, mitigating the distortive effects associated with DEPS’s exclusion of renewables and its implicit subsidy on output.

Consequently, with higher elasticity, the need for overlapping renewable subsidies or indirect emissions pricing to support DEPS decreases. This is evident from the diminishing difference in the relative cost of DEPS-R2 and DEPS-NO compared to CAT-NO in Table D1.

> 27 The estimated substitution elasticities between the energy composite and the factor composite for non-electricity sectors in China range from 0.4 to 1.2 (Cao et al., 2020; Feng & Zhang, 2018; Su et al., 2012; Zha & Zhou, 2014). This wide range is due to the level of sector aggregation and the time scope of the empirical studies. The model adopts the lower bound of this range because of our model’s detailed sectoral disaggregation, recognizing the increased challenge of input substitution at more disaggregated levels as highlighted by recent empirical studies (Oberfield & Raval, 2021). More information on the parameter settings can be found in Goulder _el al._ (2023).

62
**Table D1. Sensitivity Analysis with Different Settings of Energy-Factor Elasticities**

|**Policy Case**|**Emissions**<br>**Reduction**|**Cost per**|**Ton Abatemen**|**t (yuan/t)**|**Cost**<br>**DEPSR2/**|**Ratio**<br>**DEPSNO/**|
|---|---|---|---|---|---|---|
||**(%)**|**CAT-NO**|**DEPS-R2**|**DEPS-NO**|**-**<br>**CAT-NO**|**-**<br>**CAT-NO**|
|**Halved**<br>|||||||
|Phase 1|-2.4|6.7|18.6|29.2|2.8|4.3|
|Phase 2|-5.1|10.5|20.8|28.9|2.0|2.7|
|Phase 3|-10.2|16.4|29.5|43.0|1.8|2.6|
|All|-8.0|15.2|28.0|40.7|1.8|2.7|
|**Central**|||||||
|Phase 1|-2.6|5.4|15.3|19.6|2.8|3.6|
|Phase 2|-5.5|8.8|17.3|21.0|2.0|2.4|
|Phase 3|-11.0|14.1|22.5|32.0|1.6|2.3|
|All|-8.7|13.1|21.5|30.2|1.6|2.3|
|**Doubled**<br>|||||||
|Phase 1|-2.9|4.0|12.2|12.2|3.0|3.0|
|Phase 2|-6.3|8.8|13.9|14.3|1.6|1.6|
|Phase 3|-12.7|14.1|16.3|22.4|1.2|1.6|
|All|-10.0|13.1|15.9|21.0|1.2|1.6|

Capital transformation elasticities determine the flexibility of shifting production across different subsectors within a sector. In our central case, the capital transformation elasticity is set at 3 for different subsectors within a sector and 1.5 for different sectors, based on estimates from the GTAP database (Aguiar, 2019). This indicates that capital incurs adjustment costs when reallocating across subsectors and sectors, and the adjustment cost is lower for capital between firms producing the same product (subsectors within a sector) than between firms producing different products (sectors).

We explore the uncertainties related to this parameter. Higher capital transformation elasticity leads to lower abatement costs by reducing the capital adjustment cost of shifting from plants with higher emission intensity to plants with lower emission intensity. However, its influence on the cost gap between DEPS-NO and CAT-NO is uncertain. Increased elasticity increases the response of subsector electricity output to the implicit output subsidy under DEPS, implying greater distortion. However, it also reduces the allowance price, which in turn lowers 63
the size of the implicit output subsidy under the DEPS. The net impact depends on which effect predominates.

We found that changing this parameter does not significantly affect the importance of overlapping policies. Overlapping policies such as RPS and IEP improve the cost-effectiveness of DEPS by enabling more renewable electricity production and increasing cost pass-through. Changing capital transformation elasticity within a sector does not significantly impact these channels, because the supply elasticity of renewables is also affected by their own subsectorspecific resource input. This resource input accounts for the special integration costs associated with renewables and is a fixed factor, limiting the extent of renewables’ output change due to capital transformation elasticity. Also, capital transformation elasticity within a sector affects the supply elasticity of output from a subsector but does not directly affect the elasticity of the total output from that sector. Consequently, the response of results to overlapping policies does not vary significantly with changes in capital transformation elasticity.

**Table D2. Sensitivity Analysis with Different Settings of Capital Transformation Elasticities**

||**Emissions**<br>|**Costper**|**Ton Abateme**|**nt(yuan/t)**|**Cost**<br>|**Ratio**<br>|
|---|---|---|---|---|---|---|
||**Reduction**||||**DEPS-R2/**|**DEPS-NO/**|
||<br>**(%)**|**CAT-NO**|**DEPS-R2**|**DEPS-NO**|<br>**CAT-NO**|<br>**CAT-NO**|
|**Halved**|||||||
|Phase 1|-2.7|6.3|17.2|22.4|2.7|3.6|
|Phase 2|-5.8|10.2|20.1|23.7|2.0|2.3|
|Phase 3|-11.8|16.9|24.5|36.6|1.4|2.2|
|All|-9.3|15.7|23.7|34.6|1.5|2.2|
|**Central**|||||||
|Phase 1|-2.6|5.4|15.3|19.6|2.8|3.6|
|Phase 2|-5.5|8.8|17.3|21.0|2.0|2.4|
|Phase 3|-11.0|14.1|22.5|32.0|1.6|2.3|
|All|-8.7|13.1|21.5|30.2|1.6|2.3|
|**Doubled**|||||||
|Phase 1|-2.5|4.7|14.1|17.2|3.0|3.7|
|Phase 2|-5.4|8.8|15.7|18.8|1.8|2.1|
|Phase 3|-10.7|14.1|21.1|28.9|1.5|2.1|
|All|-8.4|13.1|20.1|27.2|1.5|2.1|

Table D3 presents the results with varying settings for electricity-non-electricity substitution elasticity. In our central parameter setting, this elasticity is calibrated based on data for the price elasticity of demand for electricity, which is -0.5 following Hu et al. (2019). To account for uncertainties, we consider two alternative cases: (1) Setting the electricity-non64
electricity substitution elasticity to zero, which implies an electricity demand elasticity of around 75% of the central case. (2) Setting the electricity-non-electricity substitution elasticity to five times the central parameter value, which implies an electricity demand elasticity twice that of the central case.

Higher electricity demand elasticity generally lowers the cost per ton abatement, except in Phase 1, where it raises unit costs due to greater emissions leakage under CAT-NO. The effect of higher electricity demand elasticity on the cost gap of DEPS-NO and CAT-NO is also ambiguous. It depends on the combined influences of carbon price changes and supply elasticity. A higher elasticity increases the impact of the implicit output subsidy under DEPS but also reduces the size of the implicit output subsidy by lowering the carbon price.

Additionally, higher elasticity makes electricity use more sensitive to price changes, enhancing the benefits of implementing an electricity consumption tax. Consequently, overlapping policies become more critical when the substitution elasticity is larger.

**Table D3. Sensitivity Analysis with Different Settings of Substitution Elasticity between Electricity and Non-Electricity Inputs**

|**Policy**<br>|**Emissions**<br>**Reduction**|**Cost per T**|**on Abateme**|**nt (yuan/t)**|**Cost**<br>**DEPSR2/**|**Ratio**<br>**DEPSNO/**|
|---|---|---|---|---|---|---|
|**Case**|**(%)**|**CAT-NO**|**DEPS-R2**|**DEPS-NO**|**-**<br>**CAT-NO**|**-**<br>**CAT-NO**|
|**Zero**|||||||
|Phase 1|-2.5|5.2|15.9|20.0|3.1|3.9|
|Phase 2|-5.4|9.0|18.4|21.7|2.0|2.4|
|Phase 3|-11.0|14.6|24.5|32.6|1.7|2.2|
|All|-8.6|13.5|23.4|30.8|1.7|2.3|
|**Central**|||||||
|Phase 1|-2.6|5.4|15.3|19.6|2.8|3.6|
|Phase 2|-5.5|8.8|17.3|21.0|2.0|2.4|
|Phase 3|-11.0|14.1|22.5|32.0|1.6|2.3|
|All|-8.7|13.1|21.5|30.2|1.6|2.3|
|**Five times**|**of the central**||||||
|Phase 1|-2.7|5.8|13.6|18.8|2.4|3.2|
|Phase 2|-5.6|8.8|14.2|17.9|1.6|2.0|
|Phase 3|-11.1|14.1|16.6|27.4|1.2|1.9|
|All|-8.7|13.1|16.2|25.9|1.2|2.0|

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Overall, the sensitivity analysis underscores the key insight of our paper: current overlapping policies can significantly reduce the cost disparity between China’s DEPS and CAT largely for the period of 2020-2035. This conclusion remains valid across a range of parameter settings, although the extent to which overlapping policies interact with China’s ETS is influenced by these settings.

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