Back Matter
  • 1, International Monetary Fund

VII. References

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Annex I. Household Incidence of a Carbon Tax

The incidence of carbon tax changes depends on changes in: i) energy prices, ii) prices for other goods and services, and iii) wages. The derivation below follows the approach proposed by Coady (2006).

Production and pass through to non-energy goods

Assume profits of a representative firm are given by


with pjthe supplier price of good j, q a 1 x n row vector of user prices for intermediate inputs and Aja n x 1 column vector of quantities, r and Ej the price and quantity of energy, and with labor costs WjLj. The element Aij denotes the quantify of input i needed to produce output yj We assume Leontief production Yj = f(Aj Ej, Lj) so that input shares are fixed. Producer and user prices are related by q = p + t, with t general sales and excise taxes, tariffs and subsidies.

A carbon tax τ directly affects the user price of energy r and indirectly the prices of other domestic inputs q


with xj=XjYj1. For domestic suppliers, we further assume that:

  • Higher input costs are fully passed on through higher producer prices pjd

  • Profits are constant through a no-arbitrage condition

  • User prices of imported goods are not affected. This implies


with α diagonal matrix that denotes the share of goods that are produced domestically. When other taxes remain constant, changes in producer prices of non-energy goods are equal to changes in user prices. Re-expressing price changes in Eq. (3) in percentage terms and concatenating across goods yields


with x˙x/x the percentage price changes, the matrix A an input-output coefficient matrix of size n x n and 1 x n row vector of energy intensity Σ=[rE1p1dY1,rE2p2dY2,...,rEnpndYn]..1

Rearranging, we can solve for changes in user prices


with Leontief inverse matrix K = (I – α)-1. In the case of exporters, we further assume

  • Perfect substitutability with foreign goods so that higher input costs are instead passed back to wages

  • No labor relocation between exporters and domestic suppliers. From Eq. (2),


which can be re-expressed as


where the elements of the diagonal matrix A are equal to the labor intensity of production wjLj/pldYj

Household incidence

The impact of a carbon tax on household welfare is then given by


where the percentage changes in user prices are weighted by their final consumption budget shares ωi. As mentioned above, we assume only the price of energy and domestically produced non-energy goods are affected by the carbon tax, while only wages paid by exporters are reduced. The final incidence in partial equilibrium on households is given by


where α˜i is the share of final consumption of good i that is produced domestically and βi the export share of good i.

For the empirical implementation, we use energy price changes resulting from a carbon tax from the model developed by Parry and others (2014). The price changes of other domestic supplies is calculated from an input-output table for Denmark using Eq. (2) and matched to consumption tables by income quintiles from Eurostat. Wage changes for exporters by sector are calculated from Eq. (3) and matched to household survey data to calculate changes in wages throughout the income distribution.

Annex II. Burden of Carbon Mitigation Policies on Eite Industries

The burden—or increase in private production costs—for EITEs from carbon mitigation policies is depicted graphically in the Figure. Here the upper, middle, and lower curves are respectively the marginal cost of reducing emissions through reducing domestic industry output, reducing the emissions intensity of output and the envelope of these two curves. A carbon pricing policy reduces emissions by ΔEtot, with ΔEint and ΔEout coming from reduced emissions intensity and reduced output respectively. The burden of the carbon price on EITE industries has two components. One is the second-order efficiency cost of the behavioral responses (the red triangle in the Figure) reflecting the resource cost of adopting cleaner (but costlier) production methods. The other is the first-order transfer payment (e.g., tax payment to the government) reflecting the charge on remaining emissions (the blue rectangle). Free allowance allocation offsets the transfer payment component of the burden, though this is a smaller share of the total burden at higher levels of emissions reduction.

Burden of Carbon Mitigation Policies on Industry

Citation: IMF Working Papers 2020, 235; 10.5089/9781513560960.001.A999

Alternative mitigation instruments to carbon pricing are less efficient but may impose a much smaller burden on EITE industries. A feebate applied to an EITE industry reduces emissions intensity but (to an approximation) has no impact on output as, unlike a carbon price, it does not charge for remaining emissions. The burden of the feebate—assuming the industry emissions reduction is the same as under the carbon price—includes a higher efficiency cost (the extra green triangle in the Figure) but there is no transfer payment. The efficiency cost of the feebate (again from simple geometry) is equivalent to that under carbon pricing (the red triangle) times ΔEtot/ΔEint. But the overall burden is generally lower under the feebate, especially for relatively low abatement levels, as there is no transfer payment under these policies. For example, if ΔEtot/ΔEint = 1.5 (i.e., two-thirds of the emissions reduction under the carbon price comes from reduced emissions intensity) the burden of the feebate is 21, 50, and 90 percent of that of carbon pricing for emissions reductions of 25, 50, and 75 percent respectively.


We are grateful to Juan Carlos Benitez and Khamal Clayton for contributions to the paper and for very helpful comments and suggestions from Miguel Segoviano, Peter Birch Sørensen, Ulla Blatt Bendtsen, Ralph Chami, Cory Hillier, Signe Krogstrup, Lars Haagen Pedersen, Eva Smidt, Vimal Thakoor, several reviewers from various IMF departments as well as colleagues from the Danish Ministry of Finance, Danmarks Nationalbank, Danish Economic Councils, Ministry of Taxation, Danish Council on Climate Change, Ministry of Climate, Energy and Utilities and Ministry of Industry, Business, and Financial Affairs. We also wish to thank Nicholas Werquin for helpful discussions on the generalized compensation approach and for sharing his code. All errors remain our own.


These emissions targets are in line with the goal of containing global warming to 1.5ºC.


To net zero emissions by around 2050 and 2070 respectively for the 1.5oC and 2oC targets. See IPCC (2018).


See NCEP (2019) for a detailed overview of Denmark’s emissions objectives and a (high-level) discussion of envisioned strategies for achieving these objectives.


Denmark led a coalition of 11 EU countries calling for a concrete plan from the European Commissions with proposals for policy initiatives and incentives for the transition to a fleet of zero-emission passenger cars.


See Article 1(1) and 3(4) of Directive 2012/27/EU.


Mostly straw, wood pellets, chips, and biodegradable waste.


GDP growth is more than offset by a drop in the carbon intensity of GDP reflecting improving energy efficiency, energy demand growing by less than in proportion to GDP, and growth in renewables. The Danish Climate and Energy Outlook (2019) projects GHG emissions in 2030 will be 46 percent below 1990 levels, though this includes the effects of scaling up renewable energy and energy efficiency measures.


From All prices below are expressed in year 2020 $ or thereabouts.


Price floors might be implemented through allowance auctions with a minimum auction price or making the MSR subject to a price trigger (see Flachsland and others 2018)—either way, allowances should be permanently withdrawn from the system whenever needed to prevent the price falling below the floor. Alternatively, the Danish government can unilaterally purchase and retire allowances to ensure domestic emissions reductions translate into reductions at the EU level, though this would involve Denmark “paying twice” for those reductions. Both elements would make the ETS more robust and transparent as well at the EU level.


This abstracts from pre-existing road fuel taxes.


For comparison a Tesla Long Range AWD Model 3 is comparable to an Audi A5 but the base price for the former is $75,000 while that for the latter is $40,000—the price gaps is closing all the time however, not least because the capacity of electric batteries is increasing, while battery prices are falling. 4,618 (private and commercial) EVs were purchased in 2019 but EVs are still less than 2 percent of the on-road fleet. Figures are from Automobile Commission (2020).


Ownership taxes are also paid semi-annually with rates varying between $53 (for vehicles with fuel economy above 50 km/liter) and $1,870 (for vehicles with fuel economy below 4.4km/liter). EVs are classified at the top of the fuel economy scale.


IEA (2019), pp. 94–95.


For example, Automobile Commission (2020) proposed a fuel tax increase of $0.16 per liter starting in 2021.


Some level of fuel taxation is efficient to reflect external costs of driving, including traffic congestion, accidents, local air pollution, and road maintenance—at least until more efficient instruments like km-based charging systems are comprehensively applied (see below and Parry and others 2014 on methodologies for quantifying externalities and efficient fuel taxes). Although the registration tax system provides incentives for smaller (i.e., lower value) vehicles and EVs, unlike road fuel taxes, it does not provide incentives to economize on vehicle use.


Denmark also imposes taxes on the energy content of oil products, natural gas, and coal used outside the power sector. A Public Service Obligation Scheme has also imposed a levy on electricity paid by all consumers (where revenues have funded renewables) though this levy is phasing out between 2017 and 2021.


NCEP (2019), Table 8.


Staff calculation based on: (i) the average cost of charging stations in McKinsey (2018) (about $1,150 per station); (ii) an assumption that one charging point is needed for each five vehicles (Ministry of Transport Building and Housing 2017); and (iii) the eventual size of the EV fleet is the same as the current vehicle fleet.


If agricultural emissions were also priced the proportionate reduction in nationwide emissions would likely be greater.


The current tax is £18 ($23) per tonne. See Hirst (2018).


Government of the Netherlands (2019). At the EU level, the Danish government is pushing for a strengthening and expansion of the ETS to other sectors ahead of the review of the ETS directive in summer of 2021 (see


These include: (i) a clearly announced and gradually rising carbon price trajectory which allows households and firms time to adjust (e.g., by making energy-efficiency investments); (ii) extensive consultations with stakeholders to build support for the reform and an effective communications program informing the public of the rationale for reform; (iii) assistance measures for vulnerable regions and workers; and (iv) complementary clean energy infrastructure investments. See Clements and others (2013) and Coady and others (2018) for further discussion.


For refrigerators, for example, the energy consumption rate is kWh/cubic foot cooled. Promoting electricity conservation is still important, even if power generation were decarbonized, to ensure demand/supply balance given constraints on renewable generation sites.


Capacity for measuring forest carbon inventories from a combination of satellite imagery, aerial photography, and on-the-ground tree sampling is presently being developed in many countries, for example, for 47 tropical countries under the REDD+ Readiness program (see Over time the program might be expanded to include carbon stored in soils as metering technologies evolve.


More expensive vehicles pay more tax, but CO2 emission rates are only loosely related to vehicle prices.


For example, postponing timber harvesting, planting of larger trees, thinning to increase forest growth, fertilizing. See Parry (2020) for more discussion on the rationale for, and design of, feebates for the forestry sector.


Meeting sectoral targets (e.g., EVs) will imply some differentiation of carbon prices. This need not increase economywide mitigation costs very much however, if the sector with lower prices (e.g., power) is only a small share of nationwide emissions.


An alternative would be to base the pivot point on EU average emission rates which this would help mitigate carbon leakage, since Danish firms would be rewarded to the extent that their emission rates are low relative to their (EU) trading partners which is especially advantageous in the absence of a BCA.


This is proposed in Automobile Commission (2020).


For a single-firm industry, the firm could be taxed on the difference between its emission rate and a target emission rate with the latter becoming progressively more stringent over time.


In fact, the price of EVs should not be too low as this might encourage car ownership among households that previously relied on other transport modes.


See, for example, ACEA (2018), Bunch and others (2011), pp. 59–61.


This assumes 7 percent of the fleet is replaced each year (i.e., vehicle lifespans are 15 years) and initially 2 percent of new vehicle sales are EVs, rising linearly to 100 percent by 2030.


In principle, the emissions impacts of feebates could be estimated using cross-price elasticities between EVs and conventional vehicles but there is not much solid evidence on this to date and most likely the elasticity will increase in future as, for example, EVs become more reliable and charging infrastructure expands.


For example, setting off before or after the peak of the rush hour, shifting to off-peak travel, less congested roads, or public transport, carpooling, reducing trip frequency.


Automobile Commission (2020). Information on people’s driving patterns could be collected by a private firm which passes on only information about motorists’ total tax liability to the government to help address privacy concerns.


See Coady (2006) for a discussion in the context of energy price reforms.


The full pass back to wages for exporters is consistent with mobile capital and firms and with exporters being price-takers on world markets. Changes in wages and the return to capital might also result from general equilibrium effects as production is re-allocated from carbon intensive activities to other sectors that may have different capital to labor ratios, but these effects are difficult to predict. As an approximation, it seems reasonable to assume carbon pricing for other (non-trade-exposed) sectors is fully passed forward to domestic users given that energy demand curves tend to be inelastic while (medium to longer term) energy supply curves tend to be elastic. Consistent with this, changes in gasoline and diesel prices tend to be fully passed forward in advanced countries (IMF 2020, pp. 4) while carbon pricing tends to be fully reflected in higher consumer prices for electricity in EU countries (e.g., Sijm and others 2012).


A $100 carbon tax increases retail prices for gasoline and diesel by $0.23 and $0.27 per liter respectively (relative to no carbon tax) which is smaller than price fluctuations due to changes in international oil prices. For comparison, a decline in international oil prices from their peak of $100 per barrel in 2014 to their current level of about $40 per barrel, reduced retail gasoline and diesel prices by about $0.50 per liter.


These small price impacts imply that carbon pricing will probably do little to discourage the electrification of transportation and other sectors.


Treatment of imputed rent for owner-occupied housing and some financial services are the main source of discrepancies (see Eurostat 2020 for details). For 2015 in Denmark, the ratio of total household consumption expenditure as estimated from the household budget survey to the national accounts was 0.89.


Under a full BCA with export rebates, the price of imports increases in proportion to their carbon content, while wages paid by exporting firms are unaffected. If foreign production is more carbon intensive than domestic production—which is the case for Denmark—then the incidence on households through higher consumer prices would be larger. Accurately estimating this incidence would require inter-country input-output tables with country-sector specific carbon emission intensity of production.


Wier and others 2005 and Danish Economic Councils 2009 find similar results from green taxes in Denmark when households are classified according to consumption levels.


The burden on households also includes the efficiency loss from the carbon price, approximately one-half the product of the emissions reduction and the carbon price. Given the emission reduction of 20 percent, the size of the efficiency loss is equal to 16 percent of the revenue raised.


The specific parameters of the reform will depend on household’s real income changes, the elasticities of labor supply and demand and features of the income distribution (Tsyvinski and Werquin 2019).


Essentially all workers face a positive marginal tax rate given that the personal allowance for labor income was only about $1,500 in 2015.


Holmlund and Soderstrom (2011).


These simulations assume short run elasticities of labor supply of 0.3 and labor demand of 0.6. In the long run, the labor supply elasticity is 0.5 while labor demand is assumed to be flat, consistent with constant returns to labor and capital. The current (average) marginal tax rate schedule is estimated by a functional relation using microdata from the Danish Law Model 2016 (see Tsyvinski and Werquin 2019 for details).


Danish Council on Climate Change (2020). The first reform would lower average tax rates for workers and encourage labor force participation but not (as under cuts in marginal tax rates) extra hours worked on the job. Empirical labor supply studies find however that most of the labor supply elasticity is due to the participation response.


That is, the percent of the domestic emissions reductions from carbon mitigation that is offset by increased emissions in other countries.


Only one BCA has been implemented to date, applying to the embodied carbon in imported electricity under California’s ETS (see Pauer 2018).


Danish Economic Council (2019) finds overall carbon leakage rate of around 0.5 percent when including the agricultural sector. Note that leakage can also arise though reductions in international fuel prices (induced by mitigation policies) leading to increased fuel demand in other countries. This second channel would likely be small for a country like Denmark but would potentially be larger for EU-wide mitigation policies. Going forward, both sources of leakage could be reduced if trading partners are meeting binding emissions targets under the Paris Agreement. See Böhringer and others (2012) and Branger and Quirion (2014) for literature reviews on leakage.


From OECD, Trade in Embodied CO2 Database (TECO2). These embodied foreign emissions are not covered by Denmark’s 70 percent reduction target, which only includes domestic emissions.


For example, the OECD TECO2 database estimates embodied carbon in imports for EU and advanced countries for 36 sector classifications (ISIC Rev. 4) and by exporting country. But measuring embodied carbon is challenging and there is a need for international collaboration to improve data standards and methodologies. See Sato (2014) for a review of the empirical literature.


See Nordhaus (2015), Böhringer and others (2016).


This phased approach is also being considered as an option in the context of incorporating BCAs into the EU ETS.


Examples of such certifications include the World Resource Institute/World Business Council on Sustainable Development GHG Protocol or the ISO 14064 standard.


See for instance Böhringer and others (2017).


WTO rules (which generally look to legal form of relevant measures) in general permit border adjustments on “indirect” taxes only. Given the stronger link between carbon taxes with BCA and a firm’s underlying production activities, it is not necessarily the case that all BCAs would be accepted as being legally equivalent to “indirect” taxes. According to the WTO’s Agreement on Subsidies and Countervailing Measures (SCM Agreement), these are defined as “sales, excise, turnover, value added, franchise, stamp, transfer, inventory and equipment taxes, border taxes and all taxes other than direct taxes and import charges.”


In 2018, the share in Denmark was 22 percent versus 10 percent in other EU countries. See Eurostat (2020). Total emissions include all sectors and indirect CO2 (excluding emissions from land use resulting from direct human-induced land use such as settlements and commercial uses, land use change and forestry activities, i.e. ‘LULUCF’, emissions from post-production waste of food and crop, and memo items). Greenhouse gases include CO2, N2O in CO2 equivalent, CH4 in CO2 equivalent, HFC in CO2 equivalent, PFC in CO2 equivalent, SF6 in CO2 equivalent, NF3 in CO2 equivalent).


Increased fat content in feed for conventional dairy cows and heifers (-); Frequent slurry of manure in pig houses (-) Increased and further afforestation; nitrogen targets.


Batini and Pointereau (forthcoming). The government’s Ministry of Food, Agriculture and Fisheries’ 67-point plan, dubbed “Økologiplan” focuses heavily on a more organic public sector and aims to strengthen cooperation between municipalities, regions and ministries to speed up the transition from conventional to organic production on publicly owned land with a long line of new initiatives to strengthen both development and conversion working with alternative ownership and operation models.


Even after the outbreak of coronavirus cases registered in 2020 in various mink farms, unlike the Netherlands, Denmark has not passed legislation aimed at closing its massive mink sector, but it did begin to phase out its fox fur market in 2009 (with plans to phase it out completely by 2023). Several EU countries have ended their fur farm industries in recent years, often in response to animal welfare concerns. Austria, Belgium, Luxembourg, Slovenia, Croatia, Czech Republic, Slovakia, and the United Kingdom have banned fur farming, and Ireland is in the process of passing a ban on fur production. Legislative proposals to end fur farming have recently been introduced in Bulgaria and Lithuania.


Indeed, the Council estimates only modest gains from feed additives for example, based on newest data from Aarhus University indicating that enteric methane emissions from cattle can be reduced by a mere 8 percent by adding more fat from rapeseed to the fodder. See Bovaer, for example, is a feed additive containing rapeseed oil, that could potentially reduce methane emissions by up to 1/3, likely less, but its ultimate impact is highly uncertain, and the drug is not on the market yet pending EU approval expected for 2021.Similarly, the Council proposal of “better slurry management,” that involves a combination of increased acidification where this is the preferred option, gasification, cooling and rapid removal of slurry from the barn, is not estimated to lead to significant mitigation. For more details see


Calculations in Figure 14 assumed that beef emits 14.7kg CO2-eq/kg CW and pigs between 3.55–4.74kg CO2-eq/kg CW where CW stands for ‘carcass weight’ based on hot carcass weight values (HCW) These figures reflect standard estimates in McLeod et al., (2013) and Opio et al. (2013) and capture all GHG emissions from enteric fermentation, manure management and feed crops. The estimates have been averaged with estimates by Kool et al., 2009 and Darlgaard (2007) using Data from Danish farms. It is also assumed that each beef carcass weighs on average 363kgs and each pig carcass weighs 80kgs. These are conservative estimates. Latest data on cattle and pig populations in Denmark are 2018 and taken from Eurostat. These estimates seem to suggest that emission from livestock in Denmark may be higher than what currently reported by Eurostat for 2018 for comparable GHGs in CO2-eq metrics (6.63 million tons of CO2 eq.), implying that total emissions excluding land use, land use change and forestry (LULUCF) may be also proportionally higher than what reported by Eurostat for 2018.


The EU recently launched “Farm to Fork” strategic envisages a halving of both pesticides and antibiotics in use in EU farms by 2030, plus a 1/5 cut in fertilizers and an increase of organically-farmed land by 25 percent in the EU on average plus changes to animal welfare legislation both on land and at sea. See


Red meat includes beef, goat, lamb, mutton, pork and venison.


Contrary to other parts of the world, livestock emissions in Western Europe from grassland systems (extensive) are similar to emissions from industrial systems (intensive) so a shift from the latter to the former would not erode gains obtained by shrinking the size of herds bred. See FAO’s GLEAM 2.0 (2017).


Government-led research in the Netherlands suggested mink farms were the first known site of likely animal-to-human coronavirus transmission. See:


WHO recommends that farmers and the food industry stop using antibiotics routinely to promote growth and prevent disease in healthy animals. See


Air pollution has received less attention than it merits in agricultural debates. Yet it is considered the largest environmental health risk in the EU and it is estimated that one in four Europeans will die or fall sick due to air pollution during their lifetime (WHO Regional Office for Europe and OECD, 2015).


Under standard assumptions about sex ratios and fertility and mortality rates, considering a logistic population growth rule, the kill of one fertile Great whale female specimen in a given year can lead to the potential loss of around 70–80 new specimens over thirty years, as her female offspring, in turn, reach sexual maturity and start giving birth during that period. Great whales leave on average 90 years and calve every 1–3 years under favorable conditions, beginning at around 7–10 years of age, all depending on the species (Safina, 2020).


This proposal is similar in spirit to earlier proposals by the Danish Council (Danish Council on Climate Change, 2016) also involving a (proxy) carbon tax at the farm level based on number of livestock, fertilizer use, feedstock, etc.


The tax was a surcharge on foods that are high in saturated fat. Butter, milk, cheese, pizza, meat, oil and processed food became subject to the tax if they contained more than 2.3 percent saturated fat.


As a member of the EU, Danish agricultural production is subject to the EU’s Common Agricultural Policy (CAP), and it is thus heavily affected by changes to the CAP. Introduced in 1962, the CAP has undergone several changes since then to reduce the cost (from 71 percent of the EU budget in 1984 to 39 percent in 2013) and to also consider rural development in its aims. The CAP works through a system of agricultural subsidies and price/market support programs and has long exerted a strong influence on agricultural and land change practices in Europe.


See Batini (2019) for similar recommendations for the case of France, another EU country subject to the CAP.


The Danish Council on Climate Change (2020) estimates that halting peatland drainage could cut 1.4 million tons of CO2-eq by 2030.


If adopted globally, this could shave yearly global GHGs by up to 15 percent.


According to the World Bank, farming seaweed in 5% of U.S. waters, for example, has the potential to create 50 million jobs—the biggest job creator since World War II (World Bank, 2016).


The International Fund for Animal Welfare estimated the value of this business at $2.1 billion back in 2008. This eco-business has been increasing exponentially in Europe, Asia, the Caribbean, and South America since then.


A standard input-output matrix would also include energy inputs. The notation used here effectively precludes second-round effects on energy price themselves. Both approaches are equivalent however when the carbon policy targets the total energy price change.

Climate Mitigation Policy in Denmark: A Prototype for Other Countries
Author: Nicoletta Batini, Ian Parry, and Mr. Philippe Wingender