Deriving optimal carbon policies for biomass utilization 9.12.2014 - - PowerPoint PPT Presentation

Forests, land use and climate change:

Deriving optimal carbon policies for biomass utilization

9.12.2014 IEA Task 38 Workshop on Forests Aapo Rautiainen Jussi Lintunen Jussi Uusivuori

In this presentation…

We present a model which includes:

– The allocation of land to competing uses – The allocation of biomass to competing uses – Carbon storage in biomass, soils and products

We use it to derive an efficient (tax) policy for regulating of biomass emissions

What its based on

Lintunen, J. and Uusivuori, J. 2014. On the economics of Forest Carbon: Renewable and Carbon Neutral But Not Emission

• Free. Fondazione Eni Enrico Mattei

Working Paper Series. 13.2014. Rautiainen, A. Lintunen, J. and Uusivuori,

• J. (Work in Progress)

Stand-level analysis:

– van Kooten ym. 1995, Hoen & Solberg 1994

National-level analysis:

– Tahvonen 1995

Substitution vs. Carbon storage:

– Marland ja Schlamadinger 1997

Bioenergy emissions:

– Fargione ym. 2008, Searchinger ym. 2009 ja Repo

• ym. 2011

5.11.2014

Earlier Research (e.g.)

I Model properties

The carbon cycle

Carbon fluxes Carbon pools Atmospheric carbon pool Living forest biomass Oceanic carbon pool Emissions from fossil fuel use in energy production Emissions from production of non- renewable materials and fertilizer Energy use Decay Growth Consumption

• f crops

and residues Annual carbon cycling in agriculture Energy use, short-lived wood products, waste from producing long-lived products Growth Long-lived wood products Harvested Wood Products Waste Landfill

Legend:

Decay Soil carbon Uncollected residues Litter Uncollected residues

EOM for atmospheric C

1 − 𝜀𝐵𝑈𝑁 𝑇𝑢

𝐵𝑈𝑁

𝑇𝑢+1

𝐵𝑈𝑁 =

+𝜁𝑔𝑔

𝑢 + 𝜁𝑨𝑨𝑢 + 𝜁𝑤 𝑗=1 𝑂

𝑤𝑗𝑢𝑦𝑗1𝑢 +

𝑗=1 𝑂+1 𝑏=1 𝐵𝑗 𝑘=1 𝐾𝑗

𝜀𝑗𝑘

𝑇𝑇𝑗𝑏𝑘𝑢 𝑇

+ 𝜀𝑀𝐺𝑇𝑢

𝑀𝐺

−

𝑗=1 𝑂

𝜁𝑗

𝑑𝐻𝑗𝑢 𝐷 + 𝜁𝑗 𝑠𝐻𝑗𝑢 𝑆 + 𝑗=1 𝑂

𝜁𝑗

𝑑𝑏𝑗𝑢 𝐺 + 𝜁𝑗 𝑑𝑏𝑗𝑢 𝐹 + 𝜁𝑗 𝑠𝑏𝑗𝑢 𝑆𝐹𝑇

−𝜁𝑥𝐻𝑢

𝑋 + 𝜁𝑥 𝑥𝑢 𝑄 + 1 − 𝛽 𝑥𝑢 𝑀 + 𝑥𝑢 𝐹 + 𝑥𝑢 𝑆𝐹𝑇 + 𝑥𝑢 𝐼𝑋𝑄

EOM for atmospheric C

1 − 𝜀𝐵𝑈𝑁 𝑇𝑢

𝐵𝑈𝑁

𝑇𝑢+1

𝐵𝑈𝑁 =

+𝜁𝑔𝑔

𝑢 + 𝜁𝑨𝑨𝑢 + 𝜁𝑤 𝑗=1 𝑂

𝑤𝑗𝑢𝑦𝑗1𝑢 +

𝑗=1 𝑂+1 𝑏=1 𝐵𝑗 𝑘=1 𝐾𝑗

𝜀𝑗𝑘

𝑇𝑇𝑗𝑏𝑘𝑢 𝑇

+ 𝜀𝑀𝐺𝑇𝑢

𝑀𝐺

−

𝑗=1 𝑂

𝜁𝑗

𝑑𝐻𝑗𝑢 𝐷 + 𝜁𝑗 𝑠𝐻𝑗𝑢 𝑆 + 𝑗=1 𝑂

𝜁𝑗

𝑑𝑏𝑗𝑢 𝐺 + 𝜁𝑗 𝑑𝑏𝑗𝑢 𝐹 + 𝜁𝑗 𝑠𝑏𝑗𝑢 𝑆𝐹𝑇

−𝜁𝑥𝐻𝑢

𝑋 + 𝜁𝑥 𝑥𝑢 𝑄 + 1 − 𝛽 𝑥𝑢 𝑀 + 𝑥𝑢 𝐹 + 𝑥𝑢 𝑆𝐹𝑇 + 𝑥𝑢 𝐼𝑋𝑄

Atmospheric C in period t+1 Atmospheric C in period t minus decay into oceans

EOM for atmospheric C

1 − 𝜀𝐵𝑈𝑁 𝑇𝑢

𝐵𝑈𝑁

𝑇𝑢+1

𝐵𝑈𝑁 =

+𝜁𝑔𝑔

𝑢 + 𝜁𝑨𝑨𝑢 + 𝜁𝑤 𝑗=1 𝑂

𝑤𝑗𝑢𝑦𝑗1𝑢 +

𝑗=1 𝑂+1 𝑏=1 𝐵𝑗 𝑘=1 𝐾𝑗

𝜀𝑗𝑘

𝑇𝑇𝑗𝑏𝑘𝑢 𝑇

+ 𝜀𝑀𝐺𝑇𝑢

𝑀𝐺

−

𝑗=1 𝑂

𝜁𝑗

𝑑𝐻𝑗𝑢 𝐷 + 𝜁𝑗 𝑠𝐻𝑗𝑢 𝑆 + 𝑗=1 𝑂

𝜁𝑗

𝑑𝑏𝑗𝑢 𝐺 + 𝜁𝑗 𝑑𝑏𝑗𝑢 𝐹 + 𝜁𝑗 𝑠𝑏𝑗𝑢 𝑆𝐹𝑇

−𝜁𝑥𝐻𝑢

𝑋 + 𝜁𝑥 𝑥𝑢 𝑄 + 1 − 𝛽 𝑥𝑢 𝑀 + 𝑥𝑢 𝐹 + 𝑥𝑢 𝑆𝐹𝑇 + 𝑥𝑢 𝐼𝑋𝑄

Fossil fuel emissions Material emissions (from non-renewables) Fertilizer emissions (from agriculture)

EOM for atmospheric C

1 − 𝜀𝐵𝑈𝑁 𝑇𝑢

𝐵𝑈𝑁

𝑇𝑢+1

𝐵𝑈𝑁 =

+𝜁𝑔𝑔

𝑢 + 𝜁𝑨𝑨𝑢 + 𝜁𝑤 𝑗=1 𝑂

𝑤𝑗𝑢𝑦𝑗1𝑢 +

𝑗=1 𝑂+1 𝑏=1 𝐵𝑗 𝑘=1 𝐾𝑗

𝜀𝑗𝑘

𝑇𝑇𝑗𝑏𝑘𝑢 𝑇

+ 𝜀𝑀𝐺𝑇𝑢

𝑀𝐺

−

𝑗=1 𝑂

𝜁𝑗

𝑑𝐻𝑗𝑢 𝐷 + 𝜁𝑗 𝑠𝐻𝑗𝑢 𝑆 + 𝑗=1 𝑂

𝜁𝑗

𝑑𝑏𝑗𝑢 𝐺 + 𝜁𝑗 𝑑𝑏𝑗𝑢 𝐹 + 𝜁𝑗 𝑠𝑏𝑗𝑢 𝑆𝐹𝑇

−𝜁𝑥𝐻𝑢

𝑋 + 𝜁𝑥 𝑥𝑢 𝑄 + 1 − 𝛽 𝑥𝑢 𝑀 + 𝑥𝑢 𝐹 + 𝑥𝑢 𝑆𝐹𝑇 + 𝑥𝑢 𝐼𝑋𝑄

Forest growth Emissions from wood use

PULP, LOGS, ENERGY WOOD, RESIDUES, HWP

EOM for atmospheric C

1 − 𝜀𝐵𝑈𝑁 𝑇𝑢

𝐵𝑈𝑁

𝑇𝑢+1

𝐵𝑈𝑁 =

+𝜁𝑔𝑔

𝑢 + 𝜁𝑨𝑨𝑢 + 𝜁𝑤 𝑗=1 𝑂

𝑤𝑗𝑢𝑦𝑗1𝑢 +

𝑗=1 𝑂+1 𝑏=1 𝐵𝑗 𝑘=1 𝐾𝑗

𝜀𝑗𝑘

𝑇𝑇𝑗𝑏𝑘𝑢 𝑇

+ 𝜀𝑀𝐺𝑇𝑢

𝑀𝐺

−

𝑗=1 𝑂

𝜁𝑗

𝑑𝐻𝑗𝑢 𝐷 + 𝜁𝑗 𝑠𝐻𝑗𝑢 𝑆 + 𝑗=1 𝑂

𝜁𝑗

𝑑𝑏𝑗𝑢 𝐺 + 𝜁𝑗 𝑑𝑏𝑗𝑢 𝐹 + 𝜁𝑗 𝑠𝑏𝑗𝑢 𝑆𝐹𝑇

−𝜁𝑥𝐻𝑢

𝑋 + 𝜁𝑥 𝑥𝑢 𝑄 + 1 − 𝛽 𝑥𝑢 𝑀 + 𝑥𝑢 𝐹 + 𝑥𝑢 𝑆𝐹𝑇 + 𝑥𝑢 𝐼𝑋𝑄

Growth in agriculture Emissions crop and residue use

FOOD AND ENERGY CROPS, RESIDUES

EOM for atmospheric C

1 − 𝜀𝐵𝑈𝑁 𝑇𝑢

𝐵𝑈𝑁

𝑇𝑢+1

𝐵𝑈𝑁 =

+𝜁𝑔𝑔

𝑢 + 𝜁𝑨𝑨𝑢 + 𝜁𝑤 𝑗=1 𝑂

𝑤𝑗𝑢𝑦𝑗1𝑢 +

𝑗=1 𝑂+1 𝑏=1 𝐵𝑗 𝑘=1 𝐾𝑗

𝜀𝑗𝑘

𝑇𝑇𝑗𝑏𝑘𝑢 𝑇

+ 𝜀𝑀𝐺𝑇𝑢

𝑀𝐺

−

𝑗=1 𝑂

𝜁𝑗

𝑑𝐻𝑗𝑢 𝐷 + 𝜁𝑗 𝑠𝐻𝑗𝑢 𝑆 + 𝑗=1 𝑂

𝜁𝑗

𝑑𝑏𝑗𝑢 𝐺 + 𝜁𝑗 𝑑𝑏𝑗𝑢 𝐹 + 𝜁𝑗 𝑠𝑏𝑗𝑢 𝑆𝐹𝑇

−𝜁𝑥𝐻𝑢

𝑋 + 𝜁𝑥 𝑥𝑢 𝑄 + 1 − 𝛽 𝑥𝑢 𝑀 + 𝑥𝑢 𝐹 + 𝑥𝑢 𝑆𝐹𝑇 + 𝑥𝑢 𝐼𝑋𝑄

Soil carbon emissions by Landfill emissions (discarded HWP)

• Land use class
• Age class
• Decay class

The Economy

Final consumption Aggregation of consumption good Energy production Forestry Agriculture Non-renewable material Energy Wood Fossil fuel Residues Land Residues Inputs and

• utputs

Legend:

Good Discarded wood products Production and consumption processes Fertilizer Aggregation of food composite Crops Food

Objective function

max

𝐞t 𝑢=0

∞

𝑢=0 ∞

𝛾𝑢 𝑣𝐺 𝑧𝑢

𝐺 + 𝑣𝐷 𝑧𝑢 𝐷 − 𝐸 𝑇𝑢 𝐵𝑈𝑁 − 𝐷𝑢 ,

𝐷𝑢 = 𝑞𝑨𝑨𝑢 + 𝑞𝑔𝑔

𝑢 + 𝑗=1 𝑂

𝑞𝑤𝑤𝐺𝑢 + 𝑑𝑗

𝐺𝐷 𝑦𝑗1𝑢 + 𝑑𝑗 𝑏𝑆𝐹𝑇 + 𝑑𝐼𝐼𝑢 𝑋 + 𝑑𝑥𝐺𝑆𝐹𝑇 + 𝑑𝑥𝐷𝑆𝐹𝑇

+

𝑘=1 𝑂 𝑙=1 𝑂+1

𝑑

𝑘𝑙𝑢 𝐷𝑃𝑂𝑡 𝑘𝑙𝑢 𝑦𝑘1𝑢 + 𝑙=1 𝑂+1

𝑑𝑂+1,𝑙,𝑢

𝐷𝑃𝑂

𝑡𝑂+1,𝑙,𝑢 𝑦𝑂+1,0,𝑢 +𝑑𝐼𝑋𝑄 + 𝑑𝑀𝐺 𝑋

𝑢 𝐼𝑋𝑄 − 𝑥𝑢 𝐼𝑋𝑄

𝐞𝑢 = 𝑨𝑢, 𝑔

𝑢, 𝑤𝑗𝑢, 𝐛t 𝐆, 𝐛t 𝐅, 𝐛t 𝐒𝐅𝐓, 𝑥𝑢 𝑀, 𝑥𝑢 𝑄, 𝑥𝑢 𝐹, 𝑥𝑢 𝐺𝑆𝐹𝑇, 𝑥𝑢 𝐷𝑆𝐹𝑇, 𝑥𝑢 𝐼𝑋𝑄 , 𝛊t, 𝑦𝑂+1,0,𝑢 , 𝐲t+1, 𝐭jkt,

𝐓t

AR, 𝑇𝑢 𝐺𝑈, 𝑇𝑢 𝐷𝑈, 𝐓iaj,t+1 S

, 𝑇𝑢+1

𝐵𝑈𝑁, 𝑇𝑢+1 𝐼𝑋𝑄 , 𝑇𝑢+1 𝑀𝐺

Utility from food Utility from good Disutility from atmospheric C Total costs Periodic Social Welfare

Contains substitution between energy, non-renewable and renewable materials Capture the substitution between food and other consumption Contains: Cost of fossil fuels, Nonrenewable materials, Agriculture, Forestry, Land use conversions HWP collection Landfilling Simplified form! Could be made more complex.

Objective function

max

𝐞t 𝑢=0

∞

𝑢=0 ∞

𝛾𝑢 𝑣𝐺 𝑧𝑢

𝐺 + 𝑣𝐷 𝑧𝑢 𝐷 − 𝐸 𝑇𝑢 𝐵𝑈𝑁 − 𝐷𝑢 ,

𝐷𝑢 = 𝑞𝑨𝑨𝑢 + 𝑞𝑔𝑔

𝑢 + 𝑗=1 𝑂

𝑞𝑤𝑤𝐺𝑢 + 𝑑𝑗

𝐺𝐷 𝑦𝑗1𝑢 + 𝑑𝑗 𝑏𝑆𝐹𝑇 + 𝑑𝐼𝐼𝑢 𝑋 + 𝑑𝑥𝐺𝑆𝐹𝑇 + 𝑑𝑥𝐷𝑆𝐹𝑇

+

𝑘=1 𝑂 𝑙=1 𝑂+1

𝑑

𝑘𝑙𝑢 𝐷𝑃𝑂𝑡 𝑘𝑙𝑢 𝑦𝑘1𝑢 + 𝑙=1 𝑂+1

𝑑𝑂+1,𝑙,𝑢

𝐷𝑃𝑂

𝑡𝑂+1,𝑙,𝑢 𝑦𝑂+1,0,𝑢 +𝑑𝐼𝑋𝑄 + 𝑑𝑀𝐺 𝑋

𝑢 𝐼𝑋𝑄 − 𝑥𝑢 𝐼𝑋𝑄

𝐞𝑢 = 𝑨𝑢, 𝑔

𝑢, 𝑤𝑗𝑢, 𝐛t 𝐆, 𝐛t 𝐅, 𝐛t 𝐒𝐅𝐓, 𝑥𝑢 𝑀, 𝑥𝑢 𝑄, 𝑥𝑢 𝐹, 𝑥𝑢 𝐺𝑆𝐹𝑇, 𝑥𝑢 𝐷𝑆𝐹𝑇, 𝑥𝑢 𝐼𝑋𝑄 , 𝛊t, 𝑦𝑂+1,0,𝑢 , 𝐲t+1, 𝐭jkt,

𝐓t

AR, 𝑇𝑢 𝐺𝑈, 𝑇𝑢 𝐷𝑈, 𝐓iaj,t+1 S

, 𝑇𝑢+1

𝐵𝑈𝑁, 𝑇𝑢+1 𝐼𝑋𝑄 , 𝑇𝑢+1 𝑀𝐺

Periodic Social Welfare Discounted Summed over infinite time horizon

Objective function

max

𝐞t 𝑢=0

∞

𝑢=0 ∞

𝛾𝑢 𝑣𝐺 𝑧𝑢

𝐺 + 𝑣𝐷 𝑧𝑢 𝐷 − 𝐸 𝑇𝑢 𝐵𝑈𝑁 − 𝐷𝑢 ,

𝐷𝑢 = 𝑞𝑨𝑨𝑢 + 𝑞𝑔𝑔

𝑢 + 𝑗=1 𝑂

𝑞𝑤𝑤𝐺𝑢 + 𝑑𝑗

𝐺𝐷 𝑦𝑗1𝑢 + 𝑑𝑗 𝑏𝑆𝐹𝑇 + 𝑑𝐼𝐼𝑢 𝑋 + 𝑑𝑥𝐺𝑆𝐹𝑇 + 𝑑𝑥𝐷𝑆𝐹𝑇

+

𝑘=1 𝑂 𝑙=1 𝑂+1

𝑑

𝑘𝑙𝑢 𝐷𝑃𝑂𝑡 𝑘𝑙𝑢 𝑦𝑘1𝑢 + 𝑙=1 𝑂+1

𝑑𝑂+1,𝑙,𝑢

𝐷𝑃𝑂

𝑡𝑂+1,𝑙,𝑢 𝑦𝑂+1,0,𝑢 +𝑑𝐼𝑋𝑄 + 𝑑𝑀𝐺 𝑋

𝑢 𝐼𝑋𝑄 − 𝑥𝑢 𝐼𝑋𝑄

𝐞𝑢 = 𝑨𝑢, 𝑔

𝑢, 𝑤𝑗𝑢, 𝐛t 𝐆, 𝐛t 𝐅, 𝐛t 𝐒𝐅𝐓, 𝑥𝑢 𝑀, 𝑥𝑢 𝑄, 𝑥𝑢 𝐹, 𝑥𝑢 𝐺𝑆𝐹𝑇, 𝑥𝑢 𝐷𝑆𝐹𝑇, 𝑥𝑢 𝐼𝑋𝑄 , 𝛊t, 𝑦𝑂+1,0,𝑢 , 𝐲t+1, 𝐭jkt,

𝐓t

AR, 𝑇𝑢 𝐺𝑈, 𝑇𝑢 𝐷𝑈, 𝐓iaj,t+1 S

, 𝑇𝑢+1

𝐵𝑈𝑁, 𝑇𝑢+1 𝐼𝑋𝑄 , 𝑇𝑢+1 𝑀𝐺

Vector of choice variables

Non-ren. materials Fossil fuels Fertilizer Food crops Energy crops Residues Harvests (logs, pulp, energy) Harvesting residues (coarse, fine) Collected discarded HWP Land allocation Land conversions Clear-cuts (By age class / as total area) C stocks (Soils, Atmosphere, HWP, Landfills)

What we can derive from this:

Optimality conditions:

– Optimal land allocation and conversions – Optimal harvesting rule for forests – Optimal biomass allocation conditions

• …which include the valuation of the carbon

impacts

→ Our focus in this presentation

II Policy recommendations

Social Cost of Carbon (SCC)

First, we derive SCCt for each period

– It is the discounted damage from emitting a unit of C into the atmosphere (in period t), summed over the infinite time horizon. – It can be interpreted as ”the periodic carbon price”.

Then, we show how the social cost of burning or using different varieties of biomass can be expressed relative to SCC

– We obtain optimal taxes on biomass use

Social Cost of Carbon

Assuming time-invariant decay:

𝑇𝐷𝐷𝑢 = 𝜇𝑢

𝑇𝐵𝑈𝑁 = 𝑗=1 ∞

𝛾𝑗 1 − 𝜀𝐵𝑈𝑁 𝑗−1 𝐸′(𝑇𝑢+𝑗

𝐵𝑈𝑁)

Decay Damage Discounting

Social Cost of Carbon

Assuming time-invariant decay: Assuming time-variant decay:

𝑇𝐷𝐷𝑢 = 𝜇𝑢

𝑇𝐵𝑈𝑁 = 𝑗=1 ∞

𝛾𝑗 1 − 𝜀𝐵𝑈𝑁 𝑗−1 𝐸′(𝑇𝑢+𝑗

𝐵𝑈𝑁)

𝑇𝐷𝐷𝑢 =

𝑗=1 ∞

𝛾𝑗 𝜈𝑢+𝑗𝐸′(𝑇𝑢+𝑗

𝐵𝑈𝑁)

𝜈𝑢+𝑗 = 1 𝑥ℎ𝑓𝑜 𝑗 = 1

𝑘𝑢=1 𝑗−1

1 − 𝜀

𝑘𝑢 𝐵𝑈𝑁 𝑥ℎ𝑓𝑜 𝑗 ≥ 2

where Time-invariant decay Time-variant decay

Social Cost of Carbon

Assuming time-invariant decay: Assuming time-variant decay:

𝑇𝐷𝐷𝑢 = 𝜇𝑢

𝑇𝐵𝑈𝑁 = 𝑗=1 ∞

𝛾𝑗 1 − 𝜀𝐵𝑈𝑁 𝑗−1 𝐸′(𝑇𝑢+𝑗

𝐵𝑈𝑁)

𝑇𝐷𝐷𝑢 =

𝑗=1 ∞

𝛾𝑗 𝜈𝑢+𝑗𝐸′(𝑇𝑢+𝑗

𝐵𝑈𝑁)

𝜈𝑢+𝑗 = 1 𝑥ℎ𝑓𝑜 𝑗 = 1

𝑘𝑢=1 𝑗−1

1 − 𝜀

𝑘𝑢 𝐵𝑈𝑁 𝑥ℎ𝑓𝑜 𝑗 ≥ 2

where

How does SCC compare with GWP?

Global Warming Potential* Social Cost of Carbon Time horizon Damage indicated by Time preference indicated by

* The treatment of CO2 in the calculation of GWP for other GHGs

Finite (Fixed to e.g. 20 or 100 years) Infinite Warming effect, i.e. the time- integrated radiative forcing caused by an instantaneous release of CO2 Discount rate A high discount rate → short- term impacts emphasized A low discount rate → long-term impacts emphasized Time horizon Short time horizon → short-term impacts emphasized Long horizon → long-term impacts emphasized Damage function indicating the disutility caused by atmospheric CO2 and its warming effect

Deriving optimal taxes Background: Temporary C stocks

The C stocks

• Soils
• Products
• Landfills

Carbon is released gradually

• The carbon releases are harmful

– They are valued at the current SCC when they occur – The social costs are discounted to present value… – …and summed over the infinite time horizon.

Deriving optimal taxes: Assumptions

Assumptions:

– Fluxes are accounted as they occur

• or at least treated ”as if”
• As noted on the previous slide: Emissions of from temporary

stocks are valued at the current SCC (when the occur), discounted to present value and summed over the infinite time horizon

– The regulations directly target the actions that cause the emissions

• Optimal tax on a given action =

+ The Social cost of C releases due to the taken given action

• The Social cost C release without taking the given action

(i.e. the opportunity cost)

Optimal taxes on actions

Fossil fuel burning Burning logs Logs as raw material Energy wood Residues Burning HWP Burning food/energy crop Burning residues 𝑇𝐷𝐷𝑢

𝐵𝑈𝑁𝜁𝑔

1 − 𝛽 𝑇𝐷𝐷𝑢

𝐵𝑈𝑁 + 𝛽𝑇𝐷𝐷𝑢 𝐼𝑋𝑄 − 𝑇𝐷𝐷𝑢 𝐸𝑃𝑁𝐷 𝜁𝑥

𝑇𝐷𝐷𝑢

𝐵𝑈𝑁 − 𝑇𝐷𝐷𝑢 𝐸𝑃𝑁𝐷 𝜁𝑥

𝑇𝐷𝐷𝑢

𝐵𝑈𝑁 − 𝑇𝐷𝐷𝑢 𝐸𝑃𝑁𝐷 𝜁𝑥

𝑇𝐷𝐷𝑢

𝐵𝑈𝑁 − 𝑇𝐷𝐷𝑢 𝐸𝑃𝑁𝑙 𝜁𝑥

𝑇𝐷𝐷𝑢

𝐵𝑈𝑁 − 𝑇𝐷𝐷𝑢 𝑀𝐺 𝜁𝑥

𝑙 = 𝐺 𝑝𝑠 𝐷 𝑇𝐷𝐷𝑢

𝐵𝑈𝑁 − 𝑇𝐷𝐷𝑢 𝐸𝑃𝑁𝑗 𝜁𝑗 𝑑

𝑇𝐷𝐷𝑢

𝐵𝑈𝑁 − 𝑇𝐷𝐷𝑢 𝐸𝑃𝑁𝑗 𝜁𝑗 𝑠

Effective emission factors

Example: Residues

𝑇𝐷𝐷𝑢

𝐵𝑈𝑁 − 𝑇𝐷𝐷𝑢 𝐸𝑃𝑁𝑗 𝜁𝑥=

1 −

𝑇𝐷𝐷𝑢

𝐸𝑃𝑁𝑗

𝑇𝐷𝐷𝑢

𝐵𝑈𝑁

𝜁𝑥 × 𝑇𝐷𝐷𝑢

𝐵𝑈𝑁

Effective Emission Factor (EEF) ”Carbon price”

1/28/2017

Emissions from harvest residues

”Short horizon” ”Long horizon”

EEF: Time-invariant SCC

1 − 𝑇𝐷𝐷𝑢

𝐸𝑃𝑁𝑗

𝑇𝐷𝐷𝑢

𝐵𝑈𝑁

𝜁𝑥

1/28/2017

Emissions from harvest residues

”Short horizon” ”Long horizon”

EEF: SCC increases 1% per period

1 − 𝑇𝐷𝐷𝑢

𝐸𝑃𝑁𝑗

𝑇𝐷𝐷𝑢

𝐵𝑈𝑁

𝜁𝑥

Kiitos