The Price of Carbon

Topics in Economics, ESCP, 2023-2024

Pablo Winant

2024-01-22

Plan

• Global Warming and the Carbon Budget
• The Price of Carbon
• Estimating the price of carbon
• Conclusion

Don’t worry too much…

The concept of global warning was created by and for the Chinese, in order to make U.S. manufacturing non competitive.

Donald Trump

   

⚠ Disclaimer: I was being sarcastic…

And yet, economists working in american universities devised the consensus on the best way to fight climate change.

William Nordhaus

2018: William Nordhaus received the nobel prize for his contributions for integrating climate change into long-run macroeconomic analysis.

William Nordhaus

His work setup the consensus among economists about the most efficient way to fight climate change…

…at least in theory

For those interested in the history of climate change economics, I recommend the work / teaching of Beatrice Cherrier

Global Warming and the Carbon Budget

Global Warming

Temperature Projection (ICCP)

Temperature is measured as difference to preindustrial level.

No action scenario: >+4 compared to preindustrial levels

Global Warming

How much is too much?

• 4 was glaciation. What about >+4?
• checkout (ICCP 2022)

Past temperatures (from CO2 trapped in ice cores)

Main Cause of Global Warming

Consensus from Earth Science

• burning of fossil fuels (oil, gas, ) -> emission Carbon Dioxyde CO2
  • on of the main Greenhouse gases
• GHG accumulate in the atomosphere
• warms land and oceans
• more evaporation -> feedback effects

Carbon Budget

Global Temperature and Carbon Dioxide (from globalchange.gov)

Carbon Budget

Global Temperature and Carbon Dioxide (from globalchange.gov)

There is an approximately linear relationship between:

• cumulative emissions of CO₂ in the atmosphere
• global temperature (with some lag)

Immediate conclusion:

• over the long-run, the world needs to target zero-emission

Climate Clock

We can associate a maximum amount of cumulative emissions to each maximum change in temperature.

This is the global carbon budget:

\(\Delta T\)	Global Carbon Budget
1.5	420 Gt
2	1170 Gt

In 2018, emissions amounted to 42.1Gt.

At this rate we have <10 years left!

We should aim to reach carbon neutrality by 2030.

What are the options?

Yoichi Kaya

The Kaya identity:

\[F = P \frac{G}{P} \frac{E}{G} \frac{F}{E}\]

• F: global CO₂ emissions
• P: global population
• G: world GDP
• E: global energy consumption

What are the options?

The Kaya identity:

\[F = P \frac{G}{P} \frac{E}{G} \frac{F}{E}\]

• \(\frac{G}{P}\): GDP per capita
• \(\frac{E}{G}\): energy intensity of GDP
• \(\frac{F}{E}\): emission intensity of energy

What are the options?

The Kaya identity works in logs:

\[\Delta^{\%} F =\Delta^{\%} P + \Delta^{\%} \left( \frac{G}{P}\right) + \Delta^{\%}\left(\frac{E}{G}\right) + \Delta^{\%}\left(\frac{F}{E}\right)\]

• \(\frac{G}{P}\): GDP per capita
• \(\frac{E}{G}\): energy intensity of GDP
• \(\frac{F}{E}\): emission intensity of energy

What are the solutions?

• ↘ population (growth)
  • a solution for developing countries
  • delicate issue…
• ↘ production (growth)
  • arguable for developed countries
  • quite unpopular so far
  • use alternative welfare metric?

• ↘ energy intensity (growth)
  • production must use less energy
  • new supply chains (circular economy, recycling)
  • change consumption patterns
• ↘ carbon content of energy

Who must take the decision?

• the state
  • ex: by 2035, all new cars sold in EU will be carbon neutral
  • ex: french state will construct new nuclear power plants
• the society
  • ex: social norms could deconsider meat-eating
  • ex: we stop taking the plane (our cars) to go on holidays
• the market
  • consumption and production are private decisions consistent with market equilibrium

We focus today on market solutions

The Price of Carbon

A stable global climate is a global public good¹

  

Carbon emissions can be thought of as a global public bad:

• non-excludable: not possible to exclude a country from its effects
• non-rivalrous: once emitted everybody bears its consequences

1. On can also think of the 420Gt stock of remaining carbon emissions as a common good which is then subject to the tragedy of commons

The core incentive issue (1/2)

Externality and free-riding

• all agents (producers/consumers) benefit from stable climate
• all agents don’t receive any marginal benefit when emitting less CO₂
• ->Generalized temptation to free ride

The core incentive issue (2/2)

The problem exists at all scales:

• within a country

• between countries:

  • all countries benefit from policies against global warming
  • no country has a personal interest in implementing (costly) abattement policies

Externalities

Externality

An externality is an indirect cost or benefit to an uninvolved third party that arises as an effect of another party’s activity.

When agents (firms, consumers) maximize their objective they ignore the negative effect.

Externalities

Examples of Externality

• smoking in public
• a firm training workers
• laptops in class

If their objective is modified such as to account for the negative effects, we say that the objective has been internalized.

How can you make the authors of the above externalities internalize them?

Externality and prices

In the context of market interactions, externalities imply that prices of goods don’t reflect their true cost.

This leads to the notion of Pigouvian Taxation:

• if the price of a good is incorrect it must be modified…
• … with a tax meant to incorporate its true social cost

Theoretically, it can be shown (under very mild assumptions) that there exists an optimal Pigou tax.

The Carbon Tax

In principle, a carbon tax is the first best solution

• it gives a price to a good (carbon emission) which is overconsumed
• this provides all the right¹ incentives for producers and consumers…
• … to reduce carbon production in the most efficient way
• … to change consumption in a way that favours less carbon production

1. nondistortive incentives

The Carbon Tax

It is also easy to implement:

• just tax the production of energy instead of all steps of the production process

Problems of the Carbon Tax

There are other market imperfections which the carbon tax doesn’t solve

• R&D: is it fostering R&D in clean technology or just reducing consumption?
• Rebound effect: money saved by energy efficiency can be spent on more consumption
• Leakages:
  • it can lead to more imports of carbon-intensive goods
  • it must be complemented by a border carbon tax

Problems of the Carbon Tax

There are other market imperfections which the carbon tax doesn’t solve

But most importantly:

• public opinion is very averse to it.

The french experiment

A carbon tax was introduced in 2015: the “Climate-Energy Contribution”

• a tax on CO₂ content of energies
• initially very low rate
• increased over time to \(44.6E/ T CO₂\)

Yellow vests

=> The yellow vests movement forced the government to back down.

The french experiment (2)

Citizen’s convention for the climate: try to build consensus

• Ocober 2019: 150 citizens drawn at random
• Mandate: define series of measures to achieve 40% reduction in GHG by 2030
• 7 sessions of 3 days

The french experiment (3)

Results:

• everything except carbon tax!!
• price incentives: VAT reduction on train tickets
• regulatory constraints: ban polluting vehicles, mandatory house renovation, on peri-urban shoping areas
• public green investment: train, housing, infrastructure

Point of view from most economists

Doesn’t matter with which policy, a price must be put on carbon emissions:

It is the only way to

• leave the market efficiently reallocate efforts across sectors
• encourage good investments over time

There is a wide consensus among economists (from Nordhaus, Stern, Aglietta…)

Tote Bags vs Plastic Bags

(a) A super nice plastic bag

(b) A dark and boring cotton tote bag

Figure 1: Which one do you use?

Let’s compare CO2 content:

• tote bag: 270Kg of CO2e
  • mostly production of cotton
• one-use plastic bag: 1.36Kg of CO2e

That means that you would need to use the tote bag 172 times for it to be less carbon intensive

More dilemmas

Should you:

• plant grass or vegetables in you garden?
• take shower or bath?
• use liquid or solid soap?
• buy an electric car?
• …

How can you know ? Other examples at co2everything

It is much easier if information is incorporated in the price.

Price signal

We need a price signal for production, consumption, investment

Market failure:

• markets don’t determine the right price for CO2 emission.
• because of the common bad tragedy

The government(s) could intervene to set the price

  

But which price should be fixed?

Estimating the price of carbon

Integrated Assessment Models

Nordhaus was rewarded for his work on the DICE model

• DICE: Dynamic Integrated model of Climate and the Economy
• several variants

Integrated Assessment Models

Cost-Benefit Analysis

• cost: reduced economic activity
• benefit: damage avoided

Result is a so-called Integrated Assessment Model

It is multidisciplinary:

• economic models reused for the modelisation of costs
• results from earth science incorporated to measure damage

Damages

Damage function \(D(T)\) is estimated with engineers/earth scientists

It evaluates the effect of global warming on many systems:

• natural quantitites
  • ex: water temperature, probability of storms…
• production functions
  • ex: crops become less productive

Tipping points create sudden/irreversible damage

• \(D(T)\) is highly nonlinear

The Damage Functions

Results from damage estimation exercises:

• impacts are nonlinear and cumulative
• early studies: 1 or 2 degrees innocuous
• more recent ones: (ex 2018 IPCC report on 1.5)
  • even 2 degrees highly disruptive

In the DICE model damages are market and non-market

• converted in consumption equivalent
• 2% of permanent consumption at 3 degrees
• 8% at 6

Meta-Analysis

Howard and Sterner: meta analysis

• damages 3 times higher

The DICE Model

\[\max_{c_t} W = \max _{c_t} \int_0^{\infty} U[c(t)] e^{-\rho t} dt\] s.t. \(c(t) = M(y(t), z(t); α, ε(t))\)

• maximize welfare made of
  • utility \(U()\) of world consumption \(c(t)\) overtime
  • with a time discount \(\rho\)
• subject to many complicated constraints
  • about 20 independent equations

The DICE Model

\[\max_{c_t} W = \max _{c_t} \int_0^{\infty} U[c(t)] e^{-\rho t} dt\] s.t. \(c(t) = M(y(t), z(t); α, ε(t))\)

This is known as a Ramsey problem, a variant of neoclassical growth problem

• there is a social planner maximizing welfare
• not the same as “planification”: planner takes into account reaction of free markets

IAM: theoretical finding (1/2)

The problem just described produces two kinds of outputs:

• the optimal path for policies (for instance carbon taxes)
• the social price of carbon

IAM: theoretical finding (2/2)

The social price of carbon is the shadow price (or lagrange multiplier) associated to the carbon budget constraint:

• by how much welfare would be increased if the carbon budget was slightly higher
• it is the value of leaving carbon in the ground ¹
• or the price that should be given as a compensation to a firm for not using carbon

1. it is similar to Tobin’s q.

Circular Flow

Simplified (!) model

Concretely

DICE 2016 in GAMS

Look at the endogenous variables and exogenous parameters

• description of the economy is very crude

Play with an interactive version based on DICE 2010

 

Conclusions?

GAMS is a modeling language that is often used for general computional equilibrium modeling models, including many trade models.

Results from the actual 2018 model

Three scenarios

• Business as usual (minimal policies)
• Cost-benefit optimum (two damage functions)
• Limit temperature increase (to 1½ , 2, 2½ °C) with hard cap
• Limit temperature increase (to 1½ , 2, 2½ °C) over 100-year or 200-year averaging period

Main Results

• compare with baby-model

  • DICE: 1.5 infeasible

• result of cost-benefit: 3 degrees in 2100

• slow emissions as soon as possible

• uniformity of prices

  • equalize marginal cost of reducing emissions everywhere
  • carbon price should be equal everywhere

• social cost of carbon rising over time

• policy ramp up over time

Controversies around the DICE model

• discount factor
  • in the formula \(\max _{c_t} \int_0^{\infty} U[c(t)] e^{-\rho t} dt\) there is discount factor \(\rho>0\) for future generations.
  • this discount is priced by the market and probably reflects our current preferences
  • but is it ethical to discount the future when trying to save the planet?
  • other economists (famously Nick Stern) have advocated using discount \(\rho=0\)

Controversies around the DICE model

• it monetizes all activities
  • can you associate a value to a lost island, to house damaged by hurricane
  • traditional answer: we need a metric to do cost-benefit analysis¹
• damage function does not correctly account for tail events (cf Weitzman)

1. Keynes: better to be vaguely right than precisely wrong

Social cost of carbon

Despite raising some legitimate doubts about optimal carbon policy IAM models yield estimates for the price of carbon which are used as a basis for policy discussions.

Conclusion

Conclusion

Integrated Assessment Models are not perfect

Yet:

• they provide a clean conceptual framework
• natural, actionable, policy recommendations
• first best is a carbon tax
• and a measure of carbon price which is increasingly used in negotiations

Now, there are many ways to raise the carbon price…