Global Climate Change Part II
Social Cost of Carbon

Econ 2277

Prof. Richard L. Sweeney

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UN Report suggests putting a high price on carbon


Source: IPCC 2018 Figure 2.26

Say we wanted to use a price instrument, what is the right tax?

[Note: How is this different from IPCC graph]

In 2009 the US formed an inter-agency working group (IAWG) to come up with a number for the social cost of carbon (SCC).

How much should we pay to reduce CO2 by one ton today?

  • Necessary for conducting mandatory RIAs
  • Differences in implicitly SCCs used across agencies at the time.

Four steps in estimating the consequences of CO2 emissions

  1. the future emissions of GHGs
  2. the effect of past and future emissions on climate
  3. the impact of changes in climate on the physical and biological environment
  4. translation of those impacts into economic damages

This section based on Greenstone et. al. 2013

Integrated assessment models (IAMs)


Three IAMs used by the US IAWG

Common IAM features

  • IAMS combine insights from science and economics

  • Emissions $\rightarrow$GHG concentrations $\rightarrow$Temperature $\rightarrow$Economic Damages

  • Come at the cost of simplification

All three models:

  • Baseline emissions based on projected socioeconomic paths (GDP, pop)
  • Carbon cycle explicitly modeled
  • Temp changes monetized with one or more "damage" functions

Step 1: Predicting baseline

  • Socioeconomic paths:

    • How many people will there be in 2100?
    • How rich will they be?
  • What will baseline emissions look like?

    • This answer has changed dramatically in the past 10 years...
    • Technological change?
    • Moving to cities?

Step 2: Map emissions to climate changes

Climate sensitivity parameter = average surface warming resulting from a doubling of CO2, in equilibrium


There is enormous uncertainty in these models

Source: Heal and Miller 2014

Note: Socioeconomic responses also very uncertain

Even if temp and climate changes are known, how will societies react?

  • sea level rise

  • internal and external displacement

  • agricultural disruption

  • Technological uncertainty

    • Nuclear fusion has been just around the corner for decades

The economic importance of tail events

This section based on Nordhaus 2011

  • For some policy problems, our main concern is with very extreme outcomes


  • Hiroshima
  • 9/11
  • Financial collapse

In these situations, the shape/ tail of the distribution matters more than the mean

Skinny vs. fat tails

  • Standard deviation "sigma" captures the likelihood of tail outcomes

  • Typically think in terms of normal distribution:

    • $p(>1\sigma)\approx.32$
    • $p(>2\sigma)\approx.05$
    • $p(>3\sigma)\approx.0027$

Example: height of US women is well approximated by a normal distribution with mean 64 inches and s.d. of 3 inches

  • a 6 foot tall woman is 2.66 sigma event
    • 1 out of every 100 women you see

Multi-sigma events

  • Although we're conditioned to think of the normal distribution, we have experienced enough costly 4 or 5 sigma events to know that other distributions must be considered

  • Example: US stock prices fell 23% on October 19, 1987

    • Daily s.d. from 1950-1986: $\sigma\approx1\%$
    • This is the equivalent of an 11 foot tall woman
    • If stock returns were normal, even a 5% crash would only be observed once every 14,000 years

Alternative Distributions Exist

Example: Earthquakes

  • Seismologists believe earthquakes follow a power law (Gutenberg-Richter law)
    • Magnitude (energy) distributed Pareto with $a=1$
  • Japan earthquake 2011
    • If we thought distribution was normal, event that large would occur ever $10^{13}$ years
    • Under Pareto distribution, it would occur once every 100 years

If things are normally distributed, we will never really be that surprised. However, if the problem has fat tails, we may experience surprise shocks orders of magnitude larger than anything we've every experienced before

Policy choice and fat tails

Why does this matter?

  • When the probability of infinite damages is nonzero, the expected BCA framework breaks down

  • Even a small possibility of infinite damages causes us to spend infinite amount on abatement today

Is this challenge unique to climate change?

  • Catastrophic tail events considered in other settings:
    • biotechnology; runaway computer systems; nuclear proliferation; rogue weeds and bugs; nanotechnology; asteroids etc
  • All of these have non-zero chance of "infinitely bad" outcomes

Example: Strangelets

  • Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL) in Long Island, scientists study high-speed ion collisions that reveal what the universe may have looked like moments after the Big Bang
  • Several physicists raised concerns that ``possibility that the collider will generate strangelets, hypothetical particles consisting of up, down, and strange quarks. Some hypotheses suggest that strangelet production could ignite a chain reaction converting everything into strange matter."

Uncertainty summary

  • Uncertainty much more worrisome than risk

  • Introspection and experience tells use that extremely costly events may be more likely than we think

  • Yet the prospect of extinction invalidates the BCA exercise

  • Neither approach totally satisfying

  • Economics is still trying to figure out the way forward

Global SCC Estimates by Model (2007$/ton CO2)

Step 3: Mapping Temperature to Damages

How would you go about doing this?

  • We discussed measuring benefits earlier in the course

  • How would you go about applying that in this context?






We also need to put all this in present value terms

What is the "right" discount rate to use?

Two reasons to discount across generations:

  1. we value current generation more
  2. future generations will be better off

Ramsey (1928) inter-generational discount rate formula:

$$r=\eta g+\rho$$

  • $\rho$ is the pure rate of time preference

    • $\rho=2\%\rightarrow$person born in 2008 = .5 person born in 1973
    • Common Assumptions: $0<\rho<3$
    • Why not zero?
  • $g$ is the growth in per capita consumption ($g\approx2\%$)

  • $\eta$ is the absolute value of the marginal utility of consumption

    • $\eta=0\rightarrow$ marginal utility of $ does not change w/ income
    • $\eta=1\rightarrow$ 1% increase income reduces marginal utility by 1%
    • Common Assumptions: $.05<\eta<3$

These yield discount rates between 0 and 9%!


Discount rate wrapup

Question: Why don't we invest in capital markets now, earn those returns, and then use that money to abate the carbon problem later?

Put differently: We are going to leave a stock of capital to our children. Should we invest in the market or invest in carbon abatement?

Many social investments involve large up front costs and long term benefits

  • education, poverty alleviation, disease eradication
  • ethically tempting to set a low discount rate for GCC
  • however we need to be consistent
  • can't invest in everything

Model Comparison


SCC estimates by discount rate


  • estimates for 2010 in 2007 dollars
  • Obamas scc about $50 per ton
  • Trump admin recently reduced this to 7