Irreversibility, Learning, Deep Uncertainty

• The problem• The solution

– What will it cost?– What to do?

Optimal emission reduction• Climate change is long-term, global,

uncertain problem• If you do not care about the distant

future, far-away lands, remote probabilities, you do not care about climate change

Uncertainty• Expected damage

E s ss

D pD

The marginal damage costs of carbon dioxide emissions.

all 3% 1% 0% SCC Pigou

mode 91 27 87 240 31 24 median 310 35 156 471 43 30 mean 422 40 208 590 50 34 st dev 688 36 285 685 38 32 skewness 2 1 2 2 1 1 kurtosis 13 4 8 11 4 5

Uncertainty• Expected damage

• Certainty equivalent damage

• Risk premium

E s ss

D pD

1CE , ( , )s ss

D U C pU C D

=CE -ERP D D

impact initial income impact initial income100 1000 100 1000

p=50% 10 4.50 6.90 10 4.50 6.90p=50% 20 4.38 6.89 99 0.00 6.80

4.44 6.89 2.25 6.8515 15.15 15.01 54.5 90.51 55.55

italic numbers are in utils , other numbers in pounds

Optimal Climate Policy• If everything is known with certainty

– in a static problem, marginal costs should equal marginal benefits

– in a dynamic problem, marginal net present costs should equal marginal net present benefits

• If probability distributions are known– in a static problem, marginal expected costs

should equal marginal expected benefits– in a dynamic problem

• without either irreversibilities or learning, marginal expected net present costs should equal marginal expected net present benefits

• with both irreversibilities and learning, things are different

Irreversibility• If current decisions have no implications

for the future – that is, the consequences can be undone or reversed – the problem is not really dynamic

• The problem is a series of static problems

• Few economic problems are static or serially static– Capital is long lived– Carbon dioxide stays in the atmosphere for

a long time

Learning• We do not know what the future will

bring, we do not know what we will learn, but we do know that we will learn

• That means that we will improve our decisions as we gather more information

• In turn, we can relax a little today: Because future decisions are more accurate, we do not need to be so risk averse today

Dismal Theorem• Weitzman (2009): the uncertainty about

climate change may be too large for expected utility maximisation

• Ramsey rule: r = ρ + ηg• Non-zero chance that impact of climate

change is so large that economy shrinks – Ramsey discount rate could go negative – net present welfare loss is large – impact grows faster than its probability falls

• The expectation is unbounded• The Pigou tax is arbitrarily large

Policy Implications• Some see the Dismal Theorem as a

formalisation of the Precautionary Principle, others as a justification of stringent climate policy

• That’s not true: The Dismal Theorem only says that you cannot use cost-benefit analysis in certain circumstances

• Weitzman does not indicate what to do instead

• Fossil fuels are an essential input in the short run, so an arbitrarily large carbon tax would do a lot of harm

Minipercentile Regret• Minimax regret is a standard decision

criterion in case of large uncertainty• For every state of the world, find the

optimum tax• For every tax in each state of the world,

calculate the welfare difference from the optimum

• Across states of the world, find the tax that minimises regret

• As continuous on the real line, we here use percentiles rather than the maximum

9.40E+12

9.42E+12

9.44E+12

9.46E+12

9.48E+12

9.50E+12

9.52E+12

9.54E+12

9.56E+12

0.0E+00

2.0E+11

4.0E+11

6.0E+11

8.0E+11

1.0E+12

1.2E+12

1.4E+12

0 50 100 150 200 250 300 350 400 450 500

99.9%99.5%99%95%90%75%50%Average

Alternatives• In minimax regret, you do the best you

can in each state of the world, and make sure you are robust to uncertainty

• There is no guarantee, however, that the outcome will be acceptable: Regret may be a small difference between very low levels of welfare

• Regret is a measure of the slope of the welfare function, rather than its level

• Therefore, minimize the fatness of the tail

9.495E+12

9.505E+12

9.515E+12

9.525E+12

9.535E+12

9.545E+12

9.555E+12

9.435E+12

9.445E+12

9.455E+12

9.465E+12

9.475E+12

9.485E+12

9.495E+12

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

$0/tC (left axis)

$500/tC (right axis)

$50/tC (right axis)

0.05

0.06

0.07

0.08

0.09

0.10

0.11

0.12

0 50 100 150 200 250 300 350 400 450 500

dollar per tonne of carbon

p-value of the ADF test =Probability of observing the dataunder the null hypothesis ofnon-stationarity / fat-tails

Implications• There is dangerous climate change• There is dangerous climate policy too• We characterise the Dismal Theorem in

a Monte Carlo analysis of a numerical model

• We use three alternative decision criteria, “Pigou with fat tails” tax should be between $50 and $170/tC

• That’s a large range, but it is not an arbitrary number