Model Selection and Uncertainty in Climate Change Mitigation Research Martin Sewell mvs25@cam.ac.uk

1. Model Selection and Uncertainty inClimate Change Mitigation ResearchMartin Sewellmvs25@cam.ac.uk All models are wrong... Model uncertainty & selection in complex models 14–16 March 2011 Groningen The Cambridge Centre for Climate Change Mitigation Research (4CMR)

2. Uncertainty Uncertainty is best described using a probability distribution, and the wider the distribution, the greater the uncertainty. Aspects of climate change about which we are: • almost certain: the physical chemistry • very uncertain: the effect of clouds, the ocean, the response of biological processes, climate change mitigation

3. Reductionism • Reductionism is a theory that asserts that the nature of complex things is reduced to the nature of sums of simpler or more fundamental things. • Anthropology is reducible to sociology, sociology is reducible to psychology, psychology is reducible to biology, biology is reducible to chemistry, chemistry is reducible to physics. • I posit that there exists what an economist would call a structural break between the natural sciences and the social sciences. • Uncertainty decreases as we move through the disciplines from anthropology to physics (excepting at the atomic and subatomic scales, where, ironically, the only true uncertainty lies).

4. What is science? • Hume (1739–40) pointed out that ‘even after the observation of the frequent or constant conjunction of objects, we have no reason to draw any inference concerning any object beyond those of which we have had experience’. • One can never generalize beyond one’s data without making subjective assumptions, so science always involves a degree of uncertainty. • If we insist upon intimating one’s degree of uncertainty and self-consistent reasoning, science becomes applied subjective Bayesian inference (observing some common sense criteria, science should also be constrained by exchangeability (de Finetti 1937), the Reflection Principle (van Fraassen 1984, 1995) and the Principal Principle (Lewis 1980)). • Science involves putting probabilities on hypotheses.

5. Science in practice • Using a scientist’s abstraction, a hypothesis is not simple, complex, popular, fashionable, left wing, right wing, racist, sexist, equitable, politically correct, dangerous, or abhorrent, it is merely surprising to a certain degree. • A scientist should be free of any ideology. • A principled approach to science involves Bayesian model selection (originally due to Jeffreys (1939)), which in practice may involve the easy to calculate approximation the Bayesian information criterion (BIC) (Schwarz 1978), followed by Bayesian model averaging. • Science, in practice, progresses by peer review, and the Intergovernmental Panel on Climate Change (IPCC) assessment reports are arguably the most peer reviewed documents in the history of science. This makes the IPCC reports excellent science, and more so if and when any mistakes (e.g. melting Himalayan glaciers) come to light, they are promptly corrected.

6. Science of climate change • Starting with the physics and chemistry, there is no significant doubt that CO2 is a greenhouse gas, and that levels of anthropogenic CO2 in the atmosphere are increasing. • The theory of anthropogenic global warming is built on peer reviewed science that has accumulated since Fourier in the 1820s. • In 2004, Naomi Oreskes analysed 928 abstracts, selected using the keywords ‘global climate change’, published in refereed scientific journals and found that none of the papers disagreed with the theory of anthropogenic climate change. • How can we trust climate models when we can’t even forecast next week’s weather? Think of climate as the signal and weather as the noise.

7. Uncertainty and climate change According to the IPCC it is • extremely likely (> 95% probability) that human activities have exerted a substantial net warming influence on climate since 1750, • very likely (> 90% probability) that anthropogenic greenhouse gas increases caused most of the observed increase in global average temperatures since the mid-20th century, and • virtually certain (> 99% probability) that global warming shall continue in the future. The apparently counter-intuitive result that the past is less certain than the future implies that we’re pretty sure of the physics, less sure of historical measurements, and the forecast into the future of the global temperature must be steeper than the rise in the past.

8. A more surprising hypothesis requires more evidence • Laplace asserted that ‘the weight of evidence for an extraordinary claim must be proportioned to its strangeness’. • A more surprising hypothesis requires more evidence. • Bayes’ theorem makes this explicit. • The present-day form of Bayes’ theorem is actually due to Laplace, Thomas Bayes only proved a special case. • It is known with certainty that CO2 is a greenhouse gas and that levels of anthropogenic CO2 in the atmosphere are increasing. • So, a priori, it would be surprising if anthropogenic CO2 was not contributing to global warming. • This puts the onus on the climate sceptics.

9. Utility • When hypotheses affect our utility, the expected utility hypothesis informs us that we should seek to maximize the sum of the products of the utility and the probability. • Therefore the probabilities should be multiplied by the utility associated with each cost/benefit to determine the best course of action. • If mitigating anthropogenic global warming has an associated cost, economically, the onus may move towards the proponents of anthropogenic global warming.

10. Scepticism • Note the reversal of the onus of weight of evidence as we move from the science to policy, this is a source of some of the antagonism and confusion between the consensus view and the sceptics. • It makes no sense to be a climate sceptic, but a lot of sense being a climate change mitigation sceptic. • As with science in general, healthy scepticism is great, but climate change denial is malicious mischief.

11. Altruism • Some policy decisions should depend on our degree of altruism. • National governments have a duty to act in the interests of their citizens, but need a policy regarding giving aid to other nations, for example for climate change adaptation. • Using a gene-based biological approach, Salter (2006) estimates that the relative investment that individuals allocate to their self is 70%, their offspring 20%, their ethny 7% and humanity 3% (the numbers are merely indicative). • This account is descriptive, but as we cannot transcend our genes (Moxon 2010), policy decisions should accommodate our innate altruism (or lack thereof).

12. Social discount rate • How much do we care about the future? • If we wish to perform a cost-benefit analysis on a future public sector project, such as climate change mitigation, we must choose a discount rate that reflects society’s preference for present benefits over future benefits. • The discount rate used in the Stern Review on the Economics of Climate Change was approximately 1.4%, and was criticized for being too low. • A colleague, Tim Joslin, wrote ‘I can see no justification whatsoever for using a discount rate of greater than zero. Arguably it should be negative.’

13. The social discount rate—my prescription • An individual’s discount function is hyperbolic and reaches 100% at the end of their lifetime. An equitable social discount function should average the population’s individual discount functions. • The social discount rate is a crucial variable in models of the economics of climate change mitigation, and there is no consensus.

14. Climate sensitivity • Climate sensitivity is a measure of how responsive the temperature of the climate system is to a change in the radiative forcing. • It is usually expressed as the temperature change associated with a doubling of the concentration of CO2 in the Earth’s atmosphere. • Climate sensitivity has a positive skew. • The compounding effect of essentially linear feedbacks dominates system sensitivity, and the uncertainty here does not diminishing with time, the estimates are not expected to improve. • We’re pretty certain of the uncertainty.

15. Economics of climate change mitigation • Economics is a social science and an approximation of psychology. • Economic models contain greater uncertainty than climate models. • Economic forecasting is notoriously difficult, largely because we can’t predict human creativity in innovation—if we knew what the next innovation would be, we’d have already invented it. • The efficient market hypothesis dictates that stock market returns approximate a martingale, rendering financial markets inherently uncertain. • Energy-environment-economy (E3) models contain greater uncertainty still.

16. Carbon tax and emissions trading Two popular solutions to the problem of how to mitigate climate change are 1) a carbon tax and 2) emissions trading (cap and trade). They are theoretically equivalent except that they’re logically opposed regarding where the uncertainty lies. • A carbon tax fixes the rate of taxation and allows emissions to vary. • Emissions trading fixes emissions and allows the cost of compliance to vary. • The physical science solution would be to fix emissions (implying a preference for emissions trading). • The economist’s solution would be to internalize an externality with a carbon tax. It would be a mistake to discount human behaviour, so my preference lies with taxation.

17. Prisoner’s dilemma • Finally turning to anthropology, we introduce greater uncertainty still when considering climate change mitigation in terms of the behaviour of different cultures, with their varying degrees of intelligence and ability to demonstrate a capacity for altruism. • Human-induced climate change is a classic case of Garrett Hardin’s tragedy of the commons—the benefits of burning fossil fuels accrue to individuals, companies and nations, whilst the costs accrue to the planet as a whole. • The tragedy of the commons is a multi-player generalization of the prisoner’s dilemma. • The best overall outcome in a prisoner’s dilemma is one of cooperation, but economic theory informs us that the rational choice is for players to always defect.

18. Martin Sewell mvs25@cam.ac.uk