Thursday, 1 March 2012

Climate Change Economics

Our February energy meeting was on the subject of climate change economics and specifically the Weitzman Nordhaus debate that was conducted in a series of papers in 2009: Weitzman, Nordhaus, Weitzman.

This debate is on the treatment of low probability, high impact events in cost benefit analysis (CBA). The standard approach to climate change economics as pioneered by Nordhaus is essentially deterministic. It evaluates the price of carbon that a social planner would have to set in order to implement the policy programme that maximises their objective function (usually lifetime CRRA utility), in a world where high temperatures damage production and production in the absence of abatement technology causes high temperatures. Weitzman's contribution was to show that if instead of calculating the carbon price by putting central assumptions into a deterministic model, we took the expected value of the carbon price given our uncertainty on the assumptions, then the price should be infinite.

This is a consequence of there being some non-zero probability of catastrophe and our infinite valuation of zero consumption (which is what catastrophe equates to in this framework). That there is a non-zero probability of catastrophe seems to be unarguable (*), so if we are to argue for anything other than the entirety of current output going towards climate change mitigation and prevention, then we must be arguing with some feature of the CBA framework. This also applies to other catastrophe risk like asteroid impacts. See also Millner and Ikefuji et al for recent work in this area.

A solution to the problem of infinite results is is to truncate the valuation of bad events i.e. so that we value another unit of consumption when we have a very low consumption level at a high but not infinitely high rate. However Weitzman shows that this truncation becomes the dominant factor in the CBA calculation (so for example the size of the median impact does not really effect the calculation, all weight is put on the impact at the extreme downside). This may be true (avoiding catastrophe perhaps should indeed be the policy target) but it is contrary to our usual understanding of the value of an investment program (e.g. the value that we might put on a company share will be closely related to the expected income stream rather than the tail of the income stream distribution).

An interesting side-issue to this debate is that Nordhaus's 1996 paper, 'The Value of Scientific Knowledge' which has a limited monte-carlo simulation of the deterministic CBA model, produces much higher estimates for the cost. My suspicion is that the value so produced was actually a function of the size of the grid over which it was estimated, and that as the grid got larger and more representative of the distribution of the parameters of the model, the the value would also have tended to infinity.

The criticisms that Weitzman effectively makes of the standard approach to climate change economics seem valid to me. However, my main problem with these models is that they produce 'optimal' projections of output, consumption, emissions and atmospheric CO2 that leads to CO2 concentration peaking at over 650ppm (see figure 5.7 of Nordhaus's 'A Question of Balance'). Despite the claimed inputs from IPCC projections etc to Nordhaus's models, I don't believe that many climate scientists would agree that this represented an optimum (see Hansen et al 2008) - rather it's a prescription for passing tipping points which are not in Nordhaus's models.

(*) Two recommendations for books credibly outlining future catastrophe:
# Hansen 'Storms of my Grandchildren' (2009)
Hansen is a climate scientist who has basically turned into an activist because he is so concerned. Has testified to Congress on numerous occassions. Works for NASA. Very credible guy who's at the top of his profession. A section from this book is copied below (**).
# Ward 'Under a Green Sky' (2008)
Ward is a paleontologist and astrobiologist who has studied mass extinctions and concluded that most of the extinction events in the geological record are 'greenhouse extinctions' associated with anoxic oceans. An amazon review (from the above link) outlines the thesis:
"That an asteroid caused the mass extinction at the end of the Cretaceous period is widely accepted and also widely disseminated to the public. Less well known to the public are the other mass extinctions. Ward contends that they all have a common cause: climate change caused by carbon dioxide increase. This can in turn release methane (a more powerful greenhouse gas than carbon dioxide) from methane hydrates creating a runaway effect. At the end of the Permian period 250 million years ago this was severe enough to kill over 90% of all species on Earth.
Now Ward is not the first to relate the devastation of the Permian-Triassic extinction to modern day human-induced climate change to show us what could happen (see for example When Life Nearly Died: The Greatest Mass Extinction of All Time), but just when you thought that the devastation could not possibly get any worse, Ward introduces a new element into the equation: photosynthetic sulphur bacteria.
The effects of the climate change causes the oceans to become increasingly anoxic. In these conditions the only life to thrive is sulphur-producing bacteria. The boundary between the oxygenated and anoxic water comes closer and closer to the surface, to the point where photosynthetic sulphur bacteria, which use the sulphur from below, thrive in the surface waters and give off large quantities of hydrogen sulphide. Apart from being very poisonous in itself to surface life, the hydrogen sulphide also destroys the ozone layer of the Earth. Ward paints a picture of the Earth at the end of the Permian: most life is dead; the oceans are purple from a thick layer of bacteria; the hydrogen sulphide has changed chemistry of the atmosphere such that cloud formation has altered drastically - clouds form in the upper atmosphere far above where clouds normally form, giving the sky a green colour."
Also consistent with this thesis is the recent New Scientist news story that almost all the fish in the sea have fresh water ancestors.

(**) "As global warming continues, storm effects will ratchet upward in three major ways. One of these ratchetings will be the development of more powerful and destructive midlatitude or frontal cyclones. Frontal storms will be more powerful, because they depend upon the temperature difference between the cold and warm air masses as well upon the amount of moisture in the atmosphere behind a warm front. This intensification of frontal cyclones will be an effect of melting ice sheets, once ice sheets begin to disintegrate rapidly enough to keep regional ocean surface temperature from rising as fast as continental temperatures and temperatures at lower latitudes. The most important point is that there will be places and occasions in which the warm air masses will be loaded with far more water vapour than would be the case in a cooler world. ...
This first ratcheting, though, will pale in comparison to the effects of the second ratcheting: when ice sheets' rapid disintegration causes a sea level rise measured in meters. ...
Ice sheets eventually begin to disintegrate at rates of several meters of sea level per century, even with the slow pace at which natural climate forcings change. But predicting when ice sheet mass loss will accelerate in the twenty-first century is a notoriously difficult ``nonlinear'' problem. We could "lock in" disastrous sea level rise very soon, that is, create conditions that guarantee its occurrence, but it is likely to be several decades before a rapid sea level rise begins. On the other hand, we have been surprised by how fast some other climate changes have occurred - such as disappearance of Arctic sea ice ... For the moment, the best estimate I can make of when large sea level change will begin is during the lifetime of my grandchildren - or perhaps your children. ...
With the combination of a higher sea level, even of only a meter or so, and increased storm strength, the consequences of future storms will be horrendous to contemplate. ... Social and economic devastation could be unprecedented. It is not necessary to put the entire island of Manhattan under water to make the city dysfunctional and, given prospects for continuing sea level rise, unsuitable for redevelopment. ...
The timing of the third ratcheting effect of global warming, the melting of methane hydrates, is as unpredictable as the others. Warning signs are beginning to appear already, with bubbling of methane from melting tundra and from the seafloor on continental shelves. So far the amounts of methane released in this way have been small. The methane hydrates of greatest concern are those in sediments on the ocean floor, because of their great volume. ...
The flooding of the ocean floor with warmer Pacific Ocean water may have been a key factor in the melting of methane hydrates during the PETM [Paleocene-Eocene Thermal Maximum - 54 million years ago, when temperatures suddenly (i.e. over millennial rather than geological timescales) rose by between 5 and 9 degC]. Could a change of ocean circulation happen again in the near future? Global models of today's climate sometimes have a problem with spurious formation of deep water in the Pacific Ocean, which suggests that it would not take much change in the densities of ocean surface waters to alter the location of deep water formation. The instigation for such a change could be freshwater additions to both the North Atlantic and Antarctic Oceans, after the rate of ice sheet disintegration in both hemispheres has reached high levels. ...
When deep water formation begins in the Pacific Ocean, the inertia of the climate system, specifically ocean circulation, will be far too great for humans to stop, even if social systems are still in order. Once large sea level rises begin to devastate coastal cities around the world, creating hundreds of millions of refugees, there may be a breakdown of global governance. But regardless of that, if ocean circulation changes, such that warmer Pacific Ocean water begins sinking to the ocean floor and melting methane hydrates, there will be no plausible way for humans to reverse that change of ocean circulation.
While we can't predict the details of short-term human history, changes will be momentous. China, despite its growing economic power, will have great difficulties as hundreds of millions of Chinese are displaced by rising seas. With the submersion of Florida and coastal cities, the United States may be equally stressed. Other nations will face greater or lesser impacts. Given global interdependencies, there may be a threat of collapse of economic and social systems.
Physical science is easier to foresee. While the timing of the three ratcheting effects is difficult to predict, their effects are not. With methane hydrate emissions added on top of those from conventional and unconventional fossil fuels, the future is clear. Diminishing feedbacks that help to keep the magnitude of natural long-term climate changes within bounds, such as the ability of the long-term carbon cycle to limit atmospheric carbon dioxide, will have no time to counter amplifying feedbacks. The huge planetary energy imbalance caused by the high levels of atmospheric carbon dioxide and methane will take care of any remaining ice in a hurry. The planet will quickly get on the Venus Express. ...
A devastated, sweltering Earth purged of life may read like far-fetched science fiction. Yet its central hypothesis is a tragic certainty - continued unfettered burning of all fossil fuels will cause the climate system to pass tipping points, such that we hand our children and grandchildren a dynamic situation that is out of their control.''

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