1 Replicating Stern – The Costs of Climate Change and Policy Graph

One aspect of neoclassical economics that is extremely useful is the representation of an economic theory in a graphical form. Where would any introductory course be without Alfred Marshall’s supply and demand curves? For many years, the ideas of John Maynard Keynes’s ideas were synthesised in the Sir John Hicks’s IS-LM curves. These graphs have the advantage of enabling analysis of the logical consequences of changes in the overall context of the problem under consideration. In climate, there is a lot of shouting between the different camps, but what appears to be a complete inability to put the consequences of global warming and the mitigation policy option of globally constraining the growth of greenhouse gas emissions into their proper context. Therefore, when assumptions are changed, or new information becomes available, it is difficult to put those into the overall context of the “climate change” issue.

Sir Nicholas (now Lord) Stern’s report of 2006 (In the Summary of Conclusions) had the two ideas separated when it claimed

Using the results from formal economic models, the Review estimates that if we don’t act, the overall costs and risks of climate change will be equivalent to losing at least 5% of global GDP each year, now and forever. If a wider range of risks and impacts is taken into account, the estimates of damage could rise to 20% of GDP or more. In contrast, the costs of action – reducing greenhouse gas emissions to avoid the worst impacts of climate change – can be limited to around 1% of global GDP each year.


This leads to two offsetting sets of costs. The first is the “do-nothing approach” of letting greenhouse gas emissions spiral out of control, raising global temperatures by a number of degrees and throwing the weather systems out of control. The other is the policy costs of constraining the rise in emissions by switching to “cleaner” forms of living in general and energy-production in particular. It is should not be confused with a cost-benefit approach. Stern is proposing to exchange a very high set of costs in the distant future, with a much lower set of policy costs now. His proposal is not to incur costs in exchange for a stream of benefits (like when constructing a new motorway), but to minimize total costs of climate change and policy.

Constructing the graph

We are told by the climate scientists that some of the minor consequences of around 0.8oC of warming over the last century are already visible. But their climate models project this is utterly insignificant compared to what will happen if greenhouse gases continue to increase unchecked for the next century or more. The large increases in temperature – around 4oC to 7oC or higher – would cause massive disruption to the climate system. It is fair to say that as global temperatures increase, these costs would increase exponentially. These “costs” are in the broadest sense. They are not just the human costs of property damage, failed harvests, population migrations and land being submerged by rising seas. These include the damage to the eco-systems and species extinction. Assuming a top end of 7oC the cost curve would look something like this.

The relative cost scales 7oC of warming are set to be twenty times the costs of constraining global warming to 3oC, or the mid-range of estimates by the IPCC for a doubling of CO2 from pre-industrial levels of 280ppm, and an approximate policy target.

Conversely, the cost of stopping any more warming will be huge. Hugely aggressive policies would quickly stop any increases in emissions and could bring about major reductions. But such policies would bring to a halt the fast-growing economies of China and India, and would considerably worsen the recession in much of Europe. However, it is possible to postulate that low-cost policies that give the odd nudge here and there over a long period could reap large rewards. In line with climate costs, I have set the relative cost of constraining the rise in global temperatures to 3oC above the pre-industrial levels to 1. So the curve might look like the one below.

Combining the two curves gives a total cost graph.

The total costs curve is derived by the addition of the climate and policy cost curves.

This replicates Stern’s statement above. The “do-nothing” scenario is ten times more expensive than the optimal cost-minimization scenario.

Some points to note.

First is that the total cost curve has quite a wide minimum area. Even if a lot of the main policy targets are missed, doing something looks to be far better than doing nothing at all.

Second, is that cost minimization strategy is at a higher temperature level than the intersection of the curves. However, a risk-averse strategy (which most people would expect in avoiding a prospective global catastrophe) would aim for a somewhat lower temperature increase.

Third is that “policy” should be called mitigation policy. That is preventing climate change costs from occurring by constraining the rise in greenhouse gases. As will be seen later, the alternative (or complementary) adaptation policies are included within the climate costs curve. The full reasons will be explained later, but the main one is that climate mitigation is something that, by definition, needs to be tackled at a global level, whereas adaptation can be done at the local, country or regional levels.

Fourth, is a clear separation of mitigation policy considerations from the projections of climate science. Yet new information from the science and policy areas can be put into a total context of acting in the best interests of the planet and the human population.

Fifth, an issue with the policy curve is the change in gradient. There must exist a set of policy options which are low cost, high impact (LC-HI) as well as the high cost, low impact (HC-LI). There are two possible types of policies which should be avoided. First are those with costs, but with zero impact (C-ZI) and second are those with a net negative impact (NNI).

Sixth, any look at climate projections and policy options show they are all over the place. The assumptions of single curves are highly restrictive ones. But like in

Finally, on climate costs there is an issue with projections about future costs. The data we have is from less than one degree of warming, and a minute fraction of projected costs. As shall be shown, the handling of this issue is crucial.

Kevin Marshall

2 Climate Change Policy Choices

The risks from policy are becoming increasingly well-known. The question is how to manage these risks. Assuming there is a genuine problem, which is possible to overcome through policy, what are we doing to make a real difference? The policy curve gradient assumes there must exist a set of policy options which are low cost, high impact (LC-HI) as well as the high cost, low impact (HC-LI).

There are two possible types of policies which should be avoided. First are those with costs, but with zero impact (C-ZI) and second are those with a net negative impact (NNI). All of these costs may include unintended consequences, which may not be fully recognized.

The choice is quite clear. Policy creation and policy implementation requires a high degree of focus in driving through effective emission reductions.

3 The Mitigation Policy Curve – Part 1

One of the aspects of neoclassical economics is that you make a whole host of assumptions, some of which are highly unrealistic. This enables one to look at the consequences of removing or changing the assumptions one at a time. For this exercise, let us assume the global cost curves are correct. That is to assume that if no policy is enacted that there will be significant global warming with catastrophic consequences for the planet and the people upon it, whilst there are a set of feasible global policies that mitigate against this.

As stated above, for a viable mitigation policy curve to exist, there must exist a set of low cost, high impact (LC-HI) policies. If you believe, as I do, that public policy should aim to make the maximum positive difference, and at a minimum to avoid net harm, then for climate change there is a duty of care in creation and implementation of policy that this truly happens.

The Small Country Problem

A small country is faced with the same climate cost curve as the entire planet. That is, if nothing is done to constrain the growth in greenhouse gas (GHG) emissions this country will face the same escalating costs of climate change. The only difference is that this cost is no longer relative to total gross world product (GWP), but relative to its own GDP. Assuming that the country’s emissions are an insignificant part of the total world amount to begin with, no matter how effective that country is in constraining its own emissions growth path, or even in cutting its total emissions, its policy cost curve will be vertical. It will move to the right with the relentless rise in global temperatures.

The total costs curve, for any temperature level will simply be the addition of the climate change costs and the money spent on emissions reductions.

The more spent by this small country, the greater its prestige in the green movement for unilaterally leading the way on “saving the planet.” But if nobody follows the small country’s example, then its “conspicuous impoverishment”(1) will be in vain.

Avoiding the small country example

How do we avoid the small country example, where the total costs are just added to by wasted effort on cutting emissions?

The standard answer is along the lines of saying if everybody does their bit, with the rich countries taking the lion’s share of the responsibility, then everything will be just fine. What is more, Britain already has some of most draconian emissions reductions targets in the world, as imposed by the Climate Change Act 2008 and others, such as the EU and Australia are also contributing. The small country argument does not hold.

The minority of countries pursuing emission reduction policies I will term the PC1 group. Still assume for the moment that the policy cost curve is correct. The current issue is to enlarge that group to make it the PC2 group. Eventually it is to convince every country to join making the policy curve truly global. As the group enlarges the policy curve shifts to the left.

If all PC1 countries commit to restrain global warming to 3oC, then they can only do so by crippling their economies. The relative cost is a global one after all. They still could cripple their economies if they went to the climate costs equal policy costs point. If the PC1 countries accounted for 25% of GWP, then they would have a benefit a quarter of all the countries acting together. So should the in the economic interests of an outsider country to help create an enlarged group PC2, that represents 50% of GWP? The PC1 group will rid the planet of over 75% of the climate change costs. The PC2 group could halve that again.

Would it be in the economic interests of a country to join the PC2 group, or stay outside?

My Excel graph gets a bit blocky here – sorry.

Let’s do the maths, with approximate numbers. Enlarging the policy-enacting group moves from point A to point B.

PC1 group members have a climate cost of 3.1 plus a policy cost of 3.1/25% = 12.4

Non PC1 members have a climate cost of 3.1 = 3.1

PC2 group members have a climate cost of 1.7 plus a policy cost of 1.7/50% = 5.1

Non PC1 members have a climate cost of 1.7 = 1.7.

So to join the enlarged PC2 group, would increase costs from 3.1 to 5.1. To stay outside the policy countries would be better for the citizens of that country, even if there is a workable policy to adopt and the clear prospect of catastrophic global warming if no mitigation policy is enacted.

Later arguments on the effectiveness of policy and prospective costs of climate will make this choice look even more unambiguous. This aspect of all countries not acting together to share proportionately the costs has not, as far as I am aware, been seriously looked at in the literature. This is why the annual COP meetings – conferences in exotic locations – will never get anywhere. Any leaders that are persuaded to join the policy-enactors, unless their country will be disproportionately made worse by climate change, are acting against their own national interests.


Policy Risk

Policies carry risks. There is a risk of them not being effective, and costs running out of control. There is also a risk of a ratchet effective. That is once the policy is implemented, vested interests are created that make it very difficult to withdraw the policy even if results fall far short of those expected. The above assumes policy success. Policy failure within PC1 countries will demonstrate to potential PC2 countries that they should avoid adopting mitigation policies, no matter how great they believe in the looming climate catastrophe.


  1. Thorstein Veblen attacked in the rich for the “conspicuous consumption”. The “conspicuous impoverishment” of the global warming movement is a variant on this, the difference is that the “prestige” that Veblen went to those wasting their money. The “prestige” heaped on the unilateralist country by the green movement on those implementing the policy and not those suffering the policy consequences.


4 The Mitigation Policy Curve – Part 2 – Counter-Examples

In the first part on the mitigation policy curve I looked at

  • The Small Country Problem. How one small country acting unilaterally will make an insignificant impacts of global climate change.
  • How it is very likely to be against the economic interests of any country to join the small group of countries already with climate mitigation policies.

In this section I will look at two examples that go completely against logical thinking. There can be instances (like in Britain) where bold policies increase global warming at great cost to that economy, but the shale gas, which constrains global warming at net benefit to the gas-producing country?

To see the effect of policy, there is a need for analysis both at the front-end (prior to implementation), during and after. The question is about the gradient of the policy cost curve, at the point

Policy increasing global emissions?

We know that policy countries are in a minority of countries. With the structure of global growth this amount will fall.

Look at the long-term. Implementing a policy, you are saying to businesses that, ceteris paribus, your energy costs are going to rise year-on-year relative to those in non-policy countries. There will be a bigger incentive to make technological efficiency gains in these countries, but those gains can be transplanted to non-policy countries. In this global emissions may decrease more rapidly than they would have done, but the policy countries bear well over 100% of the costs and it becomes a policy benefit to the non-policy countries. By implication they will achieve around 200% of the global decline in emissions.

Question is, will it be more or less than 200% of the decline? Could it be that the policy countries energy-efficient factories are replaced by less energy-efficient factories in the non-policy countries?
There is some economic theory needed here. The Solow growth model shows a technological growth curve. Developing countries can achieve rapid growth by adapting to higher-productivity by adapting existing technologies. Their lower-unit labour costs will enable to undercut the more advanced economies, but the growth in these economies will grow the global economy as well. Most of this is unit labour costs. But by adapting previous generation technologies and exploiting labour costs less than a tenth those of the rich countries, they can under-cut the rich world. Greater technological advance is mostly in unit labour costs, but it can also mean lower unit energy costs. The portion of global output transferred from the rich countries to the poorer developing countries could result in higher total energy use, and ceteris paribus, higher CO2 emissions.

What is clear is that policy countries will increase unit energy costs. There is a two-pronged approach in Britain. The European-wide carbon-trading scheme will restrict supply of energy, bidding up the price. But also renewables cost more than fossil fuels. So the two-pronged approach doubly increases unit energy costs. Increasing unit energy costs accelerates the switching of manufacturing to developing countries, mostly China. The blue bit above postulates that energy per unit of output is globally could increase. But that is part of the problem. China has much higher CO2 emissions per unit of output as Britain. If Britain’s aggressive rush to renewables is successful, then this gap will increase, as much of Chinese energy output is from coal. A de-carbonised British economy will also be a de-industrialised one. But overall global emissions will have increased through switching of output to China.

The biggest cost of the policy for Britain is nothing to do with switching low-CO2 emitting production to high CO2 emitting countries. It is the restriction on economic growth. Loss of jobs from manufacturing, and pushing up higher energy costs elsewhere constrains growth. Due to the long-term consequences of that pushes policy costs through the roof. In the sectors where jobs are lost overseas, the policy curve is positive. If British Climate Change Act 2008 is massively unsuccessful in meeting the carbon targets, it could be a very expensive policy to increase global CO2 emissions.

The Shale-Gas Counter Example

In the USA, a consequence of the shale gas revolution has been to drastically reduce unit energy costs to industry. But also there has been a switch away from coal. As CO2 emissions of gas are around half that of coal, US CO2 emissions have been falling with electricity prices. The US is enjoying both cheaper and cleaner energy. Consequently, some chemical factories that relocated to China have returned to the USA. China has a greater proportion in its electricity production than USA, and the gap is widening. So the switching of a factory from USA reduces global CO2 emissions, even though the total energy usage remains the same.

Let me show this graphically.

Suppose (as is likely at present), the Climate Change Act 2008 falls a long way short of its target but unintentionally moves a substantial part of manufacturing to China through higher costs. For Britain this will be a large cost relative to British, but may be a net contributor to global warming. The policy curve points gets a positive slope! Conversely, “free market” shale gas in the USA has constrained global carbon emissions doubly by reducing US carbon emissions per unit of output, and switching production from China, where carbon emissions per unit of output are higher. It is having positive benefits on the US economy as well (hence negative costs), whilst constraining (slightly) the top-end of global warming.

5 The Climate Cost Curve

This is a draft proposal in which to frame our thinking about the climatic impacts of global warming, without getting lost in trivial details, or questioning motives. It is an updated version of a draft posted on 26/10/2012.

The continual rise in greenhouse gases due to human emissions is predicted to cause a substantial rise in average global temperatures. This in turn is predicted to lead severe disruption of the global climate. Scientists project that the costs (both to humankind and other life forms) will be nothing short of globally catastrophic.

That is

CGW= f {K}                 (1)

The costs of global warming, CGW are a function of the change in the global average surface temperatures K. This is not a linear function, but of increasing costs per unit of temperature rise. That is

CGW= f {Kx} where x>1            (2)


The curve is largely unknown, with large variations in the estimate of the slope. Furthermore, the function may be discontinuous as, there may be tipping points, beyond which the costly impacts of warming become magnified many times. Being unknown, the cost curve is an expectation derived from computer models. The equation thus becomes

E(CGW)= f {Kx}                (3)

The cost curve can be considered as having a number of interrelated elements of magnitude M, time t and likelihood L. There are also the adaptation costs/benefits (which should lead to a planned credit) along with the costs involved in taking actions based on false expectations. Over a time period, costs are normally discounted by r. Then there are two subjective factors – The collective risk factor R, and, when considering a policy response, a weighting W should be given to the scientific evidence. That is

E(CGW)=f {M,1/t,L,A,│Pr-E()│,r,R,W}    (4)

Magnitude M is the both severity and extent of the impacts on humankind or the planet in general in a physical sense.

Time t is highly relevant to the severity of the problem. Rapid changes in conditions are far more costly than gradual changes. Also impacts in the near future are more costly than those in the more distant future due to the shorter time horizon to put in place measures to lessen those costs.

Likelihood L is also relevant to the issue. Discounting a possible cost that is not certain to happen by the expected likelihood of that occurrence enables due unlikely but catastrophic events to be considered alongside near certain events.

Adaptation A is for a project to adapt to the changed climate, to lessen or null the costs. It is the difference between the actual costs spent and the climate impacts saved. Upon completion, a project should have a net credit value.

│Pr-E()│ is the difference between the predicted outcome, based on the best analysis of current data at the local level, and the expected outcome, that forms the basis of adaptive responses. It can create a cost in two ways. If there is a failure to predict and adapt to changing conditions then there is a cost. If there is adaptation to an anticipated future condition that does not emerge, or is less severe than forecast, there is also a cost. │Pr-E()│= 0 when the outturn is exactly as forecast in every case. Given the uncertainty of future outcomes, there will always be costs incurred if the climate cost savings from adaptation is a unitary value. If there are a range of possible scenarios, then this value could be a credit.

Discount rate r is a device that recognizes that people prioritize according to time horizons. Discounting future costs or revenue enables us to evaluate the discount future alongside the near future.

Collective risk factor R, is the risk preference weighting. If policy-makers assume a collective risk-neutral position, then this weighting will be 1. Risk lovers – the gamblers and many self-made billionaires – have a weighting of less than one. Those who take out insurance are risk averse. Insurance gives a certain premium to compensate if a much greater probabilistic loss occurs. For instance, the probability of a £200,000 house being completely destroyed in a year is around 1 in 10,000. So the expected loss is just £20 in any year. Most people are risk averse when it comes to their most valuable asset, so would pay a premium of far greater than £20 compensate for this unlikely loss. With respect to potential catastrophes, we usually expect governments to take a risk-averse approach. That is to potentially spend more on certain costs (like flood defences) than the total expected losses from letting catastrophes from happening. For any problem on a vast scale, we need to articulate the risk preference weighting. The “precautionary principle”, used in arguing for tough and immediate mitigation policies, effectively creates a collective risk factor many times greater than 1. NB, as the costs of climate change will increase with time, a risk averse weighting is the equivalent of a negative discount rate r. That is, you could assume R = f {-r}.

Finally the Weighting (W) is concerned with the strength of the evidence. How much credence do you give to projections about the future? Here is where value judgements come into play. I believe that we should not completely ignore alarming projections about the future for which there is highly circumstantial evidence, but neither should we accept such evidence as the only possible future scenario. In fact, by its very nature the “evidence” will be highly circumstantial. Consider the costs of climate change graph again. The data we have (which needs to converted into evidence) is for a very short section, and for miniscule fluctuations in costs, compared to the predicted catastrophe.

This leads to a vast area of evidence quality as

  • Small errors or biases in temperature measurement will have huge impacts on future projections. (Impacts on historical climate sensitivity)
  • Small errors or biases in distinguishing between natural and human-caused extreme weather events or short-run climatic changes will have huge impacts on projected costs.

If we assume that some sort of climate catastrophe is going to happen, convincing an independent third-party could include

  • Science building a clear track record of short-run predictive successes, both on warming trends and damage impacts.
  • Learning from the errors and exaggerations.
  • Be very clear as to the quality and relevance of the evidence.
  • Corroborating evidence. Show the coherence of one part of the picture with another. For instance, trying to reconcile with estimates of polar ice cap rate of melt with the rate of sea level rise reveals some very interesting questions.
  • Corroboration of between different techniques and evaluation methods.
  • For a junior science, show the underlying methodology draws upon the best of the mature sciences and philosophies of science.

The prediction of catastrophe is highly emotive. There are comparisons here with the justice system in has Britain failed where there are highly emotive crimes, for instance the IRA bringing their bombing campaign to the British mainland in the early 1970s.

  • Clear separation of the understandable emotion, from the evidence gathering.
  • Developing, and continually improving, quality standards for evidence gathering
  • A dim view taken for tampering with, or suppression of evidence.
  • A dim view taken on influencing the jury.
  • Allowing the accused a strong defence. The lack of any credible defence argument, despite a strong defence team, will remove any “reasonable doubt” in the minds of the jury, where the accused is in denial of the overwhelming evidence of their guilt.

6 A halving of climate sensitivity

Lord Lawson, in a spirited attack on the Energy Bill passing through parliament, said in the House of Lords on 18th June 2013

There is an emerging consensus among scientists that the climate sensitivity of carbon is probably less than they thought. That means, importantly, that any dangers from warming, if they occur, are postponed well into the next century. It means that there is no urgency to go ahead in this way, not only because the uncertainties are in the distant future but because we have no idea what technologies will develop over the next 100 years.

The analysis I have developed shows Lord Lawson understates how significant the climate sensitivity issue to the problem of catastrophic warming and mitigation policy.

In my analysis, the maximum warming would be 7oC. There can be a case for warming topping out at some level, as

  • There are diminishing returns to increases in greenhouse gas on temperature.
  • There are diminishing returns at some point for unit rises in emissions on levels of GHGs. That is, higher levels of GHGs in the atmosphere will lead to higher levels of absorption.

I will assume that climate sensitivity is halved, but will assume that temperatures eventually reach 5oC above pre-industrial levels.

The simple curve to work out the consequences is the policy curve. Any constraint of greenhouse gas levels will only have half the impact on temperature. The policy curve will shift to the right to PC1.

The climate costs curve is somewhat more difficult. The elements to consider in the curve are

E(CGW)=f {M,1/t,L,A,│Pr-E()│,r,R,W}

I have highlighted the elements to consider.

Time t will be doubled. Warming rates will therefore be halved. Some of the harmful consequences of warming are from unprecedented rapid change. For many animals and plants, it is speculated sudden change is much more damaging than a slower change. More importantly, sudden changes in average temperature could jolt climate systems into different patterns. Savannahs could become deserts, or the monsoon could shift. Another aspect to consider is that rapid warming of the tundra could release massive amounts of CH4 into the atmosphere, further accelerating warming. Or rapid warming could lead to rapid disintegration and breakup of the polar ice caps, leading to rapid acceleration of sea level rise. The slower warming will make us much less likely to cross these climate tipping points.

Adaptations A
can be phased in more gradually. For instance, with sea level rise, the Thames Barrier will no longer be adequate. A replacement to last 50 years will need to be much less extensive. If warming causes crop yields to fall by increased drought there is more time to adjust.

With changes happening more slowly, (and less chaotically), the adaptation cost errors, │Pr-E()│, are likely to be less.

For any positive rate of discount r, then the current net present value will be lower for the much extended warming period. However, as Stern had a discount value of not much different to zero, allowing for a discount rate would totally cover the other issues.

For all of these reasons, the climate cost curve will move down to CC1 and total cost curve to TC1. The point where policy costs equals climate change costs moves from A to B. That is at a significantly higher temperature, and for a much lower level of policy cost.

I have steered away from the weighting W issues. But given that sensitivity is a core issue that the climate models have got consistently wrong, then any weighting given to other predictions should be viewed with greater scepticism.

7 Appendix – Deriving the Policy and Forecast Graph

In the introduction, the derivation of the graph to replicate the claim that the costs of catastrophic global warming will be many times greater than mitigation policy costs was logically incomplete. This is a derivation of the two cost functions from a series of PowerPoint slides, which I find somewhat more satisfactory.

Slide 1

First draw two axis’s – for temperature and relative cost.

Slide 2

Next, add in five points.

A. If there had been no rise in human greenhouse gases, there would be no rise in temperatures and thus no consequential costly climate impacts.

B. With “business as usual”, there will be a huge amount of warming, with hugely costly consequential climate impacts.

C. Globally, policy could be used to stop any further rise in greenhouse gases, but with huge global cost.

D. No policy and no policy costs.

E. Intersection of two curves, which in Stern’s view is at the point of constraining warming to about 3 degrees above pre-twentieth century levels.

Slide 3

Connecting up the points AB (climate costs) and CD (Policy costs) with straight lines (linear functions), creates an intersection at point F.

To replicate Stern, we need cost functions that intersect at point E. That is the climate cost curve connects AEB and the policy costs curve connects CED.

Slide 4

Drawing curves within PowerPoint is beyond my current skills. Simple curves have symmetrical properties. The required cost curves do not have such properties.

Slide 5

Above is the actual graph used.

Slide 6

On my graphs the cost curves are unstable functions

For climate costs

RC = f(T4)

For policy costs

RC = f((10-T)5)

To justify policy

  1. Must have reliable consequences of warming beyond human experience. Climate models must be robust for the high temperature rise forecast and have a phenomenal degree of precision on the shorter-term cost impact forecasts.
  2. Must be sure that got achievable high-impact low-cost policies, with a highly results-driven approach to policy implementation.