Sternly bemused

Ever since the Stern Review report came out last year I’ve been baffled by the debate on discount rates. Something bothers me, but until now I haven’t been able to put my finger on it.

Effect on GDP of catastrophic events due to global warming

My gut feel is that the costs of catastrophic events have somehow been underestimated.

What I’m worried about in particular is the effect on cities (aka concentrations of fixed capital) of rising sea levels exacerbated by storms (though the loss of other resources – farmland, roads etc – is of course important too, and could cumulatively be even more significant). Some time ago my finger in the air estimate was that the loss of capital due to the forced evacuation of a great city – Shanghai was the one I came up with – would be around $1trn a pop, at today’s prices. My point is: how could the global economy keep growing if such losses become a regular occurrence?

Looking back at the Stern Report I see that there is a section on this very point – section 5.4 Impacts of extreme events (p.149ff in my CUP print copy). “Costs of extreme weather alone could reach 0.5 – 1% of GDP”, it says – currently they are 0.2% or $60bn p.a. on average. In 2005 the loss was $200bn, largely due to Katrina. Stern also notes that “Miami alone has $900bn worth of total capital stock at risk.” (p.150). On the other hand “developed economies… invest a considerable amount in fixed capital each year (20% of GDP or $5.5trn…)” of which $1.5trn goes into construction. Now I am able to quantify my qualms. Bear with me here: I freely admit I’m in a bit of a qualm quantification quandary!

1. GDP includes both consumption and capital formation. Now, it is the capital formation that allows us to grow GDP. To put it simply, it is all the new factories we build this year that allow us to consume more next year. If we stop forming capital (i.e. net investment goes to zero), then GDP growth will also fall to zero. We can’t (say) provide more transport without building more transport infrastructure, factories to produce vehicles etc.

2. Now, Stern notes that capital formation is around 20% of GDP in developed countries. I see no reason to suppose that this type of GDP (aka economic activity) can displace consumption. What I mean is, the resources that support consumption (private cars, say) cannot be diverted into the production of fixed capital (car factories, say) – at least not easily. To put it another way, if buildings are destroyed in a storm flood, they can either be rebuilt or other buildings can be built elsewhere (as intended before the catastrophic event) – you can’t do both unless you have spare construction resources.

3. So, I suggest, long-term GDP growth depends on the growth rate of capital formation.

4. It follows that average annual losses of fixed capital of Stern’s 0.5% – 1% of GDP will reduce the rate of fixed capital formation – which is only 20% of GDP – by 100%/20% times the proportional GDP loss, that is by 2.5% – 5%.

5. So GDP growth will in the long-run be 2.5% – 5% less than otherwise, not the 0.5% – 1% range Stern refers to.

6. Compound this effect on growth and GDP, even at the lower end (an average reduction in capital formation of 2.5% p.a.), if we allow global warming to happen, will only be around 75% of what it would be otherwise after a mere decade and less than a third after 40 years – so anyone starting out on their working life now will have a retirement living standard 1/3 of what it would otherwise have been. If we allow global warming to happen, that is.

7. Sanity check: refugees from a city rendered uninhabitable will move somewhere else and either:

  • be poor (reducing total GDP that way), or,
  • if fully insured, push up the price of housing etc, in effect lowering everyone’s standard of living, and again reducing total GDP.

8. I guess ultimately the economy might respond and allocate more resources to construction and other fixed capital formation. But if the losses are scattered moreorless randomly through time and around the world, it may be very inefficient to permanently maintain a larger pool of construction resources (how will the market do this?). One year they’d be needed, another not, the next they’d be needed on the other side of the world. Furthermore, for such a change in resource allocation to have no effect on overall GDP growth rates would imply that capital formation is not at present proceeding at an optimal rate. If it is possible to permanently increase the rate of capital formation without other repercussions for the economy – and note that high rates of capital formation tend to be associated with the accumulation of environmental debt, which is what’s getting us in this mess in the first place! – then there would nevertheless certainly be a permanent reduction in consumption as a percentage of GDP.


Response to “The Ethics of Climate Change”

In the last couple of days, an article, “The Ethics of Climate Change” by John Broome in Scientific American (June 2008 ) has led me to take a somewhat different tack and suggest that economists are making a category error when they model the reduction of carbon emissions as a cost that can, if necessary, be deferred. It is surely not a case of the “sacrifices the present generation will have to make to reduce greenhouse gases” (as John Broome puts it in Scientific American) but one of the environmental debt that will continue to be run up as long as we fail to internalise the costs of our emissions.

It is the science that tells us that the elevated level of greenhouse gases is an example of an environmental debt. For example, because the annual amount of carbon dioxide the ocean can absorb has levelled off (according to the IPCC, and as discussed previously in Uncharted Territory) then, at the margin, an extra tonne of carbon dioxide emitted now by the burning of fossil fuels or land-use change will remain in the atmosphere indefinitely. Each year the extra tonne of atmospheric carbon will cause the Earth to gain more heat than it would have done otherwise, causing environmental or financial damage (or at least increasing the risk of such damage in any given year).

Carbon dioxide emissions effectively incur an (until now unaccounted) interest charge payable in perpetuity in terms of environmental damage. It may make sense to establish an international trade in cuts in emissions compared to notional business as usual levels, so that emission reductions are made most efficiently (or at least more politically expediently than would otherwise be the case), but, when we are trying to determine the optimal global emissions reduction path, it is (IMHO) a mistake to consider emission cuts as a form of expenditure. Overall emission reduction targets must rather be motivated by a consideration of the cost of increasing our collective environmental debt that would otherwise be incurred.

And this isn’t the same thing at all. No, no, no!

The problem cannot be analysed as if it were that of an individual deferring costs over their lifetime, on the grounds (say) that they’ll have more money when their career takes off. To put it bluntly, (and think about the analogy of an individual’s lifetime spending profile) deferring forgoing consumption is simply not postponing a cost (as Stern et al would have us believe) – it’s consuming now and taking on debt. And as we – the post credit crunch generation – know only too well, debts can get out of hand. Am I starting to make sense?

Consider further that the existing international consensus is to implicitly attribute the global warming debt to individual nation states on the basis of their “historical emissions” through consumption of fossil fuels. (One might argue that fossil fuel producer countries and those that have caused carbon emissions through land‑use change have also incurred a debt). Instead of philosophising we can simply look at how international debt is managed today. Government debt is rarely written off – that of developed countries almost never. It follows that we should be temporally impartial (see the Scientific American article for an explanation) in assessing when to make emission reductions. In other words, it would be very imprudent to apply a discount rate on the basis that the cost of damage caused by today’s emissions will be less in the future. This is why it’s so important that we don’t treat a debt as a cost. If I borrow a dollar today I have to pay back more than a dollar in the future. But if I spend a dollar today that is worth more than to me than if I spend a dollar in future.

The question remains as to whether we should be prioritarian (again, see the Scientific American article). To determine this we must look at the present balance sheet of Earth Enterprises inc., taking into account the net present value of the environmental debt. Taking on the environmental debt results in at least some capital investment. The interest on the environmental debt represents future destruction of capital. How should this destruction be discounted in deciding the optimal path of future carbon emissions? The loss of a city in 50 years time due to rising sea levels and more intense storms will cause the loss of today’s capital represented by the city as well as the investment made over the next 50 years. However many bathrooms there are in each house (the article suggests that we can discount because we’ll have more bathrooms in the future), they’ll all be destroyed. The same proportion of global capital will be lost by the destruction of the city in 50 years as would be lost if it were destroyed tomorrow. As for the temporal consideration, we must simply use present-day costs – a discount rate of zero.

As pointed out in the Stern Review, the cost of – or rather, the environmental debt incurred as a result of – greenhouse gas emissions depends on their level in the atmosphere at the time. That is, because of the limited ability of natural systems to absorb increased emissions and eventual positive carbon cycle feedbacks, the marginal cost of a tonne of carbon emissions increases (in real terms) as atmospheric greenhouse gas levels and the temperature increase. This conclusion suggests two possible international conversations:

  • First, responsibility for historical emissions can be quantified if politicians wish to attempt such an exercise, but at a lower cost to present emissions.
  • Second, the cost of future emissions will be higher than even present-day emissions. My bank manager would have little sympathy if I asked him to grant me a cheap mortgage simply because I missed the opportunity to borrow before the credit crisis, when money was cheap. Similarly, the fact that carbon emissions were cheap in the past is not a valid argument against them being made very expensive for everybody now.


The conventional economic approach – as espoused by Stern and characterised by a discourse focussing on the “costs” of global warming and, as a consequence, making use of discount rates – is deeply suspect.

An alternative approach which is more in tune with the international consensus perception of global warming (and other environmental externality problems) is to characterise the elevation of levels of greenhouse gases as an environmental debt, attributable to nation states or as may otherwise be politically determined.

Such an approach immediately exposes the fallacy of temporal discounting – international debts are typically never forgiven, or, if they are, this is seen as akin to an act of charity. We must be temporally impartial in assessing the costs of global warming (and other environmental debts).

Neither can we be prioritarian and plead present-day poverty. The debt-based approach also reveals that capital losses cannot be simply equated with the loss of consumption opportunities. The error is akin to a company trying to convince the investment community that a loss of $100m in a financial year is tiny compared to its turnover of $5bn. It is only relevant to compare the scale of the loss with the company’s capital. Additionally, losses of capital will be proportionate to the total capital at the time of the loss – any more optimistic assumption would be reckless.

The correct approach therefore is to use a discount rate of zero for global warming losses, and account for all global warming debts at present-day prices. That is, if the emission of a tonne of carbon now increases the risk of the 50% loss of the fixed capital investment represented by a given city in 50 years time by 0.000001%, then the cost of (=the debt incurred by emitting) that carbon is 0.000001% of 50% of the value of the city now, not 0.000001% of 50% of the value of the city discounted by a factor of the order of some percent raised to the power 50 (i.e. multiplied by for example 98.6% – Stern’s figure – or 94% – Nordhaus’ estimate for each of 50 years – try this one at home to see the effect!). To put it bluntly, if Miami has to be permanently evacuated and 50% of the cumulative fixed capital investment in the city ($900bn at present-day prices) is lost, then it is 50% whether the event happens tomorrow, in 50 years time or in 150 years time. Whenever it happens we still have to build New Miami. If you happen to be responsible for some of the environmental debt that causes this to happen, I hope you’ve invested the carbon wisely!

In translating the risk of future losses – that is, the total environmental debt due to greenhouse gas emissions – into a price of carbon we must also take into account that the warming effect of a tonne of emissions at a given time depends on the total amount of emissions up to that point in time. As in any financial market, the cost of a commodity (in this case the right to emit) depends on the behaviour of all other participants in the market.