While the title of this thought piece might appear a little strange (“as small as possible please!”), my original (more accurate) title was even stranger: “When it comes to damage functions, are you a quadratic or logistic person?” All will become clear, very soon.
I have previously suggested that our breaching of various planetary boundaries is proof that we are increasing systemic risk. In this piece I aim to explore what might be the consequences of breaching planetary boundaries and triggering systemic risk. Specifically, I will focus on the carbon emissions boundary, because that is where most of the modelling is.
The phrase ‘damage functions’ is part of the jargon used within the modelling of climate risk. The damage function in a model relates the amount of predicted warming to an amount of predicted economic damage. The choice of damage function matters. They can be more, or less, aggressive. So, different models of climate risk will show a different amount of economic damage for the same amount of warming. It is therefore important to understand the damage function, and choose one that corresponds with your climate beliefs.
To illustrate this with examples, a really aggressive model (eg Burke et al 2015) would suggest a 23 per cent loss of GDP at 4C of warming. A less aggressive model (eg Khan et al 2019) would suggest a 7 per cent loss of GDP at 4.5C of warming. These answers are materially different, and we would expect different impacts on asset prices. However, both these models – and, in fact, the majority of models of climate risk – use what is known as a ‘quadratic’ damage function.
Our TAI paper Pay now or pay later? argued that the results above were substantial underestimates. And in a previous thought piece, Climate tipping points change everything, I argued that the wrong baseline was being used. Instead, I suggested a better baseline was to consider a 100% loss of GDP as currently measured due to unmanaged climate change and to work back from there.
Now seems a good time to push harder on that idea. It is clear to me at least, that there is some level of warming at which all economic activity ceases. Sometime before that, it would appear reasonable to assert that humans will lose interest in measuring GDP or other conventional measures of growth because survival is more pressing. At what temperature might this occur? In the appendix of our Pay now or pay later? paper we listed physical damage as set out by the IPCC. Among other effects, a temperature rise between 2.5 and 4.5C is expected to lead to the ‘widespread death of trees’ and ‘reduced provision of ecosystem services’. I will leave you to decide the level of warming associated with a 100 per cent loss of GDP – but it could be as low as 5C.
The question now is what shape of damage function should we draw between where we are and a 100 per cent loss of GDP. It could be linear, but I would suggest a ‘logistic’ function (sigmoidal, or S-curve) is more realistic. Damage will accumulate slowly in the near term and then accelerate. How quickly it accelerates will depend on the temperature limit you chose above. But for any reasonable range of temperature limits, a logistic damage function will suggest a loss of GDP that is a multiple of the damage suggested by a quadratic function. In turn, this would suggest that the potential risk to asset prices is way, way higher than any modelling results you have seen to date.
So, what do you believe about climate? Do you believe the physical damage it will cause will rise at a faster rate (non-linear) as temperature rises? Do you believe that indoor work will be adversely affected, as well as outdoor work? Do you believe that climate tipping points exist, and some could be triggered at low levels of warming? The more strongly you believe these, and similar aspects, the more I would suggest you consider a logistic damage function. Forewarned is forearmed.
 From the IPCC WGII Sixth Assessment Report’s Technical Summary
 Over the decade to 2020, annual climate damage was estimated to be around 0.2% of world GDP (Equity Investors Must Pay More Attention to Climate Change Physical Risk, IMF blog, May 29, 2020). This level of damage was associated with a level of warming rising from around +1C to +1.1C. A Grantham Institute policy publication dated 30 May 2022 estimated climate damage in the UK at 1.1% of GDP (What will climate change cost the UK? Risks, impacts and mitigation for the net-zero transition)
 Many models, and their damage functions, assume that 85-90% of GDP will be unaffected by warming because the activities are performed indoors
Tim Hodgson is co-founder of the Thinking Ahead Institute at WTW, an innovation network of asset owners and asset managers committed to mobilising capital for a sustainable future.