126.96.36.199 Implications of assumptions concerning damage functions in cost-benefit analysis
What is remarkable in cost-benefit studies of the optimal timing of mitigation is that the shape (or curvature) of the damage function matters even more than the ultimate level of damages – a fact long established by Peck and Teisberg (1995). With damage functions exhibiting smooth and regular damages (such as power functions with integer exponents or polynomial functions), GHG abatement is postponed. This is because, for several decades, the temporal rate of increase in marginal climate change damage remains low enough to conclude that investments to accelerate the rate of economic growth are more socially profitable that investing in abatement.
This result changes if singularities in the damage curve represent non-linear events. Including even small probabilities of catastrophic ‘nasty surprises’ may substantially alter optimal short-term carbon taxes (Mastrandea and Schneider, 2004; Azar and Lindgren, 2003). Many other authors report similar findings (Azar and Schneider, 2001; Howarth, 2003; Dumas and Ha-Duong, 2005; Baranzini et al., 2003), whilst Hall and Behl (2006) suggest a damage function reflecting climate instability needs to include discontinuities in capital stock and the rate of return on capital, and hysteresis with respect to heating and cooling – resulting in a non-convex optimization function such that economic optimization models can provide no solution. But these surprises may be caused by forces other than large catastrophic events. They may also be triggered by smooth climate changes that exceed a vulnerability threshold (e.g. shocks to agricultural systems in developing countries leading to starvation) or by policies that lead to maladaptations to climate change.
In the case of an irreversible THC collapse, Keller et al. (2004) point out another seemingly paradoxical result: if a climate catastrophe seems very likely within a short-term time horizon, it might be economically sound to accept its consequences instead of investing in expensive mitigation to avoid the inevitable. This shows that temporary overshoot of a pre-determined target may be preferable to bearing the social costs of an exaggerated reduction in emission, as well as the need to be attentive to ‘windows of opportunity’ for abatement action. The converse argument is that timely abatement measures, especially in the case of ITC, can reduce long-term mitigation costs and avoid some of the catastrophic events. In this respect, limited differences in GMT curves for different emissions pathways within coming decades are often misinterpreted. It does not imply that early mitigation activities would make no material difference to long-term warming. On the contrary, if the social value of the damages is high enough to justify deep emission cuts decades from now, then early action is necessary due to inertia in socio-economic systems. For example, one challenge is to avoid further build-up of carbon-intensive capital stock.