Expected Utility and Catastrophic Risk in a Stochastic Economy-Climate Model

Abstract

Expected Utility and Catastrophic Risk in a Stochastic Economy-Climate ModelIkefuji, M.; Laeven, R.J.A.; Magnus, J.R.; Müris, C.H.M. General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.-Users may download and print one copy of any publication from the public portal for the purpose of private study or research -You may not further distribute the material or use it for any profit-making activity or commercial gain -You may freely distribute the URL identifying the publication in the public portal Take down policyIf you believe that this document breaches copyright, please contact us providing details, and we will remove access to the work immediately and investigate your claim. Chris MurisCentER, Tilburg University * We are grateful to Graciela Chichilnisky, John Einmahl, Reyer Gerlagh, Johan Eyckmans, Sjak Smulders, Peter Wakker, Aart de Zeeuw, Amos Zemel, and seminar participants at the Tilburg Sustainability Center for helpful comments. This research was funded in part by the JSPS under grant C-22530177 (Ikefuji) and by the NWO under grant Vidi-2009 (Laeven). E-mail addresses: ikefuji@iser.osaka-u.ac.jp (Ikefuji), r.j.a.laeven@uvt.nl (Laeven), magnus@uvt.nl (Magnus), chrismuris@gmail.com (Muris). Abstract: In the context of extreme climate change, we ask how to conduct expected utility analysis in the presence of catastrophic risks. Economists typically model decision making under risk and uncertainty by expected utility with constant relative risk aversion (power utility); statisticians typically model economic catastrophes by probability distributions with heavy tails. Unfortunately, the expected utility framework is fragile with respect to heavy-tailed distributional assumptions. We specify a stochastic economyclimate model with power utility and explicitly demonstrate this fragility. We derive necessary and sufficient compatibility conditions on the utility function to avoid fragility and solve our stochastic economy-climate model for two examples of such compatible utility functions. We further develop and implement a procedure to learn the input parameters of our model and show that the model thus specified produces quite robust optimal policies. The numerical results indicate that higher levels of uncertainty (heavier tails) lead to less abatement and consumption, and to more investment, but this effect is not unlimited.JEL Classification: D81; Q5.

DICE Simplified

“…A number of equations are redundant and have been deleted. A new variable ω t has been introduced, some equations have been combined, and the equations have been reordered; see [14] for the details. Still, this is precisely the same model as Nordhaus' 2016R model.…”

“…The alternative specification is of interest because we may wish to randomize ξ, as in [14]; see also [12,13]. This is difficult under the DICE specification because 1 − ω t − ξH 2 t could become negative (under extreme circumstances), while the alternative specification is always positive provided ξ > 0.…”

Scrap Value Functions in Dynamic Decision Problems

“…The main advantage of using scrap value functions becomes apparent in a stochastic framework, for example a stochastic version of the DICE model, as proposed by Ikefuji et al (2010a) in the context of catastrophic risk in economy-climate models. Suppose again that T = 2 and that there is only one random shock, ǫ, with some known cumulative distribution function F .…”

Climate Policy Under Fat-Tailed Risk: An Application of Dice

“…Costello et al (2010) put an upper bound on temperature increases, and Pindyck (2011) places an upper bound on marginal utility. Ikefuji et al (2010) use a bounded utility function (e.g. 'Burr' function) instead of the constant relative risk aversion (CRRA) function.…”