Mean Variance Approach to Environmental Risk

  • Margaret Insley, Department of Economics, University of Waterloo
  • Tracey Snoddon, Department of Economics, Wilfrid Laurier University
  • Peter A. Forsyth, David R. Cheriton School of Computer Science, University of Waterloo
climate change risk banner


Climate change caused by human activity represents a particularly intractable “tragedy of the commons” which can only be addressed by cooperative actions of key decision makers representing nations or regional governments. The likely success of the cooperative actions is hampered by the large incentives for free riding by those who are motivated to delay significant cuts in carbon emissions in hopes that others will do the “heavy lifting”. Further complicating the problem are the enormous uncertainties inherent in predicting climate responses to the buildup in atmospheric carbon stocks and resulting impacts on human welfare, including the prospects for adaptation and mitigation. These huge uncertainties and the need for cooperative global action have been used by some as justification for delaying aggressive unilateral policy actions. This research seeks to gain a better understanding of the impact of the strategic interactions of decision makers on the ability of the world community to make meaningful global reductions in green house gases. We develop an economic model of the optimal decisions of two large emitters of green house gases given uncertainty in future temperature levels. A summary of the model and preliminary results are presented below.

  • The global average temperature is modelled as a mean-reverting stochastic process driven by the stock of atmospheric carbon. Emissions of carbon result in short-term economic gains. However, increasing carbon levels result in long-term increasing temperature, which causes damage to the global economy.
  • We consider two large competing regional economies, which individually choose a level of carbon emissions on a bi-annual basis. We model the choice of emission level as a non-cooperative Stackelberg game, i.e. there is a leader (who chooses the emission level first) and a follower.
  • We compare the results of the non-cooperative game to the choice of a Social Planner who chooses emission levels which maximize the sum of the utilities for the two regions.Standard economic models pay insufficient attention to the possible disastrous Effects of large temperature changes. We have modified the standard damage functions to address these issues. We find that the stochastic temperature effects cannot be ignored: Temperature changes of (0:5 – 1:0)C can occur solely due to volatility, regardless of the current stock of atmospheric carbon.
  • Our results indicate that the leader has an advantage compared to the follower, particularly in the case that the leader and follower have a asymmetric damage functions due to increasing temperature.
  • The results of the non-cooperative game are in sharp contrast to the results obtained assuming a Social Planner. The Social Planner cuts back on emissions much more aggressively than in the Stackelberg game, thus indicating a classic tragedy of the commons.We also observe a form of Green Paradox: if the follower cuts back on emissions due to more environmentally friendly preferences, the leader takes advantage of this and increases her emissions, thus counteracting the environmentally friendly sentiments of the follower.

This report is part of the larger GRI funded research project, “Multi-Period MV Approach to Risk & Return in Climate Change Policy.”