Expectations of linear functions with respect to truncazted multinormal distributions, with applications for uncertainty analysis in environmental modelling

Uncertainty can hamper the stringency of commitments under cap and trade schemes. We assess how well intensity targets, where countries' permit allocations are indexed to future realised GDP, can cope with uncertainties in a post-Kyoto international greenhouse emissions trading scheme. We present some empirical foundations for intensity targets and derive a simple rule for the optimal degree of indexation to GDP. Using an 18-region simulation model of a 2020 global cap-and-trade treaty under multiple uncertainties and endogenous commitments, we estimate that optimal intensity targets could achieve global abatement as much as 20 per cent higher than under absolute targets, and even greater increases in welfare measures. The optimal degree of indexation to GDP would vary greatly between countries, including super-indexation in some advanced countries, and partial indexation for most developing countries. Standard intensity targets (with one-toone indexation) would also improve the overall outcome, but to a lesser degree and not in all cases. Although target indexation is no magic wand for a future global climate treaty, gains from reduced cost uncertainty might justify increased complexity, framing issues and other potential downsides of intensity targets.linear functions, truncazted multinormal distributions, uncertainty analysis, environmental modelling

Towards a more inclusive and precautionary indicator of global sustainability

We construct a hybrid, economic indicator of the sustainability of global well-being, which is more inclusive than existing indicators and incorporates an environmentally pessimistic, physical constraint on global warming. Our methodology extends the World Bank's Adjusted Net Saving (ANS) indicator to include the cost of population growth, the benefit of technical progress, and a much higher, precautionary cost of current CO2 emissions. Future warming damage is so highly unknowable that valuing emissions directly is rather arbitrary, so we use a novel, inductive approach: we modify damage and climate parameters in the deterministic DICE climate-economy model so it becomes economically optimal to control emissions in a way likely to limit warming to an agreed target, here 2 degrees Celsius. If future emissions are optimally controlled, our ANS then suggests that current global well-being is sustainable. But if emissions remain uncontrolled, our base-case ANS is negative now and our corresponding, modified DICE model has an unsustained development path, with well-being peaking in 2065. Current ANS on an uncontrolled path may thus be a useful heuristic indicator of future unsustainability. Our inductive method might allow ANS to include other very hard-to-value, environmental threats to global sustainability, like biodiversity loss and nitrogen pollution

OPTIMAL GROWTH, GENUINE SAVINGS AND LONG-RUN DYNAMICS

Green accounting theories have shown that negative genuine savings at some point in time imply unsustainability. Consequently, recent studies advocate the use of the genuine savings measure for empirical testing: a negative index implies that sustainability be rejected. However, this criterion cannot ascertain sustainability, because positive current genuine savings do not rule out genuine dissaving in the future. This paper derives a one-to-one relationship between the sign of long-run genuine savings and the limiting condition for sustained utility in the capital-resource growth model, assuming technical progress and resource renewability. This result suggests to extend the genuine saving method to include a test of the limiting condition: if this condition is empirically rejected, positive current genuine savings are delivering a false message

Sustainable Development, Renewable Resources and Technological Progress

Conflicts between optimality and sustainability are typical in the literature on sustainable development. Using the “capital-resource” growth model, Pezzey and Withagen (1998, Scandinavian Journal of Economics 100 (2), 513–527) have proved that if natural resources are exhaustible, the time-path of consumption is single-peaked, declining from some point in time onwards. This paper extends the model to include technical progress, resource renewability, extraction costs and population growth. The main result is that, for any constant returns to scale technology, optimal paths can be sustainable only if the social discount rate does not exceed the sum of the rates of resource regeneration and augmentation. The development of resource-saving techniques is crucial for sustaining consumption per capita in the long run, whereas capital depreciation and extraction costs are neutral with respect to this sustainability condition. Copyright Springer 2005optimal growth, renewable resources, sustainable development, technological progress,