We investigate the optimal policy response to the possibility of abrupt, irreversible shifts in system dynamics. The welfare cost of a tipping point emerges from the policymaker's response to altered system dynamics. Our policymaker also learns about a threshold's location by observing the system's response in each period. Simulations with a recursive, numerical climate-economy model show that tipping possibilities raise the optimal carbon tax more strongly over time. The resulting policy paths ultimately lower optimal peak warming by up to 0.5 • C. Different types of post-tipping shifts in dynamics generate qualitatively different optimal pre-tipping policy paths.JEL: Q54, D90, H23

The paper explores the consequences of limited substitutability in welfare between environmental and produced goods for long-term evaluation. I show how the magnitude and time development of optimal social discount rates depend on the substitutability between the different classes of goods. I relate the degree of substitutability to the notions of weak and strong sustainability in a way suggested in the literature.I show that a strong notion of sustainability results in lower weights given to long-run service and consumption streams compared to a weak notion of sustainability. The paper develops an alternative definition of weak and strong sustainability preferences that incorporates the intertemporal concern of sustainability.

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The current generation has to set mitigation policy under uncertainty about the economic consequences of climate change. This uncertainty governs both the level of damages for a given level of warming, and the steepness of the increase in damage per warming degree. Our model of climate and the economy is a stochastic version of a model employed in assessing the US Social Cost of Carbon (DICE). We compute the optimal carbon taxes and CO 2 abatement levels that maximize welfare from economic consumption over time under di erent risk states. In accordance with recent developments in finance, we separate preferences about time and risk to improve the model's calibration of welfare to observed market interest. We show that introducing the modern asset pricing framework doubles optimal abatement and carbon taxation. Uncertainty over the level of damages at a given temperature increase can result in a slight increase of optimal emissions as compared to using expected damages. In contrast, uncertainty governing the steepness of the damage increase in temperature results in a substantially higher level of optimal mitigation. T he DICE integrated assessment model 1,2 couples a growing global economy to a simple climate model. The economy produces emissions that accumulate in the atmosphere, change the radiative forcing, and warm the planet's surface. This warming feeds back into economic production and consumption (goods and services humans care about). The climate-economy interactions are nonlinear and delayed. Integrated assessment models such as DICE inform us about the long-term economic loss resulting from current carbon emissions and help us evaluate climate policy. Many of the interactions within and between climate and the economy are uncertain and an increasing number of studies simulate the consequences of given policies under uncertainty 2-10 . We follow Kelly and Kolstad 11 , Keller et al. 12 and Leach 13 in building a stochastic integrated assessment model that evaluates the optimal policy response to uncertainty. Optimality means that resources within and across periods are distributed to maximize the expected stream of global welfare. Our contribution is twofold. First, our optimal trade-off among consumption, emissions, and capital investment treats the damage parameters governing the relation between climate change and economic impact as stochastic. Second, we use a more sophisticated approach to evaluate the uncertain impact of climate change on economic and human welfare. Uncertainty evaluationNordhaus 2 estimates the DICE damages as a function of the global average temperature increase T t above the level prevailing in 1900. In these estimates, the fraction of global economic production lost to climate change isDICE's damage function and similar variations are widespread in the integrated assessments of climate change. The damage coefficient b 1 captures the level of damages at a 1 • C warming (damage level). The damage exponent b 2 captures the steepness of the damage increase as temperature rises (dam...

Greenhouse gas emissions can trigger irreversible regime shifts in the climate system, known as tipping points. Multiple tipping points affect each other's probability of occurrence, potentially causing a "domino effect". We analyze climate policy in the presence of a potential domino effect. We incorporate three different tipping points occurring at unknown thresholds into an integrated climate-economy model. The optimal emission policy considers all possible thresholds and the resulting interactions between tipping points, economic activity, and policy responses into the indefinite future. We quantify the cost of delaying optimal emission controls in the presence of uncertain tipping points and also the benefit of detecting when individual tipping points have been triggered. We show that the presence of these tipping points nearly doubles today's optimal carbon tax and reduces peak warming along the optimal path by approximately 1 degree Celsius. The presence of these tipping points increases the cost of delaying optimal policy until mid-century by nearly 150%.The threat of climate tipping points plays a major role in calls for aggressive emission reductions to limit warming to 2 degrees Celsius 3-6 . The scientific literature is particularly concerned with the possibility of a "domino effect" from multiple interacting tipping points [7][8][9][10][11][12] . For instance, reducing the effectiveness of carbon sinks amplifies future warming, which in turn makes further tipping points more likely. Nearly all of the preceding quantitative economic studies analyze opti-