We are working on robust control in simple climate models coupled with economic growth, finance, and macro models. This effort is important for carbon pricing, understanding the impacts of robustly accounting for climate change, technical change, and other sources of uncertainty, not only on economic growth and macroeconomics, but also on asset prices as well as insurance pricing and green-house gas emission pricing.

Within the context of climate models are three contrasting approaches to robustness:

adapting to potential model misspecification
robustness adjustments for prior/posterior uncertainty
“smooth” models of ambiguity aversion

Decision theoretic frameworks exist for all of these applications, but their full consequences for economic models with climate change remains to be explored. To accomplish this we are developing numerical methods to support these analyses. In terms of discounting, our focal point is on the consequences of uncertainty. There is an extensive literature from asset pricing and macroeconomics that uses stochastic discounting as a device to adjust discount rates for cash flow riskiness. We are drawing on this literature and incorporating compensations for aversion to ambiguity and concerns about model misspecification into models that feature explicit uncertainty and climate impacts on the economy. We are also contrasting pricing implications from market economies with social valuation.

Coupled Economic-Climate Models with Carbon-Climate Response: The economics of global climate change is characterized by fundamental uncertainties including the appropriate reduced forms for climate dynamics, the specification of economic damages resulting from climate change, and mechanisms by which these damages will affect long-run economic growth. We have developed and implemented a novel theoretical and computational integrated assessment modeling approach that is a well-grounded means of summarizing the fundamental relationship between human activity and the global climate for purposes of economic analysis. Using a dynamic integrated assessment framework, this project makes several contributions to improving the analysis of these uncertainties:

First, we incorporate the cumulative climate response (CCR) function developed by Matthews et al. for representing the basic relationship between anthropogenic carbon emissions and increases in global mean temperature in a manner that is more directly policy relevant than the usual approach based on the equilibrium climate sensitivity.
Second, we adapt the tools developed by Hansen, Sargent and others for robustness analysis to address underlying model uncertainty in both economic and climate dynamics.
Third, we allow climate change to affect economic growth directly, in addition to its effect on output

We then develop and study a simple analytical model that yields insights and results on the key implications of these assumptions, as well as facilitating the interpretation of numerical results from a more general model. Among our findings is that the presence of robustness may result in either a decrease or increase in the optimal carbon tax and energy usage, depending among other factors on societal preferences.

Numerical Methods: In order to perform robustness analysis over a variety of fundamentally different models, we are developing PDE-based numerical method for solving robust stochastic equilibrium models in continuous time with optimal control. This approach allows us to uncover solutions for the entire state space and to perform a quick sweep over variety of models and parameters.

Energy modeling, numerical modeling based on economic principles, has become the dominant analytical tool in U.S. energy policy. Energy models are widely used by researchers across the public and private sectors. However, the widespread application of these models in policy analysis poses challenges to decision-makers. We are developing a framework and analysis that demonstrate how non-Bayesian decision rules can address fundamental model uncertainty in the domain of energy policy, technological change, and greenhouse gas abatement.

Numerical modeling based on economic principles has become the dominant analytical tool in U.S. energy policy. Energy models are now used extensively by public agencies, private entities, and academic researchers, and in recent years have also formed the core of integrated assessment models used to analyze the relationships among the energy system, the economy, and the global climate. However, fundamental uncertainties are intrinsic in what has become the typical circumstance of multiple models embodying different representations of the energy-economy, and producing different policy-relevant outputs that model users are compelled to interpret as equally plausible and/or valid. Because the policy implications of these outputs can diverge substantially, policy-makers are confronted with a significant degree of model-based uncertainty and little or no guidance as to how it should be addressed.

This problem of “model uncertainty” has recently been the focus of work in macroeconomics, where scholars have studied the problem of how a decision-maker should proceed in the face of uncertainty re- garding the correct model of an economic system that is the object of policy. We focus on analyzing a low-dimensional numerical integrated assessment model using the “minimax regret” metric. Specifically, we have demonstrated that deep uncertainty regarding energy-related technological change can be addressed using this approach. Our findings include comparison with expected cost minimization, to show how the interaction of solution methods and model structure affect the influence of this form of deep uncertainty on low-run CO2 emissions abatement policies. We also examined other methods assuming some prior distribu- tions over uncertain parameters for analyzing the difference between our robust solution and the non-robust solution from those methods.

We demonstrate that the fundamental model uncertainty can be represented and analyzed in the context of energy policy problems determining optimal CO2 abatement strategies. The robust solution from min-max regret method is significantly different with any solutions from sensitivity analysis over uncertain parameters or those methods assuming prior distributions over uncertain parameters. The following figure shows the difference of the robust min-max regret solution over all three uncertain parameters (the red line) and others with min-max regret solution over only one uncertain parameter, Technical Change level, while the other two parameters are used for sensitivity analysis.