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Can you trust a model whose output keeps changing? Interpreting changes in the social cost of carbon produced by the DICE model

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Abstract

The social cost of carbon (SCC) measures the present value of the economic damages caused by emitting one marginal ton of carbon dioxide into the atmosphere. It plays a crucial role in climate policy analysis, where it is used to suggest optimal carbon prices or quantify the benefits of actions that reduce emissions. One prominent framework used to estimate the SCC is the Dynamic Integrated Climate-Economy (DICE) model. As updated versions of DICE have been introduced, its SCC estimates have changed, sometimes by amounts that would appear significant. For example, the SCC in 2020 produced by DICE rose 54% from its 2013R version to its 2016R2 version. We address two important questions. First, what changes to DICE explain this increase in its SCC? Second, how surprising is the magnitude of this increase, relative to the uncertainty present in DICE’s input parameters? We find that changes in scientific parameters and updated initial conditions due to near-term forecasting errors accounted for the largest shares of the SCC increase. The later SCC estimate falls within the 80% probability interval produced using the earlier model with uncertainty. Therefore, the 54% increase should not be considered surprising or dispositive regarding the quality of DICE itself.

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Notes

  1. Under no controls, we cannot use shadow prices to estimate the SCC according to Eq. (1) like we do throughout the rest of this paper, where we estimate the SCC under optimal controls. For the no-controls SCC estimates in Table 2, we approximate the numerator and denominator of Eq. (1) by introducing discrete perturbations of \(E\left( t \right)\) and \(C\left( t \right)\), respectively, and observing the resulting changes in \(W\).

  2. The order in which the changes are implemented certainly affects the magnitudes of their impacts on the SCC. For example, if we change initial conditions first and then economic model parameters second, their respective effects on the SCC would be a $6.74 increase and a $4.49 decrease. Introduced in the reverse order, these effects would be a $6.43 increase due to initial conditions and a $4.18 decrease due to economic model parameters.

  3. If we choose the order of the parameter packages by dynamically introducing whichever package has the largest impact on the SCC at each step, then the effect of each package on the SCC (in order of introduction) is an $8.81 increase due to scientific model parameters, a $6.74 increase due to initial conditions, a $4.49 decrease due to economic model parameters, and a $1.48 increase due to projection parameters.

  4. We would have ideally included a greater number of iterations, but solving DICE as a nonlinear optimization problem at each iteration is computationally expensive and time-consuming. Furthermore, after 1000 iterations, we find that the SCC output distribution is already stable. Schwanitz (2013) previously noted the challenges that computational complexity presents for conducting large-scale uncertainty analysis with IAMs.

  5. While the Gillingham et al. journal article was published in 2018, an earlier version with the same uncertainty estimates was published as a National Bureau of Economic Research working paper in 2015. The DICE-2013R model was the current version at that time, and the version to which the paper’s uncertainty estimates apply.

  6. The one exception is the Initial Factor Productivity Growth Rate in DICE-2016R2, for which we consider the 60th percentile (a value of 0.086) instead of the 90th percentile to prevent the model from projecting negative atmospheric CO2 concentrations.

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Authors and Affiliations

  1. Operations Research and Industrial Engineering, The University of Texas at Austin, 204 E. Dean Keeton St., Stop C2200, Austin, TX, 78712, USA

    Milad Eghtedari Naeini, Benjamin D. Leibowicz & J. Eric Bickel

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  1. Milad Eghtedari Naeini
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  2. Benjamin D. Leibowicz
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  3. J. Eric Bickel
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Corresponding author

Correspondence to Benjamin D. Leibowicz.

Appendix

Appendix

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Table 5 Descriptions and values of DICE parameters included in each of the four packages. For more information about the parameters and their roles in the model, see Nordhaus and Sztorc (2013)
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Naeini, M.E., Leibowicz, B.D. & Bickel, J.E. Can you trust a model whose output keeps changing? Interpreting changes in the social cost of carbon produced by the DICE model. Environ Syst Decis 40, 301–320 (2020). https://doi.org/10.1007/s10669-020-09783-y

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