Abstract
The social cost of carbon (SCC) and the climate-economic models underlying this prominent US climate policy instrument are heavily affected by modeler opinion and therefore may not reflect the views of most climate economists. To test whether differences exist, we recalibrate key uncertain model parameters using formal expert elicitation: a multi-question online survey of individuals who have published scholarship on the economics of climate change, with 165 to 216 respondents, depending on the question. Survey questions on the magnitude of climate impacts and appropriate discount rates revealed that prevailing views differ from prominent IAMs, including DICE. We calibrate the DICE damage functions and discount rates to reflect the mean and median survey responses, respectively, recognizing these two parameters’ differing sources of uncertainty (positive versus normative). We find a 16-fold higher SCC than the base DICE-2013R assumptions, with a range of 11- to 24-fold under alternative modeling assumptions (using the DICE-2016R2 model version and calibrating damages to median rather than mean responses). Our findings support a 7- to 13-fold SCC increase for different respondent subgroups even when we exclude the potential for catastrophic climate impact shocks. Our results reveal a significant disparity between IAMs and the broader community of scholars publishing in this field.
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Notes
As an alternative, Pindyck (2019) develops a “simplified” model whose calibration requires economists to provide information outside their area of expertise, specifically the CO2 emission reductions necessary to avoid a 20% loss of GDP; this is problematic as expert judgment is “not appropriate when a field does not have relevant scientific expertise and related measurements” (Colson and Cooke 2018). In comparison, maintaining IAM structure allows our survey to avoid overly complex questions for which respondents do not have a prior benchmark.
The social choice–based approach starts with a group of individuals with heterogeneous preferences who must dynamically manage a consumption asset. To bridge the divide between the competing policy positions, a “representative” SDR is derived to ensure a Pareto-efficient consumption allocation over time. Differing setups and initial assumptions result in differing aggregation rules (Gollier and Zeckhauser 2005; Heal and Millner 2014).
In the setup of Millner and Heal (2018), a series of committees must each come to an agreement over the pure rate of time preference over which they disagree. As all committee members share the same elasticity of marginality utility of consumption by assumption, this is equivalent to selecting the social discount rate (by the simple Ramsey rule). According to the Millner-Heal voting procedure, the committee selects the median pure rate of time preference of its committee members.
Therefore, we calculate the more policy-relevant marginal SCC instead of an average SCC.
The DICE-2013R’s warming scenario is a 3 °C increase by 2080, regardless of the preference and damage function assumptions that we apply. Therefore, our damage function (and corresponding SCC estimates) should be considered a lower bound, as society will have 10 years less to adapt to a 3 °C change than our survey implies.
Placing open-ended questions on the second page of the survey likely leads to a reduced response rate for these questions, as some respondents did not complete the entire survey.
While DICE-2013R and DICE-2016R2 employ quadratic damage functions, earlier DICE models employed an inverse quadratic function that ensured damages were less than output. Nordhaus calibrated these earlier models using an enumerative method, which included a measurement of certainty-equivalent damages of catastrophic events. For DICE-2013R and DICE-2016R2, Nordhaus moved to a meta-analysis strategy that essentially omits catastrophic impacts (Howard 2014). As we did not ask respondents about the appropriate functional form or about climate damages for a higher temperature scenario (enabling the calibration of the DICE damage function’s exponent), we believe that it is prudent to maintain Nordhaus’ current assumptions.
Applying the arithmetic mean is the standard approach for aggregating survey responses and distributions (Lorenz et al. 2011) including for climate damage surveys (Nordhaus 1994b; Roughgarden and Schneider 1999; Gerst et al. 2010; Pindyck 2019). The popularity of the mean is based on the approach’s ability to minimize forecast error: (1) the sample mean collapses around the true value as sample size increases, according to the central limit theorem (Freeman and Groom 2015), and (2) recent work demonstrates that aggregating expert assessments using the mean outperforms the median in terms of accuracy of prediction (Colson and Cooke 2018).
This assumption is in line with 97% of responses to Question 5, but not strictly with the 3% of responses predicting that climate change will most likely have a 0% impact on GDP this century (according to their responses to Questions 5 and 13).
A potential interpretation of our calibrations of δ and η, which internalize these alternative discount rules, is as rough approximations of the representative rule (see Online Resource 4).
Additionally, Millner and Heal (2018) have a simple and transparent decision rule, and its setup of committees deciding on a “representative” SDR matches our structure of a survey of experts.
In Drupp et al. (2018), the coefficient of variation is 1.3 for δ and 0.6 for η. Additionally, in DICE, growth rates decline over time to steady state making uncertainty over η less relevant over time to the uncertainty of the social discount rate. Given the 300-year time horizon of DICE, the uncertainty over δ should be expected to dominate.
For example, our survey scenario focuses on a 3 °C increase by 2090 following Nordhaus (1994a); this 3 °C comes earlier in DICE-2016R2 than in DICE-2013R, i.e., 2075 instead of 2080, moving it further from our survey scenario.
Running DICE-2016R2 on its optimal setting, we find that a maximum temperature increase of 2 °C is impossible for any level of climate damages and preference parameter values. Exploring the damage and preference parameters, we find a minimum of 2.32° for the maximum temperature increase. This infeasibility limit is the result of Nordhaus (2018) recalibrating DICE-2016R2 to replicate long-run climate dynamics instead of short-run climate dynamics. As the infeasibility of a 2 °C maximum temperature breaks from mainstream global policy and diverges drastically from DICE-2013R (published only 3 years earlier), we are wary of this recalibration. As recalibrating the climate model is beyond the scope of this paper, we believe providing an SCC range with modeling from both DICE-2013R and DICE-2016R2 is more transparent for policymakers.
While Crost and Traeger (2013) find that running Monte Carlo simulations over uncertain parameters in deterministic IAMs can lead to incorrect optimal taxes, their results do not apply to the BAU emissions path upon which the SCC is calculated.
We find that our results are robust to recalibrating the initial level of capital; see Online Resource 7.
When we run DICE with a normative discount rate, the model shifts slightly off its traditional BAU scenario. As we cannot impose a descriptive rate, an alternative is to maintain DICE’s socioeconomic scenario (capital, output, population, and emissions) by constraining the savings rate to its base value. Essentially, this allows for a difference between private and social discount rates. We find our SCC estimates are robust (see Online Resource 7).
There was almost universal agreement that there will be a negative effect by the end of the century (97%).
The mean responses for different subgroups of respondents (as defined by the number, type, and topic of their publications) ranged from − 6.3 to − 10.6%.
The mean responses for different subgroups of respondents ranged from 8.6 to 16%.
Assuming a normal distribution, we estimate this probability using the mean and standard deviation provided in the Supplementary Material of Nordhaus (2018). As Nordhaus never conducted a similar uncertainty analysis for DICE-2013R, a comparison with DICE-2013R is not possible.
Except for Question 15 on the probability of a catastrophic climate outcome, the above damage results are relatively unaffected by trimming inconsistent responses. For Question 15, trimming decreases the untrimmed mean of 22% by one-third. This highlights the need for careful attention in construction of climate surveys related to catastrophic impacts.
Given the equivalence of our results and Drupp et al. (2018) with respect to the SDR, it is safe to assume that the mean and median found in Drupp et al. (2018) with respect to the pure rate of time preference (δ) also apply to our sample. This supports our earlier assumption that the median δ equals the median value in Drupp et al. (2018).
For economist who responded, Pindyck (2019) finds mean and median discount rates of 2.7% and 2.0%, respectively.
The median value is unaffected by alternative trimming assumptions. However, the mean value is sensitive to trimming, with a value of 3.1% with no trimming.
This should be less of a concern for the SDR given our results match SDR experts from Drupp et al. (2018).
The ideal parameter is “measurable in theory but not in practice” with “related measurements” available (Colson and Cooke 2018).
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Howard, P.H., Sylvan, D. Wisdom of the experts: Using survey responses to address positive and normative uncertainties in climate-economic models. Climatic Change 162, 213–232 (2020). https://doi.org/10.1007/s10584-020-02771-w
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DOI: https://doi.org/10.1007/s10584-020-02771-w