The influence of negative emission technologies and technology policies on the optimal climate mitigation portfolio

Abstract

Combining policies to remove carbon dioxide (CO₂) from the atmosphere with policies to reduce emissions could decrease CO₂ concentrations faster than possible via natural processes. We model the optimal selection of a dynamic portfolio of abatement, research and development (R&D), and negative emission policies under an exogenous CO₂ constraint and with stochastic technological change. We find that near-term abatement is not sensitive to the availability of R&D policies, but the anticipated availability of negative emission strategies can reduce the near-term abatement optimally undertaken to meet 2°C temperature limits. Further, planning to deploy negative emission technologies shifts optimal R&D funding from “carbon-free” technologies into “emission intensity” technologies. Making negative emission strategies available enables an 80% reduction in the cost of keeping year 2100 CO₂ concentrations near their current level. However, negative emission strategies are less important if the possibility of tipping points rules out using late-century net negative emissions to temporarily overshoot the CO₂ constraint earlier in the century.

Appendix: Model parameterization

This appendix presents the parameterizations of the portfolio selection model. It describes the probability distributions for technological outcomes, the functional representation of induced technological change (ITC), and the cost functions used in the objective function.

The state variables α _t , γ _t , and ϕ _t record the technology outcomes that apply to period t (Table 1). These outcomes are each drawn from a three-point probability distribution similar to the one in Baker and Adu-Bonnah (2008). The main differences are that here the distribution is anchored by the previous period's realized outcome and that here the targeted level of technology depends not just on the previous period's R&D funding but also on its abatement policy. Abatement can induce technological change via functions $ITC_{\alpha}:\mu_t \rightarrow [0,\bar{\alpha}]$ for carbon-free R&D and $ITC_{\gamma}:\mu_t \rightarrow [0,\bar{\gamma}]$ for emission intensity R&D. ITC may occur through private R&D or through learning-by-doing. The technology target for a given period comes from summing the targets produced by abatement via ITC and by public R&D, provided the total target does not exceed the exogenously fixed maximal level. The three possibilities are that technology does not change, that the technology target is attained, and that the technology target is surpassed to yield the best possible outcome:¹⁰

$$Pr[\alpha_t=\alpha_{t-1}] = p_{\alpha}(1- \min[\hat{\alpha}_{t-1} + ITC_{\alpha}(\mu_{t-1}),\bar{\alpha} ] ) \label{equ_prob_alpha_target}\\[3pt] $$

(3)

$$Pr[\alpha_t=\min(\hat{\alpha}_{t-1}e+ ITC_{\alpha}(\mu_{t-1}),\bar{\alpha} )] = 1-p_{\alpha} \label{equ_prob_alpha_exact}\\[3pt] $$

(4)

$$Pr[\alpha_t=\bar{\alpha}]e= p_{\alpha}(\min[\hat{\alpha}_{t-1} + ITC_{\alpha}(\mu_{t-1}),\bar{\alpha} ])\label{equ_prob_alpha_high}\\[3pt] $$

(5)

$$Pr[\gamma_t=\gamma_{t-1}]e= p_{\gamma}(1-\min[\hat{\gamma}_{t-1} + ITC_{\gamma}(\mu_{t-1}),\bar{\gamma} ]) \label{equ_prob_gamma_target}\\[3pt] $$

(6)

$$Pr[\gamma_t=\min(\hat{\gamma}_{t-1}e+ ITC_{\gamma}(\mu_{t-1}),\bar{\gamma} )] = 1-p_{\gamma} \label{equ_prob_gamma_exact}\\[3pt] $$

(7)

$$Pr[\gamma_t=\bar{\gamma}]e= p_{\gamma}(\min[\hat{\gamma}_{t-1} + ITC_{\gamma}(\mu_{t-1}),\bar{\gamma} ]) \label{equ_prob_gamma_high}\\[3pt] $$

(8)

$$Pr[\phi_t=\phi_{t-1}]e= p_{\phi}(1-\hat{\phi}_{t-1}) \label{equ_prob_phi_target}\\[3pt] $$

(9)

$$Pr[\phi_t=\hat{\phi}_{t-1}]e= 1-p_{\phi} \label{equ_prob_phi_exact}\\ $$

(10)

$$Pr[\phi_t=\bar{\phi}]e= p_{\phi} \hat{\phi}_{t-1} \label{equ_prob_phi_high} $$

(11)

TheeITC functions allow us to see how beliefs about the effectiveness of abatement at producing each type of technological change affect optimal policy. Unfortunately, the relationship between ITC and public R&D cannot be specified using empirical results (Pizer and Popp 2008). Instead, we translate the fraction of emissions abated into the equivalent of some fraction of maximal R&D funding. First, 0% abatement does not affect the R&D targets. Second, we require ``perfect'' ITC to translate a given percentage abatement into R&D targets that are the same percentage of their maximal levels. This implies that $\mu=ITC_{\alpha}(\mu)/\bar{\alpha}=ITC_{\gamma}(\mu)/\bar{\gamma}$ under perfect ITC. A parameter ν controls the effectiveness of ITC and proxies for the severity of innovation market failures. If ν = 0, then ITC for that technology is ``perfect'' in the sense that a percentage of full abatement produces an equivalent percentage of the maximal technology target. If ν > 0, then ITC for that technology is ``imperfect'' in the sense that a percentage of full abatement translates into a smaller percentage of the maximal technology target:

$$ITC_{\alpha}(\mu_t) = \max (0,(\mu_t-\nu_{\alpha})\bar{\alpha}) \label{equ_itc_alpha}\\ $$

(12)

$$ITC_{\gamma}(\mu_t)e= \max (0,(\mu_t-\nu_{\gamma})\bar{\gamma}) \label{equ_itc_gamma} $$

(13)

Wheneν _α and ν _γ are positive, abatement may not produce any ITC unless it reaches a sufficiently high level. This representation enables us to vary the effectiveness of ITC across scenarios and also to make ITC differentially effective for emission intensity technologies and carbon-free. Under the assumption that emission intensity technologies represent incremental changes that are more responsive to carbon price signals, the base case parameterization assumes that ITC is stronger for emission intensity technologies than for carbon-free technologies.

It remains to define cost functions for abatement, NET deployment, and public R&D targets. First, the cost of abatement depends on the level of abatement and on available technologies. c(μ _t ,α _t ,γ _t ) is the average cost in the base case of abating fraction μ _t of BAU emissions e _t given R&D outcomes α _t and γ _t :

$$ c(\mu_t,\alpha_{t},\gamma_{t}) = \ \left\{ \begin{array}{ll} \min \big[ \frac{z_t}{\mu_t}d\left( z_t \right),(1-\alpha_{t})d(\mu_t) \big] & \text{for base case abatement cost} \\ \min \big[ \frac{z_t}{\mu_t}\tilde{d}\left( z_t \right),(1-\alpha_{t})\tilde{d}(\mu_t) \big] & \text{for low-cost abatement} \\ \end{array} \right. $$

(14)

where $z_t \equiv \max \left[ (\mu_t - \gamma_{t})/(1-\gamma_{t}),0 \right]$ as in Baker and Adu-Bonnah (2008). The top expression holds for the base case parameterization and for most others, but the two parameterizations with low-cost abatement use the bottom expression. Both expressions give abatement cost with time t technology as a function of abatement cost with initial technology, but they differ in the function (d(·) or $\tilde{d}(\cdot)$) used to assign the cost with initial technology. In either case, zero abatement costs nothing ($d(0)=\tilde{d}(0)=0$), and the normalization is d(1) = 100. The range of c(·) is [0,100]. The two terms inside the minimization operators give the effect of emission intensity technologies and carbon-free technologies, and the use of the minimization operator assumes that the cheapest type of technology is used at each level of abatement (compare Blyth et al. 2009). Hoogwijk et al. (2008) reported the carbon price yielding aggregate global abatement of 25% to be between $10/tCO₂ and $40/tCO₂ and the carbon price yielding aggregate global abatement of 50% to be between $60/tCO₂ and some level well above $100/tCO₂. We develop the base case and the low-cost average cost representations by assuming that marginal costs follow a geometric progression at the discretized points and increase linearly between those points.¹¹ This yields the normalized values:

$$\text{Base case: } \;d(0.25)=2.4, \, d(0.50)=8.4, \, d(0.75)=28, \, d(1)=100 $$

$$\text{Low-cost: } \;\tilde{d}(0.25)=2.4, \, \tilde{d}(0.50)=6.0, \, \tilde{d}(0.75)=12, \, \tilde{d}(1)=27 $$

When z _t falls between the above discretization for μ, we define the cost function by assuming average cost is linear between these discretized points. We only model endogenous technological change, so abatement cost does not change unless carbon-free or emission intensity technology changes as described in Eqs. 3 through 11.

A second type of cost function applies to deployment κ _t of NETs. We represent NETs as having constant marginal cost, which is determined by adjusting the base case average cost of an exogenous level x of period 1 abatement for the outcome ϕ _t of NET R&D:

$$ f(\kappa_t,\phi_t)=\kappa_t (1-\phi_t) \, d(x) $$

(15)

Converted to non-normalized costs, x = 0.75 in a low-cost parameterization corresponds to NETs costing $115/tCO₂, which is near the low end of recent estimates, and x = 1 in the base case parameterization corresponds to NETs costing $415/tCO₂, which is above many recent estimates (e.g., Rhodes and Keith 2005; Keith et al. 2006; Uddin and Barreto 2007; Stolaroff et al. 2008; Keith 2009; Pielke 2009).

Finally, a third type of cost function determines how much R&D funding it takes to select a technology target. We assume that the funding that it takes to aim for the chosen public target depends not on the level of the target but on the percentage of the maximal target that it represents. We treat the cost of reaching a percentage of the maximal level of R&D as being an exogenous fraction (specifically: y _g , y _h y _g , or y _j ) of the base case cost for abating the same percentage of period 1 emissions:

$$g\left(\frac{\hat{\alpha}_t}{\bar{\alpha}}\right) = y_g*d\left(\frac{\hat{\alpha}_t}{\bar{\alpha}}\right)*\frac{\hat{\alpha}_t}{\bar{\alpha}}*e_1 \\ $$

(16)

$$h\left(\frac{\hat{\gamma}_t}{\bar{\gamma}}\right)e= y_h*g\left(\frac{\hat{\gamma}_t}{\bar{\gamma}}\right) \\ $$

(17)

$$j\left(\frac{\hat{\phi}_t}{\bar{\phi}}\right)e= \frac{y_j}{y_g}*g\left(\frac{\hat{\phi}_t}{\bar{\phi}}\right) $$

(18)

We represent carbon-free R&D costs in terms of average abatement cost because this provides a natural reference point while satisfying the desired property of decreasing returns, and we define the cost of emission intensity R&D as some fraction y _h of the cost of carbon-free R&D. We make abatement cost and R&D cost of similar magnitude because, first, we are looking at the cost of shifting the whole abatement cost curve and, second, we aim to gain more insight than would be obtained by making R&D very cheap or very expensive.

The base case parameters in these functions and probability distributions are chosen to represent values that accord with intuition about, for instance, emission intensity technology being more responsive to abatement than is carbon-free technology. This model's parameterizations are used as demonstrations to aid intuition and to provide a framework for assessing the implications of different beliefs; the results should not be read as either predictive or prescriptive. Fourteen alternative parameterizations reflect different beliefs about technological change, cost functions, or discounting (Table 3). If all parameterizations produce similar results, then we have more confidence that the results are robust to specific values. A more thorough assessment of robustness should also include structural variation in, for instance, the form of the cost functions, the form of the ITC functions converting abatement into R&D targets, and the form of the probability distribution for technological change.

Table 3 The 15 parameter scenarios explored with the numerical model