Pricing Monitoring Uncertainty in Climate Policy

Abstract

This article assesses the environmental and economic efficiency of three different approaches to treat monitoring uncertainty in climate policy, namely prescribing uncertainty, setting minimum certainty thresholds and pricing uncertainty through a discount. Our model of the behavior of profit-maximizing agents demonstrates that under the simplest set of assumptions the regulator has no interest in reducing monitoring uncertainty. However, in the presence of information asymmetry, monitoring uncertainty may hamper the economic and environmental performance of climate policy due to adverse selection. In a mandatory policy, prescribing a reasonable level of uncertainty is preferable if the regulator has enough information to determine this level. For voluntary mechanisms, such as carbon offsets, allowing agents to set their own monitoring uncertainty below a maximum threshold or discounting carbon revenues in proportion to monitoring uncertainty are the best approaches for the regulator to mitigate the negative effects of information asymmetry. These conclusions are much more pronounced when agents do not accrue revenues from their mitigation action, other than carbon. Our analysis of monitoring uncertainty under information asymmetry, which results in heterogeneity in the agents’ benefits from abatement, generalizes the classical trade-off between production efficiency and information rents.

Appendices

Appendices

1.1 Appendix 1: Details on the Empirical Values Used in Simulations

For our simulations, we use the data publicly available for energy efficiency and landfill gas flaring (LFG) CDM projects, assuming that they represent a typical investment to reduce GHG emissions. The parameter sets are given in Table 1. The method to derive these parameters from existing databases is described below.

Carbon price p is assumed to be equal to EUR 30 per t $\hbox {CO}_{2}\hbox {e}$, roughly the price of USD 40 at which the price-containment reserve of the Californian ETS is released (EDF 2013) and slightly above the average pre-crisis carbon prices in the EU ETS.

Non-carbon benefits b in energy efficiency projects are assumed to be equal to EUR 150 per t $\hbox {CO}_{2}\hbox {e}$, the potential cost-savings from reduced electricity consumption at the average grid carbon intensity of 0.5 t $\hbox {CO}_{2}\hbox {e}$ per MWh—the average level in the OECD countries in 2010 (Brander et al. 2011)—and the electricity price of EUR 75 per MWh —the average electricity price for industry in the OECD in 2009 (IEA 2012). For landfill gas flaring projects $b = 0$ as there are no additional revenues other than carbon.

Variable monitoring costs parameter m is obtained by fitting the function “$\hbox {costs} = \hbox {m/(relative error)}^\wedge {}2$” on the estimates provided by Powell (1999) for a forestry project. We generalize it to energy efficiency and LFG projects based on two comforting points: the rationale of Powell (1999)—decreasing uncertainty through increased sample size—is consistent with our modelling approach and the resulting variable monitoring costs for a typical uncertainty of 10 % is EUR 30,000, that is half the average total MRV costs (including fixed costs) for these project types, as estimated for the CDM (Shishlov 2015).

Table 1 Parameter sets for numerical simulations

Fixed and variable abatement costs parameters $c_0$ and c are obtained from investments costs in CDM projects of type “Energy efficiency own generation” and “Landfill gas flaring”, as estimated by UNEP Risoe (2014). For each project in the database, an estimate of investment costs per $\hbox {tCO}_{2}\hbox {e}$ abated excluding variable monitoring costs is obtained by subtracting EUR 30,000 to total investment costs (see above). The resulting cumulative marginal abatement cost curve (MACC), obtained from many different projects—245 for energy efficiency and 52 for LFG—is scaled down to a single project to be consistent with our modelling approach. To this end, we assume that the marginal abatement costs of our single project—the size of which is the average size of existing projects of the same type²—are assumed to be proportional to those of the cumulative MACC. $c_{0}$ and c are then obtained by fitting the relevant equation ($\hbox {cost} = \hbox {c}_{0} + \hbox {c} * \hbox {q}^{\wedge } 2$) to this “scaled-down” MACC.

Plugging all parameters in the model results in the production of 9 Mt $\hbox {CO}_{2}\hbox {e}$ for energy efficiency projects and 0.27 Mt $\hbox {CO}_{2}\hbox {e}$ for landfill gas flaring projects under no information asymmetry, both of which are within the range of existing projects in the database (0.08-20 Mt $\hbox {CO}_{2}\hbox {e}$ and 0.07–6 Mt $\hbox {CO}_{2}\hbox {e}$ respectively).

1.2 Appendix 2: Comparison of Outcomes Under Different Scenarios (Analytical Results)

Scenario	Policy option	${{ q}}_{i}^{*}$	${u^{*}}$	${W^{*}}$	UT	$\beta *$
1. No asymmetry	(a) u prescribed	$\frac{p+b}{2c}$	$+\infty$	$\frac{\left( {p+b} \right) ^{2}}{2c}-2c_0$	$+\infty$	NA
2. Asymmetry	(a) u prescribed	$\frac{p\times \left( {1+2u_i \times \varepsilon _i } \right) +b}{2c}$	$\root 4 \of {\frac{cm}{p^{2}}}$	$\frac{\left( {p+b} \right) ^{2}}{2c}-2c_0 -\frac{4pm}{\sqrt{cm}}$	$4\sqrt{p}\times q_i \times \root 4 \of {\hbox {cm}}$	NA
	(b) u limited	$\frac{p\times \left( {1+2u_i \times \varepsilon _i } \right) +b}{2c}$	No obvious solution	No obvious solution	No obvious solution	NA
	(c) u discounted	$\frac{p\times \left( {1+2u_i \times \varepsilon _i } \right) \times \left( {1-\beta } \right) +b}{2c}$	No obvious solution	No obvious solution	No obvious solution	No obvious solution
3. Information bias	(a) u prescribed	$\frac{p\times \left( {1+2u_i \times \varepsilon _i } \right) +b}{2c}$	$\root 4 \of {\frac{4cm}{p^{2}}}$	$\frac{\left( {p+b} \right) ^{2}}{2c}-2c_0 -\frac{4pm}{\sqrt{cm}}$	$4\sqrt{p}\times q_i \times \root 4 \of {\hbox {cm}}$	NA
	(b) u limited	$\frac{p\times \left( {1+2u_i \times \varepsilon _i } \right) +b}{2c}$	$\root 4 \of {\frac{4cm}{p^{2}}}$	$\frac{\left( {p+b} \right) ^{2}}{2c}-2c_0 -\frac{4pm}{\sqrt{cm}}$	$4\sqrt{p}\times q_i \times \root 4 \of {\hbox {cm}}$	NA
	(c) u discounted	$\frac{p+b}{2c}$	$+\infty$	$\frac{\left( {p+b} \right) ^{2}}{2c}-2c_0$	0	$1/\left( {0.5+u} \right)$

1.3 Appendix 3: Comparison of Outcomes Under Different Scenarios (Numerical Results for EE Projects)

	Q1*(Kt $\hbox {CO}_{2}\hbox {e}$)	Q2*(Kt $\hbox {CO}_{2}\hbox {e}$)	Q*(Kt $\hbox {CO}_{2}\hbox {e}$)	W* (M€)	W loss (%)	P2* (M€)	W2* (M€)	UT1 (M€)	UT2 (M€)	UTA (M€)	u1* (%)	u2* (%)	t* (%)	Beta*
Case 1a	9.06	9.06	18.13	1628	0.00	542.02	813.92	271.90	-271.90	0.00	50.00	50.00	50.00	NA
Case 2a	9.19	8.93	18.13	1627	-0.04	790.72	813.59	23.53	-22.87	0.66	4.27	4.27	4.27	NA
Case 2b	9.19	9.03	18.22	1625	-0.19	805.50	811.11	23.52	-5.61	17.92	4.27	1.03	4.27	NA
Case 2c	9.18	9.02	18.20	1624	-0.24	802.54	810.13	78.02	-4.78	73.24	17.91	0.89	NA	1.17
Case 3a	9.19	9.19	18.38	1627	-0.04	837.12	813.59	23.53	23.53	47.05	4.27	4.27	4.27	NA
Case 3b	9.19	9.19	18.38	1627	-0.04	837.12	813.59	23.53	23.53	47.05	4.27	4.27	4.27	NA
Case 3c	9.06	9.06	18.13	1628	0.00	813.92	813.92	0.00	0.00	0.00	50.00	50.00	NA	1/($\mathrm{u}+0.5$)

1.4 Appendix 4: Comparison of Outcomes Under Different Scenarios (Numerical Results for LFG Projects)

	Q1*(Kt $\hbox {CO}_{2}\hbox {e}$)	Q2*(Kt $\hbox {CO}_{2}\hbox {e}$)	Q*(Kt $\hbox {CO}_{2}\hbox {e}$)	W* (M€)	W loss (%)	P2* (M€)	W2* (M€)	UT1 (M€)	UT2 (M€)	UTA (M€)	u1* (%)	u2* (%)	t* (%)	Beta*
Case 1a	0.27	0.27	0.55	4.30	0.00	-6.09	2.15	8.24	-8.24	0.00	50.00	50.00	50.00	NA
Case 2a	0.31	0.24	0.55	4.02	-6.49	1.07	2.01	1.22	-0.94	0.28	6.53	6.53	6.53	NA
Case 2b	0.31	0.26	0.57	3.88	-9.72	1.35	1.87	1.22	-0.52	0.70	6.53	3.39	6.53	NA
Case 2c	0.29	0.25	0.54	3.90	-9.34	1.08	1.78	2.35	-0.43	1.92	16.77	2.97	NA	1.21
Case 3a	0.31	0.31	0.62	4.02	-0.04	3.23	2.01	1.22	1.22	2.43	6.53	6.53	6.53	NA
Case 3b	0.31	0.31	0.62	4.02	-0.04	3.23	2.01	1.22	1.22	2.43	6.53	6.53	6.53	NA
Case 3c	0.27	0.27	0.55	4.30	0.00	2.15	2.15	0.00	0.00	0.00	50.00	50.00	NA	1/($\mathrm{u}+0.5$)

1. Q1*, Q2* and Q* are the amount of emissions reductions in Mt $\hbox {CO}_{2}\hbox {e}$ from Agent 1, Agent 2 and both agents respectively. W* is the total welfare in M€. W loss is the welfare loss compared to case 1a (no asymmetry). P2* is the profit of Agent 2, and W2* the welfare generated by his participation. UT1, UT2 and UTA are the undue wealth transfers from society to Agent 1, Agent 2 or both agents respectively (undue wealth transfers corresponds to the payments of non-existing emissions reductions or to the unpaid emissions reductions. The latter case happens for Agent 2 whose emissions reductions are underestimated. This is why UT2 is often negative). u1* and u2* are the optimal (or prescribed in policy a) monitoring errors for Agent 1 and Agent 2 respectively. t* is the optimal (or prescribed in policy a) maximum tolerated error. Beta is the optimal discount rate

1.5 Appendix 5: Derivations for Case 1a

$$\begin{aligned} E(\pi _{\mathrm{i}} )= & {} p\times q_{\mathrm{i}} +b\times q_{\mathrm{i}} -c_0 -c\times q_{\mathrm{i}}^{2}-\frac{m}{u^{2}}\\ \frac{\partial \pi }{\partial q}= & {} p+b-2cq\\ q_1^{*}= & {} q_2^{*}=\frac{p+b}{2c}\\ q^{*}= & {} q_1^{*}+q_2^{*}=\frac{p+b}{c}\\ W= & {} 2(q_1^{*}\times \left( {p+b} \right) -c_0 -c\times q_1^{{*}^{2}}-\frac{m}{u^{2}})\\ \frac{\partial W}{\partial u}= & {} \frac{4m}{u^{3}}>0\\ u^{*}= & {} +\infty \\ W^{*}= & {} \mathop {\lim }\limits _{u\rightarrow \infty } 2\left( q_1^{*}\times \left( {p+b} \right) -c_0 -c\times q_1^{{*}^{2}}-\frac{m}{u^{2}}\right) \\= & {} 2\left( q_1^{*}\times \left( {p+b} \right) -c_0 -c\times q_1^{{*}^{2}}\right) =\frac{\left( {p+b} \right) ^{2}}{2c}-2c_0 \end{aligned}$$

Note that our assumption that $\varepsilon$ and q are independent is crucial here. Although we think it is generally warranted as $\varepsilon$ is the relative standard error, it may not always be the case.

1.6 Appendix 6: Derivations for Case 2a

Profit of agent i:

$$\begin{aligned} \pi _{\mathrm{i}}= & {} p\times q_{r\hbox {i}} +b\times q_{\mathrm{i}} -c_0 -c\times q_{\mathrm{i}}^{2}-\frac{m}{u^{2}}\\= & {} p\times q_{\mathrm{i}} \times \left( {1+2u\varepsilon _i } \right) +b\times q_1 -c_0 -c\times q_{\mathrm{i}}^{2}-\frac{m}{u^{2}}\\ \frac{\partial \pi _{\mathrm{i}} }{\partial q_{\mathrm{i}} }= & {} p\times \left( {1+2u\varepsilon _i } \right) +b-2cq_{\mathrm{i}}\\ q_{\mathrm{i}}^{*}= & {} \frac{p\times \left( {1+2u\varepsilon _i } \right) +b}{2c} \end{aligned}$$

Welfare:

$$\begin{aligned} W= & {} q_1^{*}\times \left( {p+b} \right) -c_0 -c\times q_1^{{*}^{2}}-\frac{m}{u^{2}}+q_2^{*}\times \left( {p+b} \right) -c_0 -c\times q_2^{{*}^{2}}-\frac{m}{u^{2}}\\= & {} \left( {p+b} \right) \left( {\left( {\frac{p\left( {1+2u} \right) +b}{2c}} \right) +\left( {\frac{p\left( {1-2u} \right) +b}{2c}} \right) } \right) \\&-\,c\left( {\left( {\frac{p\left( {1+2u} \right) +b}{2c}} \right) ^{2}+\left( {\frac{p\left( {1-2u} \right) +b}{2c}} \right) ^{2}} \right) -2c_0 -\frac{2m}{u^{2}}=\frac{\left( {p+b} \right) ^{2}}{2c}\\&-\,\frac{2p^{2}u^{2}}{c}-2c_0 -\frac{2m}{u^{2}}\\ \frac{\partial W}{\partial u}= & {} \frac{4\left( {cm-p^{2}u^{4}} \right) }{cu^{3}}\\ u^{*}= & {} \root 4 \of {\frac{cm}{p^{2}}}\\ W^{*}= & {} \frac{\left( {p+b} \right) ^{2}}{2c}-2c_0 -\frac{2p^{2}\sqrt{\frac{cm}{p^{2}}}}{c}-\frac{2m}{\sqrt{\frac{cm}{p^{2}}}}=\frac{\left( {p+b} \right) ^{2}}{2c}-2c_0 -\frac{4pm}{\sqrt{cm}} \end{aligned}$$

Modelling this situation with a continuum of agents whose $\varepsilon _i$ are equally distributed over [-1;1] leads to a similar result on welfare:

$$\begin{aligned} W= & {} {\int }_{-1}^1 q^{*}\times \left( {p+b} \right) -c\times q^{{*}^{2}}-c_0 -\frac{m}{u^{2}}d\varepsilon \\= & {} {\int }_{-1}^1 \frac{\left( {p+b} \right) }{2c}\left( {p+b} \right) +\frac{\varepsilon up}{c}\left( {p+b} \right) -c\left[ {\frac{\left( {p+b} \right) }{2c}+\frac{\varepsilon up}{c}} \right] ^{2}d\varepsilon -2\left( {c_0 -\frac{m}{u^{2}}} \right) \\= & {} {\int }_{-1}^1 \frac{\varepsilon up}{c}\left( {p+b} \right) -c\left[ {\frac{\left( {p+b} \right) ^{2}}{4c^{2}}+\frac{\varepsilon ^{2}u^{2}p^{2}}{c^{2}}+\frac{2\varepsilon up}{2c^{2}}\left( {p+b} \right) } \right] d\varepsilon \\&+\,2\left( {\frac{\left( {p+b} \right) ^{2}}{2c}-c_0 -\frac{m}{u^{2}}} \right) \\= & {} -\frac{1}{4c}{\int }_{-1}^1 4\varepsilon ^{2}u^{2}p^{2}+\left( {p+b} \right) ^{2}d\varepsilon +2\left( {\frac{\left( {p+b} \right) ^{2}}{2c}-c_0 -\frac{m}{u^{2}}} \right) \\= & {} -\frac{1}{4c}\left( {\frac{8u^{2}p^{2}}{3}+2\left( {p+b} \right) ^{2}} \right) +2\left( {\frac{\left( {p+b} \right) ^{2}}{2c}-c_0 -\frac{m}{u^{2}}} \right) \\= & {} \frac{\left( {p+b} \right) ^{2}}{2c}-\frac{2u^{2}p^{2}}{3c}-2c_0 -\frac{2m}{u^{2}}\\ \frac{\partial W}{\partial u}= & {} \frac{4\left( {cm-p^{2}u^{4}} \right) }{3cu^{3}} \end{aligned}$$

First order condition:

$$\begin{aligned} u^{*}=\root 4 \of {\frac{3cm}{p^{2}}} \end{aligned}$$

The solution is therefore very similar to the representation with two opposite agents:

$$\begin{aligned} u^{*}_{{ continuum}} =u^{*}_{2\,{ agents}} \root 4 \of {3} \end{aligned}$$

Quite intuitively, a uniform distribution of agents over [-1;1] decreases the inefficiency generated by monitoring uncertainty compared to a distribution where $\varepsilon _i$ clusters on {-1;1} since the effect of adverse selection is lower for values of $\varepsilon _i$ closer to zero. As a result, the cost of monitoring weights relatively more on welfare and u* is 30 % higher.

1.7 Appendix 7: Derivations for Case 2b

For the case of underestimation of emissions reductions:

$$\begin{aligned} \frac{\partial \pi }{\partial u_{2b,2} }= & {} -2pq_{2b,2} +\frac{2m}{u_{2b,2}^{3}}\\ u_{2b,2}^{*}= & {} \root 3 \of {\frac{m}{pq_{2b,2} }} \end{aligned}$$

1.8 Appendix 8: Derivations for Case 2c

$$\begin{aligned} \pi _i= & {} p\times q_i \times \left( {1+2\varepsilon _i u_i } \right) \times \left( {1-\beta u_i } \right) +b\times q-c_0 -c\times q^{2}-\frac{m}{u_i^{2}}\\ \frac{\partial \pi _i }{\partial q}= & {} p\times \left( {1+2\varepsilon _i u_i } \right) \times \left( {1-\beta u_i } \right) +b-2cq\\ q_i^{*}= & {} \frac{p\times \left( {1+2\varepsilon _i u_i } \right) \times \left( {1-\beta u_i } \right) +b}{2c} \end{aligned}$$

1.9 Appendix 9: Derivations for Cases 3a and 3b

For both agents:

$$\begin{aligned} \pi _1 =\pi _2= & {} p\times q\times \left( {1+2u} \right) +b\times q-c_0 -c\times q^{2}-\frac{m}{u^{2}}\\ \frac{\partial \pi }{\partial q}= & {} p\times \left( {1+2u} \right) +b-2cq \\ q^{*}= & {} \frac{p\times \left( {1+2u} \right) +b}{2c} \end{aligned}$$

Welfare:

$$\begin{aligned} W= & {} 2\left[ {\left( {p+b} \right) \left( {\frac{p\left( {1+2u} \right) +b}{2c}} \right) -c\left( {\frac{p\left( {1+2u} \right) +b}{2c}} \right) ^{2}-c_0 -\frac{m}{u^{2}}} \right] \\= & {} \frac{\left( {p+b} \right) ^{2}}{2c}-\frac{2p^{2}u^{2}}{c}-2c_0 -\frac{2m}{u^{2}}\\ \frac{\partial W}{\partial u}= & {} \frac{4\left( {cm-p^{2}u^{4}} \right) }{cu^{3}}\\ u^{*}= & {} \root 4 \of {\frac{cm}{p^{2}}}\\ W^{*}= & {} \frac{\left( {p+b} \right) ^{2}}{2c}-2c_0 -\frac{2p^{2}\sqrt{\frac{cm}{p^{2}}}}{c}-\frac{2m}{\sqrt{\frac{cm}{p^{2}}}}=\frac{\left( {p+b} \right) ^{2}}{2c}-2c_0 -\frac{4pm}{\sqrt{cm}} \end{aligned}$$

1.10 Appendix 10: Derivations for Cases 3c

For both agents:

$$\begin{aligned} \pi= & {} p\times q\times \left( {1+2\varepsilon u} \right) \times \left( {1-\beta u} \right) +b\times q-c_0 -c\times q^{2}-\frac{m}{u^{2}}\\ \frac{\partial \pi }{\partial q}= & {} p\times \left( {1+2u} \right) \times \left( {1-\beta u} \right) +b-2cq\\ q^{*}= & {} \frac{p\times \left( {1+2u} \right) \times \left( {1-\beta u} \right) +b}{2c} \end{aligned}$$