Endogenizing the Cap in a Cap-and-Trade System: Assessing the Agreement on EU ETS Phase 4

Abstract

In early 2018, a reform of the world’s largest functioning greenhouse gas emissions cap-and-trade system, the EU Emissions Trading System (ETS), was formally approved. The reform changed the main principles of the system by endogenizing the emissions cap. We show that the emissions cap is now affected by the allowance demand and is therefore no longer set directly by EU policymakers. As a consequence, national policies that reduce allowance demand can now reduce long-run cumulative emissions, which is not possible in a standard cap-and-trade system. Using a newly developed dynamic model of the EU ETS, we show that policies that reduce allowance demand can have substantial effects on cumulative emissions after the reform. Model simulations also suggest that the reform reduces long-run cumulative emissions and, to a lesser extent, reduces emissions in the short run. Even so, the reform has a small short-run impact on the currently large allowance surplus.

Appendices

Appendix 1: Model with Explicit Allowance Market

In the main text, we abstract from modeling the allowance market. This appendix shows that an inclusion of the allowance market would not affect the simulation outcomes presented in the main text.

Let the profit function of the representative firm, $F(\cdot )$, be given by:

$$F(e_{t} ,A_{t} ,y_{t}^{All} ,y_{t} ) = f(e_{t} ,A_{t} ) - p_{t} (y_{t} - y_{t}^{All} ),$$

where ${p}_{t}$ is the market price for emission allowances, ${y}_{t}^{All}$ is the amount of freely allocated allowances, and ${y}_{t}$ is the net allowance demand of the firm: the sum of freely allocated allowances and allowances purchased by the representative firm (the latter may be negative). A net purchase of allowances (${y}_{t}>{y}_{t}^{All}$) has a negative effect on the firm’s profits and vice versa. Note that the firm takes both ${p}_{t}$ and ${y}_{t}^{All}$ as given.

The representative firm maximizes $F(\cdot )$ subject to the dynamic allowance constraint with respect to emissions and the net allowance intake. Assuming an interior solution, the first-order conditions associated with the problem imply:

$$\lambda_{t} = p_{t}$$

$$f_{e}^{^{\prime}} (e_{t} ,A_{t} ) = \lambda_{t}$$

$$\lambda_{t + 1} = (1 + r)\lambda_{t}$$

where ${\lambda }_{t}$ is the shadow price of emission allowances. It is easy to derive the optimality conditions from Sect. 3.2 from these equations.

The first condition shows that if there is allowance trading, the price of allowances equals the shadow price of emission allowances, which equals the marginal profit of emissions as stated in the main text.

The arbitrage condition ${p}_{t}={f}_{e}^{^{\prime}}({e}_{t},{A}_{t})$ ensures an equilibrium on the market for allowances. The condition ensures that along the optimal emission path, the firm is indifferent between selling an allowance, earning ${p}_{t}$, and using the allowance, earning ${f}_{e}^{^{\prime}}({e}_{t},{A}_{t})$. If it was the case that ${p}_{t}>{f}_{e}^{^{\prime}}({e}_{t},{A}_{t})$, the firm would sell as many allowances as possible, while the firm would demand more allowances if ${p}_{t}<{f}_{e}^{^{\prime}}({e}_{t},{A}_{t})$. As there is only one agent demanding allowances in the model – the representative firm – and since the amount of actioned allowances, ${y}_{t}^{Auc}={y}_{t}-{y}_{t}^{All}$, is determined by the trading system (and unaffected by the firm’s behavior in period $t$), it must be such that in equilibrium ${p}_{t}={f}_{e}^{^{\prime}}({e}_{t},{A}_{t})$.

As the first-order conditions boil down to the same optimality condition as in the model presented in the main text, the solution to the firm’s problem is unchanged by the inclusion of the allowance market. Accordingly, the extended model leads to the same simulation outcomes as the model presented in the main text.

One potential concern is that when the firm stops saving allowances, ${B}_{t+1}=0$, one could end in a situation where $F(\cdot )$ is negative while $f(\cdot )$ is positive. In this case, the two models would have different solutions: the firm would shut down production in the extended model, while it would continue production in the model presented in the main case.

However, one can show that this situation will never occur. Plotting the equilibrium allowance price into the per period profit function:

$$F(e_{t} ,A_{t} ,y_{t}^{All} ,y_{t} ) = f(e_{t} ,A_{t} ) - f_{e}^{^{\prime}} (e_{t} ,A_{t} )y_{t}^{Auc} .$$

The amount of auctioned allowances can be expressed as: ${y}_{t}^{Auc}={\eta }_{t}{y}_{t}$, where ${\eta }_{t}\in \left[\mathrm{0,1}\right].$ When there is no allowance saving, ${B}_{t+1}=0$, then ${e}_{t}\ge {y}_{t}$. Since $f(\cdot )$ is a concave function and $f\left(0,{A}_{t}\right)=0$ it must hold that: $f\left({e}_{t},{A}_{t}\right)-{f}_{e}^{^{\prime}}\left({e}_{t},{A}_{t}\right){e}_{t}>0.$ It then follows that:

$$F(e_{t} ,A_{t} ,y_{t}^{All}, y_t ) = f(e_{t} ,A_{t} ) - f_{e}^{^{\prime}} (e_{t} ,A_{t} )\eta_{t} y_{t} > 0.$$

Accordingly, when ${B}_{t+1}=0$ then $F(\cdot )$ is positive whenever $f\left(\cdot \right)$ is positive.

We also note that the concavity of $f(\cdot )$ ensures that the firm can always ensure that $F(\cdot )$ is positive. This follows from the fact that the firm can always set $e_{t} = y_{t}^{Auc}$ in which case:

$$F(y_{t}^{Auc} ,A_{t} ,y_{t}^{All} ,y_{t} ) = f(y_{t}^{Auc} ,A_{t} ) - f_{e}^{^{\prime}} (y_{t}^{Auc} ,A_{t} )y_{t}^{Auc} > 0.$$

Appendix 2: Actual and simulated emissions for the period 2008–2017

This appendix shows that the calibrated model leads to a good fit between simulated and historical EU ETS emissions. Specifically, we focus on the period 2008–2017, as the first phase of the EU ETS (2005–2007) was a test phase and emission allowances from this phase could not be saved for future phases. The simulation, therefore, starts in 2008, where the allowance surplus was zero, and it ends in 2110. The MSR is absent in this simulation, as the introduction of the MSR was unexpected in 2008. We also disregard the change to the linear reduction factor from 2021, as this revision is part of the latest reform and probably unexpected in 2008, although this assumption has little effect on the emission levels for the period 2008–2017 found here. One limitation of this exercise is that we ignore the impact of actual and expected revisions to the ETS through the first part of the simulated period like the MSR reform from 2015.

Figure 4 shows the simulated emission path and actual emissions for the period 2008–2017. The two emission paths follow each other closely over the period. The simulation overestimates emissions toward the end of the period. This is expected, as the simulation does not take the MSR reform from 2015 and the expectations about the latest ETS reform into account. Both reforms reduce the available amount of allowances in the short and medium run, resulting in lower short-run emissions.

Fig. 4

Source: Own calculations and European Environment Agency (2018)

Actual and simulated CO₂ emissions, 2008–2017