We now shift our focus to the impact of increased variability/uncertainty on the cost of regulation and the value of managerial flexibility. Assessing the impact of an environment with increased uncertainty is important in our setting, as we consider a dynamic investment decision problem over a long time horizon. We will focus on some main sources of uncertainty in the context of an ETS designed to reach emission reduction targets in an industry. In particular, we examine the impact of uncertainty concerning pollution demand, regulatory requirement, and regulatory penalty intensity. It is of interest to understand how these different risk sources influence the decision problem concerning investments in clean technologies. Such an analysis can also yield im-portant policy implications by shedding light on how the ship owner’s incentive to invest under the industry-wide ETS is affected by certain policy design choices and by changes in the uncertainty
of the environment.
3.6.1 Increased uncertainty in regulatory intensity
In this subsection, we examine the impact of increased uncertainty in regulatory intensity and its impact on the value of investing in clean technologies. Even though policy makers have formalized their ambitious commitments to the green transition process, it is unclear what the appropriate consequences should be if the emission reduction targets are not met. From an economics perspec-tive, the policy maker is deemed to incorporate certain consequences, such as a monetary penalty in a maritime ETS mechanism at the end of the regulation horizon to make its commitment to the defined reduction targets credible to ship owners. As this section shows, incorporating a convex penalty function in the policy design and the uncertainty around its intensity have far-reaching consequences for ship owners.
Recall that the regulatory penalty intensity is expressed by the random variableδ ∈∆ = (1, M] with E[δ] =µδ and finite variance σδ, where σδ can be interpreted as a measure of the uncer-tainty concerning regulatory intensity. To capture an increase in the unceruncer-tainty, we consider our base model and examine two scenarios for the regulatory intensity. In particular, we reflect an increase in regulatory intensity uncertainty by adding an independent, zero-mean disturbance to the random variableδ, i.e. a mean-preserving spread (for a formal definition of a mean-preserving spread please refer to the appendix). Note that this impliesE[ ¯δ] =E[δ] and ¯σδ ≥σδ. In other words, this allows us to capture the scenario where the uncertainty concerning the regulatory inten-sity is increased while preserving the ship owner’s expectations with regard to the penalty inteninten-sity.
Theorem 2: If uncertainty in the regulatory intensity increases, then (i) the costs of regulation J0(x0) and (ii) the value of managerial flexibility increase. Hence, the incentive to invest in clean technologies increases.
Theorem 2 highlights the effect of increased uncertainty in regulatory intensity. The “added noise”
, , Penalty Pollution
Demand
Figure 3.3: Graphical representation of an increase in regulatory intensity
in the higher uncertainty scenario increases the variability of δ, if compared to the lower uncer-tainty scenario. Scrutinizing the convex shape of the penalty function, this higher variability leads to an increase in the expected penalty at the end of the regulation horizon T. Since this increase converts to higher expected costs at stage t = 0 and a higher value of managerial flexibility, the incentive to invest in clean technologies increases.
Figure (3.3) provides intuition about the impact of increased regulatory intensity on the terminal penalty as a function of pollution demand. In the graph, the red curve indicates the high intensity case and the blue curve the low intensity one. Similar to this illustrative example, increasing the uncertainty in regulatory intensity leads to, informally speaking, an increase in the “convexity” of the expected terminal penalty function and, thus, a higher expected penalty. It is worth noting that the magnitude of the effect stated in Theorem 2 depends on the initial pollution demand x0. Moreover, the expected costs and value of managerial flexibility are monotone nondecreasing in x0. Hence, the investment incentive due to uncertainty around the regulatory intensity is also monotone nondecreasing inx0. For instance, if a ship owner’s initial pollution demand,x0, is close to the expected regulatory requirement E[c], their incentive to invest in clean technologies will be smaller when compared to a ship owner with a higher pollution demand.
In summary, higher uncertainty concerning regulatory intensity increases a ship owner’s expected costs and the value of managerial flexibility. Therefore, such a signal leads to higher investment levels under the optimal investment policy. Furthermore, the magnitude of such an incentive is monotone nondecreasing in the initial pollution demand of the ship owner. Hence, uncertainty around the regulatory intensity has a higher impact on ship owners who are further from the ex-pected emission target level.
3.6.2 Increased uncertainty in regulatory requirement
We now turn the attention to the regulatory requirement. Assume the regulator defines a certain target for emissions c to reach emission reduction goals at the terminal stage. We examine the impact of the increased uncertainty of such a measure on a ship owner’s costs of regulation and value of managerial flexibility. This is an important source of regulatory risk for ship owners. First, emission reduction targets to support global climate change goals are naturally uncertain, as they are informed by the latest projections from climate change research and the progress made globally to combat climate change over the time horizon. Second, emission reduction targets are defined for the whole maritime industry (see, e.g., IMO GHG strategy postulated by the IMO), and a ship owner’s investments in clean technologies are based on their specific reduction in carbon emissions.
How the regulator utilizes the private information about the ship owner’s demand for pollution obtained in the auction to mandate specific reduction targets is a priori uncertain for the ship owner.
In our model, a measure of regulatory requirement uncertainty is the finite variance σc of the emission targetc. To assess the impact of increased uncertainty, we examine two uncertainty sce-narios for the regulatory requirement. To ensure a meaningful comparison, we assume that the random variables concerning the regulatory requirement in the two scenarios have the same mean but different variability due to one random variable being a mean-preserving spread of the other.
In other words, we consider two scenarios characterized by E[ ¯c] = E[c], and ¯σc ≥ σc. This formulation allows us to model the scenario where the ship owners has less information about the precise regulatory requirement at the terminal stage. The next theorem describes the impact of
increased uncertainty in the regulatory requirement on the costs of regulation and value of man-agerial flexibility.
Theorem 3: If uncertainty in the regulatory requirement increases, then (i) the costs of regulation J0(x0) and (ii) the value of managerial flexibility increase. Hence, the incentive to invest in clean technologies increases.
The results of Theorem 3 might seem counterintuitive at first sight, as one could expect that the higher the uncertainty of the regulatory requirement, the more attractive it would be to defer in-vestments in clean technologies. The reason for this (myopic) intuition is that a higher uncertainty of regulatory requirements would make the effect of an (irreversible) investment in clean technolo-gies to cope with emission targets less known, which consequently could both reduce the value captured by the ship owner and the benefit for investing (i.e., the value of flexibility). It turns out this is not the case. In fact, an increase in the uncertainty of the regulatory requirement increases both the regulation costs incurred by the ship owner and the value of managerial flexibility, thus yielding increased investment levels under the higher uncertainty scenario. The additional incen-tive to invest can be interpreted as a hedge against extreme scenarios. In the face of uncertainty around the target emission values, the proposed regulation mechanism preserves its incentive for ship owners to invest and does not create an incentive to defer (irreversible) investments in clean technologies.
Figure (3.4) illustrates the impact of increased regulatory requirement uncertainty on the expected terminal penalty as a function of the regulatory requirement given xT. In this figure, the black solid line indicates the terminal penalty function, the red dashed line the high uncertainty case, and the blue dashed line the low uncertainty case. The increase in the uncertainty on regulatory requirement increases the risk concerning the target emission level at the end of the regulation horizonT. Hence, due to convexity, the expected terminal penalty is higher for every level of ter-minal pollution demandxT ∈X. Because these higher expected terminal costs transition through the intermediate review stages, the regulatory costs and the value of managerial flexibility for the ship owner are also higher in the initial stage t = 0. Therefore, the incentive to invest increases
, , Penalty Regulatory
Requirement
Figure 3.4: Graphical representation of an increase in regulatory requirement uncertainty
with uncertainty.
3.6.3 Increased uncertainty in pollution demand
This subsection deals with investigating the effect on investment decisions if the ship owner is oper-ating in an environment where the future carbon emission demand becomes more uncertain. This is relevant, as estimates about future idiosyncratic demand are usually derived by projections or forecasting models that inherently contain a forecasting error, and such an error increases with the length of the forecasting horizon. In addition, international shipping is an integral part of global supply chains, as it transports over 80% of the volume of international trade in goods (UNCTAD, 2021). A main determinant of the demand for shipping services and, in turn, the industry’s de-mand for emissions is the state of the global economy. To illustrate, disruptive events (like the COVID-19 pandemic) increase uncertainties on global markets and, in turn, increase the demand uncertainty for international shipping. Hence, future demand for emissions is inherently uncertain and largely out of the regulator’s hands, as it is idiosyncratic to the ship owner or affected by market conditions in international shipping.
Therefore, a required feature of a mechanism would be to preserve the incentive to invest in clean technologies in an environment characterized by an increased uncertainty of pollution demand.
Our results, captured by Theorem 4, indicate that the mechanism could incentivize even further investments in clean technologies under such a scenario. As discussed,ωt∈Ω captures the change in pollution demand. To investigate the impact of increased uncertainty on pollution demand, we consider our base model and focus on two uncertainty scenarios for pollution demand. Similar to before, we model the increase in uncertainty by spreading out the probability density function in one scenario, while keeping the expectation unchanged, with a mean-preserving spread. Theorem 4 summarizes the impact of increased pollution demand uncertainty on the costs of regulation and value of managerial flexibility.
Theorem 4: If uncertainty in the pollution demand increases, then (i) the costs of regulation J0(x0) and (ii) the value of managerial flexibility increase. Hence, the incentive to invest in clean technologies increases.
Figure (3.5) describes the impact of increased pollution demand uncertainty by illustrating the effect on the expected terminal penalty. The black solid line depicts the terminal penalty function, the blue dashed line the low demand uncertainty case, and the red dashed line the high demand uncertainty case. Intuitively, the increase in pollution demand uncertainty shifts more probability weight to the tails of the random variable’s ωt distribution without changing the mean. Due to the convex shape of the terminal penalty function, this leads to an overall increase in the expected terminal penalty at the end of the regulation horizon T. Similarly, the increased uncertainty in pollution demand leads to higher expected costs at the intermediate stages, thus yielding higher costs of regulation J0(x0) and a higher value of managerial flexibility. Hence, the overall incentive to invest in clean technologies increases.