Responsive market regulation in environmental economics : an agent-based stochastic equilibrium approach

The present work is concerned with stochastic modelling of markets for regulated resources. Here, we use the term regulated resource (or regulated commodity) in the sense of some tradable good, the total aggregate deployment of which is subject to control by some public or private, central entity. More precisely, we are interested in regulatory systems that can control the inflow of commodity units. Such control systems allow the regulator to force potential externalities, arising from using the resource, to be priced in on the market, without explicitly deciding on the respective premium or explicitly quantifying the economic damage avoided for each unit of the commodity. Such (quantity-based) trading systems are traditionally viewed as alternatives to conventional price-based systems such as taxes. The question whether a quantity-based or price-based system is more advantageous has first been studied by [Weitzman, 1974], whose deliberations came down to comparing the relative slopes of the marginal abatement cost curve and marginal benefit curve (of avoiding emissions). However, Weitzman appreciated that an ideal instrument would implement a contingency message, indicating what policy would be implemented, based on the current state of the system. In the present work, we pick up on this idea and examine how the costs efficiency of controlling the use of a resource can be improved by such dynamic control systems. What’s more, we construct a quantitative framework by which we can represent an entire spectrum of policies between ‘pure’ price-based and ‘pure’ quantity-based instruments. Thusly we fill a significant gap in the pertinent literature. Limitation or regulation of the inflow of commodity units to some economy can be in the collective interest of a group of economic entities, or in the interest of the society which is subjected to those entities’ externalities. While examples for the former are mainly found in the context of cartels, the latter is relevant whenever societal damages are the result of the con- sumption of a commodity – e.g. through overfishing or non-sustainable forestry. Another, particularly topical example are climate relevant commodities such as fossil fuels or emissions allowances. The main inspiration for our modelling work are Emissions Trading Systems (ETSs), the currently largest of which is the European Union ETS (EU ETS). Therein, emissions allowances (EUAs – European Emission Allowances) are made available by the regulator through regular auctions and free allocations. Those allowances can then be traded freely among market participants at the price dictated only by supply and demand on this secondary market. After a given calendar year, agents whose facilities are subject to the regulation of the EU ETS have to present a number of EUAs equal to their total emissions of greenhouse gases, measured in (metric) tonnes of CO2-equivalent (CO2e), during the respective year. For each tonne not covered in this way, each agent who is short in allowances has to pay a penalty of (currently) 100 Euros. (It shall be mentioned that paying the penalty does not absolve the agent from having to present the respective allowances in the next year.) In the wake of the economic crisis of 2007/08, we saw a strong and persistent erosion of EUA prices, which is mainly at- tributed to an oversupply resulting from an unanticipated drop in production. It was this price erosion, along with the ETS’s lack of provisions to adapt to such circumstances, that brought about doubt in the efficacy of the instrument altogether. More precisely, a number of experts in academia, politics and some stakeholders believed that the system was unable to ‘function in an orderly fashion’ [The European Commission, 2012] in the presence of such an enormous oversupply. In particular, the system lacked provisions to adapt the allocation scheme to changes in economic circumstances. Based on public consultations, the European Commission released a report in November 2012 (see [The European Commission, 2012]), presenting a number of reform options for the EU ETS, which aimed at relieving the current oversupply and, poten- tially, making the system more responsive to changes in economic circumstances. One such measure is the introduction of the so-called Market Stability Reserve (MSR), which aims at making the supply of allowances dynamic and dependent on the state of the system, rather than static and rigid, as it was. Furthermore, this supply adjustment system is designed based on a transparent set of rules, rather than discretionary interventions. The MSR has been ratified in 2016 and is set to start operating in 2020. In the present work, we construct a continuous-time stochastic equilibrium model of a market for an abstract regulated com- modity, with special interest in applications to climate-relevant resources such as emissions allowances. In doing so, we put special emphasis on a mathematically rigorous representation of stochasticity and risk-aversion on behalf of market partici- pants, as well as on a detailed (agent-based) derivation of the equilibrium dynamics in closed-form. In the process, we solve each agent’s optimisation problem, along with the associated Hamilton-Jacobi-Bellman Equation, for which we are able to find an explicit solution. Furthermore, we construct a generic regulatory mechanism of dynamic resource allocation, similar in spirit to the Market Stability Reserve. Our dynamic regulatory mechanism adjusts the resource allocation based on the current system state. The system state, however, is dependent on the allocation scheme, which implies the existence of a feed-back loop between the market and the regulation. We are, notably, able to solve this inter-dependency and derive the equilibrium under this regulation. This in turn allows us to quantify the costs associated to any given parameterisation of the mechanism, adjusting its responsiveness in order to maximise the cost-efficiency of the system. What’s more, by employing an adjustable responsiveness, we are able to represent an entire spectrum of policies between pure price instruments and pure quantity in- struments. Thereby, we fill a significant gap in the stream of literature pioneered by [Weitzman, 1974]. The present text is divided into four chapters. In Chapter 1 we describe our motivation along with the literature context of our work. In Chapter 2 we present some general concepts and observations on stochastic equilibria which will prove useful for our modelling approach. In Chapter 3 we derive our equilibrium in closed-form, before we construct our dynamic regulatory mechanism in Chapter 4. Therein, we furthermore compute total aggregate abatement costs as a function of the responsiveness of the system. This allows us to present means for the construction of a mechanism that maximises the policy’s cost-efficiency. We also provide an in-depth analysis of how the above-mentioned spectrum of policies can be represented by our mechanism’s parameterisation.


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