|dc.description.abstract||This thesis contains three essays spanning the fields of environmental economics and investment in a non-renewable resource under uncertainty. All essays relate to the analysis of the clean-up of hazardous waste resulting from natural resource extraction.
The first essay addresses the problem of inadequate hazardous waste clean-up by resource extraction firms. It compares the impacts of an environmental bond and a strict liability rule on a firm's ongoing waste abatement and eventual site clean-up decisions. The firm's problem is modeled as a stochastic optimal control problem that results in a system of Hamilton Jacobi Bellman equations. The model is applied to a typical copper mine in Canada. The resource price is modelled as a stochastic differential equation, which is calibrated to copper futures prices using a Kalman filtering approach. A numerical solution is implemented to determine the optimal abatement and extraction rates as well as the critical levels of copper prices that would motivate a firm to clean up the accumulated waste under each policy. We have found that the effect of an environmental bond relative to the strict liability rule depends on certain key characteristics of the bond - in particular whether the bond pays interest and whether the firm borrows at a premium above the risk-free rate to fund the bond. If the firm can borrow at the risk-free rate, and if the government pays the risk-free interest rate on the bond, the value of the mine prior to construction, optimal abatement rates, and optimal operating decisions are the same under the bonding policy and strict liability rule. In contrast, if no interest is paid on the bond, the value of the project is reduced compared to the strict liability rule and the firm undertakes a larger amount of waste abatement under the bond. Because the mine is less pro table, it is less likely that the firm will invest in this mine. In the more realistic case that the firm borrows to fund the bond at a premium over the risk-free rate, the value of mine is reduced further and waste abatement levels are increased. The prospect of investment in the mine is even less likely compared to the previous case.
The model developed in the first essay allows that the firm temporarily mothballs the project, but eventually clean-up must occur at the end of the project life. However, the possibility of firm bankruptcy was not explicitly included in that model, and thus
mothballing is the only option available to the firm to delay waste clean-up. The second essay contributes to our previous study by considering another important option available to the firm, i.e., the possibility of declaring bankruptcy. A firm's decision to declare bankruptcy is specified as a Poisson process that treats bankruptcy as an exogenous, risky event governed by a hazard rate. The hazard rate at a project level depends on waste stock and output prices, while at the company wide level depends on the commodity prices only. For both default scenarios, the paper demonstrates that the firm operating under a bonding policy, that covers the full cost of waste clean-up, is less able to avoid its liability costs, particularly if the bond is financed from retained earnings. If the firm borrows to finance the bond, it is possible that the firm avoids clean-up costs by defaulting on the loan following a bankruptcy. In contrast to the results of the first essay, if the firm finances the bond out of its retained earnings, and if the government pays the risk-free rate of interest on the bond, the bond and the strict liability rule do not give the same
outcome when bankruptcy is possible. Such a bond encourages a higher abatement rate and makes site clean-up more likely compared to the strict liability rule. Firms operating under the liability rule have stronger incentives to delay their clean-up costs by sitting idle and they may eventually go bankrupt at the mothballed stage. Therefore, the possibility of bankruptcy makes the firm worse off under the bonding policy, while benefits the firm under the strict liability rule.
Modelling uncertain commodity prices is a key component of the analysis of optimal firm behavior in hazardous waste clean-up. The third essay investigates the dynamics of copper prices by comparing and contrasting three different stochastic models, which are a one-factor mean-reverting model, a two-factor model, and a one-factor long-term model. These models are calibrated to copper futures prices using a Kalman filtering approach. The first model assumes spot prices are mean-reverting in drift. The second model defines two correlated stochastic factors that are spot prices and convenience yield. The third
model transforms the two-factor price model into a single factor model. We have found that the first model fails to describe the term structure of copper futures prices with long maturities. In contrast, the two-factor and the long-term models are shown to provide a reasonable fit of the term structure of copper futures prices and can be applied to long-term investment projects. The results highlight the importance of stochastic convenience yield in copper price formation.||en