Economics

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This is the collection for the University of Waterloo's Department of Economics.

Research outputs are organized by type (eg. Master Thesis, Article, Conference Paper).

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An Analysis of Optimal Agricultural Fertilizer Application Decisions in the Presence of Market and Weather Uncertainties and Nutrient Pollution
(University of Waterloo, 2023-01-12) Yang, Xinyuan; Insley, Margaret
This thesis addresses the questions of how uncertain corn market and weather factors affect optimal fertilizer application decisions of the farmer and the social planner, and what factors drive the divergence between the two. Nutrient runoff from agricultural activities has become a primary source of surface water quality deterioration worldwide. Over-application of fertilizer in agricultural production represents a non-point source pollution which is causing extensive nutrient loading in water bodies and has a severe impact on the global environment. There is evidence that farmers apply more fertilizer than is socially optimal and more than is recommended by government agencies. This thesis first investigates the farmer’s optimal fertilizer application under crop price uncertainty by constructing an inter-temporal farmer’s decision model under two alternative stochastic price processes. Closed form results are derived, which indicate that an increase in price uncertainty implies a reduction in the quantity of fertilizer applied in the farmer’s optimal decision problem. Numerous factors that could impact the optimal fertilization decision are examined as well. The farmer’s decision model is then enhanced by allowing for two possible fertilizer application times in the growing season and the inclusion of additional stochastic state variables such as rainfall and temperature, in the corn yield model. The model is parameterized for average conditions in Iowa corn growing regions. Employing a Monte Carlo approach, numerical results conclude that for a wide range of parameter assumptions the farmer’s optimal strategy is to apply fertilizer at planting rather than later as a side dressing. This thesis analyzes the impacts of price uncertainty, fertilizer cost and other economic parameters on the farmer’s optimal fertilizer application strategy. The thesis also analyzes the optimal decisions of a social planner whose objective function includes an estimate of the damages caused by nitrogen leakage and denitrification. Numerical results show that including the damages from pollution affect both the quantity and timing of fertilizer application. Assumptions about the frequency and quantity of rainfall have an important impact on the optimal decision. This is an important consideration for public policy as climate change affects weather patterns over the next decade and beyond.
The Economics of Waste Clean-Up from Resource Extraction Projects: Environmental Bonds versus Strict Liability
(University of Waterloo, 2019-01-08) Aghakazemjourabbaf, Sara; Insley, Margaret
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.
The Economics of Water Conservation Regulations in Mining: An Application to Alberta's Lower Athabasca River Region
(University of Waterloo, 2020-04-21) Huang, Yichun; Insley, Margaret
Large demands for water by the mining industry are of increasing concern around the world and access to water is seen as a significant constraint on future mine development. Citizens, environmental groups and other non-governmental organizations have called for better regulation of water consumption by the mining industry in many regions across the globe. This thesis analyzes the efficiency of a specific command and control water management policy in the Lower Athabasca River Region in Alberta, Canada applied to oil sands mining operations. This policy imposes different restrictions on water withdrawals from the river according to the severity of threat to the aquatic ecosystem due to low water levels. In developing the policy, the Alberta government focused on the potential environmental impacts of projected water use by the oil sands industry. Economic cost was considered only in terms of the cost to the oil sands industry of constructing water storage facilities. This thesis undertakes a more robust examination of economic cost by developing a stochastic optimal control model for an oil sands firm choosing production and water use rates, as well as the optimal timing to build a water storage facility. A Hamilton Jacobi Bellman equation is specified which incorporates uncertain oil prices as well as uncertain water flow volumes in the Athabasca River and a numerical solution is implemented using a finite difference approach. The price of oil is modelled as a log-mean reverting stochastic process. Uncertainty in river flows is captured by modelling the restrictions on water withdrawals as a regime switching stochastic process. The thesis estimates the economic cost of the restrictions in terms of the difference in value of the oil-producing asset with and without water restrictions. In Chapter 2, the model is used to analyze the Phase 1 water regulations, which were first applied in 2007. The Phase 1 regulations classified river water flows into green, yellow, or red zones with green implying abundant water and red implying reduced water flows. The water restrictions varied depending on river flow zone. In the thesis, the impact of these restrictions is captured by modelling the zones as different regimes with the probability of switching between regimes based on historical river flow data. The analysis also considers a number of cases in which the future river flow conditions are lower than those experienced historically. In Chapter 2, the total cost of the regulations is estimated as well as the marginal cost of increasing the water restrictions. For the Phase 1 restrictions, no information was available regarding the potential environmental benefits of the restrictions. Our conclusions show that the cost of the Phase 1 restrictions was quite small given the current reserve base and capacity of the industry. The chapter demonstrates how the marginal cost of tightening restrictions depends on the state variables, including resource stock and price. It is also shown that marginal cost is nonmonotonic with respect to price volatility. The marginal cost is shown to vary across individual oil sands projects depending on reserve levels and lease length. Chapter 3 undertakes an analysis of the Phase 2 regulations, implemented in 2015 as an update of the Phase 1 regulations. The development of the Phase 2 regulations was supported by a detailed scientific report (Phase 2 Framework Committee (P2FC) Report) outlining the likely environmental benefits of a suite of different water restrictions (rule sets) in terms of wetted area around the river. Wetted area was used as the indicator of ecosystem disturbance. The suite of water restrictions considered encompassed a much finer delineation of different water zones than in the Phase 1 regulations. The P2FC report presented an efficient frontier contrasting the effect on wetted area with the cost of water storage implied by the different restrictions. Based on their analysis the Committee chose one of the rule sets as the preferred option. This chapter uses the model developed in Chapter 2 to create a similar efficient frontier, comparing the change in wetted area with the economic cost to the oil sands. Assumptions regarding future river flows, operating costs, oil prices, future production and storage capacity and remaining established oil reserves are examined to determine their impact on the efficient frontier and the relative cost-effectiveness of the various options. The most important factors in determining the cost of the water restrictions are found to be the assumed storage capacity, cost of storage, projected river flow conditions, productive capacity and reserves. It is also found that given the significant growth of oil sands productive capacity assumed in the P2FC report, the recommended water restriction rule set is robust. However, for a smaller assumed growth in oil sands capacity, the proposed water restrictions impose very little cost on the oil sands industry. In this case, a different rule set would be recommended based on its better expected outcome in terms of maintaining the chosen ecosystem indicator. A key input to the analysis is the assumed model for oil prices. Chapter 4 applies different versions of the Kalman filter to estimate three one-factor stochastic models. The regime switching model turns out to outperform the other two single-regime models. However, the single-regime log mean-reverting model is judged to be adequate for the analysis in Chapters 2 and 3 and is preferred because it greatly reduces the complexity of the numerical computation and the interpretation of results.

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Browsing Economics by Author "Insley, Margaret"