INTERNAL CONSISTENCY IN MODELS OF OPTIMAL RESOURCE USE UNDER UNCERTAINTY

For several decades, economists have been concerned with the problem of optimal resource use under uncertainty. In many studies, researchers assume that prices evolve according to an exogenous stochastic process and solve the corresponding dynamic optimization problem to yield an optimal decision rule for exploitation of the resource. This study is motivated by our attempt to understand the relationship between efficiency in resource markets and optimal harvest decisions in which price is an exogenous state variable. The literature on optimal commodity storage finds that in a rational expectations equilibrium commodity prices are stationary and serially correlated. Yet recent papers on optimal timber harvesting that assume exogenous stationary prices generate harvest rules inconsistent with the price processes on which they are based. In this study, we investigate the appropriate form of the stochastic process governing prices of renewable resources. We develop a model in which timber is supplied by profit-maximizing managers with rational expectations and aggregate timber demand is subject to independent exogenous shocks. In contrast to earlier studies, prices are endogenously determined. Managers know the structure of the timber market and form expectations of future market equilibria in making optimal harvesting decisions. We show under general conditions that efficient timber prices are stationary and serially correlated. Stationarity and serial correlation are shown to arise from two sources: the occurrence of stock-outs (i.e., depletion of the inventory) and stock-dependent growth of the resource. Further, we show that prices retain these properties even in the absence of stock-outs. Simulations are used to further illustrate the analytical results. Our findings have implications for a large number of economic analyses of optimal resource use. First, our results reveal why extraction rules for renewable resources based on exogenous price specifications are internally inconsistent, even when the specification conforms to the stochastic behavior of prices generated by an efficient market. These prices arise in a particular structural environment, and if large numbers of resource managers adopt the harvesting rule, the underlying structural environment would change, and the price process would deviate from that used to derive the harvesting rule. Second, we show that there can be no gains from exploiting the stochasticity of resource prices in a rational expectations world, a finding that challenges the prescriptive policies for resource use found in many studies, including those on option values. Third, our results show that time-series analyses designed to test for the efficiency of renewable resource markets cannot distinguish prices generated in an efficient market from those generated in an inefficient market. Finally, we extend the literature on optimal storage. Previous models of commodity storage models are shown to be a special case of our model involving age-independent depreciation of the inventory.Resource /Energy Economics and Policy,

Contracting for Impure Public Goods: Carbon Offsets and Additionality

Governments contracting with private agents for the provision of an impure public good must contend with agents who would potentially supply the good absent any payments. This additionality problem is centrally important in the use of carbon offsets as part of climate change mitigation. Analyzing optimal contracts for forest carbon sequestration, an important offset category, we conduct a national-scale simulation using results from an econometric model of land-use change. The results indicate that for an increase in forest area of 50 million acres, annual government expenditures with optimal contracts are about $4 billion lower compared than under a uniform subsidy.Carbon Sequestration, Incentive Contracting, Offsets, Additionality

The Effects of Potential Land Development on Agricultural Land Prices

We conduct a national-scale study of the determinants of agricultural land values to better understand how current farmland prices are influenced by the potential for future land development. The theoretical basis for the empirical analysis is a spatial city model with stochastic returns to future land development. From the theoretical model, we derive an expression for the current price of agricultural land in terms of annual returns to agricultural production, the price of recently developed land parcels, and expressions involving model parameters that are represented in the empirical model by nonlinear functions of observed variables and parameters to be estimated. We estimate the model of agricultural land values with a cross-section on approximately three thousand counties in the contiguous U.S. The results provide strong support for the model, and provide the first evidence that option values associated with irreversible and uncertain land development are capitalized into current farmland values. The empirical model is specified in a way that allows us to identify the contributions to land values of rents from near-term agricultural use and rents from potential development in the future. For each county in the contiguous U.S., we estimate the share of the current land value attributable to future development rents. These results give a clearer indication of the magnitude of land development pressures and yield insights into policies to preserve farmland and associated environmental benefits.

AGRICULTURAL LAND VALUES AND FUTURE LAND DEVELOPMENT

We develop a theoretical model of land prices and urban expansion and derive a reduced-form expression for agricultural land values. This result dictates the specification of our econometric model in terms of variable choice and functional form. We find strong support for the model in an application to New York.Land Economics/Use,

Determinants of Land-Use Change In the United States 1982-1997

Changes in the use of land in the United States produce significant economic and environmental effects with important implications for a wide variety of policy issues, including protection of wildlife habitat, management of urban growth, and mitigation of global climate change. In contrast to previous descriptive and qualitative analyses of the trends in national land use, this paper uses an econometric approach to isolate the importance of historical changes in land-use profits and key government policies in determining national land-use changes from 1982 to 1997. The policies we examine are the Conservation Reserve Program (CRP) and total government payments to crop producers. We estimate a national-level discrete choice model of changes among the major land-use categories (crops, pasture, forest, urban, range, and CRP) with parcel-level observations of land use and land quality from the U.S.D.A. National Resources Inventory NRI) and measures of countylevel land-use net returns from a variety of sources. We then use fitted values from the econometric model to simulate land-use change from 1982 to 1997 under a series of factual and counterfactual scenarios that isolate the effects of different economic and policy factors. The simulations suggest how changes in economic returns and government policies have driven land-use changes in the past and will continue to affect nationwide land-use changes in the future. For example, we find that the introduction of the CRP and the decline in crop profits were the most significant explanatory factors driving the decline in cropland. Our results highlight some “unintended consequences” of government policies and the importance of net returns to a range of alternative land uses as determinants of land area change for each particular use.land use; econometric model; counterfactual simulation; Conservation Reserve Program (CRP)

POLICIES TO REDUCE FOREST FRAGMENTATION: COMBINING ECONOMETRIC MODELS WITH GIS-BASED LANDSCAPE SIMULATIONS

Forest fragmentation is a primary threat to terrestrial biodiversity. We combine a parcel-level econometric model of land-use transitions with spatially-explicit landscape simulations to predict the empirical distribution of fragmentation outcomes under given market conditions and policy scenarios. Our model explains transitions between forest, agricultural, and urban uses, allowing us to model land use change in both rural and urban areas. A Monte Carlo simulation approach links econometrically-derived transition probabilities to GIS maps for the prediction of the spatial properties of habitat change.Resource /Energy Economics and Policy,

Land-Use Change and Carbon Sinks

When and if the United States chooses to implement a greenhouse gas reduction program, it will be necessary to decide whether carbon sequestration policies — such as those that promote forestation and discourage deforestation — should be part of the domestic portfolio of compliance activities. We investigate the cost of forest-based carbon sequestration. In contrast with previous approaches, we econometrically examine micro-data on revealed landowner preferences, modeling six major private land uses in a comprehensive analysis of the contiguous United States. The econometric estimates are used to simulate landowner responses to sequestration policies. Key commodity prices are treated as endogenous and a carbon sink model is used to predict changes in carbon storage. Our estimated marginal costs of carbon sequestration are greater than those from previous engineering cost analyses and sectoral optimization models. Our estimated sequestration supply function is similar to the carbon abatement supply function from energy-based analyses, suggesting that forest-based carbon sequestration merits inclusion in a cost-effective portfolio of domestic U.S. climate change strategies.abatement; carbon; climate change; costs; forestry; greenhouse gases; land use; landuse change; sequestration

TB161: Forestry Investments and Option Values: Theory and Estimation

This bulletin considers option values related to a principal problem for forestry investors, the timing of harvests. The purpose is to present a general theory of the rotation problem under uncertainty and irreversibility and provide a methodology for empirically estimating option values. Modifications of the framework for analyzing options values related to other aspects of forestry investments are also discussed.https://digitalcommons.library.umaine.edu/aes_techbulletin/1037/thumbnail.jp

The Dynamic Behavior of Efficient Timber Prices

The problem of when to optimally harvest trees when timber prices evolve according to an exogenous stochastic process has been studied extensively in recent decades. However, little attention has been given to the appropriate form of the stochastic process for timber prices, despite the fact that the choice of a process has important effects on optimal harvesting decisions. We develop a simple theoretical model of a timber market and show that there exists a rational expectations equilibrium in which prices evolve according to a stationary ARMA(1,1) process. Simulations are used to analyze a model with a more general representation of timber stock dynamics and to demonstrate that the unconditional distribution for rational timber prices is asymmetric. Implications for the optimal harvesting literature are: 1) market efficiency provides little justification for random walk prices, 2) unit root tests, used to analyze the informational efficiency of timber markets, do not distinguish between efficient and inefficient markets, and 3) failure to recognize asymmetric disturbances in time-series analyses of historical timber prices can lead to sub-optimal harvesting rules.

URBAN SPRAWL AND OBESITY

In the U.S., urban sprawl and the rise in obesity rates have been two powerful trends during the latter half of the 20th century. Previous empirical work has found that obesity rates are influenced by labor market outcomes that are fundamentally shaped by the spatial pattern of developed land. We examine these potential linkages in an urban spatial model augmented to include time allocation and weight. Residents maximize utility defined over housing, weight, and food subject to a fixed time budget allocated to commuting, calorie expenditure, and work. We examine how weight is affected by commuting distance, food prices, and the rate of calorie expenditure; how a reduction in transportation costs affects weight throughout the city; and how initial weight affects location decisions. We identify, and explore the significance of, the conditions under which weight gain is associated with common features of sprawl.Food Consumption/Nutrition/Food Safety,