Essays on optimal extraction of groundwater in Western Kansas

Abstract

The two studies presented in this dissertation examine incentives for groundwater extraction and their resulting effect on aquifer depletion. Both studies apply dynamic optimization methods in a context of irrigated agriculture in arid and semi-arid regions such as in western Kansas. The first study examines the effects of capital subsidies aimed at increasing irrigation application efficiency. The second study examines the effects of changing incentives posed by changes in climatic patterns and by technical progress in the form of increasing crop water productivity. Both studies have significant policy and groundwater management implications. Subsidies for the adoption of (more) efficient irrigation technologies are commonly proposed and enacted with the goal of achieving water conservation. These subsidies are more politically feasible than water taxes or water use restrictions. The reasoning behind this type of policy is that increased application efficiency makes it possible to sustain a given level of crop production per acre with lower levels of groundwater pumping, all else equal. Previous literature argues that adoption of more efficient irrigation systems may not reduce groundwater extraction. Rewarding the acquisition of more efficient --and capital intensive-- irrigation equipment affects the incentives farmers have to pump groundwater. For instance, the farmer may choose to produce more valuable and water intensive crops or to expand the irrigated acreage after adopting the more efficient irrigation system. Hence, the actual impact of the policy on overall groundwater extraction and related aquifer depletion is unclear. The first chapter examines the effects of such irrigation technology subsidies using a model of inter-temporal common pool groundwater use with substitutable technology and declining well-yields from groundwater stocks, where pumping cost and stock externalities arise from the common property problem. An optimal control analytical model is developed and simulated with parameters from Sheridan County, Kansas-- a representative region overlying the Ogallala aquifer. The study contrasts competitive and optimal allocations and accounts for endogenous and time-varying irrigation capital on water use and groundwater stock. The analysis is the first to account for the labor savings from improved irrigation technologies. The results show that in the absence of policy intervention, the competitive solution yields an early period with underinvestment in efficiency-improving irrigation technology relative to the socially efficient solution, followed by a period of over-investment. This suggests a potential role for irrigation capital subsidies to improve welfare over certain ranges of the state variables. In contrast to previous work, the findings are evidence that significant returns may be achieved from irrigation capital subsidies. Finally, a policy scenario is simulated where an irrigation technology subsidy is implemented to explore whether such a program can capture significant portions of the potential welfare gain. Results indicate that the technology subsidy can improve welfare, but it captures a relatively small portion of the potential gains in welfare. The second chapter presents a dynamic model of groundwater extraction for irrigation where climate change and technical progress are included as exogenous state variables-- in addition to the usual state variable of the stock of groundwater. The key contributions of this study are (i) an intuitive description of the conditions under which groundwater extraction can be non-monotonic, (ii) a numerical demonstration that extraction is non-monotonic in an important region overlying the Ogallala Aquifer, and (iii) the predicted gains from management are substantially larger after accounting for climate and technical change. Intuitively, optimal extraction is increasing in early periods when the marginal benefits of extraction are increasing sufficiently fast due to climate and technical change compared to the increase in the marginal cost of extraction. In contrast, most previous studies include the stock of groundwater as the only state variable and, consequently, recommend a monotonically decreasing extraction path. In this study, the numerical simulations for a region in Kansas overlying the Ogallala Aquifer indicate that optimal groundwater extraction peaks 23 years in the future and the gains from management are large (29.5%). Consistent with previous literature, the predicted gains from management are relatively small (6.1%) when ignoring climate and technical change. The realized gains from management are not substantially impacted by incorrect assumptions of climate and technical change when formulating the optimal plan.