Applied Methods for Agriculture and Natural Resource Management

This contribution focuses in reviewing the development of positive mathematical programming towards econometric mathematical programming. Starting with the entropy approach it reviews alternative approaches and model specifications that appeared in the recent PMP-related literature for estimating those nonlinear terms that achieve the accurate calibration of optimisation programmes and guide the simulation response to policy scenarios. Combining recent contributions from this literature, it then proposes a possible framework to estimate and calibrate simultaneously model parameters ready to use for performing policy simulations.

This contribution uses econometric analysis to uncover the various factors driving crop choice in six states along the Mississippi River. Aside from temperature and precipitation, soil characteristics are also included as explanatory factors—which is a factor often omitted from many studies. The analysis shows soil to be a key determinant of corn and soybean area in the regions studied.

Spatial models of trade among regions require a burdensome series of information: Commodity demand and supply functions for each region and bilateral unit transaction costs. Even when this formidable amount of information is available, the trade flow matrix resulting from the model solution is typically very different from the exchanged trade flow that was realized in a previous economic cycle. This discrepancy may be attributed to two sources: incorrect measurement of transaction costs and imprecise knowledge of demand and supply function parameters. To remedy the undesirable result, we assume that the matrix of bilateral trade exchanges is observed—by the researcher—together with the realized demand and supply prices. With this additional information, we discuss the calibration of three categories of spatial models—(a) cartel behavior on the supply and export markets: This model corresponds to monopsony and monopoly behavior; (b) Nash-Cournot behavior on the supply and export markets: This model corresponds to oligopsony and oligopoly behavior; (c) perfect competition on both markets. The calibrating approach presented in this contribution is in the spirit of positive mathematical programming and its prescription: To achieve satisfactory results, it is important to use all the available information. The empirical part of the contribution is divided into two sections. First, we use only the observed matrix of bilateral trade flows to reveal the necessary adjustments to the unit transaction costs and achieve a calibrating model. Second, the observed demand and supply prices are used to reveal the adjustments to the intercepts of the demand and supply functions that correspond to a more general calibrating model.

Environmental conservation policies based on the payment for environmental services (PES) are being increasingly adopted around the world. Among several factors that may dictate the success of a PES conservation program is the payment or monetary compensation level. As participation in the program is voluntary, if payments are not enough to compensate for the eventual economic losses faced by the users, users will not participate, and conservation goals will not be achieved. Also if payments are set significantly higher than the users’ opportunity costs, conservation goals are more likely to be achieved, but the program will not be cost-effective. In this context, by using primary data from a watershed in the Brazilian Savannah, this contribution calculates opportunity costs using an agricultural net-revenue multiproduct model, parameterized with the use of positive mathematical programming (PMP) method and coupled with a hydrological model. It is shown that land and water opportunity costs not only vary from farmer to farmer due to differences in crop and input mix but also the variations in water supply affect land use opportunity costs. And, in turn, land supply affects water use opportunity costs. Given this, researchers and policy makers should not be surprised that agricultural PES programs that rely on a flat, crop-and-farmer invariant compensation value per hectare often result in failure and cost-ineffectiveness.

Despite efforts to reform management of water resources, groundwater levels have continued to decline steadily on the North China Plain, leading to serious environmental concerns and impacts. While policy makers have looked to efforts aimed at improving the efficiency of field-level irrigation and strengthening ownership and property rights in local resource management, hydrologists have asserted that more direct control of consumptive use patterns of water is needed. In this contribution, we show how both agricultural and urban demands for water can be managed, so as to ameliorate the depletion of groundwater resources in the North China Plain and promote long-run sustainability of limited water resources.

In this contribution, we explore the sensitivity of parameter estimates derived through the generalized maximum entropy (GME) approach under alternative specifications of the width of the error term supports. Although many recommend a “three-sigma” rule for setting the width of this term, there can be noticeable differences in the results if it is expanded beyond that, as others in the literature have suggested. We use a Monte Carlo analysis to see how imposing a moment-based condition into the GME problem, as an additional constraint, affects the results. We find that it removes the sensitivity of the parameter estimates to the width of the supports for the error term and that this remains robust even when the data is ill-conditioned. Based on this, we recommend that researchers impose this condition when doing GME-based estimation, to improve the performance of the estimator.

Crop rotation systems are an important part of agricultural production for managing pests, diseases, and soil fertility. Recent interest in sustainable agriculture focuses on low input-use practices which require knowledge of the underlying dynamics of production and rotation systems. Policies to limit chemical application depending on proximity to waterways and flood management require field-level data and analysis. Additionally, many supply estimates of crop production omit the dynamic effects of crop rotations. We estimate a dynamic programming model of crop rotation which incorporates yield and cost intertemporal effects in addition to field-specific factors including salinity and soil quality. Using an Optimal Matching algorithm from the Bioinformatics literature, we determine empirically observed rotations using a geo-referenced panel dataset of 14,000 fields over 13 years. We estimate the production parameters which satisfy the Euler equations of the field-level rotation problem and solve an empirically observed four-crop rotation.

Water woes are growing globally as farmers and others struggle to develop infrastructure and institutions that allow the agricultural economy to thrive in the face of competing uses for water. While not new, these struggles are deeply important, and nowhere more so than to agriculture within arid regions. This chapter uses the California water context to trace through the simple economics of how irrigation water availability and price affect prices and quantities of tradeable food products. We highlight a few key relationships within the supply chains for wine and cheese using the simplest framework possible—fixed proportions and elastic input supplies at each stage of a multi-market chain. First, we consider irrigation water used to produce grapes that are transformed into wine and highlight the role of cost shares and final product demand elasticities. We show that irrigation water is a far more important driver of prices and quantities in the low-cost San Joaquin Valley region, which faces a more elastic demand for wine than in the high-cost (and price) North Coast region, which faces a less elastic demand. When we consider the irrigation water used to produce feed crops for dairy cows—which, in turn, produce milk that is transformed into cheese, we find that water has only a moderate cost share in forage production and that forage has a moderate share in milk output. Nevertheless, because California cheese faces an elastic demand in the global market, a rise in water costs could reduce California cheese production significantly.

This study uses an updated version of the U.S. Agricultural Resource Model (USARM)—a multi-region U.S. agricultural sector programming model—to examine effects of climate change mitigation policies on U.S. water resources. One scenario considers effects of increasing prices of energy and energy-intensive inputs (primarily fertilizers) through a carbon tax or cap-and-trade program. A second scenario combines the first scenario with an agricultural offset program where farmers are paid to retire cropland for carbon sequestration. The consequences of climate mitigation policies for agricultural water use and pollution control have received relatively little attention in part because—unlike USARM—many national agricultural sector models do not explicitly include water as an input. USARM also allows for input substitution among seven inputs in a CES framework, while accounting for all major crops as well most specialty crops, federal commodity programs, and crop exports. Major results are as follows. First, climate mitigation policies have scope to significantly reduce agricultural water use. Whether domestic offsets are included has little effect on the total amount of water conserved, but has a large effect on which parts of the country the conservation takes place. Second, either carbon taxes or cap-and-trade combined with domestic offsets combines two policies often modeled as potential solutions to the hypoxic “dead zone” in the Gulf of Mexico—increased fertilizer prices and land retirement. Climate policies may have unanticipated, near-term, environmental benefits by addressing the hypoxia problem. Third, while domestic offsets reduce total fertilizer and agricultural chemical use, they increase their use per acre. Particularly in watersheds with significant land retirement, there could be unintended intensive margin effects where fertilizer and chemical use are increased. Despite this last, cautionary finding, a key insight into decision makers is that climate policies can have unanticipated, near-term benefits of water pollution control and water conservation that could be included in benefit-cost analyses of climate policy proposals.

In this chapter, we show how the current crop areas under three key staples—rice, maize, and beans—could be better aligned with the crop suitabilities that are inherent in the East African Community (EAC) region, through some key policy interventions. We take a multi-market model that was constructed for the 5 main countries in the EAC and use it to demonstrate how reducing transport costs, and increasing crop productivities can lead to market-level welfare improvements, as well as a closer alignment between the areas where the crops are cultivated, and the areas with the best agronomic suitability for those crops. At present, a significant proportion of those staples are grown in areas with limited growth potential, but opening up markets in combination with productivity-focused investments can allow countries to make better use of the crop potential they already have, and take advantage of regional market opportunities.