These models are characterized by a complex set of linear inequality constraints that represent the production possibilities available to a farmer. The simplex optimization algorithm is used to select the optimum production possibilities. One disadvantage of this approach is that the solutions are restricted to extreme points in the multidimensional decision variable space and thus it is unable to explore intermediate solutions. A major problem with linear programming models is that they need complex constraint structures to achieve some degree of calibration to base data; those constraint structures restrict alternative solutions and are difficult to implement for applications such as adoption and impact of new technologies.Econometric methods have been developed and used for single crop production function models as well as single-equation and simultaneous system models that represent input demand and output supply behavior. Early work focused on primal representations and statistical estimation , but many efforts shifted to dual representations in the 1970s and later . Both static and dynamic models have been developed. Single crop production functions are estimated directly from data on the physical quantities of inputs and outputs observed from experimental plots, or, in later stages, from comprehensive farm production surveys. Heady was an early proponent and researcher in this area. In many cases the functional form for the production functions is a quadratic or Cobb Douglas specification, both of which have implicit restrictive assumptions on the production technology. Econometric estimation of agricultural systems was expanded to represent both multi-crop production with its associated interdependencies, the endogenous nature of agricultural supply response, and the imputed value of some key agricultural inputs that are often incompletely priced. A landmark article in this literature noted that multi-crop farm businesses responded to changes in prices or technology by adjusting both the intensity of input use per acre,vertical grow system the intensive margin ; and also the allocation of land to crops, the extensive margin. This distinction is important for modeling optimal input allocation in multi-crop farming systems.
The importance of the interaction of multi-crops in a farm unit was a significant step forward in realistic economic models of farming systems. However, the approach did not include formal linkage to biophysical models of agricultural processes. The econometric approach has limitations in its ability to extrapolate responses that are outside the estimation sample, or those that employ systems that are not present in the data sample. These limitations were emphasized by Antle and Capalbo in their development of economic simulation models that combine econometric and other disciplinary simulation models into an integrated assessment framework.The importance of risk on farm decisions was recognized early in the development of linear optimization models of farming systems. Early articles on this linear approach to risk analysis are by Lin et al. and Hazell and Scandizzo . As improved algorithms to solve quadratic optimization problems were developed, specification of risk expanded to a mean-variance measure of risk and imputed a risk aversion value based on observed farmer actions or primary surveys . Just and Pope introduced a widely-used econometric risk model. Antle introduced a general moment-based representation of output distributions that has been widely used to study production risk behavior, including downside risk. Recent research has extended this approach to investigate impacts of climate change .The importance of space in agricultural production and modeling agricultural systems was first introduced in terms of trade between regions of different comparative advantages. Takayama and Judge showed that spatial equilibrium conditions and transport cost between different production locations could be characterized as a quadratic optimization problem. Spatial econometrics advanced to include rates of development and specialization of production . Only recently has the availability of remotely sensed measures of agricultural land and water use led to the use of spatial econometrics methods to address spatially varying farm production . Techniques are emerging that use both remotely sensed data and spatial econometrics to draw conclusions about resource use or the effect of spatial variation on agricultural supply response.Complex simulation models have been used for the past 45 years to describe dynamic agricultural systems.
Early examples were often based on Forrester’s concept of system dynamics that uses storage and flow variables to describe the system. However the underlying philosophy that a comprehensive and complex feedback system is stable and reproducible has never been convincingly demonstrated. Structural simulation models can be useful for representing a combination of consistent behavioral relationships based on theory and empirical measurement. They are however, subject to interpretation in the absence of robustly estimated relationships describing system behavior. Various micro-economic models have been developed to simulate the economic behavior of agricultural systems and link behavior to environmental processes and economic sustainability indicators. van Wijk et al. document the large number and diversity of such models, that include: applications of various types of linear or non-linear programming models; household models ; agent-based models that incorporate spatial and temporal interactions among households; and models that link economic models with bio-physical crop, livestock, and environmental models. Recently, agent-based modeling has been widely used as a way of modeling interactive human behavior and natural systems. Some agent-based models have a more formal dynamic and calibration structure and use mixed-integer optimization approaches for solutions. However, the generality of the approach makes it susceptible to the same difficulties of empirical verification and reproducibility that earlier complex structural simulation models had. The population-based modeling approach of Antle et al. is a more parsimonious, generic approach designed to represent agricultural system heterogeneity. It links economic simulation models to bio-physical models to evaluate impacts of technology, policy and environmental changes on sustainability.Along with more complex constrained models, researchers have developed optimization models that utilize shadow values of resources and calibration constraints to derive nonlinear calibrating functions, which are termed positive mathematical programming . In the past 10 years PMP has developed from formal calibration methods that reproduce the observed cropping pattern to those that calibrate crop supplies to prior estimates of supply elasticities , and more complex production functions that calibrate against elasticities of substitution and returns to scale. In addition, PMP models are now being formally linked with biophysical models .
These macroeconomic models spawned a series of smaller-scale models which are usually called village or household models. General equilibrium village models account for all flows in the village economy and remittances within the village to different workers and landowners. In addition, they include flows of revenue in and out of the village boundary. This is particularly useful in developing country farm economies where much of the labor is supplied by family members with little or no pay. Another advantage of village-level equilibrium models is that they account for the utility gained from subsistence food grown in a village. These CGE models are anchored by a social accounting matrix that accounts for flows within and outside the economy. Moreover, it is common practice to fit the standard functional form such as a constant elasticity of substitution production, supply, or transformation function that is calibrated against exogenously estimated elasticities . CGE models have the disadvantage of being data and computationally intensive due to their more general specification, and for the quite restrictive assumptions required for their solution. Compared with more detailed partial equilibrium models, general equilibrium models are harder to incorporate detailed process models.Flichman describes recent studies on application of models that combine bio-physical and economic models to represent agricultural systems. Flichman and Allen and van Wijk et al. also survey economic agricultural system models. They characterize bio-economic models into farm, landscape, regional, and national models. Systems in each of these scales include crops, livestock, and socioeconomics components that interact in complex ways. For example, Fig. 5 shows components that need to be included in system models at the farm scale. These components and processes encompass the crop and livestock production enterprises of a farm, the household decision and production processes, and the interactions among the household and production systems of the farm. Within these scales the cited authors address both static and dynamic specifications. In his introduction Flichman attributes growth of bio-economic modeling to two developments: improvement of biophysical agricultural simulation models, and evolution of agricultural policies that demand integrated assessments that conventional economic models cannot provide. We briefly address three prominent areas of application of integrated bio-economic models.An alternative econometric approach to measuring the impact of climate change both on agricultural crop yields and on economic variables such as land values and economic returns is to estimate statistical models based on observed behavior. These statistical models are then simulated with data from future climate projections. A justification for this approach is that it can embed realistic adaptive behavior into the model . However, this type of model also has significant weaknesses. For example, it does not incorporate effects of CO2 fertilization on crop productivity,mobile grow system cannot represent changes in socio-economic conditions, and cannot be used to identify technological adaptations distinct from climate impacts. Various researchers have used statistical econometric methods to model the effects of climate on yields and other variables .Havlik et al. provides an overview of integrated livestock modeling and its use in mitigating climate change. Their analysis is driven by a large-scale economic optimization model that assesses crop bio-energy production, land-use changes, water requirements, and greenhouse gas emissions. Their results show that improvements in livestock production systems can significantly reduce impacts on fragile land use and improve the effectiveness of climate mitigation policies. In another approach, Kobayashi et al. analyzed stocking density impacts on Kazakhstan’s extensive rangelands using a stochastic dynamic programming model for multiple livestock systems with stochastic forage production. They showed that cost of capital strongly affects herd size and productivity.There is a rich history of modeling watershed and environmental quality, however much of this has not incorporated goals related to agricultural systems and only a few efforts incorporate crop and livestock models. There are at least two different perspectives about modeling across space, including the interconnectedness of agricultural and ecological systems across the landscape. The first perspective is that human systems, including the farm, communities, and administrative and political areas in which agricultural systems interact through decisions and policies, affect production systems, markets, and trade.
The other perspective is that the interconnectedness among hydrological and biophysical processes establishes the underlying behavior of agricultural systems over the landscape. This perspective leads to an emphasis on understanding physical, chemical, and biological processes that occur in watersheds. Both perspectives are important, yet agricultural models rarely consider both in the same assessments or models. There are many applications of watershed hydrology models, in particular using the SWAT model as discussed byGassman et al. , mainly focusing on environmental quality and water resource issues. Fig. 6 shows the regional integrated assessment approach developed by AgMIP that emphasizes linkages of agricultural systems across space using the first perspective noted above . In this perspective, based in part on the impact assessment approach developed by Antle , the focus is on the economic, environmental, and social impacts of alternative systems within heterogeneous household populations. However, this framework also illustrates the feed backs from farms to agro-ecological regions to national and global scales. We often use the term “scaling up” of model results to refer to the aggregation of model results from finer spatial resolutions to a larger area. If the areas of interest are defined by hydrologists, they tend to be watersheds. In contrast, if the areas are defined by economists, they tend to be administrative and political units or socio-economic stratifications . These perspectives are not mutually exclusive, however. In fact, they lend themselves to include both human and biophysical/hydrological processes. A challenge for next generation agricultural models is to include the technical aspects of integrated modeling and a transdisciplinary approach in which scientists recognize the need for collaboration, not only on specific projects, but also in designing models and decision support tools to achieve their goals. Many current agricultural system models have been developed to evaluate practices and policies associated with environmental quality. Biophysical models typically operate at the point/field scales with an emphasis on vertical fluxes of energy, water, C, N and nutrients throughout the atmosphere, plant, and soil root-zone continuum. Upscaling from point to the landscape scale requires estimation of surface and subsurface fluxes and ecological transitions along the lateral scale.