International Trade Policies in Models of Barter Exchange

This paper is the third in a series on the linkage of national models of food and agriculture. International agreements are discussed in which given levels of world market prices are aimed at. Buffer stock agreement, various compensatory financing schemes and specific types of cartels are represented in general equilibrium models of barter exchange

Formulation and Spatial Aggregation of Agricultural Production Relationships within the Land Use Change (LUC) Model

Land Use Change (LUC) Project at IIASA in which the Centre for World Food Studies participates, is currently engaged in the development of a case study for China (Fischer et al., 1996). Its focus on land use and land cover change makes it necessary to ensure that geographic detail and statistical information on conditions prevailing within these regions be preserved to the extent possible. This raises two issues that are addressed in this paper. First, while it is not practical to formulate a regional optimization model with a very large number of sub-regions, over two thousand in the case of China, one would like to avoid the loss of information associated with aggregation. For a generalized version of the Mitscherlich-Baule yield function that is commonly used in agronomy the paper describes a consistent aggregation procedure over sub-regions, which leads to simple aggregate functions at regional level, but has the special property that, once the regional model has been solved, all results can be recovered fully at sub-regional level. Secondly, agronomy studies commonly use yield functions in which the per hectare yield of a particular crop depends on inputs per hectare. Unfortunately, in the case of China, as for most countries, input use is not available by crop and only recorded for a particular geographical unit. The paper proposes a more crude formulation whose parameters, however, can be estimated by cross-section on the basis of available data

Modeling Producer Decisions on Land Use in Spatial Continuum

The paper describes how stochastic optimization techniques can be used to model profit maximizing producer behavior in a spatial continuum. The main methodological issues to be addressed are, first, that the representation of optimal allocations in a spatial continuum naturally lead to models that contain integrals over space, and the second that the resulting model tends to have a multi-level structure, i.e. requires solving nested optimization problems because it should combine the profit maximization by individual producers with market clearing at regional level. We specify four regional model that may illustrate the approach. The first determines the optimal output level for factories that emit pollutants which reduce the crop output of neighboring farmers. The main issue is to compute the associated level of compensation to be paid by the factories to the farmers. The second model deals with optimal zoning. It computes the optimal crop routing for farmers who can choose to sell their crop to factories situated at given locations. This is an optimization problem in functional space, which can be reformulated as a dual stochastic optimization problem. In the their model, the farmer has the possibility of routing his crop along different roads or distribution nodes to the various factories for processing. It can describe the optimal choice of distribution centers at given locations, around plants or cities, and produces optimal boundaries for the zones that supply to or buy from these centers. The fourth model deals with the problem optimal land consolidation, distinguishes between consolidation processes with and without side-payments. To each of these four models we associate a decentralized, stochastic quasi-gradient (SQG-)procedure for attaining the global) optimum, which has a natural interpretation as a device for decentralized adaptive planning

Analysis of a National Model with Domestic Price Policies and Quota on International Trade

This paper is the second in the series on the linkage of national models for food and agriculture. In Section 1, the model with domestic price policy and quota, is rehearsed and reformulated. A proof is presented for the existence of domestic equilibrium at given world market prices. In Section 2, the uniqueness of the domestic equilibrium is investigated on the basis of properties of the Jacobian matrix. In Section 3, attention is centered on the actual computation of the domestic equilibrium

Computing Economic Equilibria through Nonsmooth Optimization

In the first section the problem of nonsmooth optimization is described in general terms, setting the precise hypothesis in mathematical language. Section 2 describes the principles of an example which arises in the context of the linkage of national models of food and agriculture. The general methodology is presented in Section 3, where the algorithm of solution is outlined. Section 4 reports on an extensive set of numerical experiments, both on problems known in the literature, and on the example of Section 2. Finally the paper concludes with some remarks about improvements of the algorithm, which motivate further research on the subject

Estimation of Econometric Models by Risk Minimization: A Stochastic Quasigradient Approach

The paper presents a risk minimization approach to estimate a flexible form that meets a priori restrictions on slope and curvature by means of constraints on both the estimated parameters and the function values. The resulting constrained risk minimization combines parametric and nonparametric estimation and contains integrals and implicit constraints. Within econometrics, simulation has become a common tool to solve problems of this kind. However, it appears that in our case, the simulation approach only applies when the model is linear in parameters, has simple constraints on parameters and a quadratic risk function. To deal with other cases, we use a stochastic optimization technique known as the stochastic quasi-gradient method for stationary and nonstationary problems with Cesaro averaging. This method is also applicable to an expanding series of random observations, and produces asymptotically (weakly) convergent estimates