How did farmers act? Ex-post validation of linear and positive mathematical programming approaches for farm-level models implemented in an agent-based agricultural sector model

This study evaluates linear programming (LP) and positive mathematical programming (PMP) approaches for 3,400 farm-level models implemented in the SWISSland agent-based agricultural sector model. To overcome limitations of PMP regarding the modelling of investment decisions, we further investigated whether the forecasting performance of farm-level models could be improved by applying LP to animal production activities only, where investment in new sectors plays a major role, while applying PMP to crop production activities. The database used is the Swiss Farm Accountancy Data Network. Ex-post evaluation was performed for the period from 2005 to 2012, with the 2003-2005 three-year average as a base year. We found that PMP applied to crop production activities improves the forecasting performance of farm-level models compared to LP. Combining PMP for crop production activities with LP for modelling investment decisions in new livestock sectors improves the forecasting performance compared to PMP for both crop and animal production activities, especially in the medium and long term. For short-term forecasts, PMP for all production activities and PMP combined with LP for animal production activities produce similar results.

Positive Mathematical Programming (PMP) is an approach to empirical analysis that uses all the available information, no matter how scarce. It uses sample and user-supplied information in the form of expert opinion. This approach is especially useful in situations where only short time series are available as, for example, in sectoral analyses of developing countries and environmental economics analyses. PMP is a policy-oriented approach. By this characterization we mean that, although the structure of the PMP specification assumes the form of a mathematical programming model, the ultimate objective of the analysis is to formulate policy recommendations. In this regard, PMP is not different from a traditional econometric analysis. PMP grew out of two distinct dissatisfactions with current methodologies: first, the inability of standard econometrics to deal with limited and incomplete information and, second, the inability of linear programming (LP) to approximate, even roughly, realized farm production plans and, therefore, to become a useful methodology for policy analysis. The original work on PMP is due to Howitt. After the 1960s, a strange idea spread like a virus among empirical economists: only traditional econometric techniques were considered to be legitimate tools for economic analysis. In contrast, mathematical programming techniques, represented mainly by LP (which had flourished alongside traditional econometrics in the previous decade), were regarded as inadequate tools for interpreting economic behavior and for policy analysis. In reality, the emphasis on linear programming applications during the 1950s and 1960s provided ammunitions to the critics of mathematical programming who could not see the analytical potential of quadratic and, in general, nonlinear programming.

Positive mathematical programming in agricultural economics. Principles and importance of calibrating. The modelling of agricultural producer behaviour using mathematical programming has a long tradition in agricultural economics. The linear mathematical programming approach has been prevalent in this field for a long time. But linear programming models, that are tightly constrained to reproduce agricultural producers' choices observed at the base period, are often unacceptable and also inappropriate under policy changes. Several researchers have alluded to this problem in the past and came up with several solutions such as incorporating risk or considering "flexibility" constraints. Furthermore, to solve this problem, new methodological developments also occurred, including Positive Mathematical Programming (PMP). PMP emerged more than ten years ago but its formal presentation is relatively recent. In this article, we first present the principles of PMP, using a simple example of an arable crop producer. It appears that the two main advantages of PMP are its perfect calibration to base period levels of endogenous variables and its derivation of smooth simulation results, both resulting from the incorporation of non linear terms in the objective function. Empirical implications of the standard PMP' s parameter calibration process are then discussed.

Positive Mathematical Programming (PMP) is one of the most commonly used methods of calibrating activity linear programming (LP) models in agriculture. PMP applications published thus far focus on the estimation of a farm’s nonlinear cost or profit function and rely on the recovery of unobserved or implicit information that can explain the initial model’s inability to calibrate. In this paper we use the PMP procedure to calibrate an expected utility model under the assumption that this implicit information can reveal a farmer’s profit expectations and risk attitude. The perfect calibration shows that PMP can be applied not only to LP models, but also to models that incorporate risk and this provides an interesting alternative to the traditional PMP methodology.

A bottom-up model of industrial energy system with positive mathematical programming

Using linear programming in bio‐economic farm modelling often results in overspecialised model solutions. The positive mathematical programming (PMP) approach guarantees exact calibration to base year data but the forecasting capacity of the model is affected by necessary but arbitrary assumptions imposed during calibration. In this article, a new PMP variant is presented which is based on less arbitrary assumptions that, from a theoretical point of view, are closer to the actual decision making of the farmer. The PMP variant is evaluated according to the predictions of the bio‐economic farm model, developed within the framework for integrated assessment of agricultural systems in Europe (SEAMLESS). The forecasting capacity of the model calibrated with the standard PMP approach and the alternative PMP variant, respectively, is tested in ex‐post experiments for the arable farm types of Flevoland (the Netherlands) and Midi‐Pyrenees (France). The results of the ex‐post experiments, in which we try to simulate farm responses in 2003 using a model calibrated to 1999 data, show that the alternative PMP variant improves the forecasting capacity of the model in all tested cases.

This report presents the first EU-wide individual farm level model (IFM-CAP) aiming to assess the impacts of CAP towards 2020 on farm economics and environmental effects. The rationale for such a farm-level model is based on the increasing demand for a micro simulation tool capable to model farm-specific policies and to capture farm heterogeneity across the EU in terms of policy representation and impacts. Based on Positive Mathematical Programming, IFM-CAP seeks to improve the quality of policy assessment upon existing aggregate and aggregated farm-group models and to provide assessment of distributional effects over the EU farm population. To guarantee the highest representativeness of the EU agricultural sector, the model is applied to every EU-FADN (Farm Accountancy Data Network) individual farm (83292 farms). The report provides a detailed description of the first IFM-CAP model version (IFM-CAP V.1) in terms of design, mathematical structure, data preparation, modelling livestock activities, allocation of input costs, modelling of the CAP post-2013 and calibration process. The theoretical background, the technical specification and the outputs that can be generated from this model are also briefly presented and discussed. Model capability is illustrated in this study with an analysis of the EU farmers' responses to the greening requirements introduced by the 2013 CAP reform.

The Common Agricultural Policy (CAP) has evolved throughout time reflecting the continuously changing concerns of European societies and its rural areas. The Mid-Term Review of the CAP, agreed on June 2003, represents a complete change in the way the EU support the farm sector. On the one hand, “decoupling” will make EU farmers more competitive and market oriented and, on the other hand, “cross-compliance” will ensure the respect of environmental, food safety and animal welfare standards. There is less emphasis on market and income support measures within Pillar 1 and an increasing importance of rural development programs. One of the particularities of the new CAP is that Member States have several options to implement the single payment scheme. That means that the CAP sets up the general guidelines but it will be for Member States and regions to decide the specific measures to adopt. The versatile nature of the new CAP will lead to a multiplicity of support schemes, rising the interest of developing economic tools flexible enough to take into account the different features and concerns of the rural areas. This motivates the aim of this paper to develop a methodology aimed to guide the design of regional or local strategies in the Spanish farming systems. The need to collect comprehensive field data is a serious limitation of traditional farm modelling methodologies to perform evaluation on a global scale. Most of existing analyses are restricted to the evaluation of impacts in limited areas making it difficult to establish general conclusions. In this context, the development of methodologies adapted to work with the limited databases available and that can be applied to diverse situations are highly valuable. In this paper we propose a methodological framework to assess the environmental and socio- economic impacts of different policy option in a large number of farming systems representing the heterogeneous characteristics that can be found throughout the Spanish territory. In this sense, we develop a positive mathematical programming model that allows us to simulate farmers’ behaviour under alternative policy scenarios. One of the main limitations of positive mathematical programming is that available options to the farmers are limited to the observed activities in the actual situation. We propose a cost transfer approach which allow us to overcome this difficulty. The model interface allows friendly use and easy replication to a large number of rural areas. This modelling approach allows us to evaluate environmental and socio-economic impacts of different agricultural policy scenarios. Chosen scenarios focus on some recently envisaged policy alternatives, such as the cross-compliance option in the Agenda 2000 and the decoupling scheme in the Mid Term Review of the CAP. Model results allow us to suggest that this modelling approach may be used as a management tool to assist the design of regional programs of measures within the CAP.

چکیده مدیریت منابع آب در ایران با تقاضای فزاینده برای منابع آب، افزایش قابل توجه در هزینه‌های عرضه آب و برداشت بی‌رویه از منابع آب زیرزمینی مواجه می‌باشد. برای بهبود کارایی استفاده از آب، اقتصاد‌دانان افزایش قیمت نهاده آب را پیشنهاد می‌کنند ولی سیاستگذاران به دلیل نگرانی‌های اقتصاد‌ی، فرهنگی و سیاسی این پیشنهاد را رد می‌کنند. در این تحقیق از تکنیک برنامه‌ریزی ریاضی مثبت (PMP) در سطح مزرعه برای تحلیل اثرات مختلف کاربرد سیاست‌های قیمت‌گذاری آب و همچنین سیاست‌های جایگزین آن در دشت مشهد (استان خراسان رضوی) بهره گرفته شد. سناریوهای شبیه‌سازی‌شده شامل افزایش قیمت نهاده آب، مالیات بر نهاده‌های مکمل نهاده آب و مالیات بر محصول می‌باشد. اثر سیاست‌های جایگزین بسته به گروه بهره‌بردار نماینده متفاوت بوده و اثرات آن بر درآمد، تقاضای آب و الگوی کشت هر گروه از بهره‌برداران گسترده‌ می‌باشد. سیاست قیمت‌گذاری آب و مالیات بر محصول در مقایسه با سیاست مالیات بر نهاده مکمل، مؤثرتر و مناسب‌تر می‌باشند. دو سیاست مالیات بر نهاده و محصول در نرخ‌های معینی می‌توانند به عنوان جایگزین سیاست قیمت‌گذاری آب بکار روند. واژه‌های کلیدی: آب، برنامه‌ریزی ریاضی مثبت، دشت مشهد، سیاست جایگزین

Estimating economic value of agricultural water under changing conditions and the effects of spatial aggregation

Positive mathematical programming (PMP) has renewed the interest in mathematical modelling of agricultural and environmental policies. This chapter explains first the main advantages and disadvantages of the PMP approach, followed by a presentation of an individual farm-based sector model, called SEPALE. The farm-based approach allows the introduction of differences in individual farm structures in the PMP modelling framework. Furthermore, a farm-level model gives the possibility of identifying the impacts according to various farm characteristics. Simulations of possible alternatives to the implementation of the Agenda 2000 mid-term review illustrate the value of such a model. This chapter concludes with some topics for further research to resolve some of the PMP limitations.

This study evaluates normative (NMP) and positive (PMP) mathematical programming methods for the recursive dynamic agent-based sector model SWISSland, which determines production decisions for 3400 farm-level models for the ex-post period 2005 to 2012. This study clearly shows that PMP for crop production activities improves the forecasting performance of farm based agent-based models compared to NMP. It also shows that combining PMP and NMP could be a suitable approach for agent-based sector models. For short-term forecast PMP for all production activities and PMP combined with NMP lead to similar results. The results either show that PMP calibration based on revenues and PMP calibration based on the entropy approach lead to similar results. By combining PMP with NMP some limitations of PMP could be reduced. In branches where the adoption of new production activities is expected due to market, the NMP approach could be an appropriate solution.

This paper describes the Positive Mathematical Programming (PMP), the method for calibrating models of agricultural livestock production and resource use by a nonlinear total cost function. The PMP method is applied to agricultural sectoral models to study changes in policy and market signals. The Canadian Regional Agriculture Model (CRAM) is a regional, multi-sectoral, comparative static, partial equilibrium, mathematical programming model developed and maintained by Agriculture and Agri-Food Canada (AAFC) since mid-eighties. The PMP process converts a linear model using flexibility constraints into a nonlinear model in the absence of the flexibility constraints. A component of CRAM is the beef sector. The elements of the set of total cost curves are defined as quadratic function in terms of the number of cows and calves in the beef production activities. The marginal cost curves were then approximated using the shadow values from linear programming solution with linear curves. Once the flexibility constraints were removed, the model automatically calibrates to the base year production levels. The results from four scenarios indicated the beef sector of CRAM could predict the impact of the scenarios on the size of beef herd. In Scenario 1 where cash costs were increased by 10 percent, the breeding herd size decreased from 3.73 percent in New Brunswick to 0.0 percent in Ontario and Quebec. In Scenario 2 where barley costs were decreased by 10 percent, the breeding herd size increased from 0 percent for British Columbia, Alberta, Ontario, Quebec, Prince Edward Island and Nova Scotia to 1.93 percent for New Brunswick. In Scenario 3 where carcass weight per beef cow could be increased by 10 percent, the increase in beef herd size ranged from 0 percent for Ontario and Quebec to 2.56 percent for New Brunswick. In Scenario 4 where world beef prices were increased by 10 percent increase in beef herd size ranged from 4.48 percent for Manitoba to 25.78 percent for New Brunswick.

This paper describes the Positive Mathematical Programming (PMP), the method for calibrating models of agricultural livestock production and resource use using a nonlinear total cost function. The PMP method is applied to agricultural sectoral models to study changes in policy and market signals. The Canadian Regional Agriculture Model (CRAM) is a regional, multi-sectoral, comparative static, partial equilibrium, mathematical programming model developed and maintained by Agriculture and Agri-Food Canada (AAFC) since mid-eighties. The PMP process converts a linear model using flexibility constraints into a nonlinear model in the absence of the flexibility constraints. A component of CRAM is the beef sector. The elements of the set of total cost curves are defined as quadratic function in terms of the number of cows and calves in the beef production activities. The marginal cost curves are then approximated using the shadow values from linear programming solution with linear curves. Once the flexibility constraints were removed, the model automatically calibrates to the base year production levels. The results from four scenarios indicated the beef sector of CRAM could predict the impact of the scenarios on the size of beef herd. In Scenario 1 where cash costs were increased by 10 percent, the breeding herd size decreased from 3.73 percent in New Brunswick to 0.0 percent in Ontario and Quebec. In Scenario 2 where barley costs were decreased by 10 percent, the breeding herd size increased from 0 percent for British Columbia, Alberta, Ontario, Quebec, Prince Edward Island and Nova Scotia to 1.93 percent for New Brunswick. In Scenario 3 where carcass weight per beef cow could be increased by 10 percent, the increase in beef herd size ranged from 0 percent for Ontario and Quebec to 2.56 percent for New Brunswick. In Scenario 4 where world beef prices were increased by 10 percent increase in beef herd size ranged from 4.48 percent for Manitoba to 25.78 percent for New Brunswick.

In 1956, Freund introduced the analysis of agricultural price risk in a mathematical programming framework. His discussion admitted only constant absolute risk aversion. This paper generalizes the treatment of risk preference in a mathematical programming approach along the lines suggested by Meyer (1987) who demonstrated the equivalence of expected utility of wealth and a function of mean and standard deviation of wealth for a wide class of probability distributions that differ only by location and scale. This paper extends the definition of calibration under Positive Mathematical Programming (PMP) by considering limiting input prices along with the traditional decision variables. Furthermore, it shows how to formulate an analytical specification for the estimation of the risk preference parameters and calibrates the model to the base data within small deviations. The PMP approach under generalized risk allows also the estimation of output supply elasticities and the response analysis of decoupled farm subsidies that recently has interested policy makers. The approach is applied to a sample of farms that do not produce all the sample commodities.