Sufficient Conditions for Aggregation of Linear Programming Models

Paris, Quirino; Rausser, Gordon C.

doi:10.2307/1238355

Cited by 19 publications

(5 citation statements)

References 10 publications

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“…These conditions are very restrictive and impractical. Several attempts have been made to relax these conditions (Miller 1966;Lee 1966;Paris and Rausser 1973), but the improvements have not been significant from empirical point of view.…”

Section: Exact Aggregation In Sector Modelsmentioning

confidence: 99%

“…In sector modeling, the empirical aggregation problem is to represent many firms, not necessarily homogenous, by a model of convenient size. Paris (1980) derived necessary and sufficient conditions for this more general case by extending the results of Paris and Rausser (1973) to firms with arbitrary size. However, he did not provide empirical guidance for developing the aggregate model.…”

Section: Exact Aggregation In Sector Modelsmentioning

confidence: 99%

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Exact Aggregation in Mathematical Programming Sector Models

Önal

McCarl²

1991

Canadian J Agri Economics

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This paper defines the exact aggregation problem in the sector modeling context and develops the theoretical basis of an aggregation procedure based on extreme point representation. Under the assumption of full information on all firms this procedure yields exact aggregation, irrespective of firm heterogeneity, and it also suggests empirical procedures for cases when full information is not present. Although aggregation in such cases is in general not exact, empirical evidence shows that little error is involved, and the aggregate model is rather stable under various parameter changes. Le présent document définit le problème de l'agrégation exacte dans le contexte de la modélisation d'un secteur et énonce la base théorique d'une méthode d'agrégation fondée sur la représentation des points extrêmes. Si on part de l'hypothèse qu'on détient toutes les informations sur les entreprises, la méthode proposée donne une agrégation exacte de ces dernières, peu importe leur hétérogénéité. Les auteurs suggèrent aussi des méthodes empiriques lorsque certaines données font défaut. Même si, dans ces cas, l'agrégation est rarement exacte, les résultats indiquent que les erreurs sont peu nombreuses et que le modèle agrégé garde sa stabilité meme advenant la modification de divers paramètres.

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Section: Exact Aggregation In Sector Modelsmentioning

confidence: 99%

Section: Exact Aggregation In Sector Modelsmentioning

confidence: 99%

Exact Aggregation in Mathematical Programming Sector Models

Önal

McCarl²

1991

Canadian J Agri Economics

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“…Paris and Rausser [8] have recently added to the literature on sufficient conditions, and also place their discussion in historical perspective. They make the point that Day's specifications are not only impossible to meet in practice but are also the most restrictive set of conditions conceivable.…”

Section: Australian Journal Of Agricultural Economics Aprilmentioning

confidence: 99%

Using Regression Analysis to Reduce Aggregation Bias in Linear Programming Supply Models*

Kennedy

1975

Australian Journal of Agricultural Economics

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IntroductionNormative estimates of aggregate supplies of outputs from N resource situations may be obtained by running a h e a r programming (LP) model for each resource situation and summing the resulting N output vectors. However, using this method, N may be too large to make the aggregate estimate obtained worth the cost of N LP runs, It may be possible to obtain the same result, or an approximation to the result, by summing the results of q ( < N ) LP models which are in some sense representative of the N original LP models. In general, the extent of the approximation, or aggregation, bias as it is known, is inversely proportional to q. The tradeoff between the costs saved in decreasing q at the expense of increasing the inaccuracy of estimates

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“…Such extreme solutions may be dramatically different from the observed supply responses, and would therefore not be useful for policy analysis purposes if the regional breakdown of the aggregate supply is important to policy-makers. A widely-used approach for preventing extreme specialization and obtaining diversified solutions is to impose upper/lower bounds (flexibility constraints) in activity) proposed originally by Day (1963;1969) have been relaxed to some extent by Paris and Rausser (1973). Spreen and Takayama (1980) concluded that exact aggregation is impossible in LP supply response models if there are alternative optimal solutions, but semi-exact aggregation is possible where the aggregation of the individual firm solutions belongs to the set of alternative optimal solutions of the aggregate problem.…”

mentioning

confidence: 99%

Modeling Agricultural Supply Response Using Mathematical Programming and Crop Mixes

Chen

Önal

2012

American J Agri Economics

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Mathematical programming models are widely used in agricultural sector analysis. However, the lack of micro‐level data, as well as computational requirements, necessitate the aggregation of individual producers into representative units when working at the sectoral level. This usually leads to unrealistic extreme specialization in supply responses. In 1982, McCarl introduced the “historical crop mixes” approach to avoid extreme specialization. We extend this approach by generating additional synthetic crop mixes using supply response elasticities and systematically varied commodity prices. In addition to avoiding extreme specialization, this approach provides flexibility when future supply responses can be vastly different from past responses. An application to U.S. biofuel policy analysis is presented.

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Sufficient Conditions for Aggregation of Linear Programming Models

Cited by 19 publications

References 10 publications

Exact Aggregation in Mathematical Programming Sector Models

Exact Aggregation in Mathematical Programming Sector Models

Using Regression Analysis to Reduce Aggregation Bias in Linear Programming Supply Models*

Modeling Agricultural Supply Response Using Mathematical Programming and Crop Mixes

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