Skip to main content

Towards Econometric Mathematical Programming for Policy Analysis

  • Chapter
  • First Online:
Applied Methods for Agriculture and Natural Resource Management

Part of the book series: Natural Resource Management and Policy ((NRMP,volume 50))

Abstract

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 is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Arata, L., Donati, M., Sckokai, P., & Arfini, F. (2017). Incorporating risk in a positive mathematical programming framework: A dual approach. Australian Journal of Agricultural and Resource Economics, 61(2), 265–284.

    Article  Google Scholar 

  • Arfini, F., & Donati, M. (2011). The impact of the Health Check on structural change and farm efficiency: A comparative assessment of three European agricultural regions. In C. Moreddu (Ed.), Disaggregated impacts of CAP reforms: Proceedings of an OECD Workshop. Paris, France: OECD Publishing.

    Google Scholar 

  • Arfini, F., Donati, M., Grossi L., & Paris, Q. (2008). Revenue and cost functions in PMP: A methodological integration for a territorial analysis of CAP. Paper presented at the 107th EAAE Seminar ‘Modelling of Agricultural and Rural Development Policies’. Sevilla, Spain, January 29–February 1st 2008.

    Google Scholar 

  • Arndt, C., Robinson, S., & Tarp, F. (2002). Parameter estimation for a computable general equilibrium model: A maximum entropy approach. Economic Modelling, 19, 375–398.

    Article  Google Scholar 

  • Britz, W., & Arata, L. (2019). Econometric mathematical programming: an application to the estimation of costs and risk preferences at farm level. Agricultural Economics, 50.

    Google Scholar 

  • Britz, W., Heckelei, T., & Wolff, H. (2003). Symmetric positive equilibrium problem: A framework for rationalizing economic behaviour with limited information: Comment. American Journal of Agricultural Economics, 85(4), 1078–1081.

    Article  Google Scholar 

  • Buysse, J., Fernagut, B., Harmignie, O., Henry de Frahan, B., Lauwers, L., Polomé, P., et al. (2007a). Farm-based modelling of the EU sugar reform: Impact on Belgian sugar beet suppliers. European Review of Agricultural Economics, 34(1), 21–52.

    Article  Google Scholar 

  • Buysse, J., Van Huylenbroeck, G., & Lauwers, L. (2007b). Normative, positive and econometric mathematical programming as tools for incorporation of multifunctionality in agricultural policy modelling. Agriculture, Ecosystems & Environment, 120(1), 70–81.

    Article  Google Scholar 

  • Chambers, R. G., & Just, R. E. (1989). Estimating multioutput technologies. American Journal of Agricultural Economics, 71(4), 980–995.

    Article  Google Scholar 

  • Cortignani, R., & Severini, S. (2009). Modelling farm-level adoption of deficit irrigation using positive mathematical programming. Agricultural Water Management, 96(12), 1785–1791.

    Article  Google Scholar 

  • Cortignani, R., & Severini, S. (2012). Modelling farmer participation to a revenue insurance scheme by means of the positive mathematical programming. Agricultural Economics—Czech, 58(7), 324–331.

    Article  Google Scholar 

  • Ferris, M. C., Dirkse, S. P., Jagla, J.-H., & Meeraus, A. (2009). An extended mathematical programming framework. Computers & Chemical Engineering, 33(12), 1973–1982.

    Article  Google Scholar 

  • Ferris, M. C., Dirkse, S. P., & Meeraus, A. (2002). Mathematical programs with equilibrium constraints: Automatic reformulation and solution via constrained optimization (Computing Laboratory Report No. 02/11). Oxford: England: Oxford University.

    Google Scholar 

  • Frisvold, G. B., & Konyar, K. (2012). Less water: How will agriculture in Southern Mountain states adapt? Water Resources Research, 48, W05534. https://doi.org/10.1029/2011WR011057.

    Article  Google Scholar 

  • Garnache, C., & Mérel, P. (2015). What can acreage allocations say about supply elasticities? A convex programming approach to supply response disaggregation. Journal of Agricultural Economics, 66(1), 236–256.

    Article  Google Scholar 

  • Garnache, C., Mérel, P. R., Howitt, R. E., Howitt, R. E., & Lee, J. (2017). Calibration of shadow values in constrained optimization models of agricultural supply. European Review of Agricultural Economics, 44(3), 363–397.

    Article  Google Scholar 

  • Gocht, A. (2005). Assessment of simulation behaviour of different mathematical programming approaches. In F. Arfini (Ed.), Modelling agricultural policies: State of the art and new challenges. Proceedings of the 89th European Seminar of the European Association of Agricultural Economists (pp. 48–73). Italy: University of Parma.

    Google Scholar 

  • Gocht, A., & Britz, W. (2011). EU-wide farm type supply models in CAPRI-How to consistently disaggregate sector models into farm type models. Journal of Policy Modeling, 33(1), 146–167.

    Article  Google Scholar 

  • Golan, A., Judge, G., & Miller, D. (1996). Maximum entropy econometrics. Chichester: Wiley.

    Google Scholar 

  • Gorddard, R. (2013). Profit-maximizing land-use revisited: The testable implications of non-joint crop production under land constraint. American Journal of Agricultural Economics, 95(5), 1109–1121.

    Article  Google Scholar 

  • Graindorge, C., Henry de Frahan, B., & Howitt, R. E. (2001). Analysing the effects of Agenda 2000 using a CES calibrated model of Belgian agriculture. In T. Heckelei, H. P. Witzke, & W. Henrichsmeyer (Eds.), Agricultural sector modelling and policy information systems (pp. 177–186). Kiel: Vauk Verlag.

    Google Scholar 

  • Graveline, N., & Mérel, P. (2014). Intensive and extensive margin adjustments to water scarcity in France’s cereal belt. European Review of Agricultural Economics, 41(5), 707–743.

    Article  Google Scholar 

  • Guyomard, H., Baudry, M., & Carpentier, A. (1996). Estimating crop supply response in the presence of farm programmes: Application to the CAP. European Review of Agricultural Economics, 23, 401–420.

    Article  Google Scholar 

  • Heckelei, T., & Britz, W. (2000). Positive mathematical programming with multiple data points: A cross-sectional estimation procedure. Cahiers d’Economie et Sociologie Rurales, 57(4), 28–50.

    Google Scholar 

  • Heckelei, T., & Britz, W. (2005). Models based on positive mathematical programming: State of the art and further extensions. In F. Arfini (Ed.), Modelling agricultural policies: state of the art and new challenges. Proceedings of the 89th European Seminar of the European Association of Agricultural Economists (pp. 48–73). Italy: University of Parma.

    Google Scholar 

  • Heckelei, T., & Wolff, H. (2003). Estimation of constrained optimisation models for agricultural supply analysis based on generalised maximum entropy. European Review of Agricultural Economics, 30(1), 27–50.

    Article  Google Scholar 

  • Heckelei, T., Britz, W., & Zhang, Y. (2012). Positive mathematical programming approaches—recent developments in literature and applied modelling. Bio-based and Applied Economics, 1(1), 109–124.

    Google Scholar 

  • Heckelei, T., Mittelhammer, R., & Jansson T. (2008). A Bayesian alternative to generalized cross entropy solutions for underdetermined econometric models. In Food and Resource Economics Discussion Paper 2008:2, Institute for Food and Resource Economics, University of Bonn.

    Google Scholar 

  • Helming, J. F. M., Peeters, L., & Veendendaal, P. J. J. (2001). Assessing the consequences of environmental policy scenarios in Flemish agriculture. In T. Heckelei, H. P. Witzke, & W. Henrichsmeyer (Eds.), Agricultural sector modelling and policy information systems. Proceedings of the 65th EAAE Seminar, March 29–31, 2000 at Bonn University (pp. 237–245). Kiel: Vauk Verlag.

    Google Scholar 

  • Henry de Frahan, B., Buysse, J., Polomé, P., Fernagut, B., Harmignie, O., Lauwers, L., et al. (2007). Positive mathematical programming for agricultural and environmental policy analysis: Review and practice. In A. Weintraub, C. Romero, T. Bjørndal, R. Epstein, & J. Miranda (Eds.), Handbook of operations research in natural resources, international series in operations research and management science (pp. 129–154). New York: Springer.

    Google Scholar 

  • Henry de Frahan, B., Baudry, A., De Blander, R., Polomé, P., & Howitt, R. (2011). Dairy farms without quotas in Belgium: Estimations and simulations with a flexible cost function. European review of agricultural economics, 38(4), 1–27.

    Article  Google Scholar 

  • Howitt, R. E. (1995a). Positive mathematical programming. American Journal of Agricultural Economics, 77(2), 329–342.

    Article  Google Scholar 

  • Howitt, R. E. (1995b). A calibration method for agricultural economic production models. Journal of Agricultural Economics, 46(2), 147–159.

    Article  Google Scholar 

  • Jansson, T., & Heckelei, T. (2011). Estimating a primal model of regional crop supply in the European Union. Journal of Agricultural Economics, 62(1), 137–152.

    Article  Google Scholar 

  • Jansson, T., & Heckelei, T. (2009). A new estimator for trade costs and its small sample properties. Economic Modelling, 26, 489–498.

    Article  Google Scholar 

  • Jansson, T., Heckelei, T., Gocht, A., Basnet, S. K., Zhang, Y., & Neuenfeldt, S. (2014). Analysing impacts of changing price variability with estimated farm risk-programming models. Paper presented at the EAAE 2014 Congress ‘Agri-Food and Rural Innovations for Healthier Societies’. Slovenia, Ljubljana, 26–29 Aug 2014.

    Google Scholar 

  • Júdez, L., Chaya, C., Martinez, S., & Gonsalez, A. A. (2001). Effects of the measures envisaged in “Agenda 2000” on Arable Crop Producers and Beef and Veal Producers: An application of positive mathematical programming to representative farms of a Spanish region. Agricultural Systems, 67, 121–138.

    Article  Google Scholar 

  • Kanellopoulos, A., Berentsen, P., Heckelei, T., van Ittersum, M., & Oude Lansink, A. (2010). Assessing the forecasting performance of a generic bio-economic farm model calibrated with two different PMP variants. Journal of Agricultural Economics, 61(2), 137–152.

    Article  Google Scholar 

  • Lence, H. L., & Miller, D. (1998). Recovering output specific inputs from aggregate input data: A generalized cross-entropy approach. American Journal of Agricultural Economics, 80(4), 852–867.

    Article  Google Scholar 

  • Léon, Y., Peeters, L., Quinqu, M., & Surry, Y. (1999). The use of maximum entropy to estimate input-output coefficients from regional farm accounting data. Journal of Agricultural Economics, 50, 425–439.

    Article  Google Scholar 

  • Louhichi, K., Ciaian, P., Espinosa, M., Perni, A., Vosough Ahmadi, B., Colen, L., & Gomez y Paloma, S. (2016). An EU-Wide Individual farm model for common agricultural policy analysis (IFM-CAP 1.0) (technical documentation) (JRC Science and Policy Reports). Sevilla, Spain: European Commission, Joint Research Centre, Institute for Prospective Technological Studies.

    Google Scholar 

  • Louhichi, K., Kanellopoulos, A., Janssen, S., Flichman, G., Blanco, M., Hengsdijk, H., et al. (2010). FSSIM, a bio-economic farm model for simulating the response of EU farming systems to agricultural and environmental policies. Agricultural Systems, 103(8), 585–597.

    Article  Google Scholar 

  • Marsh, T. L., Mittelhammer, R., & Cardell, N. S. (2014). Generalized maximum entropy analysis of the linear simultaneous equations model. Entropy, 16, 825–853.

    Article  Google Scholar 

  • Medellin-Azuara, J., Howitt, R., & Harou, J. (2012). Predicting farmer responses to water pricing, rationing and subsidies assuming profit maximizing investment in irrigation technology. Agricultural Water Management, 108, 73–82.

    Article  Google Scholar 

  • Mérel, P., & Bucaram, S. (2010). Exact calibration of programming models of agricultural supply against exogenous supply elasticities. European Review of Agricultural Economics, 37(3), 395–418.

    Article  Google Scholar 

  • Mérel, P., & Howitt, R. E. (2014). Theory and application of positive mathematical programming in agriculture and the environment. Annual Review of Resource Economics, 6, 451–470.

    Article  Google Scholar 

  • Mérel, P., Simon, L. K., & Yi, F. (2011). A fully calibrated generalized constant-elasticity-of-substitution programming model of agricultural supply. American Journal of Agricultural Economics, 93(4), 936–948.

    Article  Google Scholar 

  • Mérel, P., Yi, F., Lee, J., & Six, J. (2014). A regional bio-economic model of nitrogen use in cropping. American Journal of Agricultural Economics, 96(1), 67–91.

    Article  Google Scholar 

  • Mittelhammer, R. C., Cardell, N. S., & Marsh, T. L. (2013). The data-constrained generalized maximum entropy estimator of the GLM: Asymptotic theory and inference. Entropy, 15, 1756–1775.

    Article  Google Scholar 

  • Moro, D., & Sckokai, P. (1999). Modelling the CAP arable crop regime in Italy: Degree of decoupling and impact of Agenda 2000. Cahiers d’Economie et Sociologie Rurales, 53, 50–73.

    Google Scholar 

  • Oude Lansink, A. (1999). Generalised maximum entropy and heterogeneous technologies. European Review of Agricultural Economics, 26, 101–115.

    Article  Google Scholar 

  • Paris, Q. (2001a). Symmetric positive equilibrium problem: A framework for rationalizing economic behavior with limited information. American Journal of Agricultural Economics, 83(4), 1049–1061.

    Article  Google Scholar 

  • Paris, Q. (2001b). Dynamic positive equilibrium problem. Working Paper. Davis: Department of Agricultural and Resource Economics. University of California.

    Google Scholar 

  • Paris, Q. (2011). Economic foundations of symmetric programming. Cambridge: Cambridge University Press.

    Google Scholar 

  • Paris, Q. (2015). Positive mathematical programming with generalized risk: A revision. Working Paper. Davis: Department of Agricultural and Resource Economics. University of California, April 2015.

    Google Scholar 

  • Paris, Q. (2017). Cost function and positive mathematical programming. Bio-based and Applied Economics, 6(1), 19–35.

    Google Scholar 

  • Paris, Q., & Howitt, R. E. (1998). An analysis of ill-posed production problems using maximum entropy. American Journal of Agricultural Economics, 80(1), 124–138.

    Article  Google Scholar 

  • Petsakos, A., & Rozakis, S. (2015). Calibration of agricultural risk programming models. European Journal of Operational Research, 24, 536–545.

    Article  Google Scholar 

  • Preckel, P. V. (2001). Least squares and entropy: A penalty function perspective. American Journal of Agricultural Economics, 83(2), 366–377.

    Article  Google Scholar 

  • Röhm, O., & Dabbert, S. (2003). Integrating agri-Environmental programs into regional production models: An extension of positive mathematical programming. American Journal of Agricultural Economics, 85(1), 254–265.

    Article  Google Scholar 

  • Sinha, A., Malo, P., & Deb, K. (2017). A review on bilevel optimization: From classical to evolutionary approaches and applications. arXiv:1705.06270v1 [math.OC]. 17 May 2017.

  • Vicente, L. N., & Calamai, P. H. (1994). Bilevel and multilevel programming: A bibliography review. Journal of Global Optimization, 5(3), 291–306.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Bruno Henry de Frahan .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Henry de Frahan, B. (2019). Towards Econometric Mathematical Programming for Policy Analysis. In: Msangi, S., MacEwan, D. (eds) Applied Methods for Agriculture and Natural Resource Management. Natural Resource Management and Policy, vol 50. Springer, Cham. https://doi.org/10.1007/978-3-030-13487-7_2

Download citation

Publish with us

Policies and ethics