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Determining Optimal Levels of Nitrogen Fertilizer Using Random Parameter Models


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  • Tumusiime, Emmanuel
  • Brorsen, B. Wade
  • Mosali, Jagadeesh
  • Johnson, Jim
  • Locke, James
  • Biermacher, Jon T.


The parameters of yield response functions can vary by year. Past studies usually assume yield functions are nstochastic ‘‘limited’’ stochastic. In this study, we estimate rye– ryegrass yield functions in which all parameters are random. The three functional forms considered are the linear response plateau, the quadratic, and the Spillman-Mitscherlich. Nonstochastic yield models are rejected in favor of stochastic parameter models. Quadratic functional forms fit the data poorly. Optimal nitrogen application recommendations are calculated for the linear response plateau and Spillman-Mitscherlich. The stochastic models lead to smaller recommended levels of nitrogen, but the economic benefits of using fully stochastic crop yield functions are small because expected profit functions are relatively flat for the stochastic yield functions. Stochastic crop yield functions provide a way of incorporating production, uncertainty into input decisions.

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Bibliographic Info

Article provided by Southern Agricultural Economics Association in its journal Journal of Agricultural and Applied Economics.

Volume (Year): 43 (2011)
Issue (Month): 04 (November)

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Handle: RePEc:ags:joaaec:117949

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Keywords: cereal rye–ryegrass; Monte Carlo; nitrogen; random parameters; stochastic plateau; Production Economics; Q10; C12; D24;

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  1. Taylor, Karen W. & Epplin, Francis M. & Brorsen, B. Wade & Fieser, Brian G. & Horn, Gerald W., 2010. "Optimal Grazing Termination Date for Dual-Purpose Winter Wheat Production," Journal of Agricultural and Applied Economics, Southern Agricultural Economics Association, vol. 42(01), February.
  2. Gelson Tembo & B. Wade Brorsen & Francis M. Epplin & Em�lio Tost�o, 2008. "Crop Input Response Functions with Stochastic Plateaus," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 90(2), pages 424-434.
  3. Roberts, David C. & Brorsen, B. Wade & Solie, John B. & Raun, William R., 2011. "The effect of parameter uncertainty on whole-field nitrogen recommendations from nitrogen-rich strips and ramped strips in winter wheat," Agricultural Systems, Elsevier, vol. 104(4), pages 307-314, April.
  4. Jon T. Biermacher & B. Wade Brorsen & Francis M. Epplin & John B. Solie & William R. Raun, 2009. "The economic potential of precision nitrogen application with wheat based on plant sensing," Agricultural Economics, International Association of Agricultural Economists, vol. 40(4), pages 397-407, 07.
  5. Babcock, Bruce A., 1992. "Effects of Uncertainty on Optimal Nitrogen Applications (The)," Staff General Research Papers 10588, Iowa State University, Department of Economics.
  6. Kaitibie, Simeon & Epplin, Francis M. & Brorsen, B. Wade & Horn, Gerald W. & Krenzer, Eugene G., Jr. & Paisley, Steven I., 2003. "Optimal Stocking Density for Dual-Purpose Winter Wheat Production," Journal of Agricultural and Applied Economics, Southern Agricultural Economics Association, vol. 35(01), April.
  7. Pollak, R.A. & Wales, T.J., 1990. "The Likelihood Dominance Criterion: A New Approach To Model Selection," Discussion Papers in Economics at the University of Washington 90-10, Department of Economics at the University of Washington.
  8. B. Brorsen & Francisca Richter, 2012. "Experimental designs for estimating plateau-type production functions and economically optimal input levels," Journal of Productivity Analysis, Springer, vol. 38(1), pages 45-52, August.
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Cited by:
  1. Park, Seong Cheol & Vitale, Jeffrey D. & Turner, Jason Clemn & Stoecker, Arthur L. & Hattey, Jeffory A., 2011. "Economic Potential of Swine Effluent in Intensified Forage Systems in the Southern Plains," Journal of the ASFMRA, American Society of Farm Managers and Rural Appraisers.
  2. Park, Seong Cheol & Brorsen, B. Wade & Stoecker, Arthur L. & Hattey, Jeffory A., 2012. "Forage Response to Swine Effluent: A Cox Nonnested Test of Alternative Functional Forms Using a Fast Double Bootstrap," Journal of Agricultural and Applied Economics, Southern Agricultural Economics Association, vol. 44(04), November.
  3. Boyer, Christopher N. & Larson, James A. & Roberts, Roland K. & McClure, Angela T. & Tyler, Donald D. & Zhou, Vivian, 2013. "Stochastic Corn Yield Response Functions to Nitrogen for Corn after Corn, Corn after Cotton, and Corn after Soybeans," Journal of Agricultural and Applied Economics, Southern Agricultural Economics Association, vol. 45(04), November.


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