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Determining Optimal Levels of Nitrogen Fertilizer Using RandomParameter Models

Published online by Cambridge University Press:  26 January 2015

Emmanuel Tumusiime ,
Brorsen B. Wade ,
Jagadeesh Mosali ,
Jim Johnson ,
James Locke  and
Jon T. Biermacher
Brorsen B. Wade
Affiliation:
Department of Agricultural Economics at Oklahoma State University
Jon T. Biermacher
Affiliation:
Agricultural Division of The Samuel Roberts Noble Foundation, Inc.
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Abstract

The parameters of yield response functions can vary by year. Past studiesusually assume yield functions are nonstochastic or “limited” stochastic. Inthis study, we estimate rye–ryegrass yield functions in which all parametersare random. The three functional forms considered are the linear responseplateau, the quadratic, and the Spillman-Mitscherlich. Nonstochastic yieldmodels are rejected in favor of stochastic parameter models. Quadraticfunctional forms fit the data poorly. Optimal nitrogen applicationrecommendations are calculated for the linear response plateau andSpillman-Mitscherlich. The stochastic models lead to smaller recommendedlevels of nitrogen, but the economic benefits of using fully stochastic cropyield functions are small because expected profit functions are relativelyflat for the stochastic yield functions. Stochastic crop yield functionsprovide a way of incorporating production, uncertainty into inputdecisions.

Keywords

cereal rye—ryegrassMonte Carlonitrogenrandom parametersstochastic plateauQ10C12D24
Type
Research Article
Information
Journal of Agricultural and Applied Economics , Volume 43 , Issue 4 , November 2011 , pp. 541 - 552
Copyright
Copyright © Southern Agricultural Economics Association 2011

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References

Akaike, H. “A New Look at the Statistical Model Identification.” IEEE Transactions on Automatic Control 19(1974):716–23.10.1109/TAC.1974.1100705Google Scholar
Altom, W., Rogers, J.L., Raun, W.R., Johnson, G.V., and Taylor, S.L. “Long-Term Wheat-Ryegrass Forage Yields as Affected by Rate and Date of Applied Nitrogen.” Journal of Production Agriculture 9,1(1996):510–16.10.2134/jpa1996.0510Google Scholar
Babcock, B.A. “The Effects of Uncertainty on Optimal Nitrogen Applications.” Review of Agricultural Economics 14(1992):271–80.10.2307/1349506Google Scholar
Belanger, G., Walsh, J.R., Richards, J.E., Milburn, P.H., and Zaidi, N. “Comparison of Three Statistical Models Describing Potato Yield Response to Nitrogen Fertilizer.” Agronomy Journal 92(2000):902–8.10.2134/agronj2000.925902xGoogle Scholar
Belasco, E.J., Taylor, M.R., Goodwin, B.K., and Schroeder, T.C. “Probabilistic Models of Yield, Price, and Revenue Risks for Fed Cattle Production.” Journal of Agricultural and Applied Economics 41(2009):91–105.S1074070800002571Google Scholar
Berck, P., and Helfand, G. “Reconciling the von Liebig and Differentiable Crop Production Functions.” American Journal of Agricultural Economics 72(1990):985–96.10.2307/1242630Google Scholar
Biermacher, J.T., Brorsen, B.W., Epplin, F.M., Solie, J.B., and Raun, W.R. “The Economic Potential of Precision Nitrogen Application with Wheat Based on Plant Sensing.” Agricultural Economics 40(2009):397–407.10.1111/j.1574-0862.2009.00387.xGoogle Scholar
Brorsen, B.W., and Richter., F.G.C. “Experimental Designs for Estimating Plateau-Type Production Functions and Economically Optimal Input Levels.” Journal of Productivity Analysis 35(2011):DOI: 10.1007/sl 1123-010-0204-0.Google Scholar
Cerrato, M.E., and Blackmer, A.M. “Comparison of Models for Describing Corn Yield Response to Nitrogen Fertilizer.” Agronomy Journal 82(1990):138–43.10.2134/agronj1990.00021962008200010030xGoogle Scholar
Coulibaly, N, Bernardo, D.J., and Horn, G.W. “Energy Supplementation Strategies for Wheat Pasture Stocker Cattle Under Uncertain Forage Availability.” Journal of Agricultural and Applied Economics 28(1996):172–79.S1074070800009597Google Scholar
Davidson, R., and Mackinnon, J.G. “Several Tests for Model Specification in the Presence of Alternative Hypothesis.” Econometrica 49(1981):781–93.10.2307/1911522Google Scholar
DeVuyst, E.A., and Preckel, P.V. “Gaussian Cubature: A Practitioner's Guide.” Mathematical and Computer Modelling 45(2007):787–94.10.1016/j.mcm.2006.07.021Google Scholar
Frank, M.D., Beattie, B.R., and Embleton, M.E. “A Comparison of Alternative Crop Response Models.” American Journal of Agricultural Economics 72(1990):597–603.10.2307/1243029Google Scholar
Greene, W.H. Econometric Analysis. 6th ed. Upper Saddle River, NJ: Prentice-Hall, 2008.Google Scholar
Grewal, R., Lilien, G.L., and Mallapragada, G. “Location, Location, Location: How Network Embeddedness Affects Project Success in Open Source Systems.” Management Science 52,7(2006):1043–56.10.1287/mnsc.1060.0550Google Scholar
Grimm, S.S., Paris, Q., and Williams, W.A. “Avon Liebig Model for Water and Nitrogen Crop Response.” Western Journal of Agricultural Economics 12(1987):182–92.Google Scholar
Heady, E.O., and Pesek, J. “A Fertilizer Production Surface With Specification of Economic Optima for Corn Grown on Calcareous Ida Silt Loam.” Journal of Farm Economics 36(1954):466–82.10.2307/1233014Google Scholar
Ishrat, H., Epplin, F.M., and Krenzer, E.G. Jr., “Planting Date Influence on Dual-Purpose Winter Wheat Forage Yield, Grain Yield, and Test Weight.” Agronomy Journal 95(2003):1179–88.10.2134/agronj2003.1179Google Scholar
Kaitibie, S., Epplin, F.M., Brorsen, B.W., Horn, G.W., Krenzer, E.G. Jr., and Paisley, S.I. “Optimal Stocking Density for Dual-Purpose Winter Wheat Production.” Journal of Agricultural and Applied Economics 35(2003):29–38.S1074070800005915Google Scholar
Krenzer, E.G. Jr., Tarrant, A.R., Bernardo, D.J., and Horn, G.W. “An Economic Evaluation of Wheat Cultivars Based on Grain and Forage Production.” Journal of Agriculture Production 9(1996):66–73.10.2134/jpa1996.0066Google Scholar
Lanzer, E.A., and Paris, Q. “A New Analytical Framework for the Fertilization Problem.” American Journal of Agricultural Economics 63(1981):93–103.10.2307/1239815Google Scholar
Makowski, D., and Wallach, D. “It Pays to Base Parameter Estimation on a Realistic Description of Model Errors.” Agronomie 22(2002):179–89.10.1051/agro:2002002Google Scholar
Mooney, D.F., Roberts, R.K., English, B.C., Tyler, D.D., and Larson, J.A. “Switchgrass Production in Marginal Environments: A Comparative Economic Analysis across Four West Tennessee Landscapes.” Selected paper, American Agricultural Economics Association Annual Meeting, Orlando, FL, 2008.AMBIGUOUS (830868 citations)Google Scholar
National Research Council. Nutrient Requirements of Beef Cattle. 6th ed. Washington, DC: National Academy Press, 1984.Google Scholar
Paris, Q. “The Von Liebig Hypothesis.” American Journal of Agricultural Economics 74(1992):1019–28.10.2307/1243200Google Scholar
Pinheiro, J.C., and Bates, D.M. “Approximations to the Log-likelihood Function in the Nonlinear Mixed-Effects Model.” Journal of Computational and Graphical Statistics 4(1995):12–35.Google Scholar
Pollak, A.R., and Wales, T.J. “The Likelihood Dominance Criterion: A New Approach to Model Selection.” Journal of Econometrics 47(1991):227–42.10.1016/0304-4076(91)90100-RGoogle Scholar
Roberts, D.C., Brorsen, B.W., Solie, J.B., and Raun, W.R. “The Effect of Parameter Uncertainty on Whole-Field Nitrogen Recommendations from Nitrogen-Rich Strips and Ramped Strips in Winter Wheat.” Agricultural Systems 104(2011):307–14.10.1016/j.agsy.2010.12.002Google Scholar
SAS Institute Inc. SAS OnlineDoc® 9.1. Cary, NC: SAS Institute Inc., 2003.Google Scholar
Schwarz, G. “Estimating the Dimension of a Model.” Annals of Statistics 6(1978):461–64.10.1214/aos/1176344136Google Scholar
Spillman, W.J. “Application of the Law of Diminishing Returns to Some Fertilizer and Feed Data.” Journal of Farm Economics 5(1923):36–52.10.2307/1230266Google Scholar
Taylor, K.W., Epplin, F.M., Brorsen, B.W., Fieser, B.G., and Horn, G.W. “Optimal Grazing Termination Date for Dual-Purpose Winter Wheat Production.” Journal of Agricultural and Applied Economics 42(2010):87–103.S107407080000331XGoogle Scholar
Tembo, G., Brorsen, B.W., Epplin, F.M., and Tostão, E. “Crop Input Response Functions With Stochastic Plateaus.” American Journal of Agricultural Economics 90(2008):424–34.10.1111/j.1467-8276.2007.01123.xGoogle Scholar
The Samuel Roberts Noble Foundation, Inc. 1997-2008. “Pasture & Range Information: Forage Yields from Ryegrass Varieties and Strains.” Internet site: http://www.noble.org/Ag/Research/Forages.htm (Accessed June 2009).AMBIGUOUS (453405 citations)Google Scholar
Tumusiime, E., Brorsen, B.W., Mosali, J., and Biermacher, J.T. “How Much Does Considering the Cost of Lime Affect the Recommended Level of Nitrogen?” Agronomy Journal 103(2011):404–12.10.2134/agronj2010.0355Google Scholar
Vuong, Q. “Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses.” Econometrica 57(1989):307–34.10.2307/1912557Google Scholar