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The Expanded Johnson System: A Highly Flexible Crop Yield Distribution Model

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  • Ramirez, Octavio A.
  • McDonald, Tanya U.

Abstract

The expanded form of the Johnson system advanced in this paper can model any theoretically possible combination of the first four central moments of a random variable, i.e. any mean-variance-skewness-kurtosis combination exhibited by a yield, price or any other distribution that may be encountered in practice. None of the probability distribution models previously in the literature come close to achieving such property. An application involving Illinois farm-level corn yields is presented to illustrate the estimation, characteristics and use of the proposed system. Although the yield data analyzed is from the same state and crop, the skewness and kurtosis combinations implied by the best fitting non-normal models extend over a large region of the S-K plane, corresponding to both the SU and the SB families. Theoretically, it is known that several of these S-K combinations can not be accommodated by the most commonly used parametric models based on the Beta and the Gamma distributions, which corroborates the need for probability distribution models that can span larger areas of this space.

Suggested Citation

  • Ramirez, Octavio A. & McDonald, Tanya U., 2006. "The Expanded Johnson System: A Highly Flexible Crop Yield Distribution Model," 2006 Annual meeting, July 23-26, Long Beach, CA 21455, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    • Handle: RePEc:ags:aaea06:21455
    DOI: 10.22004/ag.econ.21455
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    References listed on IDEAS

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    1. Keith H. Coble & Thomas O. Knight & Rulon D. Pope & Jeffery R. Williams, 1996. "Modeling Farm-Level Crop Insurance Demand with Panel Data," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 78(2), pages 439-447.
    2. Octavio A. Ramirez & Sukant Misra & James Field, 2003. "Crop-Yield Distributions Revisited," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 85(1), pages 108-120.
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    5. Octavio A. Ramírez, 1997. "Estimation and Use of a Multivariate Parametric Model for Simulating Heteroskedastic, Correlated, Nonnormal Random Variables: The Case of Corn Belt Corn, Soybean, and Wheat Yields," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 79(1), pages 191-205.
    6. Charles B. Moss & J. S. Shonkwiler, 1993. "Estimating Yield Distributions with a Stochastic Trend and Nonnormal Errors," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 75(4), pages 1056-1062.
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    8. Octavio A. Ramírez & Tanya McDonald, 2006. "Ranking Crop Yield Models: A Comment," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 88(4), pages 1105-1110.
    9. Bailey Norwood & Matthew C. Roberts & Jayson L. Lusk, 2004. "Ranking Crop Yield Models Using Out-of-Sample Likelihood Functions," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 86(4), pages 1032-1043.
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    Cited by:

    1. Tack, Jesse, 2013. "A Nested Test for Common Yield Distributions with Applications to U.S. Corn," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 38(1), pages 1-14, April.
    2. Ozaki, Vitor & Campos, Rogério, 2017. "Reduzindo a Incerteza no Mercado de Seguros: Uma Abordagem via Informações de Sensoriamento Remoto e Atuária," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 71(4), December.
    3. Ramirez, Octavio A. & Carpio, Carlos E. & Rejesus, Roderick M., 2011. "Can Crop Insurance Premiums Be Reliably Estimated?," Agricultural and Resource Economics Review, Northeastern Agricultural and Resource Economics Association, vol. 40(1), pages 1-14, April.

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