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On the Distribution of Crop Yields: Does the Central Limit Theorem Apply?

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  • Phoebe Koundouri
  • Nikolaos Kourogenis

Abstract

In this article, we investigate the applicability of the central limit theorem (CLT) to aggregate crop yields. We argue that the aggregation of elementary crop yields is likely to produce nonnormal distributions if, contrary to the standard CLT case, the number of crop acres exhibits substantial time variation. This case is covered by limit theorems for random sums of random variables, which predict nonnormal limiting distributions. The case of substantial variation in the number of summands produces an empirical hypothesis that we test using data from U.S. aggregate state crop yields. The results provide empirical support against the applicability of the CLT. Copyright 2011, Oxford University Press.

Suggested Citation

  • Phoebe Koundouri & Nikolaos Kourogenis, 2011. "On the Distribution of Crop Yields: Does the Central Limit Theorem Apply?," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 93(5), pages 1341-1357.
  • Handle: RePEc:oup:ajagec:v:93:y:2011:i:5:p:1341-1357
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    File URL: http://hdl.handle.net/10.1093/ajae/aar055
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    1. Richard E. Just & Quinn Weninger, 1999. "Are Crop Yields Normally Distributed?," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 81(2), pages 287-304.
    2. Bruce J. Sherrick & Fabio C. Zanini & Gary D. Schnitkey & Scott H. Irwin, 2004. "Crop Insurance Valuation under Alternative Yield Distributions," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 86(2), pages 406-419.
    3. Hennessy, David A., 2009. "Crop Yield Skewness and the Normal Distribution," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 34(1), April.
    4. Joseph Atwood & Saleem Shaik & Myles Watts, 2002. "Can Normality of Yields Be Assumed for Crop Insurance?," Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, Canadian Agricultural Economics Society/Societe canadienne d'agroeconomie, vol. 50(2), pages 171-184, July.
    5. Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," The Journal of Business, University of Chicago Press, vol. 47(2), pages 244-280, April.
    6. Alan P. Ker & Barry K. Goodwin, 2000. "Nonparametric Estimation of Crop Insurance Rates Revisited," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 82(2), pages 463-478.
    7. Joseph Atwood & Saleem Shaik & Myles Watts, 2003. "Are Crop Yields Normally Distributed? A Reexamination," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 85(4), pages 888-901.
    8. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    9. 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.
    10. Barry K. Goodwin & Alan P. Ker, 1998. "Nonparametric Estimation of Crop Yield Distributions: Implications for Rating Group-Risk Crop Insurance Contracts," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 80(1), pages 139-153.
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    Cited by:

    1. Phoebe Koundouri & Nikolaos Kourogenis & Nikitas Pittis, "undated". "Statistical Modeling of Stock Returns: A Historical Survey with Methodological Reflections," DEOS Working Papers 1226, Athens University of Economics and Business.
    2. Gerlt, Scott & Thompson, Wyatt & Miller, Douglas, 2014. "Exploiting the Relationship between Farm-Level Yields and County-Level Yields for Applied Analysis," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 39(2), August.
    3. Xiaodong Du & David A. Hennessy & Cindy L. Yu, 2012. "Testing Day's Conjecture that More Nitrogen Decreases Crop Yield Skewness," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 94(1), pages 225-237.
    4. Phoebe Koundouri & Nikolaos Kourogenis & Nikitas Pittis, 2016. "Statistical Modeling Of Stock Returns: Explanatory Or Descriptive? A Historical Survey With Some Methodological Reflections," Journal of Economic Surveys, Wiley Blackwell, vol. 30(1), pages 149-164, February.
    5. Wyatt Thompson & Joe Dewbre & Patrick Westfhoff & Kateryna Schroeder & Simone Pieralli & Ignacio Perez Dominguez, 2017. "Introducing medium-and long-term productivity responses in Aglink-Cosimo," JRC Working Papers JRC105738, Joint Research Centre (Seville site).
    6. Gerlt, Scott & Westhoff, Patrick, 2013. "Analysis of the Supplemental Coverage Option," 2013 AAEA: Crop Insurance and the Farm Bill Symposium, October 8-9, Louisville, KY 156704, Agricultural and Applied Economics Association.
    7. Christopher N. Boyer & B. Wade Brorsen & Emmanuel Tumusiime, 2015. "Modeling skewness with the linear stochastic plateau model to determine optimal nitrogen rates," Agricultural Economics, International Association of Agricultural Economists, vol. 46(1), pages 1-10, January.
    8. Gerlt, Scott & Westhoff, Patrick, "undated". "Comparison of County ARC and SCO," 2014 AAEA: Crop Insurance and the 2014 Farm Bill Symposium: Implementing Change in U.S. Agricultural Policy, October 8-9, Louisville, KY 184289, Agricultural and Applied Economics Association.

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