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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.

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File URL: http://hdl.handle.net/10.1093/ajae/aar055
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Bibliographic Info

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

Volume (Year): 93 (2011)
Issue (Month): 5 ()
Pages: 1341-1357

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Handle: RePEc:oup:ajagec:v:93:y:2011:i:5:p:1341-1357

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References

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  1. Hennessy, David A., 2012. "Crop Yield Skewness and the Normal Distribution," Staff General Research Papers 35019, Iowa State University, Department of Economics.
  2. Zanini, Fabio C. & Sherrick, Bruce J. & Schnitkey, Gary D. & Irwin, Scott H., 2001. "Crop Insurance Valuation Under Alternative Yield Distributions," 2001 Conference, April 23-24, 2001, St. Louis, Missouri 18953, NCR-134 Conference on Applied Commodity Price Analysis, Forecasting, and Market Risk Management.
  3. 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 244-80, April.
  4. Weninger, Quinn & Just, Richard E., 1999. "Are Crop Yields Normally Distributed?," Staff General Research Papers 5064, Iowa State University, Department of Economics.
  5. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January.
  6. 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.
  7. 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.
  8. 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.
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Cited by:
  1. Phoebe Koundouri & Nikolaos Kourogenis & Nikitas Pittis, . "Statistical Modeling of Stock Returns: Explanatory or Descriptive? A Historical Survey with Some Methodological Reflections," DEOS Working Papers 1331, Athens University of Economics and Business.
  2. Xiaodong Du & David A. Hennessy & Cindy L. Yu, 2010. "Testing Day's Conjecture that More Nitrogen Decreases Crop Yield Skewness," Center for Agricultural and Rural Development (CARD) Publications 10-wp511, Center for Agricultural and Rural Development (CARD) at Iowa State University.
  3. 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.
  4. Phoebe Koundouri & Nikolaos Kourogenis & Nikitas Pittis, . "Statistical Modeling of Stock Returns: A Historical Survey with Methodological Reflections," DEOS Working Papers 1226, Athens University of Economics and Business.

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