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

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  • Phoebe Koundouri

    (Dept. of International and European Economic Studies, Athens University of Economics and Business)

  • Nikolaos Kourogenis

    ()
    (Department of Banking and Financial Management, University of Piraeus.)

Abstract

In this paper we take issue with the applicability of the central limit theorem (CLT) on aggregate crop yields. We argue that even after correcting for the effects of spatial dependence, systemic heterogeneities and risk factors, aggregation does not necessarily lead to normality. We show that aggregation is also likely to lead to nonnormal distributions, which exhibit both skewness and excess kurtosis. In particular, we consider the case in which the number of summands is not constant but varies with time, which corresponds to the empirically relevant situation where the number of acres used for cultivation of a particular crop exhibits substantial variation over time. In this case, the CLT is not applicable while the limit theorems for random sums of random variables, which apply, predict that the limiting distribution of the sum is not normal and depends on the postulated distribution of the number of summands. Using data from aggregate US states crop yields, we provide empirical support regarding the deviation of aggregate crops yields from normality.

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Paper provided by Athens University of Economics and Business in its series DEOS Working Papers with number 1007.

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Handle: RePEc:aue:wpaper:1007

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  1. 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, Agricultural and Applied Economics Association, vol. 86(2), pages 406-419.
  2. Richard E. Just & Quinn Weninger, 1999. "Are Crop Yields Normally Distributed?," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, Agricultural and Applied Economics Association, vol. 81(2), pages 287-304.
  3. Alan P. Ker & Barry K. Goodwin, 2000. "Nonparametric Estimation of Crop Insurance Rates Revisited," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, Agricultural and Applied Economics Association, vol. 82(2), pages 463-478.
  4. 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, University of Chicago Press, vol. 47(2), pages 244-80, April.
  5. Hennessy, David A., 2009. "Crop Yield Skewness and the Normal Distribution," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, Western Agricultural Economics Association, vol. 34(1), April.
  6. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, Econometric Society, vol. 41(1), pages 135-55, January.
  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, Agricultural and Applied Economics Association, vol. 80(1), pages 139-153.
  8. Joseph Atwood & Saleem Shaik & Myles Watts, 2003. "Are Crop Yields Normally Distributed? A Reexamination," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, Agricultural and Applied Economics Association, vol. 85(4), pages 888-901.
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Cited by:
  1. Du, Xiaodong & Hennessy, David A. & Yu, Cindy, 2012. "Testing Day's Conjecture That More Nitrogen Decreases Crop Yield Skewness," Staff General Research Papers, Iowa State University, Department of Economics 35022, Iowa State University, Department of Economics.
  2. 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.
  3. 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.
  4. 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, Agricultural and Applied Economics Association 156704, Agricultural and Applied Economics Association.

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