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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. 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.
  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. Hennessy, David A., 2012. "Crop Yield Skewness and the Normal Distribution," Staff General Research Papers 35019, Iowa State University, Department of Economics.
  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. 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.
  8. 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, . "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, 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.
  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 156704, Agricultural and Applied Economics Association.

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