Department of Agricultural, Food, and Resource Economics Elton R. Smith Endowment

The basic idea here is that there is some rhyme and reason to the distribution of crop yields as contemplated prior to planting. These distributions are important to understand for food security and insurance rate-setting purposes. It is well understood that certain cropland, whether due to soils, climate or management opportunities available, face higher harvest-time yield variability. The line of work below seeks to explain other factors. The paper,

• Hennessy, D.A. “Crop Yield Skewness under Law of Minimum Technology.” American Journal of Agricultural Economics, 91(February, 2009):197-208. Link

argues that yield skewness has to do with ‘reliability’ as in how many things can go wrong. In a reliable system (with better land/climate, with irrigation in arid areas and when the region’s cropping infrastructure is more developed) yields will tend to be negatively skewed because things will typically go right. Another way to think about it is as removing constraints in an optimization problem. The paper

• Hennessy, D.A. “Crop Yield Skewness and the Normal Distribution.” Journal of Agricultural and Resource Economics, 34(April, 2009):34-52. Link

shows that when the weather suitability to yield relation demonstrates a declining response (and there is ample evidence that it does), then there will be a tilt toward negative skewness. It also seeks to sort out much confusion regarding the appropriateness of a normal yield distribution assumption. The central limit theory does not provide support for this assumption.

The above theory about reliability and skewness is tested in,

• Du, X., D.A. Hennessy, and C. Yu. “Testing Day’s Conjecture that More Nitrogen Decreases Crop Yield Skewness.” American Journal of Agricultural Economics, 94(January, 2012):225-237. Link
• Du, X., Cindy L. Yu, D.A. Hennessy, and R. Miao. “Geography of Crop Yield Skewness.” Agricultural Economics, 46(4, 2015):463-473. Link

The first paper looks at removing a nitrogen fertilization constraint, showing that skewness becomes more negative as nitrogen use increases. The second paper shows that the moments of yield distributions perform as expected (higher mean, lower variability, more negatively skewed) whenever land is better, or less constraining.

A separate take on ‘geography is yield distribution destiny’ is given in:

• Du, X., D.A. Hennessy, H. Feng, and G. Arora. “Land Resilience and Tail Dependence Among Crop Yield Distributions.” Forthcoming at American Journal of Agricultural Economics. Link

There the matter is systemic risk. Yield is viewed as a function of land quality, water availability and good/bad heat in the form of growing degree days and stress degree days. It is argued that better soils should complement good heat in determining yield because the growing season is longer. However, land quality and soil moisture are substitutes because good land promotes storage of precipitation in the soil. We use data to demonstrate that this is the case, and we use related insights to argue that aggregate crop yields in an area will become more systemically risky whenever area land is marginal for cropping. The work

• Du, X., D.A. Hennessy, and H. Feng. “A Natural Resource Theory of U.S. Crop Insurance Contract Choice.” American Journal of Agricultural Economics, 96(January, 1, 2014):232-252. Link

addresses a related theme, namely that ‘geography is crop insurance demand destiny.’

One further paper in the set is:

• Hennessy, D.A. “A Crop Yield Expectation Stochastic Process with Beta Distribution as Limit.” Journal of Agricultural and Resource Economics, 36(April, 2011):177-191. Link

in which a very mechanical characterization of crop yield formation is provided. Yield is viewed as a martingale process emerging over the course of the crop year as good and bad news events are realized. Perhaps surprisingly, the beta distribution emerges as a result. There is a reliability theory underpinning to this too, but that is not explored in the paper. The work is intended as a way for modeling yield expectations over the course of the growing season, and so helping commodity market analysts. But only a few people have shown interest. Whether that is because I didn’t communicate well or because few think much of the idea, well that is for others to relate to you on the off chance that you find someone who has read this work.

Work under the ERS chair is ongoing in this area, where the emphasis is on understanding why crop insurance participation rates in Michigan and other northern tier cropping states are so low.