Utilizing Extreme Value Theory to Uncover Yield Distributions from Farm and County Level Historical Corn Yields

Authors

Gerald H. Van Tassell, University of Nebraska-LincolnFollow

First Advisor

Cory G. Walters

Date of this Version

6-2024

Document Type

Thesis

Citation

A thesis presented to the faculty of the Graduate College at the University of Nebraska in partial fulfillment of requirements for the degree of Master of Science

Major: Agricultural Economics

Under the supervision of Professor Cory G. Walters

Lincoln, Nebraska, June 2024

Comments

Copyright 2024, Gerald H. Van Tassell. Used by permission

Abstract

Yield risk represents a major portion of the financial risk facing corn producers and is found in the left tail of the yield distribution. Traditional methods for generating yield distributions fall into two categories: parametric and non-parametric. The shape and behavior of the tail of parametric yield distributions are determined by distributional assumptions. Non-parametric distributions fail to account for the possibility of as yet unseen extreme events, often referred to as “Black Swans”. Extreme Value Theory (EVT) rectifies these issues by providing an empirical, parametric estimate of the risk of extreme events, regardless of the underlying distribution of corn yields.

A new method for generating complete yield distributions using EVT and Kernel Density Estimation (KDE) is proposed. EVT is used to estimate the tails of the yield distribution and KDE is used to estimate the body of the yield distribution. The new method combines the EVT estimate of the tails of the yield distribution with the KDE of the body of the yield distribution into a complete yield distribution.

County-level yield data is often used instead of farm-level yield data due to the paucity of farm-level yield data. The aggregation from farm to county-level data changes the shape of the yield distribution and reduces its variance. The new method for generating complete crop yield distributions is implemented on four datasets from three aggregation levels. Data from Preston Farms in Hardin County, Kentucky is compared to county-level yield data from Hardin County. Data from the Knorr-Holden Plot, a research plot in Scotts Bluff County, Nebraska is compared to county-level yield data from Scotts Bluff County. This paper showcases best practices for the application of EVT to small sample crop yield data.

The relationship between farm, field, and county-level yield distributions is heterogenous. While the Hardin County yield distribution well approximates the Preston Farms yield distribution, the Scotts Bluff County yield distribution is a poor approximation of the Knorr-Holden Plot yield distribution.

In the future, the improved method for estimating yield distributions will be applied to a net income model to improve producer decision making under uncertainty.

Advisor: Cory G. Walters