Estimating Farm-Level Yield Distributions For Corn And Soybeans In Illinois

Many yield modeling approaches have been developed in attempts to provide accurate characterizations of farm-level yield distributions due to the importance of yield uncertainty in crop insurance design and rating, and for managing farm-level risk. Competing existing models of crop yields accommodate varying skewness, kurtosis, and other departures from normality including features such as multiple modes. Recently, the received view of crop yield modeling has been challenged by Just and Weninger who indicate that there is insufficient evidence to reject normality given data limitations and potential methodological shortcomings in controlling for deterministic components (trend) in yields. They point out that past empirical efforts to estimate and validate specific-farm distributional characterizations have been severely hampered by data limitations. As a result, they argue in favor of normality as an appropriate parameterization of crop yields. This paper investigates alternate representations of farm-level crop yield distributions using a unique data set from the University of Illinois Endowment farms, containing same-site yield observations for a relatively long period of time, and under conditions that closely mirror actual farm conditions in Illinois. Results from alternate econometric model specifications controlling for trend effects suggest that a linear trend provides an adequate representation of crop yields at the farm level during the period covered by the estimations. Specification tests based on a linear-trend model suggest significant heteroskedasticity is present in only a few farms, and that the residuals are white noise. With these data, Jarque-Bera normality test results indicate that normality of detrended yield residuals is rejected by a far greater number of fields than would be explained due to randomness. Thus, to further clarify the issue of yield distribution characterizations, more complete goodness-of-fit measures are compared across a larger set of candidate distributions. The results indicate that the Weibull distribution consistently ranks better than the normal distribution both in fields where normality is rejected and in fields where normality is not rejected. The results highlight the fact that failing to reject normality is not the same as identifying normality as a "best" parameterization, and provide guidance for progressing toward better representations of farm-level crop yields.