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.Productivity Analysis, Research Methods/ Statistical Methods, Teaching/Communication/Extension/Profession,

CROP INSURANCE VALUATION UNDER ALTERNATIVE YIELD DISTRIBUTIONS

Considerable disagreement exists about the most appropriate characterization of farm-level yield distributions. Yet, the economic importance of alternate yield distribution specifications on insurance valuation, product designs and farm-level risk management has not been investigated or documented. The results of this study demonstrate that large differences in expected payments from popular crop insurance products can arise solely from the parameterization chosen to represent yields. The results suggest that the frequently unexamined yield distribution specification may lead to incorrect conclusions in important areas of insurance and risk management research such as policy rating, and assessment of expected payments from policies.Risk and Uncertainty,

A quasilinear differential inclusion for viscous and rate-independent damage systems in non-smooth domains

This paper focuses on (incomplete) rate-independent damage in elastic bodies. Since the driving energy is nonconvex, solutions may have jumps as a function of time, and in this situation it is known that the classical concept of energetic solutions for rate-independent systems may fail to accurately describe the behavior of the system at jumps. Therefore we resort to the (by now well-established) "vanishing-viscosity" approach to rate-independent processes, and approximate the model by its viscous regularization. In fact, the analysis of the latter PDE system presents remarkable difficulties, due to its highly nonlinear character. We tackle it by combining a variational approach to a class of abstract doubly nonlinear evolution equations, with careful regularity estimates tailored to this specific system, relying on a q-Laplacian type gradient regularization of the damage variable. Hence for the viscous problem we conclude the existence of weak solutions, satisfying a suitable energy-dissipation inequality that is the starting point for the vanishing-viscosity analysis. The latter leads to the notion of (weak) parameterized solution to our rate-independent system, which encompasses the influence of viscosity in the description of the jump regime