Tanya U. McDonald

Bio: Tanya U. McDonald is an academic researcher from New Mexico State University. The author has contributed to research in topics: Probability distribution & Parametric statistics. The author has an hindex of 3, co-authored 6 publications receiving 56 citations.

Ranking Crop Yield Models: A Comment

Abstract: This comment discusses key specification issues that may have affected the performance and, therefore, the ranking of parametric models that were compared in a recent AJAE article. A procedure to obtain the most flexible parametric model specification possible, given the particular probability distribution function on which the model is based is presented. These specifications also allow for standardized and, therefore, more valid comparisons across parametric models that are based on different probability distributions. Finally, the comment cautions against generalization of the rankings in that AJAE article and recommends that these more flexible specifications be adopted in future comparisons and applications.

A Flexible Parametric Family for the Modeling and Simulation of Yield Distributions

Abstract: The distributions currently used to model and simulate crop yields are unable to accommodate a substantial subset of the theoretically feasible mean-variance-skewness-kurtosis (MVSK) hyperspace. Because these first four central moments are key determinants of shape, the available distributions might not be capable of adequately modeling all yield distributions that could be encountered in practice. This study introduces a system of distributions that can span the entire MVSK space and assesses its potential to serve as a more comprehensive parametric crop yield model, improving the breadth of distributional choices available to researchers and the likelihood of formulating proper parametric models.

The Expanded Johnson System: A Highly Flexible Crop Yield Distribution Model

Abstract: Replaced with revised version of paper 11/28/06 Former title: The Expanded and Re-Parameterized Johnson System: A Most Crop-Yield Distribution Model

An Empirically-Grounded Comparison of the Johnson System versus the Beta as Crop Yield Distribution Models

Abstract: Previous research established that the expanded Johnson system can accommodate any theoretically possible mean-variance-skewness-kurtosis combination. Therefore, it has been hypothesized that this system can provide for a reasonably accurate modeling approximation of any probability distribution that might be encountered in practice. In order to test that hypothesis, this manuscript develops a more flexible expanded form of the Beta distribution which, in its original form, has been widely used to model and simulate crop yields for risk analysis. Empirically grounded evaluations suggest that the Johnson system can model a variety of typical yield data-generating processes that are based on the Beta distribution much more precisely than the Beta can model representative crop yield data simulated from the Johnson system. The accuracy with which the Johnson system approximates the Beta supports the previously stated hypothesis.

Heterogeneity and Distributional Form of Farm-Level Yields

Abstract: Representing farm-level crop yield heterogeneity and distributional form is critical for risk and crop insuranceresearch.Moststudieshaveusedcountydata,understatingbothsystematicandrandomvariation. Comparison of systematic versus random intra-county variation is lacking. Few studies compare the various distributional forms that have been proposed. This study utilizes the extensive potential of government farm-level crop insurance data. Results show that systematic intra-county variation is surprisingly strong. A newly applied reverse lognormal distribution is preferred when county-wide variation is removed, but the normal distribution fits surprisingly well in the crop insurance relevant percentiles when county-wide variation is not removed. Representing and accounting for both spatial and temporal heterogeneity is a major problem in agricultural economics and policy analysis due to the fact that most data are aggregated to at least the county level (e.g., Gardner and Kramer 1986; Just and Pope 1999). Both systematic and random components of crop yields are major factors in intra-county farm-level heterogeneity that are critical for modeling risk, producer behavior, and crop insurance participation. Most studies have either used aggregate (at least county-level) data or relied on relatively few farm-level observations. The former makes results primarily illustrative, while the latter limits statistical significance. This article characterizes intra-county crop yield heterogeneity both spatially and temporally with the most extensive dataset utilized to date and evaluates a broader set of parametric distributional possibilities than previously.

Crop Yield Distributions: A Reconciliation of Previous Research and Statistical Tests for Normality

Abstract: This study revisits the large but inconclusive body of research on crop yield distributions. Using competing techniques across 3,852 crop/county combinations we can reconcile some inconsistencies in previous studies. We examine linear, polynomial, and ARIMA trend models. Normality tests are undertaken, with an implementable R-test and multivariate testing to account for spatial correlation. Empirical results show limited support for stochastic trends in yields. Results also show that normality rejection rates depend on the trend specification. Corn Belt corn and soybeans yields are negatively skewed while they tend to become more normal as one moves away from the Corn Belt.

Relaxing Heteroscedasticity Assumptions in Area-Yield Crop Insurance Rating

Abstract: This article focuses on the effect of differing heteroscedasticity assumptions on derived premium rates of area-yield crop insurance. Tests of the proportional and absolute heteroscedasticity assumptions are conducted using both in-sample and out-of-sample measures. Our results suggest that arbitrarily imposing a specific form of heteroscedasticity or homoscedasticity in insurance rate calculations limits actuarial soundness. Our results have practical implications for the federal crop insurance programs, as we reject the traditional rating assumptions for many cotton regions and lower-yielding/higher-risk corn and soybean counties but not in the heart of the Cornbelt. Copyright 2011, Oxford University Press.

On Technological Change in Crop Yields

Abstract: Technological changes in agriculture tend to alter the mass associated with segments or components of the yield distribution as opposed to simply shifting the entire distribution upwards. We propose modeling crop yields using mixtures with embedded trend functions to account for potentially different rates of technological change in different components of the yield distribution. By doing so we can test some interesting and previously untested hypotheses about the data generating process of yields. For example: (1) is the rate of technological change equivalent across components, and (2) are the probabilities of components constant over time? Our results—technological change is not equivalent across components and probabilities tend not to have changed significantly over time—have implications for modeling yields. We find estimated conditional yield densities are quite different when unique trend functions are embedded inside the mixture components versus estimating the same mixture with detrended data. Also, we prove different rates of technological change in different components lead to nonconstant variance with respect to time (i.e., heteroscedasticity). We present two applications of the proposed yield model. The first application considers climate determinants of component membership, where our results are consistent with the literature for climate determinants of yields. The second application compares the proposed yield model to USDA's current rating methodology for area‐yield crop insurance contracts and finds the proposed model may lead to more accurate rates.