Estimation and Use of a Multivariate Parametric Model for Simulating Heteroskedastic, Correlated, Nonnormal Random Variables: The Case of Corn Belt Corn, Soybean, and Wheat Yields
01 Feb 1997-American Journal of Agricultural Economics (Oxford University Press)-Vol. 79, Iss: 1, pp 191-205
TL;DR: The authors developed a multivariate, non-normal density function that can accurately and separately account for skewness, kurtosis, heteroskedasticity, and correlation among the random variables of interest.
Abstract: This study develops a multivariate, nonnormal density function that can accurately and separately account for skewness, kurtosis, heteroskedasticity, and the correlation among the random variables of interest. The statistical attributes of the underlying random variables and correlation processes are examined. The potential applications of this modeling tool are discussed and exemplified by analyzing and simulating Corn Belt corn, soybean, and wheat yields. While corn and soybean yields are found to be skewed and kurtotic and exhibit different variances through time, wheat yields appear normal but also heteroskedastic. A strong correlation is detected between corn and soybean yields.
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TL;DR: In this article, the main sources of agricultural risk are discussed and an exposition of expected utility theory and of the notion of risk aversion is provided, followed by a basic analysis of agricultural production decisions under risk, including some comparative statics results from stylized models.
Abstract: Uncertainty and risk are quintessential features of agricultural production. After a brief overview of the main sources of agricultural risk, we provide an exposition of expected utility theory and of the notion of risk aversion. This is followed by a basic analysis of agricultural production decisions under risk, including some comparative statics results from stylized models. Selected empirical topics are surveyed, with emphasis on risk analyses as they pertain to production decisions at the farm level. Risk management is then discussed, and a synthesis of hedging models is presented. We conclude with a detailed review of agricultural insurance, with emphasis on the moral hazard and adverse selection problems that arise in the context of crop insurance.
389 citations
TL;DR: In this paper, the evidence for nonnormality of crop yields is reassessed and three methodological problems are identified in typical yield distribution analyses: misspecification of the nonrandom components of yield distributions, missreporting of statistical significance, and use of aggregate timeseries (ATS) data to represent farm-level yield distributions.
Abstract: The evidence for nonnormality of crop yields is reassessed. Three methodological problems are identified in typical yield distribution analyses: (i) misspecification of the nonrandom components of yield distributions, (ii) missreporting of statistical significance, and (iii) use of aggregate timeseries (ATS) data to represent farm-level yield distributions. One or more of these problems infect virtually all evidence against normality to date. The positive contribution of the article is a set of principles that must be followed in any valid investigation of yield normality.
294 citations
TL;DR: In this article, the authors demonstrate that large differences in expected payouts from popular crop insurance products can arise solely from the parameterization chosen to represent yield distributions and suggest that the frequently unexamined yield distribution specification may lead to economically significant errors in crop insurance policy rating and assessment of expected payout from policies.
Abstract: Considerable disagreement exists about the most appropriate characterization of farm-level yield distributions. Yet, the economic importance of alternative yield distribution specifications on crop insurance valuation has not been well documented. The results of this study demonstrate that large differences in expected payouts from popular crop insurance products can arise solely from the parameterization chosen to represent yield distributions. The results suggest that the frequently unexamined yield distribution specification may lead to economically significant errors in crop insurance policy rating and assessment of expected payouts from policies.
201 citations
Posted Content•
TL;DR: In this paper, the authors examined optimal futures and put ratios in the presence of four alternative crop insurance coverages, including revenue insurance, yield insurance, crop crop insurance, and crop crop revenue insurance.
Abstract: New types of crop insurance have expanded the tools from which crop producers may choose to manage risk. Little is known regarding how these products interact with futures and options. This analysis examines optimal futures and put ratios in the presence of four alternative insurance coverages. An analytical model investigates the comparative statics of the relationship between hedging and insurance. Additional numerical analysis is conducted which incorporates futures price, basis, and yield variability. Yield insurance is found to have a positive effect on hedging levels. Revenue insurance tends to result in slightly lower hedging demand than would occur given the same level of yield insurance coverage.
160 citations
TL;DR: This paper revisited the issue of crop-yield distributions using improved model specifications, estimation, and testing procedures that address the concerns raised in recent literature, which could have invalidated previous findings of yield nonnormality.
Abstract: This article revisits the issue of crop-yield distributions using improved model specifications, estimation, and testing procedures that address the concerns raised in recent literature, which could have invalidated previous findings of yield nonnormality. It concludes that some aggregate and farm-level yield distributions are nonnormal, kurtotic, and right or left skewed, depending on the circumstances. The advantages of utilizing nonnormal versus normal probability distribution function models, and the consequences of incorrectly assuming crop-yield normality are explored.
112 citations
References
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01 Jan 1963
TL;DR: In this article, a tabular summary of parametric families of distributions is presented, along with a parametric point estimation method and a nonparametric interval estimation method for point estimation.
Abstract: 1 probability 2 Random variables, distribution functions, and expectation 3 Special parametric families of univariate distributions 4 Joint and conditional distributions, stochastic independence, more expectation 5 Distributions of functions of random variables 6 Sampling and sampling distributions 7 Parametric point estimation 8 Parametric interval estimation 9 Tests of hypotheses 10 Linear models 11 Nonparametric method Appendix A Mathematical Addendum Appendix B tabular summary of parametric families of distributions Appendix C References and related reading Appendix D Tables
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01 Jan 1980TL;DR: The Classical Inference Approach for the General Linear Model, Statistical Decision Theory and Biased Estimation, and the Bayesian Approach to Inference are reviewed.
Abstract: SAMPLING THEORY AND BAYESIAN APPROACHES TO INFERENCE. The Classical Inference Approach for the General Linear Model. Statistical Decision Theory and Biased Estimation. The Bayesian Approach to Inference. INFERENCE IN GENERAL STATISTICAL MODELS AND TIME SERIES. Some Asymptotic Theory and Other General Results for the Linear Statistical Model. Nonlinear Statistical Models. Time Series. DYNAMIC SPECIFICATIONS. Autocorrelation. Finite Distributed Lags. Infinite Distributed Lags. SOME ALTERNATIVE COVARIANCE STRUCTURES. Heteroskedasticity. Disturbance--Related Sets of Regression Equations. Inference in Models that Combine Time Series and Cross--Sectional Data. INFERENCE IN SIMULTANEOUS EQUATION MODELS. Specification and Identification in Simultaneous Equation Models. Estimation and Inference in a System of Simultaneous Equations. Multiple Time Series and Systems of Dynamic Simultaneous Equations. FURTHER MODEL EXTENSIONS. Unobservable Variables. Qualitative and Limited Dependent Variable Models. Varying and Random Coefficient Models. Non--Normal Disturbances. On Selecting the Set of Aggressors. Multicollinearity. Appendices.
4,469 citations
2,085 citations
TL;DR: In this article, the authors evaluate two transformations, the Extended Box-Cox (BC) and the inverse hyperbolic sine (IHS), to reduce the influence of extreme observations of dependent variables.
Abstract: Transformations that could be used to reduce the influence of extreme observations of dependent variables, which can assume either sign, on regression coefficient estimates are studied in this article. Two that seem reasonable on a priori grounds—the extended Box—Cox (BC) and the inverse hyperbolic sine (IHS)—are evaluated in detail. One feature is that the log-likelihood function for IHS is defined for zero values of the dependent variable, which is not true of BC. The double-length regression technique (Davidson and MacKinnon 1984) is used to perform hypothesis tests of one transformation against the other using Canadian data on household net worth. These tests support the use of IHS instead of BC for this data set. Empirical investigators in economics often work with a logged dependent variable (taking the natural logarithm of a data series is, of course, a special case of BC) to reduce the weight their particular estimation procedure might otherwise attach to extreme values of the dependent v...
1,148 citations
TL;DR: In this article, models from atmospheric science, plant science, and agricultural economics are linked to explore the sensitivity of agricultural productivity to global climate change, and the simulation suggests that irrigated acreage will expand and regional patterns of U.S. agriculture will shift.
Abstract: Agricultural productivity is expected to be sensitive to global climate change. Models from atmospheric science, plant science, and agricultural economics are linked to explore this sensitivity. Although the results depend on the severity of climate change and the compensating effects of carbon dioxide on crop yields, the simulation suggests that irrigated acreage will expand and regional patterns of U.S. agriculture will shift. The impact of the U.S. economy strongly depends on which climate model is used.
644 citations