Hostname: page-component-8448b6f56d-mp689 Total loading time: 0 Render date: 2024-04-20T03:40:03.885Z Has data issue: false hasContentIssue false
  • English
  • Français

Empirically Evaluating the Flexibility of the Johnson Family of Distributions: A Crop Insurance Application

Published online by Cambridge University Press:  15 September 2016

Yue Lu ,
Octavio A. Ramirez ,
Roderick M. Rejesus ,
Thomas O. Knight  and
Bruce J. Sherrick
Yue Lu
Affiliation:
Department of Agricultural Economics and Agricultural Business at New Mexico State University in Las Cruces, New Mexico
Octavio A. Ramirez
Affiliation:
Department of Agricultural Economics and Agricultural Business at New Mexico State University in Las Cruces, New Mexico
Roderick M. Rejesus
Affiliation:
Department of Agricultural and Resource Economics at North Carolina State University in Raleigh, North Carolina
Thomas O. Knight
Affiliation:
Department of Agricultural and Applied Economics at Texas Tech University in Lubbock, Texas
Bruce J. Sherrick
Affiliation:
Department of Agricultural and Consumer Economics at the University of Illinois at Urbana-Champaign in Urbana, Illinois
Get access

Abstract

This article examines the flexibility of the Johnson system of distributions by assessing its performance in terms of modeling crop yields for the purpose of setting actuarially fair crop insurance premiums. Using data from corn farms in Illinois coupled with Monte Carlo simulation procedures, we found that average crop insurance premiums computed on the basis of the Johnson system provide reasonably accurate estimates even when the data are normal or come from a non-normal distribution other than the Johnson system (i.e., a beta). These results suggest that there is potential for using the Johnson system to rate previously uninsured crops that do not have historical insurance performance data upon which to base premium calculations.

Keywords

crop insurancecrop yield modelingJohnson distributionpremium rate setting
Type
Contributed Papers
Information
Agricultural and Resource Economics Review , Volume 37 , Issue 1 , April 2008 , pp. 79 - 91
Copyright
Copyright © 2008 Northeastern Agricultural and Resource Economics Association 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Babcock, B.A., Hart, C.E., and Hayes, D.J. 2004. “Actuarial Fairness of Crop Insurance Rates with Constant Rate Relativities.” American Journal of Agricultural Economics 86(3): 563–575.Google Scholar
Coble, K.H., Knight, T.O., Pope, R.D., and Williams, J.R. 1997. “An Expected Indemnity Approach to the Measurement of Moral Hazard in Crop Insurance.” American Journal of Agricultural Economics 79(1): 216–226.Google Scholar
Gallagher, P. 1987. “U.S. Soybean Yields: Estimation and Forecasting with Nonsymmetric Disturbances.” American Journal of Agricultural Economics 69(4): 796–803.Google Scholar
Goodwin, B.K., and Ker, A.P. 1998. “Nonparametric Estimation of Crop Yield Distributions: Implications for Rating Group-Risk Crop Insurance Contracts.” American Journal of Agricultural Economics 80(1): 139–153.Google Scholar
Harri, A., Coble, K.H., Erdem, C., and Knight, T.O. 2005. “Crop Yield Normality: A Reconciliation of Previous Research.” Working paper, Department of Agricultural Economics, Mississippi State University, Starkville, MS.Google Scholar
Johnson, J.L., Kotz, S., and Balakrishnan, N. 1994. Continuous Univariate Distributions. New York: Wiley and Sons.Google Scholar
Jung, A.R., and Ramezani, C.A. 1999. “Valuing Risk Management Tools as Complex Derivatives: An Application of Revenue Insurance. Journal of Financial Engineering 8(March): 99–120.Google Scholar
Ker, A.P., and Coble, K. 2003. “Modeling Conditional Yield Densities.” American Journal of Agricultural Economics 85(2): 291–304.Google Scholar
Mood, A.M., Graybill, F.A., and Boes, D.C. 1974. Introduction to the Theory of Statistics (3rd edition). New York: McGraw-Hill Book.Google Scholar
Moss, C.B., and Shonkwiler, J.S. 1993. “Estimating Yield Distributions with a Stochastic Trend and Non-Normal Errors.” American Journal of Agricultural Economics 75(4): 1056–1062.Google Scholar
Nelson, C.H., and Preckel, P.V. 1989. “The Conditional Beta Distribution as a Stochastic Production Function.” American Journal of Agricultural Economics 71(2): 370–377.Google Scholar
Norwood, B., Roberts, M.C., and Lusk, J.L. 2004. “Ranking Crop Yield Models Using Out-of-Sample Likelihood Functions.” American Journal of Agricultural Economics 86(4): 1032–1043.Google Scholar
Ramirez, O.A. 1997. “Estimation and Use of a Multivariate Parametric Model for Simulating Heteroscedastic, Correlated, Non-Normal Random Variables: The Case of Corn-Belt Com, Soybeans and Wheat Yields.” American Journal of Agricultural Economics 79(1): 191–205.CrossRefGoogle Scholar
Ramirez, O.A., and McDonald, T.U. 2006a. “The Expanded and Re-parameterized Johnson System: A Most Flexible Crop-Yield Distribution Model.” Selected paper at the AAEA Annual Meetings, Long Beach, CA (July 23-26).Google Scholar
Ramirez, O.A., and McDonald, T.U. 2006b. “Ranking Crop Yield Models: A Comment.” American Journal of Agricultural Economics 88(4): 1105–1110.Google Scholar
Ramirez, O.A., Moss, C.B., and Boggess, W.G. 1994. “Estimation and Use of the Inverse Hyperbolic Sine Transformation to Model Non-Normal Correlated Random Variables.” Journal of Applied Statistics 21(4): 289–305.Google Scholar
Sherrick, B.J., Zanini, F.C., Schnitkey, G.D., and Irwin, S.H. 2004. “Crop Insurance Valuation Under Alternative Yield Distributions.” American Journal of Agricultural Economics 86(2): 406–419.CrossRefGoogle Scholar
Stokes, J.R. 2000. “A Derivative Security Approach to Setting Crop Revenue Insurance Premiums.” Journal of Agricultural and Resource Economics 25(1): 159–176.Google Scholar
Taylor, C.R. 1990. “Two Practical Procedures for Estimating Multivariate Non-Normal Probability Density Functions.” American Journal of Agricultural Economics 72(1): 210–217.Google Scholar
Turvey, C.G., and Baker, T.G. 1990. “A Farm-Level Financial Analysis of Farmers’ Use of Futures and Options under Alternative Farm Programs.” American Journal of Agricultural Economics 72(4): 946–957.Google Scholar