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Demonstration of the Use of Lower Partial Moments to Improve Safety-First Probability Limits

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  • Joseph Atwood

Abstract

A general stochastic inequality is presented which utilizes lower partial moments to generate sharp upper bounds on safety-first type probabilities. Alternative forms of the inequality often generate less conservative probability bounds than Chebychev's mean-standard error and Berck and Hihn's mean-semivariance inequalities. Of particular interest is the linear lower partial moment version which utilizes absolute deviations below a fixed reference point. A constraint is developed which, if enforced in an optimization model, guarantees that safety-first probability concerns are satisfied while selecting the least constraining level for the reference point.

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  • Joseph Atwood, 1985. "Demonstration of the Use of Lower Partial Moments to Improve Safety-First Probability Limits," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 67(4), pages 787-793.
    • Handle: RePEc:oup:ajagec:v:67:y:1985:i:4:p:787-793.
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    File URL: http://hdl.handle.net/10.2307/1241818
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    1. Lokonon, Boris Odilon & Savadogo, Kimseyinga & Mbaye, Ahmadou, 2015. "Assessing the impacts of climate shocks on farm performance and adaptation responses in the Niger basin of Benin," African Journal of Agricultural and Resource Economics, African Association of Agricultural Economists, vol. 10(3), pages 1-16, September.
    2. Atwood, Joseph & Shaik, Saleem, 2020. "Theory and statistical properties of Quantile Data Envelopment Analysis," European Journal of Operational Research, Elsevier, vol. 286(2), pages 649-661.
    3. Watts, Myles J. & Atwood, Joseph A. & Helmers, Glenn A. & Held, Larry J., 1989. "Safety First Programming- A Zero-One Approach," 1989 Annual Meeting, July 30-August 2, Baton Rouge, Louisiana 270679, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    4. Atwood, Joseph A. & Watts, Myles J. & Helmers, Glenn A. & Held, Larry J., 1988. "Incorporating Safety-First Constraints In Linear Programming Production Models," Western Journal of Agricultural Economics, Western Agricultural Economics Association, vol. 13(1), pages 1-8, July.
    5. Lambert, David K. & Harris, Thomas R., 1990. "Stochastic Dynamic Optimization And Rangeland Investment Decisions," Western Journal of Agricultural Economics, Western Agricultural Economics Association, vol. 15(2), pages 1-10, December.
    6. Cochran, Mark J., 1986. "Stochastic Dominance: The State Of The Art In Agricultural Economics," Regional Research Projects > 1986: S-180 Annual Meeting, March 23-26, 1986, Tampa, Florida 271995, Regional Research Projects > S-180: An Economic Analysis of Risk Management Strategies for Agricultural Production Firms.
    7. Lambart, David K. & Harris, Thomas R., 1991. "Multi-Period Rangeland Investment Analysis with Safety-First constraints and Uncertain Data," 1991 Annual Meeting, August 4-7, Manhattan, Kansas 271157, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    8. Mikémina Pilo & Nicolas Gerber & Tobias Wünscher, 2021. "Impacts of Adaptation to Climate Change on Farmers’ Income in the Savanna Region of Togo," Revue économique, Presses de Sciences-Po, vol. 72(3), pages 421-442.
    9. Christiaensen, Luc J.M. & Boisvert, Richard N., 2000. "On Measuring Household Food Vulnerability: Case Evidence from Northern Mali," Working Papers 127676, Cornell University, Department of Applied Economics and Management.
    10. Wetzstein, Michael E. & Szmedra, Philip I. & McClendon, Ronald W. & Edwards, David M., 1988. "Efficiency Criteria And Risk Aversion: An Empirical Evaluation," Southern Journal of Agricultural Economics, Southern Agricultural Economics Association, vol. 20(1), pages 1-8, July.
    11. Arnade, Carlos Anthony & Cooper, Joseph C., 2012. "Acreage Response under Varying Risk Preferences," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 37(3), pages 1-17.
    12. Hatch, L. Upton & Atwood, Joseph A. & Segar, James, 1989. "An Application Of Safety-First Probability Limits In A Discrete Stochastic Farm Management Programming Model," Southern Journal of Agricultural Economics, Southern Agricultural Economics Association, vol. 21(1), pages 1-8, July.
    13. Matthews, Nicolette & Grove, Bennie, 2015. "Economic-Environmental Trade-offs and the Conservativeness of the Upper Partial Moment," 2015 Conference, August 9-14, 2015, Milan, Italy 212450, International Association of Agricultural Economists.
    14. Kalashami, Mohammad Kavoosi & Sabbagi, Mohammad Aghapour & Alipour, Hamid Reza, 2011. "Using Probabilistic-Risky Programming Models in Identifying Optimized Pattern of Cultivation under Risk Conditions (Case Study: Shoshtar Region)," International Journal of Agricultural Management and Development (IJAMAD), Iranian Association of Agricultural Economics, vol. 1(1), pages 1-9, March.

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