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Least Squares and Entropy: A Penalty Function Perspective

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  • Paul V. Preckel

Abstract

Mathematical measures of entropy as defined by Shannon and cross entropy as defined by Kullback and Leibler are currently in vogue in the field of econometrics, primarily due to the comprehensive work of Golan, Judge, and Miller. An alternative interpretation of the entropy measure as a penalty function over deviations is presented, and a number of parallels are drawn with least squares estimators. It is demonstrated that both approaches may be applied to the general linear model. The causes of differences in estimated parameter values are described, and some suggestions for the formulation of entropy-based econometric problems are presented. Copyright 2001, Oxford University Press.

Suggested Citation

  • Paul V. Preckel, 2001. "Least Squares and Entropy: A Penalty Function Perspective," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 83(2), pages 366-377.
    • Handle: RePEc:oup:ajagec:v:83:y:2001:i:2:p:366-377
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    File URL: http://hdl.handle.net/10.1111/0002-9092.00162
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    1. Heckelei, Thomas & Britz, Wolfgang, 2000. "Positive Mathematical Programming with Multiple Data Points: A Cross-Sectional Estimation Procedure," Cahiers d'Economie et de Sociologie Rurales (CESR), Institut National de la Recherche Agronomique (INRA), vol. 57.
    2. Elvira Silva & Pedro Macedo & Isabel Soares, 2019. "Maximum entropy: a stochastic frontier approach for electricity distribution regulation," Journal of Regulatory Economics, Springer, vol. 55(3), pages 237-257, June.
    3. Kaplan, Jonathan D. & Howitt, Richard E. & Farzin, Y. Hossein, 2003. "An information-theoretical analysis of budget-constrained nonpoint source pollution control," Journal of Environmental Economics and Management, Elsevier, vol. 46(1), pages 106-130, July.
    4. Yi, Jing & Canning, Patrick N. & Ge, Houtian & Rehkamp, Sarah & Gomez, Miguel I., 2023. "A national database of highly perishable fresh produce production with temporal and spatial resolution," 2023 Annual Meeting, July 23-25, Washington D.C. 335590, Agricultural and Applied Economics Association.
    5. Arndt, Channing & Robinson, Sherman & Tarp, Finn, 2002. "Parameter estimation for a computable general equilibrium model: a maximum entropy approach," Economic Modelling, Elsevier, vol. 19(3), pages 375-398, May.
    6. Kuiper, Marijke & van Tongeren, Frank, 2005. "Which road to liberalization in the Mediterranean? Analyzing different regional trade liberalization scenarios for Morocco and Tunisia," Conference papers 331404, Purdue University, Center for Global Trade Analysis, Global Trade Analysis Project.
    7. Balcombe, Kelvin, 2006. "Cross-Entropy Estimation of Linear Cointegrated Equations," MPRA Paper 15100, University Library of Munich, Germany.
    8. You, Liangzhi & Wood, Stanley & Wood-Sichra, Ulrike, 2009. "Generating plausible crop distribution maps for Sub-Saharan Africa using a spatially disaggregated data fusion and optimization approach," Agricultural Systems, Elsevier, vol. 99(2-3), pages 126-140, February.
    9. Esteban Fernández-Vázquez & Matías Mayor-Fernández & Jorge Rodríguez-Vález, 2009. "Estimating Spatial Autoregressive Models by GME-GCE Techniques," International Regional Science Review, , vol. 32(2), pages 148-172, April.
    10. Rui Fragoso & Maria Leonor da Silva Carvalho, 2013. "Estimation of cost allocation coefficients at the farm level using an entropy approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(9), pages 1893-1906, September.
    11. Esteban Fernández-Vázquez, 2014. "Estimating the effect of technological factors from samples affected by collinearity: a data-weighted entropy approach," Empirical Economics, Springer, vol. 47(2), pages 717-731, September.
    12. Hansen, Heiko & Surry, Yves R., 2006. "Die Schatzung Verfahrensspezifischer Faktoreinsatzmengen Fur Die Landwirtschaft In Deutschland," 46th Annual Conference, Giessen, Germany, October 4-6, 2006 14959, German Association of Agricultural Economists (GEWISOLA).
    13. Buschena, David E. & Atwood, Joseph A., 2011. "Evaluation of similarity models for expected utility violations," Journal of Econometrics, Elsevier, vol. 162(1), pages 105-113, May.
    14. R. Carter Hill & Randall C. Campbell, 2001. "Maximum Entropy Estimation in Economic Models with Linear Inequality Restrictions," Departmental Working Papers 2001-11, Department of Economics, Louisiana State University.
    15. Hansen, H. & Surry, Y., 2007. "Die Schätzung verfahrensspezifischer Faktoreneinsatzmengen für die Landwirtschaft in Deutschland," Proceedings “Schriften der Gesellschaft für Wirtschafts- und Sozialwissenschaften des Landbaues e.V.”, German Association of Agricultural Economists (GEWISOLA), vol. 42, March.
    16. Heckelei, Thomas & Mittelhammer, Ronald C. & Jansson, Torbjorn, 2008. "A Bayesian Alternative To Generalized Cross Entropy Solutions For Underdetermined Econometric Models," Discussion Papers 56973, University of Bonn, Institute for Food and Resource Economics.
    17. Heckelei, Thomas & Wolff, Hendrik, 2002. "A Methodological Note on the Estimation of Programming Models," 2002 International Congress, August 28-31, 2002, Zaragoza, Spain 24896, European Association of Agricultural Economists.
    18. Cook, Larry & Harslett, Philip, 2015. "An introduction to entropy estimation of parameters in economic models," Conference papers 332651, Purdue University, Center for Global Trade Analysis, Global Trade Analysis Project.
    19. Jing Yi & Samantha Cohen & Sarah Rehkamp & Patrick Canning & Miguel I. Gómez & Houtian Ge, 2023. "Overcoming data barriers in spatial agri‐food systems analysis: A flexible imputation framework," Journal of Agricultural Economics, Wiley Blackwell, vol. 74(3), pages 686-701, September.
    20. Rehkamp, Sarah & Canning, Patrick & Birney, Catherine, 2021. "Tracking the U.S. Domestic Food Supply Chain’s Freshwater Use Over Time," Economic Research Report 327191, United States Department of Agriculture, Economic Research Service.
    21. You, Liangzhi & Wood, Stanley & Wood-Sichra, Ulrike, 2004. "Generating Plausible Crop Distribution Maps For Sub-Sahara Africa Using Spatial Allocation Model," 2004 Annual meeting, August 1-4, Denver, CO 19965, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    22. You, Liangzhi & Wood, Stanley & Wood-Sichra, Ulrike, 2007. "Generating plausible crop distribution and performance maps for Sub-Saharan Africa using a spatially disaggregated data fusion and optimization approach:," IFPRI discussion papers 725, International Food Policy Research Institute (IFPRI).

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