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Least Squares and Entropy: A Penalty Function Perspective

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  • Paul V. Preckel
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    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.

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    Bibliographic Info

    Article provided by Agricultural and Applied Economics Association in its journal American Journal of Agricultural Economics.

    Volume (Year): 83 (2001)
    Issue (Month): 2 ()
    Pages: 366-377

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    Handle: RePEc:oup:ajagec:v:83:y:2001:i:2:p:366-377

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    Cited by:
    1. R. Carter Hill & Randall C. Campbell, . "Maximum Entropy Estimation in Economic Models with Linear Inequality Restrictions," Departmental Working Papers 2001-11, Department of Economics, Louisiana State University.
    2. Balcombe, Kelvin, 2006. "Cross-Entropy Estimation of Linear Cointegrated Equations," MPRA Paper 15100, University Library of Munich, Germany.
    3. 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.
    4. 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.
    5. 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.
    6. 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).
    7. 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.
    8. Arndt, Channing & Robinson, Sherman & Tarp, Finn, 1999. "Parameter estimation for a computable general equilibrium model: a maximum entropy approach," TMD discussion papers 40, International Food Policy Research Institute (IFPRI).
    9. 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.
    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. 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).

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