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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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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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), INRA (French National Institute for Agricultural Research), vol. 57.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Balcombe, Kelvin, 2006. "Cross-Entropy Estimation of Linear Cointegrated Equations," MPRA Paper 15100, University Library of Munich, Germany.
    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).
    12. 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).
    13. 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.

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