IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/1809.html
   My bibliography  Save this paper

Estimation under Multicollinearity: Application of Restricted Liu and Maximum Entropy Estimators to the Portland Cement Dataset

Author

Abstract

A high degree of multicollinearity among the explanatory variables severely impairs estimation of regression coefficients by the Ordinary Least Squares. Several methods have been suggested to ameliorate the deleterious effects of multicollinearity. In this paper we aim at comparing the Restricted Liu estimates of regression coefficients with those obtained by applying the Maximum Entropy Leuven (MEL) family of estimators on the widely analyzed dataset on Portland cement. This dataset has been obtained from an experimental investigation of the heat evolved during the setting and hardening of Portland cements of varied composition and the dependence of this heat on the percentage of four compounds in the clinkers from which the cement was produced. The relevance of the relationship between the heat evolved and the chemical processes undergone while setting takes place is best stated in the words of Woods et al.: "This property is of interest in the construction of massive works as dams, in which the great thickness severely hinder the outflow of the heat. The consequent rise in temperature while the cement is hardening may result in contractions and cracking when the eventual cooling to the surrounding temperature takes place." Two alternative models have been formulated, the one with an intercept term (non-homogenous) that exhibits a very high degree of multicollinearity and the other with no intercept term (extended homogenous) that characterizes perfect multicollinearity. Our findings suggest that several members of the MEL family of estimators outperform the OLS and the Restricted Liu estimators. The MEL estimators perform well even when perfect multicollinearity is there. A few of them may outperform the Minimum Norm LS (OLS+) estimator. Since the MEL estimators do not seek extra information from the analyst, they are easy to apply. Therefore, one may rely on the MEL estimators for obtaining the coefficients of a linear regression model under the conditions of severe (including perfect) multicollinearity among the explanatory variables.

Suggested Citation

  • Mishra, SK, 2004. "Estimation under Multicollinearity: Application of Restricted Liu and Maximum Entropy Estimators to the Portland Cement Dataset," MPRA Paper 1809, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:1809
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/1809/1/MPRA_paper_1809.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Sudhanshu Mishra, 2004. "Multicollinearity and maximum entropy leuven estimator," Economics Bulletin, AccessEcon, vol. 3(25), pages 1-11.
    2. Paris, Quirino, 2001. "Mele: Maximum Entropy Leuven Estimators," Working Papers 11991, University of California, Davis, Department of Agricultural and Resource Economics.
    3. Golan, Amos & Judge, George G. & Miller, Douglas, 1996. "Maximum Entropy Econometrics," Staff General Research Papers Archive 1488, Iowa State University, Department of Economics.
    4. Dasgupta, Madhuchhanda & Mishra, SK, 2004. "Least absolute deviation estimation of linear econometric models: A literature review," MPRA Paper 1781, University Library of Munich, Germany.
    5. repec:ebl:ecbull:v:3:y:2004:i:25:p:1-11 is not listed on IDEAS
    6. Quirino Paris, 2001. "Multicollinearity and maximum entropy estimators," Economics Bulletin, AccessEcon, vol. 3(11), pages 1-9.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sudhanshu K. MISHRA, 2016. "Shapley Value Regression and the Resolution of Multicollinearity," Journal of Economics Bibliography, KSP Journals, vol. 3(3), pages 498-515, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Msangi, Siwa & Howitt, Richard E., 2006. "Estimating Disaggregate Production Functions: An Application to Northern Mexico," 2006 Annual meeting, July 23-26, Long Beach, CA 21080, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    2. Akpalu, Wisdom & Hassan, Rashid M. & Ringler, Claudia, 2008. "Climate variability and maize yield in South Africa: Results from GME and MELE methods," IFPRI discussion papers 843, International Food Policy Research Institute (IFPRI).
    3. Sudhanshu Mishra, 2004. "Multicollinearity and maximum entropy leuven estimator," Economics Bulletin, AccessEcon, vol. 3(25), pages 1-11.
    4. Howitt, Richard E. & Msangi, Siwa, 2002. "Reconstructing Disaggregate Production Functions," 2002 Annual meeting, July 28-31, Long Beach, CA 19585, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    5. Balcombe, Kelvin, 2006. "Cross-Entropy Estimation of Linear Cointegrated Equations," MPRA Paper 15100, University Library of Munich, Germany.
    6. repec:ebl:ecbull:v:3:y:2004:i:25:p:1-11 is not listed on IDEAS
    7. repec:lrk:lrkwkp:fiirs016 is not listed on IDEAS
    8. Miguel Henry & George Judge, 2019. "Permutation Entropy and Information Recovery in Nonlinear Dynamic Economic Time Series," Econometrics, MDPI, vol. 7(1), pages 1-16, March.
    9. Hyeok Lee & Yong Kyun Kim, 2018. "The effects of external shocks on the Korean economy: CGE model-based analysis," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 7(1), pages 1-14, December.
    10. Wang, Yafeng & Graham, Brett, 2009. "Generalized Maximum Entropy estimation of discrete sequential move games of perfect information," MPRA Paper 21331, University Library of Munich, Germany.
    11. Arndt, Channing & Simler, Kenneth R., 2005. "Estimating utility-consistent poverty lines," FCND briefs 189, International Food Policy Research Institute (IFPRI).
    12. Wobst, Peter & Arndt, Channing, 2004. "HIV/AIDS and Labor Force Upgrading in Tanzania," World Development, Elsevier, vol. 32(11), pages 1831-1847, November.
    13. Sudhanshu K. MISHRA, 2016. "Shapley Value Regression and the Resolution of Multicollinearity," Journal of Economics Bibliography, KSP Journals, vol. 3(3), pages 498-515, September.
    14. Thomas Brenner & Matthias Duschl, 2018. "Modeling Firm and Market Dynamics: A Flexible Model Reproducing Existing Stylized Facts on Firm Growth," Computational Economics, Springer;Society for Computational Economics, vol. 52(3), pages 745-772, October.
    15. Nicole Branger, 2004. "Pricing Derivative Securities Using Cross-Entropy: An Economic Analysis," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 63-81.
    16. Amos Golan & Enrico Moretti & Jeffrey M.Perloff, 2004. "A Small-Sample Estimator for the Sample-Selection Model," Econometric Reviews, Taylor & Francis Journals, vol. 23(1), pages 71-91.
    17. Golan, Amos & Karp, Larry S & Perloff, Jeffrey M, 2000. "Estimating Coke's and Pepsi's Price and Advertising Strategies," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(4), pages 398-409, October.
    18. Rubiera-Morollón, Fernando & Fernández-Vázquez , Esteban & Aponte-Jaramillo, Elizabeth, 2012. "Estimation and analysis of labor productivity in Spanish cities," INVESTIGACIONES REGIONALES - Journal of REGIONAL RESEARCH, Asociación Española de Ciencia Regional, issue 22, pages 129-151.
    19. You, Liangzhi & Wood, Stanley, 2006. "An entropy approach to spatial disaggregation of agricultural production," Agricultural Systems, Elsevier, vol. 90(1-3), pages 329-347, October.
    20. Golan, Amos & Perloff, Jeffrey M. & Wu, Ximing, 2001. "Welfare Effects of Minimum Wage and Other Government Policies," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt0gb7h58q, Department of Agricultural & Resource Economics, UC Berkeley.
    21. Wu, Ximing & Perloff, Jeffrey M., 2004. "China's Income Distribution Over Time: Reasons for Rising Inequality," Institute for Research on Labor and Employment, Working Paper Series qt9jw2v939, Institute of Industrial Relations, UC Berkeley.
    22. Giuseppe Ragusa, 2011. "Minimum Divergence, Generalized Empirical Likelihoods, and Higher Order Expansions," Econometric Reviews, Taylor & Francis Journals, vol. 30(4), pages 406-456, August.

    More about this item

    Keywords

    Multicollinearity; Estimator; Restricted Liu; Maximum Entropy Leuven estimator; MEL family; Modular Maximum Entropy Leuven estimator; Least Absolute Deviation; Minimum Norm Least Squares; Moore-Penrose inverse; Portland cement dataset;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:1809. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.