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Least absolute deviation estimation of linear econometric models: A literature review

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  • Dasgupta, Madhuchhanda
  • Mishra, SK

Abstract

Econometricians generally take for granted that the error terms in the econometric models are generated by distributions having a finite variance. However, since the time of Pareto the existence of error distributions with infinite variance is known. Works of many econometricians, namely, Meyer & Glauber (1964), Fama (1965) and Mandlebroth (1967), on economic data series like prices in financial and commodity markets confirm that infinite variance distributions exist abundantly. The distribution of firms by size, behaviour of speculative prices and various other recent economic phenomena also display similar trends. Further, econometricians generally assume that the disturbance term, which is an influence of innumerably many factors not accounted for in the model, approaches normality according to the Central Limit Theorem. But Bartels (1977) is of the opinion that there are limit theorems, which are just likely to be relevant when considering the sum of number of components in a regression disturbance that leads to non-normal stable distribution characterized by infinite variance. Thus, the possibility of the error term following a non-normal distribution exists. The Least Squares method of estimation of parameters of linear (regression) models performs well provided that the residuals (disturbances or errors) are well behaved (preferably normally or near-normally distributed and not infested with large size outliers) and follow Gauss-Markov assumptions. However, models with the disturbances that are prominently non-normally distributed and contain sizeable outliers fail estimation by the Least Squares method. An intensive research has established that in such cases estimation by the Least Absolute Deviation (LAD) method performs well. This paper is an attempt to survey the literature on LAD estimation of single as well as multi-equation linear econometric models.

Suggested Citation

  • Dasgupta, Madhuchhanda & Mishra, SK, 2004. "Least absolute deviation estimation of linear econometric models: A literature review," MPRA Paper 1781, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:1781
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    File URL: https://mpra.ub.uni-muenchen.de/1781/1/MPRA_paper_1781.pdf
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    References listed on IDEAS

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    1. Smith, V Kerry & Hall, Thomas W, 1972. "A Comparison of Maximum Likelihood Versus Blue Estimators," The Review of Economics and Statistics, MIT Press, vol. 54(2), pages 186-190, May.
    2. Robert Blattberg & Thomas Sargent, 2010. "Regression With Non-Gaussian Stable Disturbances: Some Sampling Results," World Scientific Book Chapters,in: Perspectives On Promotion And Database Marketing The Collected Works of Robert C Blattberg, chapter 1, pages 7-16 World Scientific Publishing Co. Pte. Ltd..
    3. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
    4. repec:cup:etheor:v:7:y:1991:i:4:p:450-63 is not listed on IDEAS
    5. repec:cup:etheor:v:7:y:1991:i:2:p:186-99 is not listed on IDEAS
    6. Weiss, Andrew A., 1991. "Estimating Nonlinear Dynamic Models Using Least Absolute Error Estimation," Econometric Theory, Cambridge University Press, vol. 7(01), pages 46-68, March.
    7. Phillips, P.C.B., 1991. "A Shortcut to LAD Estimator Asymptotics," Econometric Theory, Cambridge University Press, vol. 7(04), pages 450-463, December.
    8. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(02), pages 186-199, June.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Stephen Satchell & Wei Xia, 2005. "Estimation of the Risk Attitude of the Representative UK Pension Fund Investor," Birkbeck Working Papers in Economics and Finance 0509, Birkbeck, Department of Economics, Mathematics & Statistics.
    2. Thomas Brenner & Matthias Duschl, 2014. "Modelling Firm and Market Dynamics - A Flexible Model Reproducing Existing Stylized Facts," Working Papers on Innovation and Space 2014-07, Philipps University Marburg, Department of Geography.
    3. Thomas Brenner & Matthias Duschl, 2015. "Causal dynamic effects in regional systems of technological activities: a SVAR approach," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 55(1), pages 103-130, October.
    4. Matthias Duschl & Thomas Brenner, 2013. "Growth dynamics in regional systems of technological activities – A SVAR approach," Working Papers on Innovation and Space 2013-12, Philipps University Marburg, Department of Geography.
    5. S K Mishra, 2007. "Globalization and Structural Changes in the Indian Industrial Sector: An Analysis of Production Functions," The IUP Journal of Managerial Economics, IUP Publications, vol. 0(4), pages 56-81, November.
    6. Thomas Gries & Wim Naudé & Marianne Matthee, 2009. "The Optimal Distance To Port For Exporting Firms," Journal of Regional Science, Wiley Blackwell, vol. 49(3), pages 513-528.
    7. 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.

    More about this item

    Keywords

    Lad estimator; Least absolute deviation estimation; econometric model; LAD Estimator; Minimum Absolute Deviation; Robust; Outliers; L1 Estimator; Review of literature;

    JEL classification:

    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables

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