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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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 1781.

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Date of creation: 01 Jun 2004
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Handle: RePEc:pra:mprapa:1781

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Related research

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

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References

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  1. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
  2. 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.
  3. 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 186-90, May.
  4. Phillips, P.C.B., 1991. "A Shortcut to LAD Estimator Asymptotics," Econometric Theory, Cambridge University Press, vol. 7(04), pages 450-463, December.
  5. repec:cup:etheor:v:7:y:1991:i:2:p:186-99 is not listed on IDEAS
  6. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(02), pages 186-199, June.
  7. Blattberg, Robert & Sargent, Thomas J, 1971. "Regression with Non-Gaussian Stable Disturbances: Some Sampling Results," Econometrica, Econometric Society, vol. 39(3), pages 501-10, May.
  8. repec:cup:etheor:v:7:y:1991:i:4:p:450-63 is not listed on IDEAS
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Citations

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Cited by:
  1. S.K. Mishra, 2007. "Globalization and Structural Changes in the Indian Industrial Sector: An Analysis of Production Functions," Working Papers id:788, eSocialSciences.
  2. 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.
  3. Gries, Thomas & Naude, Wim & Matthee, Marianne, 2008. "The Optimal Distance to Port for Exporting Firms," Working Paper Series RP2008/32, World Institute for Development Economic Research (UNU-WIDER).
  4. 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.
  5. 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.

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