Dasgupta, Madhuchhanda and Mishra, SK (2004): Least absolute deviation estimation of linear econometric models: A literature review.

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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 nonnormal stable distribution characterized by infinite variance. Thus, the possibility of the error term following a nonnormal 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 nearnormally distributed and not infested with large size outliers) and follow GaussMarkov assumptions. However, models with the disturbances that are prominently nonnormally 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 multiequation linear econometric models.
Item Type:  MPRA Paper 

Institution:  NorthEastern Hill University, Shillong 
Original Title:  Least absolute deviation estimation of linear econometric models: A literature review 
Language:  English 
Keywords:  Lad estimator; Least absolute deviation estimation; econometric model; LAD Estimator; Minimum Absolute Deviation; Robust; Outliers; L1 Estimator; Review of literature 
Subjects:  C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics > C46  Specific Distributions; Specific Statistics C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models; Multiple Variables > C30  General C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models; Multiple Variables 
Item ID:  1781 
Depositing User:  Sudhanshu Kumar Mishra 
Date Deposited:  13. Feb 2007 
Last Modified:  13. Feb 2013 13:56 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/1781 