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

Listed author(s):
  • Dasgupta, Madhuchhanda
  • Mishra, SK

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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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
Handle: RePEc:pra:mprapa:1781
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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. Blattberg, Robert & Sargent, Thomas J, 1971. "Regression with Non-Gaussian Stable Disturbances: Some Sampling Results," Econometrica, Econometric Society, vol. 39(3), pages 501-510, May.
  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.
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