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On the median regression for SURE models with applications to 3-generation immigrants data in Sweden

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  • Shukur, Ghazi
  • Zeebari, Zangin

Abstract

In this paper we generalize the median regression method to be applicable to system of regression equations, in particular SURE models. Giving the existence of proper system wise medians of the residuals from different equations, we apply the weighted median regression with the weights obtained from the covariance matrix of the equations obtained from ordinary SURE method. The benefit of this model in our case is that the SURE estimators utilise the information present in the cross regression (or equations) error correlation and hence more efficient than other estimation methods like the OLS method. The Seemingly Unrelated Median Regression Equations (SUMRE) models produce results that are more robust than the usual SURE or single equations OLS estimation when the distributions of the dependent variables are not normally distributed or the data are associated with outliers. Moreover, the results are also more efficient than is the cases of single equations median regressions when the residuals from the different equations are correlated. A theorem is derived and indicates that even if there is no statistically significant correlation between the equations, using SUMRE model instead of SURE models will not damage the estimation of parameters.

Suggested Citation

  • Shukur, Ghazi & Zeebari, Zangin, 2011. "On the median regression for SURE models with applications to 3-generation immigrants data in Sweden," Economic Modelling, Elsevier, vol. 28(6), pages 2566-2578.
  • Handle: RePEc:eee:ecmode:v:28:y:2011:i:6:p:2566-2578
    DOI: 10.1016/j.econmod.2011.07.010
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    References listed on IDEAS

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    1. Amemiya, Takeshi, 1982. "Two Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, vol. 50(3), pages 689-711, May.
    2. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    3. A. Charnes & W. W. Cooper & R. O. Ferguson, 1955. "Optimal Estimation of Executive Compensation by Linear Programming," Management Science, INFORMS, vol. 1(2), pages 138-151, January.
    4. Chib, Siddhartha & Greenberg, Edward, 1995. "Hierarchical analysis of SUR models with extensions to correlated serial errors and time-varying parameter models," Journal of Econometrics, Elsevier, vol. 68(2), pages 339-360, August.
    5. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew "t"-distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389.
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    Cited by:

    1. Zeebari, Zangin & Shukur, Ghazi, 2012. "On the Least Absolute Deviations Method for Ridge Estimation of SURE Models," HUI Working Papers 69, HUI Research.

    More about this item

    Keywords

    Median regression; SURE models; Robustness; Efficiency;

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • 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

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